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Physical Layer Techniques for Wireless Communication Security

Permanent Link: http://ufdc.ufl.edu/UFE0041108/00001

Material Information

Title: Physical Layer Techniques for Wireless Communication Security
Physical Description: 1 online resource (169 p.)
Language: english
Creator: Jo, Youngho
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: blast, communication, crack, interference, jamming, mai, mimo, physical, precoding, security, spectrum, spread, stbc, tdcs, wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, we consider physical layer techniques in wireless communication security. We study how to crack an adversary's communication which uses direct-sequence spread-spectrum (DS-SS), and how to protect wireless communication systems against interference. These security measures are classified as electronic protection (EP) and electronic attack (EA) among electronic warfare (EW), respectively. EW is the use of the electromagnetic spectrum to effectively deny the use of this medium by an adversary, while optimizing its use by friendly forces. We investigate the performance of the physical layer of wireless communication systems considered in this dissertation. On the topic of eavesdropping on an adversary's secure communication, we discuss how to crack a DS-SS system. The DS-SS is a covert technique resistant to interference, interception and multipath fading. Identifying spread-spectrum signals or cracking DS-SS systems by an unintended receiver (or eavesdropper) without a priori knowledge is a challenging problem. To address this problem, we first search for the start position of data symbols in the spread signal (for symbol synchronization). After synchronization, we remove a spread sequence by a less-expensive and more accurate cross-correlation based method, and identify the spread sequence by using a matched filter. We also propose a zigzag searching method to identify a generator polynomial that reduces memory requirement and is capable of correcting polarity errors existing in the previous methods. In addition, we analyze the bit error performance of our proposed method. With regard to protecting wireless communication systems against interference, we propose an enhanced transform domain communication system (ETDCS) with narrow band interference (NBI) avoidance capability as a countermeasure for a single-carrier single-input single-output (SC-SISO) communication system, a vertical-Bell Laboratories layered space-time (V-BLAST) architecture with non-stationary interference avoidance capability as a countermeasure for a single-carrier multi-input multi-output (SC-MIMO), and a multi-carrier transform domain communication system (MC-TDCS) as a countermeasure for multi-carrier multi-input single-output (MC-MISO) systems, respectively. The TDCS is a viable solution for interference avoidance. An interference avoiding fundamental modulation waveform is synthesized at the transmitter to avoid intentional interference, and the receiver adapts its matched filter to match the transmitted fundamental modulation waveform in the frequency domain. By doing so, spectrally interfered regions are avoided altogether via adaptive spectral notching. The basic idea for the ETDCS is to synthesize an adaptive fundamental modulation waveform by a non-parametric spectral estimator, called Capon's method. The advantages of the ETDCS and a V-BLAST with the minimum mean square error (MMSE) detector are integrated to enhance bit error performance in narrow band interference (NBI) environment. The concepts of ETDCS and multi-carrier modulation are combined together in the MC-TDCS to combat multipath fading and to avoid intentional interference. In code division multiple access (CDMA) or multi-carrier CDMA (MC-CDMA) systems, because users do not use completely orthogonal spreading codes or orthogonality of the spreading codes are destroyed by multipath fading, there is residual multiple-access interference (MAI) present at the output of a matched filter. Transmitter pre-filtering techniques can be employed to mitigate the MAI and channel distortions in the downlink of the MC-CDMA. We analyze the bit error rate performance of a downlink time division duplex MC-CDMA with a pre-filtering transmitter antenna array at the base station (BS), rather than at the mobile terminals (MTs). We also incorporate a pre-filtering approach at the MC-TDCS to mitigate the MAI. In summary, this research studies physical layer measures in wireless communication security. We provide countermeasures for SISO and MIMO communication systems against jamming and unintentional interference, while we also study vulnerabilities of DS-SS systems as well as how to crack the DS-SS system.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Youngho Jo.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Wu, Dapeng.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041108:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041108/00001

Material Information

Title: Physical Layer Techniques for Wireless Communication Security
Physical Description: 1 online resource (169 p.)
Language: english
Creator: Jo, Youngho
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: blast, communication, crack, interference, jamming, mai, mimo, physical, precoding, security, spectrum, spread, stbc, tdcs, wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, we consider physical layer techniques in wireless communication security. We study how to crack an adversary's communication which uses direct-sequence spread-spectrum (DS-SS), and how to protect wireless communication systems against interference. These security measures are classified as electronic protection (EP) and electronic attack (EA) among electronic warfare (EW), respectively. EW is the use of the electromagnetic spectrum to effectively deny the use of this medium by an adversary, while optimizing its use by friendly forces. We investigate the performance of the physical layer of wireless communication systems considered in this dissertation. On the topic of eavesdropping on an adversary's secure communication, we discuss how to crack a DS-SS system. The DS-SS is a covert technique resistant to interference, interception and multipath fading. Identifying spread-spectrum signals or cracking DS-SS systems by an unintended receiver (or eavesdropper) without a priori knowledge is a challenging problem. To address this problem, we first search for the start position of data symbols in the spread signal (for symbol synchronization). After synchronization, we remove a spread sequence by a less-expensive and more accurate cross-correlation based method, and identify the spread sequence by using a matched filter. We also propose a zigzag searching method to identify a generator polynomial that reduces memory requirement and is capable of correcting polarity errors existing in the previous methods. In addition, we analyze the bit error performance of our proposed method. With regard to protecting wireless communication systems against interference, we propose an enhanced transform domain communication system (ETDCS) with narrow band interference (NBI) avoidance capability as a countermeasure for a single-carrier single-input single-output (SC-SISO) communication system, a vertical-Bell Laboratories layered space-time (V-BLAST) architecture with non-stationary interference avoidance capability as a countermeasure for a single-carrier multi-input multi-output (SC-MIMO), and a multi-carrier transform domain communication system (MC-TDCS) as a countermeasure for multi-carrier multi-input single-output (MC-MISO) systems, respectively. The TDCS is a viable solution for interference avoidance. An interference avoiding fundamental modulation waveform is synthesized at the transmitter to avoid intentional interference, and the receiver adapts its matched filter to match the transmitted fundamental modulation waveform in the frequency domain. By doing so, spectrally interfered regions are avoided altogether via adaptive spectral notching. The basic idea for the ETDCS is to synthesize an adaptive fundamental modulation waveform by a non-parametric spectral estimator, called Capon's method. The advantages of the ETDCS and a V-BLAST with the minimum mean square error (MMSE) detector are integrated to enhance bit error performance in narrow band interference (NBI) environment. The concepts of ETDCS and multi-carrier modulation are combined together in the MC-TDCS to combat multipath fading and to avoid intentional interference. In code division multiple access (CDMA) or multi-carrier CDMA (MC-CDMA) systems, because users do not use completely orthogonal spreading codes or orthogonality of the spreading codes are destroyed by multipath fading, there is residual multiple-access interference (MAI) present at the output of a matched filter. Transmitter pre-filtering techniques can be employed to mitigate the MAI and channel distortions in the downlink of the MC-CDMA. We analyze the bit error rate performance of a downlink time division duplex MC-CDMA with a pre-filtering transmitter antenna array at the base station (BS), rather than at the mobile terminals (MTs). We also incorporate a pre-filtering approach at the MC-TDCS to mitigate the MAI. In summary, this research studies physical layer measures in wireless communication security. We provide countermeasures for SISO and MIMO communication systems against jamming and unintentional interference, while we also study vulnerabilities of DS-SS systems as well as how to crack the DS-SS system.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Youngho Jo.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Wu, Dapeng.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041108:00001


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Iwouldliketoexpressmysincereappreciationtoseveralpeoplefortheircontinuoussupportandguidanceoverthecourseofmydegree.First,IwouldliketoexpressmydeepestgratitudetomyadvisorProfessorDapengOliverWuforhisexcellentguidanceandcontinualsupportduringthecoursetomydegree.Withouthisdeepinsight,advice,andwillingnesstoprovidesupport,thisworkwouldnothavebeenpossible.Hisextensiveknowledgeandcommitmenttotheexcellenceofresearchandteachingaretrulyatreasureforme.Hehasalwaysprovidedneededassistanceatanytime.IalsowouldliketothankProfessorLiuqingYang,ProfessorTaoLi,andProfessorShigangChenforservingonmydissertationcommitteeandprovidingvaluableadviceonmyresearch.IamalsogratefultoProfessorClintSlattonformentoringmyresearchduringmyrstyearattheUniversityofFlorida.MyfellowgraduatestudentshavemademylifeatUFenjoyableandmemorable.IwouldliketothankthestudentsattheMultimediaCommunicationsandNetworkingLaboratory(MCN)attheElectricalandComputerDepartmentoftheUniversityofFlorida,whohavemademydoctoralprogramexperienceallthemorerewardingtome.IwanttotakethisopportunitytothankmycolleaguesandfriendsattheDepartmentofElectricalandComputerEngineeringandattheUniversityofFlorida.Inparticular,specialthankstoChanghwanKoandhiswifeJungminfortheirdeepestfriendshiptowardmeandmyfamilyatGainesville,Florida.Asalways,Iamdeeplyindebtedtomylovelymother,myparents-in-law,andtherestofmyfamilyfortheirloveandsupportthroughoutthisdegreeprogramandmylife.IwouldliketothankmywifeJeungheeforherlove,understanding,andunwaveringbeliefinme,andwouldliketoexpressmygreatlovetomysonsSungbinandAnthony.Finally,thisdissertationisdedicatedtomyfather,inheaven,forhistearsandlove. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 13 CHAPTER 1INTRODUCTION .................................. 16 1.1Motivation .................................... 17 1.1.1CrackDirect-SequenceSpread-SpectrumSystems .......... 17 1.1.2ProtectWirelessCommunicationSystemsAgainstInterference ... 18 1.2ContributionsofthisDissertation ....................... 22 1.3OutlineoftheDissertation ........................... 23 2PERFORMANCEOFWIRELESSCOMMUNICATIONSYSTEMSUNDERINTERFERENCE .................................. 26 2.1Introduction ................................... 26 2.2InterferenceModel ............................... 27 2.2.1IntentionalInterference ......................... 27 2.2.1.1Barragenoisejamming .................... 28 2.2.1.2Partialbandjamming .................... 28 2.2.1.3Multi-tonejamming ..................... 28 2.2.1.4Swept-tonejamming ..................... 29 2.2.2UnintentionalInterference ....................... 30 2.2.2.1Multipleaccessinterference ................. 30 2.2.2.2Co-channelinterference .................... 30 2.2.2.3Adjacent-channelinterference ................ 31 2.3Single-CarrierModulationSystems ...................... 31 2.3.1Direct-SequenceSpread-SpectrumSystems .............. 31 2.3.2CodeDivisionMultipleAccess ..................... 33 2.3.3TransformDomainCommunicationSystems ............. 34 2.4Multi-CarrierModulationSystems ...................... 35 2.4.1OrthogonalFrequencyDivisionMultiplexing ............. 35 2.4.2Multi-CarrierCodeDivisionMultipleAccess ............. 36 2.5Multi-InputMulti-OutputSystems ...................... 37 2.5.1Space-TimeOrthogonalBlockCoding ................. 37 2.5.2Vertical-BellLaboratoriesLayeredSpace-Time ............ 39 2.6Multi-CarrierMulti-InputMulti-OutputSystems .............. 40 2.6.1Space-TimeOrthogonalFrequencyDivisionMultiplexing ...... 41 5

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.............. 42 2.6.3Multi-CarrierVertical-BellLaboratoriesLayeredSpace-Time .... 46 2.6.4TheEectsofJammingonMulti-CarrierV-BLASTsystems .... 48 2.7Summary .................................... 53 3ONCRACKINGDIRECT-SEQUENCESPREAD-SPECTRUMSYSTEMS .. 54 3.1Introduction ................................... 54 3.2RelatedWorks .................................. 56 3.3SignalModel .................................. 59 3.4SymbolSynchronization ............................ 59 3.5SymbolEstimation ............................... 64 3.6SpreadSequenceEstimation .......................... 67 3.7IdenticationofGeneratorPolynomial .................... 69 3.8SimulationandValidation ........................... 76 3.9Summary .................................... 83 4ENHANCEDTRANSFORMDOMAINCOMMUNICATIONSYSTEM ..... 85 4.1Introduction ................................... 85 4.2AMathematicalModelofTDCS ....................... 87 4.3Methodology .................................. 89 4.4TheEectsofVariousJammingonETDCS ................. 91 4.5Summary .................................... 98 5ANENHANCEDV-BLASTWITHNON-STATIONARYINTERFERENCEAVOIDANCECAPABILITY ............................ 100 5.1Introduction ................................... 100 5.2RelatedWorks .................................. 101 5.3SystemandInterferenceModel ........................ 102 5.4ProposedMethodology ............................. 103 5.5SimulationandAnalysis ............................ 105 5.6Summary .................................... 111 6ONTHEPERFORMANCEOFJOINTPRECODINGANDEQUALIZATIONFORTRANSMITTERANTENNAARRAYDOWNLINKTDDMC-CDMA .. 113 6.1Introduction ................................... 113 6.2SystemModel .................................. 115 6.3SingleUserEqualizationatReceiver ..................... 118 6.3.1MaximalRatioCombining ....................... 118 6.3.2EqualGainCombining ......................... 119 6.3.3OrthogonalityRestoringCombining .................. 119 6.3.4MinimumMeanSquareErrorEqualization .............. 119 6.4Space-FrequencyPrecoding .......................... 119 6.4.1FilterDesign ............................... 120 6

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....................... 121 6.4.3PerformanceAnalysis .......................... 123 6.5SimulationandVerication .......................... 125 6.6Summary .................................... 132 7MULTI-CARRIERTRANSFORMDOMAINCOMMUNICATIONSYSTEM:ANINTERFERENCEAVOIDANCEMULTI-CARRIERSYSTEM ....... 133 7.1Introduction ................................... 133 7.2MC-TDCSSystemModel ........................... 135 7.3SingleUserDetection .............................. 140 7.3.1MaximalRatioCombining ....................... 141 7.3.2EqualGainCombining ......................... 147 7.3.3OrthogonalityRestoringCombining .................. 147 7.3.4MinimumMeanSquareErrorEqualization .............. 149 7.4MultipleAccessInterferenceMitigation .................... 150 7.4.1FilterDesign ............................... 151 7.4.2PowerAllocationSchemes ....................... 153 7.4.3PerformanceAnalysis .......................... 153 7.4.4SimulationandComparison ...................... 153 7.5PerformanceunderJamming .......................... 154 7.5.1PerformanceunderBarrageNoiseJamming .............. 154 7.5.2PerformanceunderPartialBandJamming .............. 156 7.5.3PerformanceunderMulti-ToneJamming ............... 157 7.6Summary .................................... 157 8CONCLUSION .................................... 160 8.1SummaryoftheDissertation .......................... 160 8.2FutureWork ................................... 162 8.2.1CrackingSecureWirelessCommunicationSystems .......... 162 8.2.2ProtectingWirelessCommunicationSystemsAgainstInterference 162 REFERENCES ....................................... 164 BIOGRAPHICALSKETCH ................................ 169 7

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Table page 2-1IMEMclassicationbasedonbandwidthin[ 1 ] ................... 27 2-2AZF-SICV-BLASTdetectionalgorithm ...................... 40 3-1Listofnotations. ................................... 58 3-2RelationshipamongPr(K=k)in( 3{45 ),hc;^ci,and1 2erfcp 3{47 )wherekdenotesthenumberoferrorsintheestimationofthespreadsequenceofthenon-zigzagmethod. .............................. 73 4-1ComparisonoftheaverageBERperformanceofTDCS,EWDCS,andETDCSwithantipodalmodulation(Eb=N0=4dB,I=E=016dB) ........... 99 5-1V-BLAST/MMSEwithETDPDetection ...................... 105 8

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Figure page 2-1Linearfeedbackshiftregister[ 2 { 5 ] ......................... 32 2-2Performanceoftheprecodingandthereceiver-baseddecorrelatorfor=0.2,0.5,0.8,andn=100 .................................. 34 2-3AschematicofAlamoutitransmissionstrategy[ 6 ] ................. 37 2-4AhighlevelsystemdiagramofV-BLAST[ 7 ] .................... 39 2-5Ablockdiagramofspace-timeOFDMsystems[ 8 ] ................. 42 2-6PerformanceofST-OFDMsystemunderBNJwithRayleighfadingandAWGN 44 2-7PerformanceofST-OFDMsystemunder=0:5PBJwithRayleighfadingandAWGN ......................................... 45 2-8Performanceofspace-timeOFDMsystemunder=0:5MTJwithRayleighfadingandAWGN .................................. 46 2-9Multi-carrierV-BLASThighlevelsystemdiagramwherenumberoftransmittersisMandnumberofreceiversisN. ......................... 46 2-10BERperformanceofMCV-BLASTforBPSKmodulationwithMN=22MIMORayleighFadingChannel .......................... 48 2-11BERperformanceofMCV-BLASTunderBNJforBPSKmodulationwith22MIMORayleighfadingchannel .......................... 50 2-12BERperformanceofMCV-BLASTunder50%PBJforBPSKmodulationwith22MIMORayleighfadingchannel ........................ 51 2-13BERperformanceofMCV-BLASTunder50%MTJforBPSKmodulationwith22MIMORayleighfadingchannel ........................ 52 3-1Theoreticalandsimulatedspectralnorm,kykk2,in( 3{12 )withP=31andSNR=-5dB ...................................... 63 3-2ComparisonofMSE,E[(^kk)2],bythespectralnormvs.Frobeniusnorm ... 63 3-3Agraphicalillustrationofthezigzagestimatorwhere^n=blog2(P+1)cand^c=sgn(^c) ..................................... 71 3-4Symbolsynchronizationbythespectralnormwherethedasheddenotesa1,thesoliddenotesa0,thedashed-dotteddenotesa1,respectively ....... 76 3-5Datasymbolsestimationby( 3{15 ) ......................... 77 3-6Spreadsequenceestimationby( 3{25 ) ........................ 77 9

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....................... 78 3-8Histogramofhc;^ciwithP=64,L=128,andSNR=-5dB ............ 79 3-9ComparisonoftheprobabilityofcorrectestimationofthespreadsequencePr(hc;^ci=P) ........................................... 81 3-10ComparisonofthesimulatedandanalyticalprobabilityofbiterrorPab;zigzagwiththezigzagestimatorin( 3{50 ) ............................ 82 3-11Probabilityofcorrectestimationofthespreadsequencebythezigzagestimationwithn-tuplegeneratorpolynomial,P=2n1,SNR=-10dBandL=256 .... 83 4-1AblockdiagramofTDCStransmitter[ 9 { 11 ] .................... 87 4-2Spectralestimationandspectralnotching ..................... 92 4-3AntipodalsignalingBERperformancewithoutinterferencein( 4{8 ) ....... 94 4-4Theoreticalandsimulatedperformancewithoutspectralshapingin( 4{10 ) ... 94 4-5AntipodalsignalingBERperformanceunder10%partialbandjamming .... 95 4-6AntipodalsignalingBERperformanceunder70%partialbandjamming .... 96 4-7AntipodalsignalingBERperformanceundersingle-toneJamming ........ 97 4-8AntipodalsignalingBERperformanceundermulti-toneJamming ........ 97 4-9AntipodalsignalingBERperformanceunderswept-tonejamming ........ 98 5-1V-BLASTwiththeTDP[ 12 ] ............................ 102 5-2BERperformancewithoutinterference ....................... 106 5-3BERperformanceforMN=22under30%partialbandInterference ... 107 5-4BERperformanceforMN=22undersingle-toneinterference ....... 108 5-5BERperformanceforMN=22underswept-toneinterference ....... 108 5-6BERperformanceforMN=22undermulti-toneinterference ....... 109 5-7BERperformanceforMN=44under30%partialbandinterference ... 109 5-8BERperformanceforMN=44undersingle-toneinterference ....... 110 5-9BERperformanceforMN=44underswept-toneinterference ....... 110 5-10BERperformanceforMN=44undermulti-toneinterference ....... 111 6-1ArchitectureofMC-CDMAtransceiverwithmultipletransmitterantennae,precodingandreceiver-basedequalization ........................... 116 10

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.. 127 6-3EectofarraygainontheaverageBERusingPS/MRCforsingleuser(K=1)withP=1;2;4overRayleighfadingchannel .................... 127 6-4AverageBERofsynchronousMC-CDMAdownlinkusingTIR/MRCforK=8activeuserswithP=1;2;4overRayleighfadingchannel ............. 129 6-5PerformancecomparisonofsynchronousMC-CDMAdownlinkusingPDforK=8activeuserswithP=1;2;4overRayleighfadingchannel ............. 129 6-6PerformancecomparisonofsynchronousMC-CDMAdownlinkusingMRCforK=8activeuserswithP=1;2;4overRayleighfadingchannel .......... 130 6-7PerformancecomparisonofsynchronousMC-CDMAdownlinkusingEGCforK=8activeuserswithP=1;2;4overRayleighfadingchannel .......... 130 6-8PerformancecomparisonofsynchronousMC-CDMAdownlinkusingORCforK=8activeuserswithP=1;2;4overRayleighfadingchannel .......... 131 6-9PerformancecomparisonofsynchronousMC-CDMAdownlinkusingMMSEforK=8activeuserswithP=1;2;4overRayleighfadingchannel .......... 131 7-1TransmitterandreceiverarchitectureofMC-TDCSwithmultipletransmitterantennae,pre-lteringandreceiver-basedequalization ............... 136 7-2Pseudo-randomphasevectorforr,whererdenotesthenumberofrandomsequencebitsgeneratedbyLFSR ............................... 138 7-3BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuserandsingletransmitantennaoverLk;p-pathRayleighfading ...... 143 7-4BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuser(K=1)andmultipleantennaeoverLk;p=2-pathRayleighfading 145 7-5BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithtwotransmitterantennae(P=2)overLk;p=2-pathRayleighfading ...... 146 7-6BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithfourtransmitterantennae(P=4)overLk;p=2-pathRayleighfading ...... 146 7-7BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuser(K=1)overLk;p-pathRayleighfading ................. 148 7-8BERperformanceofthesynchronousMC-TDCSdownlinkusingORCwithsingleuseroverL-pathRayleighfadingwhereListhediversityorder ......... 149 7-9BERperformanceofthesynchronousMC-TDCSdownlinkusingMMSEwithsingleuser(K=1)overLk;p-pathRayleighfadingwhereLk;pisthediversityorder 150 11

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....... 153 7-11BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderBNJoverL-pathRayleighfadingwhereListhediversityorder ......... 155 7-12BERperformanceofthesynchronousMC-TDCSdownlinkusingEGCunderBNJoverL-pathRayleighfadingwhereListhediversityorder ......... 155 7-13BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunder10%PBJoverL-pathRayleighfadingwhereListhediversityorder ...... 156 7-14BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderSTJoverL-pathRayleighfadingwhereListhediversityorder ......... 158 7-15BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderMTJoverL-pathRayleighfadingwhereListhediversityorder ......... 159 12

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Inthisdissertation,weconsiderphysicallayertechniquesinwirelesscommunicationsecurity.Westudyhowtocrackanadversary'scommunicationwhichusesdirect-sequencespread-spectrum(DS-SS),andhowtoprotectwirelesscommunicationsystemsagainstinterference.Thesesecuritymeasuresareclassiedaselectronicprotection(EP)andelectronicattack(EA)amongelectronicwarfare(EW),respectively.EWistheuseoftheelectromagneticspectrumtoeectivelydenytheuseofthismediumbyanadversary,whileoptimizingitsusebyfriendlyforces. Weinvestigatetheperformanceofthephysicallayerofwirelesscommunicationsystemsconsideredinthisdissertation.Onthetopicofeavesdroppingonanadversary'ssecurecommunication,wediscusshowtocrackaDS-SSsystem.TheDS-SSisacoverttechniqueresistanttointerference,interceptionandmultipathfading.Identifyingspread-spectrumsignalsorcrackingDS-SSsystemsbyanunintendedreceiver(oreavesdropper)withoutaprioriknowledgeisachallengingproblem.Toaddressthisproblem,werstsearchforthestartpositionofdatasymbolsinthespreadsignal(forsymbolsynchronization).Aftersynchronization,weremoveaspreadsequencebyaless-expensiveandmoreaccuratecross-correlationbasedmethod,andidentifythespreadsequencebyusingamatchedlter.Wealsoproposeazigzagsearchingmethodtoidentifyageneratorpolynomialthatreducesmemoryrequirementandiscapableofcorrecting 13

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Withregardtoprotectingwirelesscommunicationsystemsagainstinterference,weproposeanenhancedtransformdomaincommunicationsystem(ETDCS)withnarrowbandinterference(NBI)avoidancecapabilityasacountermeasureforasingle-carriersingle-inputsingle-output(SC-SISO)communicationsystem,avertical-BellLaboratorieslayeredspace-time(V-BLAST)architecturewithnon-stationaryinterferenceavoidancecapabilityasacountermeasureforasingle-carriermulti-inputmulti-output(SC-MIMO),andamulti-carriertransformdomaincommunicationsystem(MC-TDCS)asacountermeasureformulti-carriermulti-inputsingle-output(MC-MISO)systems,respectively. TheTDCSisaviablesolutionforinterferenceavoidance.Aninterferenceavoidingfundamentalmodulationwaveformissynthesizedatthetransmittertoavoidintentionalinterference,andthereceiveradaptsitsmatchedltertomatchthetransmittedfundamentalmodulationwaveforminthefrequencydomain.Bydoingso,spectrallyinterferedregionsareavoidedaltogetherviaadaptivespectralnotching. ThebasicideafortheETDCSistosynthesizeanadaptivefundamentalmodulationwaveformbyanon-parametricspectralestimator,calledCapon'smethod.TheadvantagesoftheETDCSandaV-BLASTwiththeminimummeansquareerror(MMSE)detectorareintegratedtoenhancebiterrorperformanceinnarrowbandinterference(NBI)environment.TheconceptsofETDCSandmulti-carriermodulationarecombinedtogetherintheMC-TDCStocombatmultipathfadingandtoavoidintentionalinterference. Incodedivisionmultipleaccess(CDMA)ormulti-carrierCDMA(MC-CDMA)systems,becauseusersdonotusecompletelyorthogonalspreadingcodesororthogonalityofthespreadingcodesaredestroyedbymultipathfading,thereisresidualmultiple-accessinterference(MAI)presentattheoutputofamatchedlter.Transmitterpre-lteringtechniquescanbeemployedtomitigatetheMAIandchanneldistortionsinthedownlinkoftheMC-CDMA.Weanalyzethebiterrorrateperformanceofadownlinktimedivision 14

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Insummary,thisresearchstudiesphysicallayermeasuresinwirelesscommunicationsecurity.WeprovidecountermeasuresforSISOandMIMOcommunicationsystemsagainstjammingandunintentionalinterference,whilewealsostudyvulnerabilitiesofDS-SSsystemsaswellashowtocracktheDS-SSsystem. 15

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Wirelesscommunicationsareverycommonbothformilitaryandcommercialparties.Theabilitytousecommunicationwhilemobilehasgreatbenetstobothparties.However,wirelesscommunicationhasmanysecurityissues,sincecommunicationtakesplaceoverawirelesschannelwhiletheusersareusuallymobile. Suchawirelesschannelsuersfromanumberofvulnerabilities:1)Thechannelisvulnerabletoeavesdropping.2)Thedatacanbealtered.3)Theabsenceofawiredlinkmakesitmucheasiertocheatonidentities.4)Thechannelcanbeoverused.5)Finally,thechannelcanbejammed,notablyinordertoaperpetrateadenial-of-service(DoS)attack[ 13 ]. Mobilityalsobringsusseveralimplications:1)Adevicecanjeopardizeprivacy.2)Mobilitymeansthatagivendevicemustbeabletoroamacrosswirelessnetworkscontrolledbydierentoperators.3)Mobiledeviceshavelimitedstorage,computingpower,andenergy.4)Amobiledevicecanbeeasilystolensothatitcanbemisusedorreverseengineered[ 13 ]1. Duetovulnerabilitiesbythecharacteristicsofwirelesscommunications,wehaveseveralrequirementsusuallytobemetbyasecuresystem:1)Themostobviousrequirementisauthentication.2)Accesscontrolistheabilityofanorganizationtograntappropriateaccesstoresources.3)Condentialityoftheexchangedinformationisalsoanimportantrequirementsincethewirelesschannelcanbevulnerabletoeavesdropping.4)Theintegrityofdatamustbeappropriatelyprotected.5)Anotherrequirementisprivacy.6)Non-repudiationisalsoanimportantrequirement.7)Finally,thenetworkmustprovide 16

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13 ].Next,wewilldescribeourmotivationforstudyingtheseproblems. 14 ]. 2 15 16 ].TheDS-SSsignalhasthecharacteristicsofpseudo-randomnessandcorrelationprocessing,whichleadtomanyadvantagessuchasanti-noise,anti-interference,andanti-multipathfading. Intheareaofnon-cooperativecommunicationsystems,aninterceptordoesnothaveaprioriknowledgeaboutthePNsequence.Toeavesdropontheadversary'scommunicationwhichusesDS-SS,theestimationofthespreadsequencefromtheinterceptedsignalisakeytocrackingtheseDS-SSsystemsandisachallengingproblem.Theliteratureonthissubjectisnotrich.2 3.2 17

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Theseobservationsmotivateustoinvestigatethefollowingproblems: 1. CanwecrackaDS-SSsystemwithoutaprioriknowledgeaboutthatsystem? 2. Canwecorrectpolarityerrorsaswellasreducememoryrequirementsofaneavesdropper? 3. Ifsuchamethodisfeasible,canwepredicttheperformanceoftheeavesdropperwithoutmassivesimulations? Wewilladdressthesequestionsinthisdissertation. Intentionalelectromagneticinterference(IEME)canbecategorizedintofourcategories,basedonthefrequencycontentoftheirspectraldensitiesas\narrowband",\moderateband",\ultra-moderateband",and\hyperband"[ 1 ]. TheDS-SSisaradiotransmissiontechnologythathasresistancetointentionalorunintentionalinterference[ 2 16 ].Therefore,spread-spectrum,ingeneral,hasbeenused 18

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17 18 ].TheDS-SSdoesnotavoidinterferedregions,sincetheinformation-bearingsignalisstilltransmittedatthoseregions. However,asingle-carriertransformdomaincommunicationsystem(SC-TDCS)canavoidaltogetherspectrallycrowdedregionsviagenerationofanadaptiveinterferenceavoidingfundamentalmodulationwaveform(FMW)atboththetransmitterandreceiver.TheTDCS[ 9 11 ]providesaviablesolutionforinterferenceavoidance.Therefore,theforemostresearchproblemintheSC-TDCSisaccurateestimationofthespectralenvironment.Themoreaccuratetheestimationofthespectralcontent,thebettertheperformancetheTDCSwillachieve. Forsingle-inputsingle-output(SISO)communicationsystems,therewereseveralapproacheswhichincorporatedtheSC-TDCSwithdierentmethodsofestimationofthespectralenvironmentintheliterature[ 9 10 19 ].TheSC-TDCS[ 9 11 ]utilizedaparametric10th-orderautoregressive(AR)methodtoestimatethepowerspectraldensity(PSD)ofthespectralenvironment.However,theAR-estimatorfailedtoprovideaccurateestimationundernon-stationaryinterference.Thewaveletdomaincommunicationsystem(WDCS)[ 10 ]andtheenhancedWDCS(EWDCS)[ 19 ]utilizedaconceptofawaveletperiodogramandanevolutionarywaveletspectrum(EWS)forspectralestimation,respectively.Thewaveletperiodogramisnotanaccurateestimationofenvironmentalpowerspectraldensity(PSD)andisnotabletoestimateanon-stationaryinterference,whilethebiterrorrate(BER)performanceoftheEWDCSunderanon-stationaryinterferencewasrelativelysub-optimalcomparedtothatunderstationaryinterferenceswithrespecttonon-stationaryinterference.Therefore,weneedtomitigatetheproblemoftheTDCS[ 9 11 ],WDCS[ 10 ],andEWDCS[ 19 ]forSC-TDCSsystems. Multiple-inputandmultiple-output(MIMO)systemsthatusemultipleantennaeatboththetransmitterandreceiverareapromisingdevelopmentinwirelesscommunication 19

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7 20 ]. Thefundamentalconceptsoftransformdomainprocessing(TDP)oftheSC-TDCSandV-BLASTbasedonzero-forcing(ZF)detectorwascombinedintheworkof[ 12 ]tomitigateNBI.However,itfailedtomitigatenon-stationaryinterference,likeswept-toneinterference.Thelackofstationarityofanon-stationaryinterferenceaectedtheperformanceofthespectralestimator,thereforethesystemproposedin[ 12 ]didnotworkwellfornon-stationaryinterferences.Moreover,theZFdetectorcansuerfromnoiseenhancementatearlystagesoftheV-BLASTscheme.Therefore,wealsoneedtoprovidenon-stationaryaswellasstationaryinterferenceavoidancecapabilitytotheV-BLASTsystemforhighlyreliablecommunication. Acosteectivetransmissiontechniquethatcanusescarcespectralresourcesisinneedforwirelessservices.Multi-carrierCDMA(MC-CDMA)hasbeendevelopedasacandidateair-interface,especiallyfordownlink,toprovidehighbitrates.However,theperformanceofMC-CDMAisessentiallylimitedbymultipleaccessinterference(MAI),andlowcomputationalcomplexityandresourceusagesaredesiredatmobileterminals(MTs)[ 21 { 23 ]. TomitigatetheMAI,theuseofpre-lteringwithMC-CDMAsystemshasalsobeenconsideredrecently.Pre-lteringapproachesdesignedinfrequencyandspacefordownlinktimedivisionduplexMC-CDMAsystemshavebeenproposedin[ 22 24 { 27 ].However,notmuchworkhasbeendonetomitigatejammingfortheMC-CDMA.TheMC-CDMAhasanti-jammingcapabilityduetousageofspreadsequence,butdoesnothaveinterferenceavoidancecapabilitylikeDS-CDMA. Asmentioned,theTDCScanprovidetheinterferenceavoidancecapabilityforaSCcommunicationsystem[ 9 11 ].ResearchresultsaimedatcharacterizingSC-TDCS 20

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28 ]andthatperformanceundermultipathfadingwasstudiedin[ 29 ].However,themitigationoftheMAIwasnotaddressedin[ 28 29 ]. Recently,theTDCShasbeenappliedtocognitiveradio(CR)technique[ 30 ],sinceitcanutilizethespectrumecientlybylearningandadaptingitssystemtotheenvironmentalcondition.ThedevelopmentofCRtechniquehasbeenraisedbythefactthatthespectrumisnotalwaysbeingusedaccordingtothespectralmeasurementresult[ 31 ]. Anorthogonalfrequencydivisionmultiplexing(OFDM)basedTDCSinCRforcontrolmessagetransmissionwasproposedin[ 29 ].However,onlytheSISOantennacongurationwasconsideredandperformanceundertheintentionalinterferencewasnotinvestigated.AperformancecomparisonbetweentheSC-TDCSandOFDM-basedCRradioforaMIMOsystemusingtheV-BLASTreceiverarchitecturetoreconstructthetransmitteddatainRayleighfadingchannelwaspresentedin[ 32 ].Amodicationofboththetransmitterandthereceiverblockdiagramaccordingto[ 11 ]hadbeenmadeintheirsystems.TheCRwithOFDMconsistentlyoutperformstheCRwithTDCSarchitecture.Sincethezero-forcingequalizationatthereceiverremovedthefrequencyselectivityofthechanneltransferfunction,thereisnoroomforimprovementwiththeaidoffrequencydomaindiversity.Therefore,weneedtoenhancetheBERperformanceoftheTDCSunderRayleighfadingwiththehelpofthefrequencydomaindiversitycombiningtechniques. Theaforementionedobservationsmotivateustoinvestigatethefollowingproblems: 1. CanweenhancetheperformanceoftheSC-TDCSunderbothstationaryandnon-stationaryinterference? 2. Ifsuchamethodisestablished,isitapplicabletoMIMO-TDCS,especiallyfortheV-BLAST,inordertomitigatebothstationaryandnon-stationaryinterference? 3. CanweenhancetheperformanceoftheTDCSundermultipathfadingwiththehelpofthefrequencydomaindiversityandtransmitterdiversity? 21

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Ifsuchasystemispossible,canwemitigateintentionalinterferenceaswellasunintentionalinterference? 5. Canwepredictthebiterrorperformanceofthesystem? Wewilladdressthesequestionsinthisdissertation. ThecontributionsmadetowardcrackingDS-SSare:(i)ageneratorpolynomialestimatorwhichcanidentifyacodegeneratorpolynomialandcancorrectpolarityerrorsintheestimatedPNsequenceandestimateddatasymbols,(ii)atheoreticalvericationoftheprobabilityoferrorofacodegeneratorestimatorwithrespecttosignal-to-noiseratio(SNR),thenumberofdatasymbols,andthelengthofthespreadsequenceoftheinterceptedsignal,and(iii)theaccuracyofperformancepredictionofaneavesdropper. AscontributionsmadetowardprotectingSISOcommunicationsystemsagainstjamming,weproposetheenhancedTDCS(ETDCS)whichisapracticalalternativefortheSC-TDCSwithanon-parametricspectralestimationmethod[ 33 34 ].WederiveamathematicalmodeloftheTDCSandanalyzetheBERperformanceoftheTDCS.TheproposedETDCSwithCapon'smethod(CM)canproperlyestimatetheinterferenceenvironmentandoerssignicantinterferenceavoidancecapabilityforboththestationaryandnon-stationaryinterference.Moreover,theETDCSshowstheconsistentbiterrorperformanceunderboththestationaryinterferenceandthenon-stationaryinterference. Weextendourpreviousapproachin[ 34 ]toprovidenon-stationaryaswellasstationaryinterferenceavoidancecapabilitytotheV-BLASTsystem[ 35 ]ascontributionsprotectingtheMIMOcommunicationsystemagainstjamming.TheTDPbyCMandminimummeansquareerror(MMSE)detectorarecombinedwiththeV-BLASTtoenhancebiterrorperformanceintheNBIenvironment. Tomitigatethemultipleaccessinterference(MAI)andintentionalinterference,weproposethemulti-carrierTDCS(MC-TDCS)asaninterferenceavoidancemulti-carrier 22

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Wealsoanalyzetheperformanceofjointspace-frequencyprecodingapproachesintermsoftheaverageBERperformance.Severallinearpowerallocationstrategiesincorporatedtogetherwithsingleuserequalizationschemesarecomparedtoajointprecodingwithanequalpowerconstraintatthebase-stationandmaximalratiocombining(MRC)atthemobileterminals(MTs).Byconductingthesestudies,wecanpredicttheperformanceofvariousspace-frequencyprecodingschemes[ 22 24 { 27 36 37 ]withoutmassivesimulations. InChapter 2 ,westudytheBERperformanceofthewirelesscommunicationsystemsconsideredinthisdissertation.WedescribeinterferencemodelandstudystationarityofintentionalinterferenceinSection 2.2 .InSection 2.3 ,westudysingle-carriermodulationsystems.OFDMandMC-CDMAareintroducedasmulti-carriermodulation(MCM)methodsinSection 2.4 .WestudyeectsofjammingonMIMOinSection 2.5 .Theoreticalanalysistoquantifytheeectsofinterferenceonmulti-carrierMIMOsystemsisconductedinSection 2.6 .Finally,Section 2.7 summarizesthischapter. InChapter 3 ,weturnourattentiontocrackingDS-SSsystems[ 38 39 ].RelatedworksarediscussedinSection 3.2 .Section 3.3 describesthesignalmodel.Section 3.4 introducesourmethodofidentifyingthestartpositionofadatasymbolinthespreadsignal.Section 3.5 presentshowtoremovedatasymbolsfromtheinterceptedsignal. 23

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3.6 .Section 3.7 discusseshowtoidentifyaPNcodegeneratorpolynomialandhowtocorrectpolarityerrors.Section 3.8 presentssimulationresultstoshowtheeectivenessandtovalidatetheanalyticalprobabilityoferrorofourapproaches.Section 3.9 summarizesthischapter. InChapter 4 ,weproposestheETDCSwhichisapracticalalternativefortheTDCSwithanon-parametricspectralestimationmethod.InSection 4.2 ,weelaborateonamathematicalmodelofTDCS.InSection 4.3 ,anoverviewoftheTDCSarchitectureisgiven,andthelimitationsoftheTDCSandtheproposedestimationmethodareinvestigated.EectsofvariousformsofjammingontheperformanceofETDCSandcomparativebiterrorperformanceanalysisoftheproposedETDCSfollowinSection 4.4 .Finally,Section 4.5 summarizesthischapter. InChapter 5 ,weextendourpreviousapproachinChapter 4 toamulti-inputmulti-output(MIMO)communicationsystem[ 35 ].Section 5.2 presentsourpreviouswork.Section 5.3 describesaV-BLASTsystemmodelandtheinterferencemodel.Section 5.4 introducesourproposedmethodology.Section 5.5 presentssimulationresultstoshowtheperformanceofourproposedapproaches.Section 5.6 summarizesthischapter. InChapter 6 ,weanalyzetheBERperformanceof(joint)space-frequencyprecodingapproaches.Section 6.2 elaboratesonasystemmodelofaDLTDDMC-TDCS.Then,varioussingle-userequalizationmethodsarediscussedinSection 6.3 .Section 6.4 describeshowtomitigatetheMAIwithhelpofthetransmitterdiversityandtheprecodingatthetransmitter.TheperformanceanalysisandvericationbysimulationarepresentedinSection 6.4.3 andSection 6.5 ,respectively.Finally,Section 6.6 summarizesthischapter. InChapter 7 ,weproposeamulti-carriertransformdomaincommunicationsystem(MC-TDCS).Section 7.2 elaboratesonasystemmodeloftheproposedMC-TDCSanddescribesamathematicalmodeloftheproposedsystem.Then,singleuserequalizerperformanceforthesingleuserdetectionisinvestigatedinSection 7.3 .Section 7.4 describeshowtomitigatetheMAIwiththehelpoftransmitterdiversityandprecoding 24

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7.5 .Finally,Section 7.6 summarizesthischapter. InChapter 8 ,wesummarizethedissertationandpointoutfutureresearchdirections. 25

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13 17 ]1. Thepurposeofthischapteristoinvestigatetheperformanceofvariouswirelesscommunicationsystemsatphysicallayerunderinterference,sinceinterferencecandisruptcommunicationsbydecreasingthesignal-to-noiseratio(SNR).Therefore,weneedtoinvestigatetheperformanceofwirelesscommunicationsystemsunderinterferencetopredictthatperformanceortomitigateinterferenceforreliablecommunication. Thephysicallayerunderstudyincludessingle-carriersystems,multi-carriermodulationsystem,single-inputsingle-output(SISO)systems,multi-inputmulti-output(MIMO)systems,andsoon.Theperformancemeasureofinterestisthebiterrorrate(BER)inthischapter. Theremainderofthischapterisorganizedasfollows.WedescribeinterferencemodelandstudystationarityofintentionalinterferenceinSection 2.2 .InSection 2.3 ,westudysingle-carriermodulationsystems.Orthogonalfrequencydivisionmultiplexing(OFDM)andmulti-carriercodedivisionmultipleaccess(MC-CDMA)areintroducedasmulti-carriermodulation(MCM)methodsinSection 2.4 .Westudyeectsofjammingonmultiple-inputmultiple-output(MIMO)inSection 2.5 .Theoreticalanalysistoquantify 1 26

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2.6 .Finally,Section 2.7 summarizesthischapter. 1 ].Thedenitionsforbandwidthclassicationproposedin[ 1 ]isshowninTable 2-1 forreference. Table2-1. IMEMclassicationbasedonbandwidthin[ 1 ] BandratioBandtype hypoband Moderateor mesoband 1%
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PSDN=N0+NJ(2{1) whereN0isthenoisePSDofcomplexAWGNandNJisthePSDofcomplexBNJ. where'Jistherandomphase,whichisuniformlydistributedover[0;2].AJandfJaretheamplitudeandfrequency,respectively.Single-tonejamming(STJ)isaspecialcaseofmulti-tonejammingwithq=1. 28

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2dJ=0(2{3) whereE[]denotesexpectationandautocorrelationofJ(t)becomes where()denotescomplexconjugation. NotethatSWTJcombinestheadvantagesofbothspotjammingandBNJbyrapidelectronicsweepingofanarrowbandofjammingsignalsoverabroadfrequencyspectrum;thedisadvantageofSWTJisitshighsusceptibilitytoelectroniccounter-countermeasures.Whilethishastheadvantageofbeingabletojammultiplefrequenciesinquicksuccession,itdoesnotaectthemallatthesametime,andthuslimitstheeectivenessofthistypeofjamming.Although,dependingontheerrorcheckinginthedevice(s),thiscanrenderawiderangeofdeviceseectivelyuseless.Everyswept-tonecanbemodeledas withfJ=fL+twhereJisrandomphasewhichisuniformlydistributedover[0;2].AJandfJareamplitudeandfrequency,respectively.fLislowsofsweepsandtissweeptimeandissweepinterval. 29

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TheautocorrelationofJ(t)becomes Therefore,theSWTJisnotawide-sensestationary(WSS)jamming.However,theSWTJisacyclostationaryprocess.Since 2.2.2.1Multipleaccessinterference 2.3.2 andSection 2.4.2 ,respectively. 30

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40 ]. 2.3.1 introducesdirect-sequencespread-spectrum(DS-SS)andlinearfeedbackshiftregister(LFSR),anddiscussesvulnerabilitiesofthatDS-SSsystemintermsofnon-cooperativecommunication.Section 2.3.2 dealswiththeMAIofcodedivisionmultipleaccess(CDMA).InSection 2.3.3 ,atransformdomaincommunicationsystem(TDCS)isintroducedasaninterferenceavoidancesystem. 2 ]. InDS-SSsystems,theinformationsignalismodulatedbyaPNsequencepriortotransmissionresultinginawidebandsignalresistanttonarrowbandjammingandmultipath.TheDS-SStransmittersuseaperiodicalpseudo-randomsequencetomodulatethebasebandsignalbeforetransmission.ThePNspreadingsequenceistypicallyknowntothereceiver,whichusesthematchedlteringoperationandrecoversthetransmitteddata[ 15 16 ].TheDS-SSsignalhasthecharacteristicsofpseudo-randomnessandcorrelation 31

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2 16 ]. + Linearfeedbackshiftregister[ 2 { 5 ] PracticalandecientimplementationtechniquesforPNsequencescenteronshift-register.Sincecrackabilityissuchanimportantissue,itappearssensibletocategorizePNcodegenerator,accordingtoincreasingcomplexity,intheclassesof(a)linearfeedbackshiftregister(LFSR);(b)oneormoreLFSRswithnonlinearfeedforwardlogic(NFFL);and(c)generalnonlinearfeedbackshift-register(NLFSR).Otheradhoccasesarepossible. Figure 2-1 showsadiagramoftheLFSR.LFSRscangeneratelinearmaximalsequences,m-sequences,orPNsequence,usingselectedstagesofann-stageshiftregister.Thecorrectselectionofthetap-weights(orfeedbackstages)willresultinamaximalsequencelengthN=2n1.Theclassicalpropertiesofanm-sequenceare[ 4 5 15 ]:(1)maximal-lengthforann-stagegenerator;(2)maximumpossiblepeak/side-lobeautocorrelationovertheperiodN;and(3)alargenumberofmaximumcodespern-stages. However,non-cooperativecommunicationsystems,suchasspectrumssurveillanceandelectronicinterception,areentirelydierentfromcooperativecommunicationsystems.Thereceiverhasminimalknowledgeoftheinterceptedsignal.Inthiscaseonlyblind 32

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41 ].Capturinginformationfromtheinterceptedsignalisstillanimportantanddicultproblemtobesolvedinthenon-cooperativecommunicationsystem[ 38 39 42 ].InChapter 3 ,wediscusshowtocrackaDS-SSsystem.WeconsidertheLFSRastheimplementationtechniqueforPNsequencesinChapter 3 2.2 ,thedownlink(DL)multiuserCDMAsuersfromtheMAI.Therefore,theperformanceoftheCDMAispredeterminedbytheMAI.Atransmitterprecoding,asanalternativeforcombatingtheMAIinsynchronousmultiuserchannel,wasproposedin[ 43 44 ].Thetransmitterprecodingreducesthemultiuserdetectionproblemintodecoupledsingleuserdetectionproblem. AsymptoticBERofaprecodedrandomspreadingsystemin[ 44 ]is whereQ(x)=1=p n(2{10) whereKisthenumberofusers,andKn(nisthenumberofchips/bit).Moreover,theperformanceoftheprecodingandthereceiver-baseddecorrelatorwithequalorunequalpowerdistributionisasymptoticallyequivalent. Areproductionoftheasymptotictheoreticalperformanceoftheprecodingandthatofreceiver-baseddecorrelatorisshowninFigure 2-2 for=0.2,0.5,and0.8andn=100.Theresultshowsthattheirperformancearequitesimilarasexpected.Interestedreadersshouldreferto[ 44 ]andreferencestherein. 33

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Performanceoftheprecodingandthereceiver-baseddecorrelatorfor=0.2,0.5,0.8,andn=100 9 11 ]isaviableoptionforavoidingtheinterferenceconsideredinthepreviousSection 2.2.1 .InTDCS,thetransmittergeneratesaninterference-freewaveformtoavoidtheintentionalinterference,whilethereceiverneedstoadaptitsmatchedltertomatchthetransmittedwaveform.Adaptivespectralnotchingavoidsthespectrallycrowdedregions(orthejammedregions). InChapter 4 ,weproposeanenhancedTDCS(ETDCS)whichisapracticalalternativefortheTDCSin[ 9 11 ]withanon-parametricspectralestimationmethod.InChapter 5 ,weextendourapproachinChapter 4 toprovidenon-stationaryaswellasstationaryinterferenceavoidancecapabilitytoavertical-BellLaboratorieslayeredspace-time(V-BLAST)system.InChapter 7 ,weproposeamulti-carrierTDCS(MC-TDCS).Theconceptoftransformdomainprocessing(TDP)andmulti-carriermodulation(MCM)arecombinedtogetherinMC-TDCStoavoidintentionalinterferenceandtocombatmultipathfading.Wewillalsostudytheperformanceundermultiuserand 34

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2.4.1 isrobustagainstinter-symbolinterference(ISI)andfadingcausedbymultipathfading,andisalsorobustagainstnarrowbandICI.WestudytheMAIproblemofMC-CDMAinSection 2.4.2 23 ]. SinceOFDMisaveryimportantcandidateforthecoretechniqueofnextgenerationwirelesscommunicationsystems,itisnecessarytoevaluateitsperformanceunderintentionalinterferenceoverfadingchannels.In[ 45 ],acomprehensivestudyoftheeectofdierentjammingtechniquesforanOFDMsystemwasconducted.Bycomparingthebiterrorrate(BER)performanceofdierentjammingtechniques,themosteectivejammingtechniquecanbeidentiedundervariouschannelconditions.Thisisverycriticalforbothjammingandanti-jammingapplicationsforOFDMsystems.BNJ,PBJ,andMTJinatime-correlatedRayleighfadingchannelwithAWGNwereevaluatedin[ 45 ].Interested 35

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45 ]tounderstandtheeectsofvarioustypesofjammingforOFDMsystems. 2.3.2 ,wherespreadingisperformedinthetimedomain,hashighsamplingrates.ThishighsamplingratemakesDS-CDMAverysusceptibletoperformancedegradationcausedbymultipathpropagation[ 23 ].Therefore,MC-CDMAwasdevelopedtoovercomethisdrawbackoftheDS-CDMA[ 21 ].ThemainbenetofMC-CDMAincomparisontootherOFDM-basedmultipleaccessmethodsinSection 2.4.1 istheinherentprovisionoffrequencydiversity.Bycontrast,adrawbackofMC-CDMA,likeDS-CDMA,istheMAIencountered.ThesefactorspredeterminedtheperformanceofMC-CDMA[ 23 ]. BecausethelossoftheorthogonalityamongusersinmultipathenvironmentscausestheMAI,weneedtomitigatetheMAI.WhileinDLtransmissions(i.e.,fromthebasestation(BS)tothemobileterminals(MTs)),thesingleuserdetection(SUD)techniquesaretypicallyemployed,guaranteeingreasonabletrade-obetweenperformanceandsystemcomplexity,inuplink(i.e.,fromtheMTstotheBS),multiuserdetection(MUD)techniquesseemtobemandatory[ 23 ]. Theideabehindpre-equalization4[ 22 25 26 46 { 48 ]istovarythegainassignedtoeachsub-carriersothattheinterferenceisreducedandalowcomplexdetectionschemecanbeemployedatthereceiver.Inordertoworkproperly,thepre-equalizationtechniquesrequirechannelstateinformation(CSI)atthetransmitter.InChapter 6 ,weanalyzethebiterrorperformanceofvariousspace-frequencyprecodingschemesofaDLMC-CDMA. 36

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2.5.1 andavertical-BLAST(V-BLAST)inSection 2.5.2 ,respectively. AlamoutiEncoder . AlamoutiDecoder ^xi AschematicofAlamoutitransmissionstrategy[ 6 ] AverysimpleandeectiveschemefortwotransmitantennaeandasinglereceiverantennaachievingdiversityordertwowasintroducedbyAlamoutiin[ 49 ].AtransceiverarchitectureisshowninFigure 2-3 Itsendsthesequencefx1;x2gontherstantennaandfx2;x1gontheother. 37

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orinshortnotationy=Hx+n.TheresultingchannelHisorthogonal,i.e.,HHH=HHH=h2I2andthegainofthechannelh2=jh1j2+jh2j2,sincethechannelbecomes: and Thetransmittedsymbolscanbecomputedbythezero-forcing(ZF)approach: Therelevantnoisevarianceisgivenby2ntrHHH1=2n=h2.Thedenominatorh2indicatesdiversityordertwoforthereceptionofbothsymbols.TheBERperformanceofBPSKmodulationisgivenby: Pb=Z10Qr 2exp2 Pb;STBC=P2b1+2(1Pb)(2{17) 38

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7 20 ]. Vectorencoder . TX TX TX TX . Richscattering environment V-BLASTDecoder . RX RX RX RX RX RX ^a . AhighlevelsystemdiagramofV-BLAST[ 7 ] Ahigh-levelsystemdiagramofaBLASTisshowninFigure 2-4 in[ 7 ].Thereceivedsignalvectorbecomes: wherer=[r1;;rN]Tanda=[a1;;aM]Tarethereceivedsignalvectorandtransmittedsignalvector,respectively.ThechannelmatrixHis 39

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WeassumethatthereceiverhastheCSI.Afullzero-forcingsequentialinterferencecancelation(ZF-SIC)algorithmisdescribedinTable 2-2 [ 20 ]. Table2-2. AZF-SICV-BLASTdetectionalgorithm Initialization:i1G1=H+k1=argminjk(G1)jk2Recursion:wki=(Gi)kiyki=wTkiri^aki=Q(yki)ri+1=ri^aki(H)kiGi+1=H+kiki+1=argminj62(k1;;ki)k(Gi+1)jk2ii+1 ItisdesirabletoutilizetheV-BLASTinthereliablewirelesscommunicationsystemunderintentionalinterference,mentionedinSection 2.2.1 .InChapter 5 ,aTDPinSection 2.3.3 andminimummeansquareerror(MMSE)detectorin[ 50 ]arecombinedwiththeV-BLASTtoenhanceperformanceintheNBIenvironment[ 35 ]. 2.4 andMIMOinSection 2.5 willachieveunprecedentedperformance.Multi-carrierMIMO(MC-MIMO)systemsarerobustagainstfrequencyselectivefadingduetofrequencydiversityfromOFDM,frequencyatfadingowingtospacediversityfromMIMO,andhighthroughputduetoMIMO.Weconducttheoreticalanalysistoquantifytheeectsofinterferenceonbothaspace-timeOFDM(ST-OFDM)systemandamulti-carrierV-BLAST(MCV-BLAST)systeminSection 2.6.2 andSection 2.6.4 ,respectively. 40

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Atthersttransmitter,Xo,istransmittedduringthersttimeslotfollowedbyXeinthesecondtimeslot.Atthesecondtransmitter,Xe,istransmittedrstfollowedbyXo.Theequivalentspace-timeblockcodetransmissionmatrixisgivenby: i.e.,entriesofthetransmissionmatrixaretheOFDMsymbolvectorsXo,Xe,andtheirconjugates. Let1and2betwodiagonalmatriceswhosediagonalelementsaretheDFTsoftherespectivechannelimpulseresponses,h1andh2.Assumingthatthechannelresponsesareconstantduringthetwotimeslots,thedemodulatedvectorsinthecorrespondingtimeslotsaregivenby Assumingthechannelresponsesareknownorcanbeestimatedaccuratelyatthereceiver,thedecisionvariablesareconstructedbycombiningY1,Y2,andthechannelresponse 41

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^X0=1Y1+2Y2^Xe=2Y11Y2(2{23) Substituting( 2{22 )into( 2{23 )yieldsthefollowingexpressions: ^X0=j1j2+j2j2X0+1Z1+2Z2^X0=j1j2+j2j2Xe+2Z11Z2(2{24) ItisknownthattheMRCistheoptimallinearcombiningtechniqueforreceiverdiversity.Theabovedecisionequationsforthetransmitterdiversityschemearesimilarinformtothatofatwo-branchMRCreceiverdiversitysystem.Theblockdiagramofspace-timeOFDMtransmitterdiversitysystemin[ 8 ]isshowninFigure 2-5 .TheBERperformanceofthespace-timeOFDMwithoutjammingisgivenby( 2{16 )and( 2{17 ). SerialtoParallel IDFT&CP IDFT&CP ParalleltoSerial ^X(m) Combiner&Detector RemoveCP&DFT ChannelEstimation Ablockdiagramofspace-timeOFDMsystems[ 8 ] 8 ]underjamming.Thechannelismodeledasaat-fadingRayleighchannel.Foreverysub-carrier 42

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whereandareindependentRayleighrandomvariableswithvariances2sand2Jrespectively.Becausejammingandsignalareunderthesamechannelenvironment,SandJcanberegardedasthesamevalue.Therefore,wehavethefollowingsignalmodelunderjamming. whereJ1andJ2denotetheDFTsofjammingand1and1aretwodiagonalmatriceswhosediagonalelementsaretheDFTsoftherespectivejammerchannelimpulseresponse. InRayleighfadingchannel,theeectiveenergy-per-bitbecomesGSEbandtheeectivePSDoftheBNJbecomesGJNJ.Aftersimplifying,wegettheBER SincetherearetwoRayleighrandomvariables,and,withthesamevariance,theaverageBERforBPSKcanbeexpressedas: Pb=Z10Z10Qs 4exp22 Certainly,theinniteupperlimitofintegrationshouldbereplacedbyniteapproximatedvalueinpractice. 43

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2-6 showstheperformanceofthespace-timeOFDMunderBNJwithRayleighfadingandAWGN.NotethatthetheoreticalBERperformanceisdrawnby( 2{17 )with( 2{29 ).TheOFDMsystememployed256sub-carriers.Itwasassumedthattheperfectchannelestimationwasavailableatthereceiver.ThetheoreticalBERperformanceby( 2{29 )isagoodapproximationofthesimulatedBERperformance. Figure2-6. PerformanceofST-OFDMsystemunderBNJwithRayleighfadingandAWGN WeconsiderthebestjammingscenarioforPBJ:ThejammingsignalbandwidthfallsintothatoftheOFDMsignalcompletely.Theportionofjammingsignalbandwidthcanbedescribedby: whereWJisthebandwidthofthejammingsignalandWSisthebandwidthoftheOFDMsignal.Weneedtoconsiderthejammedfrequencybandsandtheun-jammedfrequencybands.GiventheaveragePSDofPBJNJ,theeectivePSDofPBJinthersttypeofbandbecomesNJ=,andthereisnojammingatallinthesecondtypeofband.Then,wehavetheBERperformanceunderthePBJasfollows: 44

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Forthetime-correlatedRayleighfadingchannel,followingthesamestepsasbefore,theaverageBERforBPSKbecomes: Pb=Z10Z10Qs 4exp22 4exp22 Figure 2-7 showstheperformanceofthespace-timeOFDMunder50%PBJwithRayleighfadingandAWGN. Figure2-7. PerformanceofST-OFDMsystemunder=0:5PBJwithRayleighfadingandAWGN ForMTJ,weassumethatthoseqjammingtonesareperfectlyalignedwithqsub-carriersoftheOFDMsystem.Thentheportionofjammingsignalbandwidthisdenedas: 45

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2{32 ).Figure 2-8 showstheperformanceofthespace-timeOFDMunder50%MTJwithRayleighfadingandAWGN. Figure2-8. Performanceofspace-timeOFDMsystemunder=0:5MTJwithRayleighfadingandAWGN Vectorencoder . OFDM OFDM ... OFDM . Richscattering environment V-BLASTDecoder . FFT FFT FFT FFT ... FFT CP CP CP CP CP . ^a . Tx1 Tx2 TxM Rx1 Rx2 Rx3 Rx4 RxN Figure2-9. Multi-carrierV-BLASThighlevelsystemdiagramwherenumberoftransmittersisMandnumberofreceiversisN. TheV-BLASTisaMIMOsystembasedonspatialmultiplexing(SM)method,whichprovidestrade-obetweensystemperformanceandsystemimplementationcomplexity[ 7 46

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].TheV-BLASTiscombinedwithOFDMmodulationschemetoachievehighdataratetransmissioninfrequencyselectivefadingchannel.SincetheOFDMeectivelydividesthefrequencyselectivefadingchannelintoanumberofatfadingsub-channels,amulti-carrier(MC)V-BLASTsystemcomprisesofnarrowbandV-BLASTsystemsondierentsub-carriers.Therefore,theMCV-BLASTcanprovidebothhighdatarateandhighthroughputtransmissionoverrichscatteringchannel[ 23 ].AV-BLASTtransceivermodelbasedonanOFDMmodulationschemeisdepictedinFigure 2-9 AMCV-BLASTsystemwithMtransmitandNreceiverantennaeconsistsofonenarrowbandV-BLASTsystemoneachsubcarrier.Therefore,wecanwritethereceivedsignalvectoronaspecicsub-carrierasfollows: wherey=[y1;;yN]Tisthereceivedsignal,x=[x1;;xM]Tisthetransmittedsignaloneachsub-carrier,andnisAWGNnoise.ThechannelmatrixHisaNMmatrixwitheachentryHmndenotingthechannelresponsebetweenmthtransmitantennaandnthreceiveantenna, AV-BLASTalgorithmwillreconstructthetransmittedinformationsignalwiththeinformationofthechannelmatrixbyremovingtheeectoffadingofthechannelinfrequencydomain[ 7 ]. Figure 2-10 showstheBERperformanceforMN=22transceiverMCV-BLASTforBPSKmodulationinaatfadingindependentRayleighchannelforthedierentequalizers[ 20 ].Weusethesamemainsimulationparametersusedin[ 45 ].WecanseethattheBERperformancewithazero-forcing(ZF)equalizerisidenticaltothatofMN=11transceiversystem,andequalizerswithsuccessiveinterference 47

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Figure2-10. BERperformanceofMCV-BLASTforBPSKmodulationwithMN=22MIMORayleighFadingChannel LetboththejammingandthesignalbeindependentlyattenuatedbythechannelandlettwoindependentrandomvariablesbedescribedbythejammingchannelpowergainGv=2andthesignalchannelpowergainGx=2whereandareindependentRayleighrandomvariableswithvariance2xand2v,respectively.Therefore,theMIMOsignalmodelin( 2{34 )underjammingcanbewrittenasfollows: 48

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23 ],theBERforBPSKisgivenby: whereEbistheaverageenergy-per-bitofOFDMsignal.InRayleighfadingchannel,theeectiveenergy-per-bitbecomesGxEbandtheeectivePSDoftheBNJbecomesGvNv.Aftersimplifying,wegettheBERunderRayleighfadingchannelasfollows: SincetherearetwoRayleighrandomvariables,and,withthesamevariance,theaverageBERofzero-forcingMCV-BLASTwithMN=22underBNJforBPSKcanbeexpressedas: Pub=Z10Z10Qs 4exp22 TheperformanceoftheMC-VBLASTislowerboundedby: Plb=Pub21+2Pub(2{40) wheresuperscriptlandudenotelowerandupperboundoftheBER.Certainly,theinniteupperlimitofintegrationshouldbereplacedbyniteapproximatedvalueinpractice.Figure 2-11 showstheperformanceofthe22MCV-BLASTunderBNJwithRayleighfadingandAWGN.NotethattheanalyticalBERperformanceisdrawnby( 2{39 )and( 2{40 ).Inthissimulation,weusethesamesimulationparametersusedinFigure 2-10 withSNR=10dB. Let=WJ=WxdenotethefractionofjammedbandwidthWJwithrespecttototalsystembandwidthWxforPBJ.Therefore,wehavetoconsiderthejammedbandsandtheun-jammedbands.TheeectivePSDofPBJinthejammedbandsbecomesNJ=given 49

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BERperformanceofMCV-BLASTunderBNJforBPSKmodulationwith22MIMORayleighfadingchannel theaveragePSDofPBJNJ,whilethereisnojammingatallintheun-jammedbands.Therefore,theaverageBERunderPBJwithAWGNbecomes: NotethattheaverageBERunderBNJin( 2{37 )isaspecialcaseof( 2{41 )with=1and( 2{38 )forPBJbecomes: andtheaverageBERforBPSKforthetime-correlatedRayleighfadingchannelbecomes: Pub=Z10Z10Pb(;;) 4exp22 4exp22 Figure 2-12 showstheperformanceofthe22MCV-BLASTunder50%(=0:5)PBJwithRayleighfadingandAWGN.NotethattheanalyticalBERperformanceis 50

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BERperformanceofMCV-BLASTunder50%PBJforBPSKmodulationwith22MIMORayleighfadingchannel drawnby( 2{43 )and( 2{40 ).Inthissimulation,weusethesamesimulationparametersusedinFigure 2-11 .In[ 45 ],asignalspacemodelwasproposedtoanalyzetheBERperformanceofOFDMunderAWGN.ThusBERperformanceof22zero-forcingMCV-BLASTforBPSKisgivenas: whereAJcanbeobtainedsimplythroughthefollowingequation 51

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BERperformanceofMCV-BLASTunder50%MTJforBPSKmodulationwith22MIMORayleighfadingchannel IftheAWGNisnegligible(W=Y)forsimplicity,wehave: h andtheaverageBERperformanceof22ZFMCV-BLASTforBPSKunderMTJwithRayleighfadingchannelandAWGNis Pub=Z10Z10Pb(2Eb;N0;;2SIR=2) 4exp2+2 Figure 2-13 showstheperformanceofthe22MCV-BLASTunder50%(=0:5)MTJwithRayleighfadingandAWGN.NotethattheanalyticalBERperformanceisdrawnby( 2{47 )and( 2{40 ).Inthissimulation,weusethesamesimulationparameterswhichinFigure 2-11 TheMCV-BLASTcombinesthemeritsofmulti-carriermodulationandMIMOsystemtoachievehighdataratetransmissionunderfrequencyselectivefadingchannel.Inthissection,weinvestigatetheeectsofvariousjammingforMCV-BLASTunder 52

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53

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2 16 18 ]. Toeavesdropontheadversary'scommunication,oneneedsto(a)identifythestartpositionofdatasymbolsintheinterceptedspreadsignalforthepurposeofsymbolsynchronization,(b)estimatedatasymbols,(c)estimatethePNsequence,and(d)estimatethecodegeneratorpolynomialofthePNsequence. Toidentifythestartpositionofdatasymbols,wepresentamethodbasedonthespectralnormwhichachievessmallerestimationerrorinSection 3.4 .Afterthesymbolsynchronization,weremoveaPNsequencefromtheinterceptedsignalsbyacorrelationmethodtoestimatedatasymbolswithoutaprioriknowledgeaboutthatPNsequenceinSection 3.5 .IdenticationofaPNsequenceisprocessedbyamatchedlterbetweentheinterceptedsignalandtheestimateddatasymbolsinSection 3.6 OneoftheharderproblemsineavesdroppingonDS-SSsignalsisthepolarityambiguityoftheestimatedspreadsequenceanddatasymbols:ErroneousreversalofpolarityofeachchipintheestimatedPNsequencecomparedtothetruePNsequenceisamajorsourceoftheperformancedegradationofaneavesdropper.Therefore,weneedtoestimateacodegeneratorpolynomialtomitigatethispolarityproblem.WeproposeasearchingmethodtoidentifythecodegeneratorpolynomialinordertocorrectpolarityerrorsaswellastoreducememoryrequirementofaneavesdropperinSection 3.7 54

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Theprobabilityoferrorperformanceofaneavesdropperisafunctionofsignal-to-noiseratio(SNR),thenumberofdatasymbols,andthelengthofthespreadsequenceoftheinterceptedsignal.Therefore,weneedtostudytheanalyticalprobabilityoferrorperformanceoftheeavesdropperwithrespecttotheseparameters.Bydoingso,wecanecientlypredicttheperformanceoftheeavesdropper. First,weuseaGaussianapproximationmethodin[ 51 ]inordertondamarginalprobabilitydensityfunctionofthesymbolestimatorinSection 3.5 andthesequenceestimatorinSection 3.6 ,respectively.Second,wendtheprobabilityoferrorofthesymboldetectorwithouttheproposedcodegeneratorestimatorasasumofproductsoferrorfunctionsandfrequenciesofthenumberoferrorsintheestimatedspreadsequence.Finally,wecomparetheprobabilityoferrorwithandwithouttheproposedgeneratorpolynomialestimatorinSection 3.7 Thecontributionsofthischapterare:(i)ageneratorpolynomialestimatorwhichcanidentifyacodegeneratorpolynomialandcancorrectpolarityerrorsintheestimatedPNsequenceandestimateddatasymbols,(ii)atheoreticalvericationoftheprobabilityoferrorofacodegeneratorestimatorwithrespecttosignal-to-noiseratio(SNR),thenumberofdatasymbols,andthelengthofthespreadsequenceoftheinterceptedsignal,and(iii)theaccuracyofperformancepredictionofaneavesdropper. Theremainderofthischapterisorganizedasfollows:RelatedworksarediscussedinSection 3.2 .Section 3.3 describesthesignalmodel.Section 3.4 introducesourmethodofidentifyingthestartpositionofadatasymbolinthespreadsignal.Section 3.5 presentshowtoremovedatasymbolsfromtheinterceptedsignal.Then,estimationofaspreadsequenceispresentedinSection 3.6 .Section 3.7 discusseshowtoidentifyaPNcodegeneratorpolynomialandhowtocorrectpolarityerrors.Section 3.8 presentssimulation 55

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3.9 summarizesthischapter. 13 14 ]. Toeavesdropontheadversary'scommunicationwhichusesDS-SS,theestimationofthespreadsequencefromtheinterceptedsignalisakeytocrackontheseDS-SSsystemsandisachallengingproblem.Theliteratureonthissubjectisnotrich.Webrieydiscusssomerelatedworkswhichhavestudiedthisproblem. First,aneavesdropperneedstodetectanytransmissionofDS-SSsignalsinordertocrackasecureDS-SSsignal.Amethodbasedontheuctuationofanautocorrelationestimator,insteadofontheautocorrelationitself,wasproposedin[ 52 ].Theuctuationoftheautocorrelationestimatorwasusedtoestimateanaccuratespreadcodeperiod.Sincetheinterceptedsignalmayexperiencedelay,theinterceptormustndthestartpositionofadatasymbolinthespreadsignal.Toidentifythestartpositionofadatasymbolinthespreadsignal,acorrelation-basedmethodwasproposedin[ 42 ].AmethodofmaximizingtheFrobeniusnormofacovarianceoftheinterceptedsignalwasproposedin[ 53 ].However,theFrobeniusnormmayresultintheincreaseofestimationerrorastheperiodofthePNsequenceincreases;hence,theirmethoddoesnotworkwellforthePNsequenceofalongperiod.Toaddressthislimitation,amethodbasedonthespectral 56

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3.4 Second,toidentifythePNsequence,severalmethodswereproposedintheliterature[ 41 42 54 55 ].In[ 41 ],amethodbasedonamultichannelidenticationtechniquewasproposedtorecovertheconvolutionbetweenthePNsequenceandthechannelresponseforblindchannelestimation;thelimitationofthismethodishighcomputationalcomplexity.In[ 55 ],amethodbasedonprincipalcomponentanalysis(PCA)wasusedtoestimatethePNsequencefromeigenvectorscorrespondingtotherstandthesecondlargesteigenvaluesofthesamplecovariancematrix;however,thecomputationalcomplexityrequiredbyPCAishigh.ToestimatethePNsequenceandtouseaparallelprocessingtocombatthepolarityambiguityinsuccessivedemodulationanddecoding,theuseofchip-by-chipdetectionwassuggestedin[ 42 ].However,theirparallelprocessingapproachhasalimitation:Itincreasesmemoryrequirementanddoesnotmitigatethepolarityerror.Amultiplesubsectioncross-correlationaveragingmethodwasproposedtoestimatethePNsequencein[ 54 ];however,themethodusedonlyhalfofthecapturedsymbols.Itisknownthatthemoredatasymbolsused,themoreaccuratetheestimationis.InSection 3.6 ,weproposeacross-correlationbasedmethodthatusesallcapturedsymbolsandachieveshigherestimationaccuracy. Third,tocorrectthepolarityambiguityintheestimatedspreadsequenceanddatasymbols,aneavesdropperneedstoestimateacodegeneratorpolynomial.Theestimatorsusedin[ 54 55 ]didnotconsidertheproblemofpolarityerrorsintheestimatedPNsequence,i.e.,erroneousreversalofpolarityofeachchipintheestimatedPNsequence(comparedtothetruePNsequence).Therefore,theprobabilityofcorrectestimationofthePNsequence,usingtheirestimators,maybelessthan50%.Thisleadstosignicantperformancedegradationintermsofbiterrorrate(BER)orsymbolerrorrate(SER).WesolvethisproblembyidentifyingthePNcodegeneratorpolynomialinSection 3.7 .NotonlyisitimportanttoestimatethePNsequence,butwealsoneedtoidentifythe 57

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54 55 ]. In[ 42 ],theprobabilityoferroroftheirsequenceestimatorwasanalyzedforeachchipofaspreadsequence.Theyfoundamarginalprobabilitydensityfunctionofthatsequenceestimatorbyanumericalintegration.However,theydidnotconsiderthepolarityambiguityintheircorrectestimationprobabilityanalysis.Therefore,theiranalysishadalimitation.InSection 3.7 ,weconsiderthepolarityambiguityintheanalysisoftheprobabilityoferrorofasequenceestimatorandasymboldetector.WealsoprovideacompleteexpressionfortheprobabilityoferrorofasymboldetectorinSection 3.7 Table3-1. Listofnotations. Pr() Probabilityof()Pb Realpartof()Im() Imaginarypartof()GF Expectationofmatrix()sgn(x) Signofxa Complementaryerrorfunctionof()kk2 58

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41 55 ]: (3{1) (3{2) whereTsisthesymbolduration,andalisaQPSKorBPSKmodulatedsymboltransmittedattimekTs1.Weassumethesymbolsalarecenteredanduncorrelated.Letn(t)denotethenoiseattheoutputofthereceivedlterandthenoiseisadditivewhiteGaussiannoise(AWGN)anduncorrelatedwiththeinformationsignalal.Theeectofthetransmitterlter,thereceptionlter,thechannelresponseandthepseudo-randomsequenceckisrepresentedbyh(t).Letp(t)denotetheconvolutionofallltersofthetransmissionchain.Tcisthechipdurationandfckgk=0;;P1isthepseudo-randomsequenceoflengthPwhereP=Ts=Tc.Inthischapter,weassumethesymboldurationTscanbeestimatedbythemethodin[ 52 ]forsimplicity.NotethatweconsidertheAWGNchannelonlyinthischapter.Ourstudycanbeextendedtomultipathenvironmentsifweuseablindchannelestimationmethodproposedin[ 41 ].However,inthecurrentwork,welimitourselvestotheAWGNchannelforsimplicity.Table 3-1 liststhenotationsusedinthischapter. 3{1 )issampledanddividedintonon-overlappingwindowswiththeeavesdropper'ssamplingdurationTev.Weassumethesamplingdurationofaneavesdropperisthechipdurationforsimplicity,howeverthisisnotarequirementofourmethod.Therefore,P(L+1)samplesareavailablebysampling(L+1)Tslongsignal 59

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wherethesuperscriptkrepresentsthekTctime-delayeddesynchronizedsignalof( 3{1 )fork=0;;P1.Letykldenoteacolumnofthedesynchronizedyk.Wemaywriteyklasfollows: where[]Tdenotesthetranspose,yl;kisthekthentryofacolumnyklandhl;kisthespreadingsequenceofyl;k.Now,wecanmodify( 3{4 )asfollows: 60

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and( 3{3 )becomes: Notethatsampleswhichbelongtoa1andaLin( 3{3 )aretruncatedinthesynchronizedinterceptedsignal( 3{7 ).LetRdenotethecovariancematrixof( 3{5 ). where[]Histheconjugatetranspose;IPrepresentsaPPidentitymatrix,E[]denotesexpectation,and2nisthenoisevariance. Toplacethestartingspreadsequencehl;0intheproperpositionin( 3{4 ),wesearchforamaximumofthespectralnormofthesamplecovariancematrixof( 3{8 ).ThespectralnormofamatrixisthesquarerootofthelargesteigenvalueofRin[ 56 ].Letkyk2denotethespectralnormofthesquarecovariancematrix. wheremax(R)standsforthelargesteigenvalueofthecovariancematrix.Then,thespectralnormof( 3{7 )is: 61

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3{5 )is: ifthesingularvaluesareexpressedindecreasingorder.Sincekh0lk2khelk2orkh0lk2khbl+1k2,wecandeterminethesynchronizedversionof( 3{3 )bymaximizingthespectralnormin( 3{9 )withrespecttok=0;;P1asfollows: ^y0=argmaxk2[0;P1]kykk2=argmaxk2[0;P1]p In[ 53 ],theFrobeniusnormwasusedtosearchforthestartpositionofadatasymbol.NotethatthesquareoftheFrobeniusnormkyk2Fisthesumofsquaresofthesingularvaluesofy.Thereareerrorsintheeigenvaluedecompositionofthesamplecovariance^Rduetothenoiseaccordingtomatrixperturbationtheory[ 56 ].TheexpectedvalueoftheperturbationerroroftheFrobeniusnormisP22n,whilethatofthespectralnormis2n[ 56 ].TheFrobeniusnormhasatendencytoincreasethemeansquareerror(MSE)asthespreadsequencelengthincreases.Thus,theirmethoddoesnotperformwellforlonglengthsequences.Tomitigatethislimitation,weusethespectralnormin( 3{12 ). Figure 3-1 showsthetheoreticalandsimulatedsquaredspectralnormkykk2in( 3{12 ).Forthecalculation,10,000trialsarecarriedoutandaveragedtogether.Inthesimulation,weuseQPSK.ThePNsequenceisanm-sequence[ 4 15 16 ]withthelengthP=31andwithageneratorpolynomialf(x)=1+x2+x5.TheSNRis-5dB.Whenk=0,thespectralnormhasapeak.Notethatthemoresamples,themoreaccurateestimationof^y0in( 3{12 )canbeachieved. WealsocomparetheMSEsintheestimationofthetime-delaykTc,E[(^kk)2],betweenthespectralnormandtheFrobeniusnorm.Thesamesimulationparametersare 62

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Theoreticalandsimulatedspectralnorm,kykk2,in( 3{12 )withP=31andSNR=-5dB BL=128;P=15;31;63 ComparisonofMSE,E[(^kk)2],bythespectralnormvs.Frobeniusnorm 63

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3-1 ,exceptthatSNRisvariedfrom-20dBto5dB.Figure 3-2 (a)showsthatthespectralnormhassmallerMSEsthantheFrobeniusnorm,whenthesequencelengthP=31isxedandthenumberofsymbolsLis128,256and512.Wecansynchronizethecapturedsignalwithfewersymbolsbythespectralnorm.Figure 3-2 (b)showsthecasewiththexednumberofsymbolsL=128andwiththevariedlengthofspreadsequenceP=15,31,and63.AsthelengthPincreases,theMSEisincreasedbyafactorofP2;thatis,theMSE,normalizedbythesquaresofthesequencelengthP2,isalmostthesame. 3{6 )toestimatetheinformationsymbolalfromthesynchronizedsignaly0lin( 3{7 ).Withthepropertyofstrongself-correlationandweakcross-correlationofspread-spectrum,weuseamethodbasedonacross-correlationbetweenatestcolumn,sayy0t,andacolumnofadatasymbolal,sayy0l,ofthesynchronizedsignalin( 3{7 ).Then,wehave: (3{13) Ifthespreadsequenceisanm-sequence[ 4 15 16 ],Cy0ty0l(=0)Cy0ty0l(6=0).Then, Nowwecanestimatethesymbolalfrom( 3{14 )asfollows: ^al=sgnhReCy0ty0l(0)i+jsgnhImCy0ty0l(0)i(3{15) whereRe()takestherealpartandIm()takestheimaginarypartofacomplex.sgn(x)isthesignfunctionwithvalue1,ifx>0,and-1otherwise.Notethattheestimatedsymbol^alin( 3{15 )isestimateduptoanunknownmultiplicativefactor.Therefore,thesignofthesymbolin( 3{15 )canbereversedbythismultiplicativefactor.Thisproblem 64

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54 55 ].WewillsolvethisproblembyestimatingacodegeneratorpolynomialinSection 3.7 Inordertoanalyzetheperformanceofthesymbolestimatorin( 3{14 ),weuseaGaussianapproximationofthesumofproductsoftworandomvariablesinordertondamarginalprobabilitydensityfunctionofthesymbolestimatorin( 3{14 ).Letql;k=yt;kyl;k,at=a0,andh0;k=hl;k=ckin( 3{14 )forsimplicity. Assumea0=1andal=1forgenerality.Then, where=jckj2,2=2n=,andnl;kisaGaussianrandomprocesswithzeromeanandaunitvariance,i.e.,nl;kN(0;1).Fromtheabovedenitions,wehavetheSNR==2n=1=2. Let+=1+n0;k,+=1+nl;k,and+=++.Sincenl;kN(0;1),+N(1;2)and+N(1;2).Wewanttondthemarginalprobabilitydensityf(+)whichisaproductoftwonormaldistributions.Tondthemarginaldensityf(+),weneedtointegratetheproductofaconditionaldistributionf(+j+)andamarginaldistributionf(+)withrespectto+. 22Z11 22++ 22Z11 22+12d+(3{18) 65

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3{18 )canbeobtainedusinganumericalintegration,aMonteCarlo,oraGaussianapproximationwithagiven[ 51 ].Amongthesethreemethods,weuseanapproximationofproductsoftwonormaldistributions.Let+denotethemeanand2+denotethevarianceof+.Since+and+areindependentofeachother,themeanandvarianceof+are: Themeanandvarianceof+are+and22+.Sincedatasymbolsfql;kgareindependentofeachotherandhavethesamedistribution,thedistributionof^alwillbeapproximatelynormallydistributedaccordingtothecentrallimittheorem[ 57 ].Therefore,thedistributionof^alisanormaldistributionN(P+;2P2+)forP1. Undertheconditionthata0=1,theprobabilityoftheerrorestimationof^alis 2erfc+s where erfc(x)=2 66

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2erfcs 2erfc+s since=+and2=2+.Thebiterrorrateofestimationofthesymbolalis: 2erfc+s 3{6 ),weuseamatchedlteroperationbetweenthesynchronizedinterceptedsignaly0in( 3{7 )andtheestimateddatasymbols^ain( 3{15 ).Thatis: ^c=sgn(3{25) whereh;idenotesinnerproduct,^a=[^a0;;^aL1]Tisavectoroftheestimatedsymbol,and^c=[^c0;;^cP1]Tstandsforavectoroftheestimatedspreadsequence.Thesignofthesequencein( 3{25 )canalsobereversedbyamultiplicativefactorin( 3{15 ). Toanalyzetheperformanceofthesequenceestimatorin( 3{25 ),weusethesameGaussianapproximationmethodinSection 3.5 .Thesequenceestimator( 3{25 )canbe 67

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^ck=L1Xl=0yl;k^al=L1Xl=0(alhl;k+nl;k)^al(3{26) Let!l;k=yl;kal,andhl;k=ckforsimplicity.Assumeck=1forgenerality.Thenwehave: where2=2n=,=jalj2.Letu+=1+nl;k,+=al,andw+=u++.Sincenl;kN(0;1),u+N(1;2).Weneedtondamarginalprobabilitydensityf(w+)whichisaproductoftwonormaldistributionsas( 3{18 ): Letw+denotethemeanand2w+denotethevarianceofw+.Sinceu+and+areindependent,themeanandvarianceofw+are: Therefore,themeanandvarianceofp 68

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57 ].Therefore,thedistributionof^ckisanormaldistributionN(p Undertheconditionthatck=1,theprobabilityoftheerrorestimationof^ckis: 2erfcw+s Forck=1,withsimilarnotationswand2wandusingthesameprocedure,wehave: 2erfcw+s sincew=w+and2w=2w+. TheprobabilityoferrorPcbinestimationofthesequenceckis: 2erfcw+s Notethattheprobabilityoferrorin( 3{24 )and( 3{33 )doesnotaccountforthepolarityerror.Wewilladdressthisprobleminthesucceedingsection. 3{25 ). 69

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4 16 ]. LetF=GF(q)whereqisaprimeorapowerofaprimewhereGF2denotesaniteeldandqiscalledtheorderoftheeldF[ 4 ].Ifthefeedbackfunctionf(x0;;xn1)isalinearfunction;thatis,ifitcanbeexpressedas wherewidenotesatapweightoftheLFSRfori=0;;n1overF.Then,sequenceshavethelinearrecursionrelation[ 4 ]: Ifwehave2nsuccessivesequencebits,wecanestimatethegeneratorpolynomialofsequencec=(c0;;cP1)overF=GF(q).Wemayrewritetherecursionrelation( 3{35 )intothefollowingmatrixrepresentation[ 4 ]: 3{36 )overGF(q)toobtaintapweightsw=(w0;;wn1).Thenextsuccessivesequencebitcanbegeneratedandtestedwiththeestimatedtapweights^wandnsuccessivesequencesusingtransformmatrixMofLFSRas 4 ]. 70

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Agraphicalillustrationofthezigzagestimatorwhere^n=blog2(P+1)cand^c=sgn(^c) follows[ 4 ]: and (^ck+1;^ck+2;;^ck+n)=(^c0;^c1;;^cn1)Mk+1(3{38) Notethatdet(M)=(1)n^w0andthusMisinvertibleifandonlyif^w06=0. Themethodweproposeiscalleda\zigzagestimator"whichsearchesforageneratorpolynomialprimarilybasedon( 3{36 )and( 3{38 )fromtheestimatedsequence^cin( 3{25 ),andalsocorrectsthepolarityerrorintheestimatedsequence^canddatasymbol^a.AgraphicalrepresentationofthezigzagestimatorisgiveninFigure 3-3 .Afundamentalideaincorrectingsignsoftheestimatedsequenceisthatthezigzagestimatorreturnsthenon-signreversedsequenceifthezigzagestimatorcanndacodegeneratorpolynomialfromtheestimatedsequence^c.Letusintroducesomemathematicalnotations.Letc=(c0;c1;)bethesetofsequenceorsymbols.Let^cdenotetheestimatedversionofcandcbethesign-ippedversionofc,i.e.,c=sgn(c).Letbncdenotethenearest 71

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3{25 ).Stores^c(stemporalmemoryof^c).InitializeTestFlag0,FlipCount0,and^nblog2(P+1)c 3{36 ). 3{38 ).IncreaseFlipCountFlipCount+1. (4a) If^ci=^i;i=2^n;;4^n1,setTestFlag1andgoto(Step6). (4b) If^ci6=^i;i=2^n;;4^n1,setTestFlag0andgoto(Step5). IfFlipCount=1,increaseFlipCountFlipCount+1.Goto(Step2). (5b) IfFlipCount=2,increase^n^n+1andresetFlipCount0.Goto(Step2). NotethatthemethodproposedinthissectioncanalsobeappliedtoGoldcodes.Somepairsofm-sequenceswiththesamedegreecanbeusedtogenerateGoldCodesbylinearlycombiningtwom-sequenceswithdierentosetsinGaloiseld.Iftheestimatedgeneratorpolynomialcanbedecomposedintotwopreferredpairsofm-sequence,wecandecomposetheestimatedgeneratorpolynomialintotwom-sequences.Forexample,aGoldcodegeneratorf(x)=1+x+x2+x3+x4+x5+x6canbefactoredintof1(x)=1+x+x3andf2(x)=1+x2+x33. Finally,weuseamatchedlteroperationbetweentheinterceptedsignalysandthesigncorrectedestimatedsequence^czigzagin(Step6).Thatis: ^azigzag=sgn(3{39) 4 ]. 72

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RelationshipamongPr(K=k)in( 3{45 ),hc;^ci,and1 2erfcp 3{47 )wherekdenotesthenumberoferrorsintheestimationofthespreadsequenceofthenon-zigzagmethod. 2erfcp 2erfcPq 22P1 2erfc(P2)q 22P1 2erfcPq 22PPr(K=k) However, ^anonzigzag=sgn(3{40) Nowwearereadytondtheprobabilityoferrorofthezigzagestimatorin( 3{39 ).First,wewillndtheprobabilityoferrorofthesymboldetectorwithoutthezigzagestimatorof( 3{40 ).Afterthat,theprobabilityofthesymboldetectorbythezigzagestimator( 3{39 )willbeanalyzed.Asymboldetectorofacooperativereceiver(Rx)canbewrittenasfollows: ^a=sgn(hy;ci)=sgn(hca+n;ci)=sgn(ahc;ci+hn;ci) (3{41) wherenN(0;1).Then,signal-to-noiseratioRxofthecooperativereceiveris: 2 Therefore,theprobabilityoferrorofthecooperativereceiverwiththeknownspreadsequencecis[ 58 ]: 2erfcr However,signal-to-noiseratioEvoftheeavesdropper(Ev)is: InSection 3.6 ,wendtheprobabilityoferrorPcbintheestimationofeachchipin 73

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3{33 ).Thenumberofincorrectestimationsofeachchipckinthespreadsequencecisanindependentyes/noexperimentwithafailprobabilityPcb.LetKdenotethenumberoferrorsintheestimationofthespreadsequencecofthelengthP.Then,wecanwriteKB(P;Pcb).TheprobabilityofgettingexactlykerrorsintheestimationofthespreadsequencecwiththelengthofPisgivenby: Pr(K=k)=f(k;P;Pcb)=0B@Pk1CA(Pcb)k(1Pcb)Pk(3{45) fork=0;1;2;;Pwiththebinomialcoecient (Pk)!k!(3{46) Ifthereisnoerrorintheestimationofthespreadsequencec,i.e.,c=^cork=0,hc;^ci=PandEv(K=0)=1=2.Ifthereisonlyoneerrorintheestimationofthespreadsequencec,i.e.,k=1,hc;^ci=P2andEv(K=1)=(P2)2=(2P).Table 3-2 showstherelationshipamonghc;^ci,EvandPr(K=k)in( 3{47 )and( 3{45 ).Therefore,theprobabilityoferrorintheestimationofsymbolwithoutthezigzagestimatorcanbewrittenasfollows: 2erfc(P2k)r 22P!Pr(K=k)(3{47) Sincef(k;P;Pcb)=f(Pk;P;1Pcb),theprobabilityofkerrorsintheestimationofthespreadsequenceisthesameasthatofPkcorrectestimationsofthespreadsequence.LetQdenotethenumberofcorrectestimationsofthespreadsequenceandq=Pk.If 74

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2erfc(P2k)r 22P!f(k;P;Pcb)+bP=2cXq=01 2erfc(2qP)r 22P!f(q;P;1Pcb)(3{48) IfPiseven, 2erfc(P2k)r 22P!f(k;P;Pcb)+0B@PP=21CA(Pcb)P=2(1Pcb)P=2+P=21Xq=01 2erfc(2qP)r 22P!f(q;P;1Pcb)(3{49) Themeaningsof( 3{48 )and( 3{49 )are(i)theprobabilitydistributionofhc;^ciissymmetric,(ii)theprobabilitydistributionofhc;^ci>0followsf(k;P;Pcb),and(iii)theprobabilitydistributionofhc;^ci<0followsf(q;P;1Pcb). Thezigzagestimatorin( 3{39 )canidentifythePNcodegeneratorpolynomialtocorrectthepolarityerrorintheestimationofthespreadsequenceifhc;^ci=Pork=Porq=0.Then,theprobabilityoferrorintheestimationofsymbolswiththezigzagestimatorPab;zigzagis: 2erfc(P2i)r 22P!Pr(K=k)+1 2erfcr 75

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3{50 )bythezigzagestimatorisenhancedbyafactoroftwo,comparedto( 3{47 )withoutthezigzagestimator,ifthezigzagestimatorcanestimateacodegeneratorpolynomial.Wewillvalidatetheprobabilityoferrorofthesymboldetectorin( 3{39 )and( 3{40 )inthefollowingSection 3.8 Symbolsynchronizationbythespectralnormwherethedasheddenotesa1,thesoliddenotesa0,thedashed-dotteddenotesa1,respectively 76

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Datasymbolsestimationby( 3{15 ) CTruesequencec Spreadsequenceestimationby( 3{25 ) 77

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Signcorrectionbythezigzagestimator First,weneedtodetermineasynchronizedversionoftheinterceptedsignalby( 3{12 ).Figure 3-4 (a)showsadesynchronizedsignalyk=26delayedby26Tc.Therefore,asamplewindowyk=261containstheendofasymbola1foradurationof5Tcfollowedbythebeginningofnextsymbolsignala0foraduration26Tc.Asynchronizedsignalyk=00by( 3{12 )isshowninFigure 3-4 (b).Notethatthedesynchronizedsampleswhichbelongtoa1aretruncated.Figure 3-4 (c)showstwosynchronizedsamplewindowsforthepurposeofcomparison. Second,estimationsofdatasymbolsandspreadsequencesarefollowedbythesymbolsynchronization.Figure 3-5 showstherst62estimateddatasymbols^aby( 3{15 ).Figure 3-6 showsthenoisyestimatedsequence^cby( 3{25 ).Notethattheestimateddata^ainFigure 3-5 (a)andtheestimatedsequenceinFigure 3-6 (b)aresignreversedversionsofthetruesymbolaandthetruesequencec,respectively.Therefore,hc;^ci=P.Wecancorrectpolarityerrorsintheestimateddatasymbol^aandthespreadsequence^cbytheproposedzigzagestimator. Third,wecancorrectpolarityerrorsintheestimateddatasymbol^aandthespreadsequences^cbythezigzagestimator.ThezigzagestimatorinSection 3.7 searchesand 78

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3{36 )andthetransformmatrixin( 3{37 ).Figure 3-7 showsthesigncorrectedsequence^czigzaganddatasymbol^azigzagbytheproposedzigzagestimator.Wealsoconducta BWiththezigzagestimator Histogramofhc;^ciwithP=64,L=128,andSNR=-5dB 79

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First,wecomparethehistogramofhc;^cibetweenwiththezigzagestimatorandwithoutthezigzagestimatortoverifytherelationbetween( 3{47 )and( 3{50 ).Inthissimulation,weusethenumberofdatasymbolL=128,thelengthofthespreadsequenceP=64,andSNR=5dB.Figure 3-8 showsthecomparisonofhistogramshc;^cibetweenwiththezigzagestimatorandwithoutthezigzagestimator.Thehorizontalaxisisthevaluehc;^ciandtheverticalaxisrepresentsthenormalizedoccurrencefrequencyofhc;^ci.Theoccurrencefrequencyofhc;^ci=Pis0.9991and0.4939forwiththezigzagestimatorandwithoutthezigzagestimator,respectively.However,theoccurrencefrequencyofhc;^ci=Pwiththezigzagestimatorandwithoutthezigzagestimatoris0.0000and0.5052.ThezigzagestimatorinSection 3.7 canidentifythePNcodegeneratorpolynomialtocorrectthepolarityerrorintheestimationofthespreadsequencewhenhc;^ci=P.Therefore,theoccurrencefrequencyhc;^ci=Pwiththezigzagestimatoristhesumofthatofhc;^ci=Pandhc;^ci=Pwithoutthezigzagestimator.Thisvalidatestherelationbetween( 3{47 )and( 3{50 ). Second,wecomparePr(hc;^ci=P)betweenwiththezigzagestimatorandwithoutthezigzagestimatorin( 3{47 )and( 3{50 ),respectively.Figure 3-9 showsthePr(hc;^ci=P)withdierentcombinationsofthenumberofdatasymbolsLandthelengthofthespreadsequenceP.NotethatthePr(hc;^ci=P)correspondstoPr(K=0)withoutthezigzagestimatorandPr(K=0)+Pr(K=P)withthezigzagestimator.ThePr(hc;^ci=P)increasesasthenumberoftheinterceptedsymbolsLincreasedandalsoincreasesasthelengthofthespreadsequencePincreased.Therefore,thePr(hc;^ci=P)obtainedbythezigzagestimatorisalmosttwotimesgreaterthanthatwithoutour 80

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BL=512,P=64,128,256 ComparisonoftheprobabilityofcorrectestimationofthespreadsequencePr(hc;^ci=P) symboldetectorin( 3{39 )andtheanalyticalprobabilityoferrorin( 3{50 ).Figure 3-10 showsthePab;zigzagwithdierentcombinationsofthenumberofdatasymbolsLandthe 81

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3{43 )withP=64forcomparison.ThePab;zigzagisenhancedasthenumberofsamplesLincreasesandasthelengthofsequencePincreases.Moreover,theanalyticalperformancePab;zigzagofthesymboldetectorin( 3{50 )isalmostthesameasthatofthesimulatedprobabilityoferrorin( 3{40 ).SincethesimulatedPr(hc;^ci=P)'1forP=64,L=128,SNR=-5dBinFigure 3-9 over10,000trials,Pab;zigzag'Pb;Rx.Therefore,theanalyticalprobabilityoferrorin( 3{50 )isagoodapproximationoftheperformanceofaneavesdropper.Thisanalyticalperformancecanprovideanecientpredictionoftheperformanceofourproposedzigzagestimator.Finally,weconducta BP=64,L=256 CP=128,L=256 DP=128,L=512 ComparisonofthesimulatedandanalyticalprobabilityofbiterrorPab;zigzagwiththezigzagestimatorin( 3{50 ) 82

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3-11 showstheprobabilityofthecorrectestimationofthespreadsequencePr(hc;^ci=P)withn=6;;13withthenumberofdatasymbolsL=256.ThePr(hc;^ci=P)increasesasthelengthofthespreadsequenceP=2n1increased. Figure3-11. Probabilityofcorrectestimationofthespreadsequencebythezigzagestimationwithn-tuplegeneratorpolynomial,P=2n1,SNR=-10dBandL=256 83

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84

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Transformdomaincommunicationsystem(TDCS)[ 9 11 ]providesaviablesolutionforinterferenceavoidance.IntheTDCS,aninterferenceavoidingwaveformisgeneratedatthetransmittertoavoidintentionalinterference,andthereceiverneedstoadaptitsmatchedltertomatchthetransmittedwaveform.Spectrallycrowdedregionsareavoidedaltogetherviaadaptivespectralnotching.Therefore,theforemostproblemintheTDCSisaccurateestimationofthespectralenvironment.Themoreaccuratetheestimationoftheinterferencespectrumis,thebettertheperformancetheTDCSwillachieve. TheTDCS[ 9 11 ]utilizedaparametric10th-orderautoregressive(AR)estimatortoestimatethepowerspectraldensity(PSD)ofthespectralenvironment.SincetheAR-lterestimatestheinterferenceundertheassumptionthattheinterferenceprocessisstationary,theAR-estimatorfailstoprovideaccurateestimationunderthenon-stationaryinterferencesuchasswept-tonejamming.Forthisreason,theTDCSbasedontheAR-estimatorperformedworseagainsttheswept-toneinterference,ascomparedtothecaseunderthestationaryinterference. Toenhancethebiterrorrate(BER)performanceoftheTDCSunderthenon-stationaryinterference,thewaveletdomaincommunicationsystem(WDCS)[ 10 ]andtheenhancedwaveletdomaincommunicationsystem(EWDCS)[ 19 ]wereproposedintheliterature.TheWDCSandtheEWDCSutilizedawaveletdomainspectralestimator.The 85

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10 ]failedtomitigateanon-stationaryinterferenceliketheswept-tone.However,theEWDCSusedtheevolutionarywaveletspectrum(EWS)whichisrelatedtothelocalauto-covariancethroughtoauto-correlationofawavelet.TheBERperformanceoftheEWDCSunderanon-stationaryinterferencewasrelativelysub-optimalcomparedtothatunderstationaryinterferences.Moreover,theBERperformanceoftheEWDCSunderstationaryinterferenceswascomparativelypoorerthanthatoftheTDCSunderstationaryinterferences[ 19 ]underthesamesimulationenvironment. TomitigatetheproblemoftheTDCS[ 9 11 ],WDCS[ 10 ],andEWDCS[ 19 ],weuseanon-parametricspectralestimator,calledCapon'smethod[ 59 { 61 ].Capon'smethod(CM)forspectralestimationisbasedonalterbankdecomposition:thespectrumofasignalisestimatedineachbandbyasimplelterdesignsubjecttosomeconstraintsandcanprovidefastspeedofconvergence.TheCMhastheabilitytocopewithacomplicatedinterferenceenvironmentinwhichthenumberofinterferingsourcesislarge.CombiningthestrengthoftheCMandaforementionedTDCS,weproposetheenhancedtransformdomaincommunicationsystem(ETDCS).TheETDCSwillprovidebetterbiterrorperformancethantheTDCS[ 9 ],WDCS[ 10 ],orEWDCS[ 19 ]forboththestationaryinterferenceandthenon-stationaryinterference. ThischapterproposestheETDCSwhichisapracticalalternativefortheTDCSwithanon-parametricspectralestimationmethod.InSection 4.2 ,weelaborateonamathematicalmodelofTDCS.InSection 4.3 ,anoverviewoftheTDCSarchitectureisgiven,andthelimitationoftheTDCSandtheproposedestimationmethodareinvestigated.EectsofvariousjammingontheperformanceofETDCSandcomparativebiterrorperformanceanalysisoftheproposedETDCSarefollowedinSection 4.4 .Finally,Section 4.5 summarizesthischapter. 86

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. EstimateSpectrum SpectrumMagnitude RandomPhase ScaleC IFFT Buer Mod Tx . . Figure4-1. AblockdiagramofTDCStransmitter[ 9 { 11 ] Inthissection,weelaborateonamathematicalmodeloftheTDCSin[ 9 { 11 ],andanalyzethebiterrorrateperformanceoftheTDCS.ThetransmitterarchitectureofTDCSsystemisshowninFigure 4-1 .TheTDCSin[ 9 { 11 ]involvesdesigningawaveforminthefrequencydomainratherthaninthetimedomain(orwaveletdomain)toavoidtheinterference.Ifthedesignedinformation-bearingwaveformcouldavoidusingbandsoccupiedbyinterferences,thecommunicationsystemwouldavoidtheinterference.Sincethemodulatedinformation-bearingsignalwouldhavelittleornospectrumattheinterferedbands,itshouldnotbeaectedbytheinterferenceandshouldnotintroducenewinterferencetootherusers.ThisinterferenceavoidingconceptservesasthebasisfortheTDCSdesign[ 9 { 11 19 ]. Weassumethatthereceiverandtransmitterantennaeexperiencethesamespectralenvironment.Thustheycangeneratethesamespectralestimationofthespectralenvironment.Thisassumptionholdsforshort-rangedatacommunications.Scenariosinwhichtheassumptionisvalidincludevehiclesoraircraftsgroupedintightformationunderdistantinterference,orcloselylocatedsecondarymobileusersofanadhocnetworksharingthesamespectrumwithaprimaryuser.Forthosescenarioswheretheassumption 87

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19 ]. Afterestimationofthespectralenvironment,abandexceedsthatofthenoiselevelbyafactorofathresholdlevel,interferenceisclaimedtobepresentandthebandisnotchedout,assigningvalue`0'.Otherwise,thebandsareretainedandsettothevalue`1'.Thatis: wherew=ej2 NisaprimitiveNthrootofunity.Consequently,aninterference-freespectrummagnitudeA0(!)inFigure 4-1 isgenerated.Afternotchingouttheinterferences,amulti-valuedcomplexpseudo-random(PN)phasevector,ej(!),isgeneratedfromalinearfeedbackshiftregister(LFSR)identicalinlengthtoA0(!)andmultipliedelement-by-elementwithA0(!)inaprocesscalledphasecoding,producingspectralvector,Bb(!),withknownamplitudeandPNphasecharacteristics.ThespectralvectorBb(!)isthenamplitude-scaledbyconstantCtoensurethecommunicationsymbolhasthedesiredsignalenergy.Thenwehave: Theresultantspectralvector,B(!),isinverseFouriertransformedtoproduceatime-domainbasisfunction,b(t),whichissubsequentlystoredandmodulatedwithdata,d(t).LetB[k]denoteafrequencydomainrepresentationofthebasisfunction,b(t)fork=0;;N1whereNisthenumberofFFTpoint.Then,wehave: Nn(4{3) Thissignaturewaveb[n]storedintoabuerinFigure 4-1 anddatamodulatedbyd(t). Anithreceivedsignalatthereceiverbecomes: 88

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Letcdenotestheconjugateofthesignaturewaveb.Anoutputofcorrelatoratthereceiverbecomes: Then,theestimateddataatthereceiverbecomes: ^di=sgn()(4{6) IfA[k]=1fork=0;;N1,thescalefactorCbecomes1=p Therefore,thebiterrorratefortheantipodalmodulationbecomes: whereEbistheaverageenergyperbitandN0isthenoisepowerdensity.TheQ-functionisthecomplementaryerrorfunction. TheTDCS[ 9 11 ]used10th-orderAR-ltertoestimatethespectralenvironment.TheAR-lterusedintheTDCSisaparametricestimationmethod.IttsanARlinearpredictionltermodeltothesignalbyminimizingtheforwardpredictionerrorintheleastsquaresense.SincethemodelintheAR-estimatordidnotttheenvironmentswell 89

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9 11 ]. Thewavelet-basedspectralestimationswerefoundtobeusedintheWDCS[ 10 ]andtheEWDCS[ 19 ].Thewaveletperiodogram,comprisedofthesquareofthewaveletcoecients,hasbeenusedintheWDCStoestimatethespectralenvironment.However,thewaveletperiodogramisanoisyestimationoftheenvironment'spowerdistributionandhencecannotestimatethenon-stationaryinterference.TheEWSusedintheEWDCSaddressedboththestatisticalandthenon-stationarynatureofthespectralestimation,howevertheEWDCSperformanceunderswept-toneinterferencewasshowntoberelativelysub-optimalcomparedtootherstationaryinterferences.Moreover,thebiterrorperformanceoftheEWDCSunderstationaryinterferenceswascomparativelypoorerthanthatoftheTDCSunderstationaryinterferences[ 19 ].Therefore,thespectralestimationtechniquesusedintheTDCS,theWDCS,andtheEWDCS,havetheirlimitations. Therearebasicallytwobroadcategoriesofthetechniquesforspectralestimation.Oneisthenon-parametricapproachbasedontheconceptofbandpasslter.Theotheristheparametricmethod,whichassumesamodelforthedata,andthespectralestimationbecomesaproblemofestimatingtheparametersintheassumedmodel.Oneofthemostwell-knownnon-parametricspectralestimationmethodsisCapon'sapproach,whichisalsoknownasminimumvariancedistortionlessresponse(MVDR)[ 59 { 61 ].AtthestageofspectralestimationintheETDCS,weusedtheCapon'smethod(CM)toestimatetheinterferenceenvironments.Capon'smethodforspectralestimationisprimarilybasedonalterbankdecomposition:Thespectrumofasignalisestimatedineachbandbyasimplelterdesignsubjectwithsomeconstraints(Interestedreaderspleasereferto[ 59 { 61 ]). 90

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4-2 showsanexampleofspectralestimationandspectralnotchingbytheCMmethod.Figure 4-2 (a)showsthespectralestimationby16th-orderCMwheretheX-axisisthenormalizedfrequencyover[0;]andtheY-axisisthepowerspectraldensity. 4-1 .Afterdatamodulation,thesignalistransmittedoverAWGNchannelundervariousinterferences.Thesymbolswerenallydemodulatedatthereceiverwiththematchedlteroperation,andthenumberofbiterrorswasrecorded.Thesimulationswereterminatedwhenthetotalnumberofbiterrorsexceeded500bitsunlessotherwisementioned;thisnumberwaschosenempiricallyandwassucienttoproducerelativelysmoothbiterrorperformance(BER)curves. Inthischapter,weuseantipodalmodulationasoursignalmappingmethod.Antipodalmodulationisaformofbinarymodulationthatusesthebasisfunctionb(t)asonesymbol,s1(t),andthenegativebasisfunctionb(t)asthesecondsymbol,s2(t). (4{9) 91

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BCorrespondingSpectrumMagnitudeA0(!) Spectralestimationandspectralnotching ThetheoreticalBERPbofantipodalmodulationoveranadditivewhiteGaussiannoise(AWGN)withoutjammingisgivenby( 4{8 ).Figure 4-3 showstheantipodalBERperformanceunderAWGNintheabsenceoftheintentionalinterferencetoensureproper 92

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However,thetheoreticalperformancewithoutspectralshapingisestimatedbyassumingconstantinterferencepowerspectraldensityNJoverthesystembandwidth,eectivelyaddingtothesystemnoiseoorandimpactingbiterrorperformanceper( 4{8 )fortheantipodalcase.Thatis[ 14 ]: whereNJistheinterferencenoisepower.Figure 4-4 showsthetheoreticalandsimulatedantipodalBERperformancewithoutspectralshapingaddingconstantinterferencepowerspectraldensityoverthesystembandwidth.TheBERperformancewassimulatedattheaveragesignal-to-noiseratio(SNR)Eb=N0=4dBandanaverageinterference-to-signalenergyperbit(I=E)rangingfrom0.0dBto16.0dB.Notethatthe\NoJamming(SNR=4dB)"performanceinFigure 4-4 andothersisthevalueof( 4{8 )fortheEb=N0=4dB(i.e.,Pb=1:25102).Theseresultsareimportantandprovideabaselineforcomparingtheperformanceswithoutspectralshapingandwithinterferenceavoidingsystem.NotethatthepurposeoftheinterferencemitigationistoenhancetheBERperformancefrom( 4{10 )to( 4{8 )undervariousjammingenvironmentswiththeproposedETDCS. Next,variousintentionalinterferencescenariosarepresentedtotheproposedETDCS.Intentionalelectromagneticinterference(IEME)canbecategorizedintofourcategories,basedonthefrequencycontentoftheirspectraldensitiesas\narrowband",\moderateband",\ultra-moderateband",and\hyperband"[ 1 ].Weconsideronlynarrowbandinterference(NBI)inthischapter.TheNBIfurthercanbecategorizedintostationaryornon-stationaryinterferencewithrespecttoitstime-varyingcharacteristicinthefrequencydomain.Partialband,single-tone,andmultitonejammingarestationaryinterferencesandswept-tonejammingisanon-stationaryinterferenceintermsofwide-sensestationarity. 93

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AntipodalsignalingBERperformancewithoutinterferencein( 4{8 ) Figure4-4. Theoreticalandsimulatedperformancewithoutspectralshapingin( 4{10 ) Asmentioned,weassumethatthetransmitterandthereceiverareabletogeneratethesamebasisfunction.First,partialbandinterference(PBJ)occupiesacontinuousrangeofsystembandwidth.ThePBJismodeledasadditiveGaussiannoisewithitspowerfocusingonaportionoftheentirebandwidthofthesystem.Sincewhitenoise 94

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AntipodalsignalingBERperformanceunder10%partialbandjamming isstationary,thePBJisalsoastationaryjamming.Figure 4-5 andFigure 4-6 showtheperformanceoftheproposedETDCSunder10%and70%PBJ,respectively.TheperformancewithoutspectralshapingunderPBJiscloselyapproximated( 4{10 )forallI=Evalueconsidered.However,thatwiththeproposedETDCSunder10%and70%isclosetothe\NoJamming(SNR=4dB)"in( 4{8 ).Therefore,theproposedETDCSsuccessfullymitigatesthePBJ. Second,multi-tonejamming(MTJ)dividesitstotalpowerintoqdistinct,equalpower,randomphasetones.Everyjammingtonecanbemodeledas: whereJisrandomphase,whichisuniformlydistributedover[0;2].AJandfJareamplitudeandfrequency,respectively.Notethatsingle-tonejamming(STJ)isaspecialcaseofmulti-tonejammingwithq=1.TheMTJisawide-sensestationaryjamming,sincethemeanE[j(t)]=0andtheautocorrelationE[j(t)j(t+)]=R()whereE[]denotestheexpectation.Figure 4-7 andFigure 4-8 showtheperformanceoftheproposed 95

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AntipodalsignalingBERperformanceunder70%partialbandjamming ETDCSunderSTJandMTJ,respectively.TheperformancewithoutthespectralshapingunderSTJisworsethan( 4{10 ).However,MTJisamoreeectivejammingscenariothanPBJandSTJintheviewpointofthejammerperformanceifthespectralshapingbyCMmethodisnotemployed.NotethattheproposedETDCSsuccessfullycountermeasurestheSTJandMTJ. Finally,theproposedETDCSisexposedtoanon-stationaryinterference,i,e.,swept-tonejamming(SWTJ)(seeFigure 4-9 ).TheSWTJiswhenajammer'sfullpowerisshiftedfromonefrequencytoanother.EverySWTJcanbemodeledas: whereJisrandomphasewhichisuniformlydistributedover[0;2].AJisamplitudeandfJ(t)isasweepingfrequency.SincethemeanE[j(t)]=0andtheautocorrelationE[j(t)j(t+)]=R(t;),theSWTJisanon-stationaryinterference.IntheTDCS[ 9 11 ],theswept-toneinterferencecouldnotbeaccuratelyestimatedduetotheparametricspectralestimationmethod,i.e.,AR-method.IntheEWDCS[ 19 ],theperformanceunder 96

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AntipodalsignalingBERperformanceundersingle-toneJamming Figure4-8. AntipodalsignalingBERperformanceundermulti-toneJamming swept-tonewassub-optimalcomparedtootherinterferencescenarios.InFigure 4-9 ,wecanseethatthesimulatedBERperformanceundertheSWTJwithoutspectralnotchingiscloselyapproximatedto( 4{10 )fortheoverallrangeofI=Econsidered.However,the 97

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AntipodalsignalingBERperformanceunderswept-tonejamming proposedETDCSsuccessfullymitigatedanon-stationaryinterferencewiththespectralestimationbyCMmethod. Insummary,Table 4-1 showsthecomparativeBERperformanceamongtheTDCS,theEWDCS,andtheproposedETDCS.TheaverageETDCSantipodalBERperformanceforallstationaryinterferencesis1:29102.TheaverageETDCSantipodalBERperformancefortheswept-toneinterferenceis1:35102.Thiskindofanon-stationaryinterferencecouldnotbehandledbytheTDCS[ 9 11 ]andmadesub-optimalperformancefortheEWDCS[ 19 ].TheproposedETDCSdemonstratestheabilitytomitigatethedierenttypesofinterferences.Inparticular,theproposedETDCSextendsthiscapabilityfromthestationaryinterferencetothenon-stationaryinterference.Moreover,theproposedETDCShasconsistentperformanceforalltypesofinterferenceconsideredinthissection.ThisisthemostnotablestrengthoftheproposedETDCS. 98

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ComparisonoftheaverageBERperformanceofTDCS,EWDCS,andETDCSwithantipodalmodulation(Eb=N0=4dB,I=E=016dB) Avg.Pb Non-stationaryinterference Overall (PBJ,STJ,MTJ) (SWTJ) Nativemode 2:62101 19 ] 1:50102 9 ] 1:38102 N/A 99

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7 20 ] Highlyreliablecommunicationhasbeendesiredbybothmilitaryandcivilianparties.Itisveryimportant,especiallyforthemilitarycommunicationsystems,tobeabletooperateunderbothunintentionalandintentionalinterferences.Therefore,itisdesirabletousetheV-BLASTsystemasahighlyreliablecommunicationsystemundertheseinterferences. Oneoftheobjectivesofacommunicationinterferer(orjammer)istodisruptordegradeperformanceofthecommunicationsystemuptothepointwhereitisnolongerreliable.Therefore,communicationsecurityresearchmainlycentersonprovidingcountermeasurestoovercomesuchintentionalcommunicationinterferences.However,themitigationoftheNBIhasnotbeenstudiedintheMIMOsystem,especiallyfortheV-BLASTarchitecture. TheNBIhasbeeninvestigatedthoroughlyforthesingle-inputandsingle-output(SISO)systembytransformdomainprocessing(TDP).AfundamentalideaoftheTDPisthedesignofaninterference-freeadaptivewaveforminfrequency-domainratherthanintime-domain.SpectrallycrowdedregionsareavoidedbyadaptivespectralnotchingintheTDP[ 9 33 ]. 100

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12 ],theycombinedthefundamentalconceptofTDPwithV-BLASTbasedonzero-forcing(ZF)detectortomitigateNBI.However,theyfailedtomitigatenon-stationaryinterference,likeswept-toneinterference.Thelackofstationarityofanon-stationaryinterferenceaectedtheperformanceofthespectralestimator,10th-orderautoregressive(AR)lter.Therefore,thesystemproposedin[ 12 ]didnotworkwellfornon-stationaryinterferences.BecausetheZFdetectorgenerallysuersfromnoiseenhancementatearlystages,theyusedhigherSNRs(15dBand25dB)intheirsimulationstudies. Inourpreviouswork[ 33 ],weproposedaviableoptionofthereliableSISOcommunicationsystem,calledETDCS.Theenhancedtransformdomaincommunicationsystem(ETDCS)oeredasignicantinterferenceavoidancecapabilityforbothstationaryandnon-stationaryinterferencewithanon-parametricspectralestimator,Capon'smethod(CM)[ 33 59 61 ]. Inthischapter,weextendourpreviousapproachinChapter 4 toprovidenon-stationaryaswellasstationaryinterferenceavoidancecapabilitytotheV-BLASTsystem.TheTDPbyCMandminimummeansquareerror(MMSE)detectorarecombinedwiththeV-BLASTtoenhancebiterrorperformanceinNBIenvironment;thatis,theTDPbyCMwillprovidebetteravoidanceofthespectrallycrowdedregionsandwillenhancethebiterrorperformanceoftheV-BLASTsystemunderareasonableSNRbyMMSEdetector. Theremainderofthischapterisorganizedasfollows:Section 5.2 presentsourpreviouswork.Section 5.3 describesaV-BLASTsystemmodelandtheinterferencemodel.Section 5.4 introducesourproposedmethodology.Section 5.5 presentssimulationresultstoshowtheperformanceofourproposedapproaches.Section 5.6 summarizesthischapter. 4 101

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5-1 showsahigh-levelsystemblockdiagramofaV-BLASTsystemmodelwithMtransmittersandNreceivers.Weassumeperfectchannelestimationatthereceiverandwedonotconsiderthepowerallocationproblemsuchthatthepowerlaunchedbyeachtransmitterisproportionalto1=M.IneachuseoftheMIMOchannel,avectora=(a1;;aM)Tofcomplexnumbersissentandavectorr=(r1;;rN)Tofcomplexnumbersisreceivedwhere[]Tdenotestranspose.Weusetherelationbetweenaandrasfollows: . ... TX TDPProcessing Copier Modulator . . ... RX V-BLASTDecoder TDPProcessing ^d(t) Figure5-1. V-BLASTwiththeTDP[ 12 ] whereHisNMmatrixrepresentingthescatteringeectsofthechannelandnisthenoisevector.WeassumethatHisarandommatrixwithindependentzeromeancomplexGaussian.Wealsoassumethatnisacomplexrandomvectorwithi.i.d.elementsanditscovariancematrixistheidentitymatrixscaledbythenoisevariance2n.Letv=(v1;v2;;vN)TdenoteonetypeoftheNBIinterferencevector.Then,theNBI 102

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5{1 )canbemodeledasfollows: Wealsoassumethesameelectromagneticenvironmentforalltransceivers.Therefore,alltransceiversexperiencedthesameinterferencevandcangeneratethesameadaptiveinterference-freewaveformatboththeMtransmittersandtheNreceiversintheTDPprocessingstage.Ifthisisnottrue,adedicatedfeedbackloopmaybeemployed.TheNBIcanbecategorizedintostationaryornon-stationaryinterferencewithrespecttoitstime-varyingcharacteristicinthefrequencydomain.partialband,single-tone,andmulti-toneinterferencearestationaryinterferencesandswept-toneinterferenceisanon-stationaryinterference. partialbandinterference(PBJ)occupiesacontinuousrangeofsystembandwidth.Multi-tonejamming(MTJ)dividesitstotalpowerintoseveraldistinct,equalpowerandrandomphasetones.Single-toneinterference(STJ)isaspecialcaseofMTJ.Swept-toneinterference(SWTJ)islikeasingle-tonechangingfrequencyovertime.Weassumethatstationaryinterferencesdonotchangethefrequencytheyoccupiedandswept-toneinterferencesweepsthebandswithacertainpatterninaspecictimeinterval. Therearebasicallytwobroadcategoriesoftechniquesforspectralestimation.Oneisthenon-parametricapproachbasedontheconceptofbandpasslter.Theotheristheparametricmethod:Itassumesamodelforthedatasothatthespectralestimationbecomesaproblemofestimatingtheparametersintheassumedmodel[ 61 ]. 103

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9 ]anditsextensiontoaV-BLASTin[ 12 ]isaparametricestimationmethod.IttsanARlinearpredictionltermodeltothesignalbyminimizingtheforwardpredictionerrorintheleastsquaresense.SincethemodelintheAR-estimatordidnotttheenvironmentswellinthecaseofanon-stationaryinterference,theTDPsueredsignicantperformancedegradationandfailedtoestimateaswept-toneinterference.Oneofthemostwell-knownnon-parametricspectralestimationmethodsisCapon'sapproachwhichisalsoknownasminimumvariancedistortionlessresponse(MVDR)[ 59 61 { 63 ].Capon'smethod(CM)forspectralestimationisprimarilybasedonalterbankdecomposition:Thespectrumofsignalsisestimatedineachbandbyasimplelterdesignsubjecttosomeconstraints.WeuseCMmethodtoestimateinterferedenvironmentattheTDPprocessingstageinourproposedV-BLAST. Afterthespectralestimation,abandwhichexceedsthenoiselevelisnotchedoutwithacertainthreshold.Otherwise,thatbandisretained.Consequently,aninterference-freespectrummagnitudeA0(!)isgenerated.Afternotchingouttheinterferences,amulti-valuedcomplexpseudo-random(PN)phasevectorisgeneratedfromalinearfeedbackshiftregister(LFSR)identicalinlengthtoA0(!)andmultipliedelement-by-elementwithA0(!)inaprocesscalledphasecoding,producingspectralvector,Bb(!),withknownamplitudeandPNphasecharacteristics.ThespectralvectorBb(!)isthenamplitude-scaledbyconstantCtoensureacommunicationsymbolhasthedesiredsignalenergy.Theresultantspectralvector,B(!),isinverseFouriertransformedtoproduceatime-domainbasisfunction,b(t). Aftergenerationofthebasisfunctionb(t),inputdatastreamd(t)isdemultiplexedandmodulatedintoMsub-streams,andnallyfedintoeachtransmitter.Weusedacycliccodeshiftkeying(CCSK)[ 64 ]whichisaformofM-arysignallingoveracommunicationchannel.Thatis,initssimplestform,abasisfunctionb(t)ischosen,andacyclically(circularly)shiftedversionofb(t)isusedtomodulateacarrier.Thereceiveralsogeneratesb(t)todemodulatethedetectedsymbolwiththecorrelationdetector. 104

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V-BLAST/MMSEwithETDPDetection Initialization:W1= MHy MHHy+2nINi=1Recursion:ki=argminj=2fk1;;ki1gk(Wi)jk2yki=(Wi)kiri^aki=Q(yki)=argmaxp=1;2;;16yki;dtpTs MHyki MHkiHyki+2nINi=i+1 TheproposedV-BLASTusesaMMSEdetector[ 50 ]atthereceiversides.SincetheZFdetectorsuersfromthenoiseenhancementattheearlystages,thedetectorwithMMSEcriterionisfavorableundertheinterference.ThedetectoralgorithmofaV-BLASTdecoderisshowninTable 5-1 .ThisversionoftheV-BLASTisbasedontheMMSEandthecorrelationdetection.NotethatthemajordierencewiththegeneralV-BLAST/MMSEdetectionandTable 5-1 isinthe3rdstepofRecursionwherethedetectedsignalcorrelateswiththecyclicshiftversionofthebasisfunctionb(t). 12 ]andaddourproposedapproachinthatplatform.Wealsousethesameinterferencemodelin[ 12 ].Ineachsimulation,werstsampledtheenvironmentforadurationof10symbolsandthefundamentalwaveformb(t)wasgenerated.Afterdemultiplexingand16-CCSKmodulation,thesignalawastransmittedbyeachtransmitteroveranMIMOchannelHwiththechannelnoisenandthevariousinterferencev.ByMMSEandcorrelation 105

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BERperformancewithoutinterference detectionatthereceivergiveninTable 5-1 ,thesymbolswerenallydemodulatedandtheBERwasrecorded. First,asimulationisrunintheabsenceoftheintentionalinterferencetoensureproperoperationoftheproposedmethod.Figure 5-2 showsthesimulationresultsfor(M;N)=(2;2)and(M;N)=(4;4).TheEb=N0israngedbetween-10dBand6dBinstepsof1dB.TheBER,Pb,iscalculatedbyterminatingthesimulationwhenthetotalnumberofbiterrorsexceeds500bits-thisnumberischosenempiricallyandissucienttoproducerelativelysmoothbiterrorperformancecurves.WeobservethattheV-BLAST/MMSEperformesbetterthantheV-BLAST/ZFforoverallrangesofEb=N0. Finally,theproposedsystemisexposedtovariousinterferences.The30%partialband,single-toneandmulti-toneinterferenceareusedforthestationaryinterferences,andtheswept-toneisusedforthenon-stationaryinterferencemodel.TheBERperformanceissimulatedatthesignal-to-noiseratioEb=N0=4dBandtheaverageinterference-to-signalenergyperbit(I=E)israngedfrom1.0dBto10.0dB. 106

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12 ]underthesamesimulationparameters.Thethresholdusedforthe10th-orderAR-estimatoris40%[ 12 ],whilethatusedforourproposed16th-orderCMis30%.Notethatwemakenoclaimthattheseparametersareorarenotoptimalforourapplication.ThesevaluesareempiricallychosenbasedontheoverallacceptableandcomparableBERperformanceversusstationaryandnon-stationaryinterferenceavoidancecapability. Figure5-3. BERperformanceforMN=22under30%partialbandInterference Figure 5-3 5-4 5-5 ,and 5-6 showsimulationresultsfor(M;N)=(2;2),whileFigure 5-7 5-8 5-9 ,and 5-10 showsthesimulationresultsfor(M;N)=(4;4),respectively.NotethatV-BLAST/MMSE/CM(orV-BLAST/ZF/AR)denotesV-BLASTwiththeMMSE(orZF)detectorandtheTDPbasedonCM(orAR),whileV-BLAST/MMSE(orV-BLAST/ZF)denotesnormalV-BLASTsystemwithouttheTDPprocessing.WealsopresenttheBERperformancewithoutinterference(nojamming)forbothV-BLAST/ZFandV-BLAST/MMSEsystemfromFigure 5-2 forcomparison. 107

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BERperformanceforMN=22undersingle-toneinterference Figure5-5. BERperformanceforMN=22underswept-toneinterference EvenwithoutTDPprocessing,V-BLAST/MMSEperformsbetterthanV-BLAST/ZF.TheperformanceofV-BLAST/ZFisunstableforcasesoftheswept-toneandmulti-toneinterferenceasshowninFigure 5-5 andFigure 5-6 for(M;N)=(2,2)andFigure 5-9 and 5-10 for(M;N)=(4,4).ThisisduetonoiseenhancementoftheZFdetector.Therefore, 108

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BERperformanceforMN=22undermulti-toneinterference Figure5-7. BERperformanceforMN=44under30%partialbandinterference themethodproposedin[ 12 ]usedhigherSNRs(15dBand25dB)intheirperformancestudies. AsshowninFigure 5-3 ,V-BLAST/MMSE/CMapproachsignicantlyimprovestheBERperformanceunderboththestationaryandthenon-stationary 109

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BERperformanceforMN=44undersingle-toneinterference Figure5-9. BERperformanceforMN=44underswept-toneinterference interferencewithrespecttoV-BLAST/ZF/AR.TheperformanceimprovementisobtainedbyboththeMMSEdetectorinV-BLASTdetectionandCMmethodintheTDPprocessingstage.V-BLAST/ZF/ARmethodimprovestheBERperformanceunderthestationaryinterference,whileitdoesnotworkwellforthenon-stationary 110

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BERperformanceforMN=44undermulti-toneinterference interferenceduetothestationarityassumptionontheARestimator.Therefore,theproposedmethodextendsitsNBIinterferenceavoidancecapabilityfromthestationaryNBItothenon-stationaryNBI,andhasconsistentperformanceforalltypeofinterferenceconsideredinthischapter. Ifwelookattheperformanceintermsofajammer(orinterferer),thesingle-toneinterferencecandisruptordegradetheperformanceoftheV-BLASTsystemmorethanotherinterferencescenarios.Sincethesingle-toneinterferencecanconcentratemoreinterferencepowerthanotherinterferences,anadaptivethresholdselectionforthistypeofNBIshouldbeprovidedbyTDPprocessinginfutureresearch. 111

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112

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13 17 ]. Direct-sequencecodedivisionmultipleaccess(DS-CDMA),wherespreadingisperformedinthetimedomain,hashighsamplingrates.ThishighsamplingratemakesDS-CDMAverysusceptibletoperformancedegradationcausedbymultipathpropagation[ 23 ].Therefore,multi-carrierCDMA(MC-CDMA)wasdevelopedtoovercomethisdrawbackoftheDS-CDMA[ 21 58 ].ThemainbenetofMC-CDMAincomparisontootherOFDM-basedmultipleaccessmethodsistheinherentprovisionoffrequencydiversity.Bycontrast,adrawbackofMC-CDMA,likeDS-CDMA,isthemultiuserinterference(MUI)encounteredduetolossoforthogonality.ThisfactorpredeterminestheperformanceofMC-CDMA[ 21 23 ]. Severaladvancedmultiuserdetectiontechniquesareavailableforinterferencemitigation[ 58 ].Despitetheeectivenessoftheirapproaches,thesemethodsarenotsuitablefordownlink(DL)applicationsduetothelimitedcomputationalpowerofmobileterminals(MTs)[ 26 ].Asanalternativetomultiuserdetection,precodingtechniquescanbeemployedtomitigatetheMAIandchanneldistortionsintheDL.Afundamentalideaoftheprecodingistovarythecomplexgainassignedtoeachsubcarriersuchthatinterferenceisreducedandthesignalatthereceiverappearsundistorted.Theuseoftheprecodinghasseveraladvantages:(i)reducingtheMAIatMTsbytheprecodingatthebasestation(BS)sothatthereceivedsignalatthedecisionpointisfreefrominterference, 113

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Inrecentyears,severallinearprecodingtechniqueshavebeenproposedformulti-inputsingle-output(MISO)DLtimedivisionduplex(TDD)MC-CDMAintheliterature[ 22 24 { 27 36 37 ].Thealgorithmdiscussedin[ 24 ]aimsatmaximizingthesignaltointerferenceplusnoiseratio(SINR)atMTs.Thisleadstoacomplicatedjointoptimizationproblemforthetransmitltersofallactiveusers,andthusasuboptimalapproachwasproposedbasedonamodiedSINR.In[ 25 ],aspace-frequencyprecodingtechniquebasedonminimizationofthetransmittedpowersubjecttoMAIeliminationwasproposed,whicheliminatesthenecessityofthenoisevariancetobeestimatedattheMTandknownattheBS.In[ 26 ],adierentpowerconstraintwasderivedfortheapproachproposedin[ 25 ].Aconstraintontheoveralltransmitpowerallocatedtoallactiveuserswasimposed,insteadofnormalizingthetransmitpowerforeachuser.Thiswasfurtherextendedin[ 27 ],wherealternativestrategiestoconstrainthetransmitpowerattheBShavebeendiscussed.Allofthesespace-frequencyprecodingschemeswerederivedconsideringthatnochannelequalizationisperformedattheMTs,whileacombinationoftheprecodingtechniquesandchannelequalizationatthereceiverwasproposedin[ 22 ]. Inthischapter,westudyananalyticalbiterrorrate(BER)performanceofaDLTDDMC-CDMAwithaprecodingtransmitterantennaarrayattheBS.In[ 44 ],asymptoticBERofaprecodedrandomspreadingCDMAsysteminadditivewhiteGaussiannoise(AWGN)channelswasanalyzed.In[ 27 ],theperformanceofdierentspace-frequencyprecodingmethodswascomparedbynumericalsimulations.In[ 22 ],twospace-frequencyschemeswithmultiuserpre-lteringtechniquesforDLMC-CDMAwereproposedandtheperformanceoftheproposedschemeswascomparedtoothertransmitterprecodingapproachesbysimulation.However,notmanyanalyticalperformancestudieshavebeendonefortheprecodedDLMC-CDMA.Byconductinganalyticalstudy,wecanpredictandcomparetheperformanceofvariousprecodingtechniques. 114

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6.2 elaboratesonasystemmodelofaDLTDDMC-TDCS.Then,varioussingle-userequalizationmethodsarediscussedinSection 6.3 .Section 6.4 describeshowtomitigatetheMAIwithhelpofthespace-frequencydiversityandtheprecodingatthetransmitter.TheperformanceanalysisandvericationbysimulationarepresentedinSection 6.4.3 andSection 6.5 ,respectively.Finally,Section 6.6 summarizesthischapter. 22 24 { 27 36 37 ]requirechannelstateinformation(CSI)atthetransmitterinordertoworkproperly.ThiscanbeachievedinTDDsystemsbyexploitingthechannelreciprocitybetweenalternativeuplinkanddownlinktransmission.Ifchannelvariationsaresucientlyslow,thechannelestimationderivedattheBSduringanuplinktimeslotcanbereusedforprecodinginthesubsequentdownlinktimeslot[ 26 43 ]. WeconsideraDLoftheMC-CDMAnetworkwherethetotalnumberofsub-carriersNcisdividedintoMsmallergroupsofLelementsofthesub-carrierswhereM=Nc=L.WeassumethattheBShasPtransmitterantennaeandusesthesub-carriersofagivengrouptocommunicateKactiveusers(KL).Thereforeeachuserk(1kK)transmitsMdatasymbolsperOFDMsymbol.Hence,eachOFDMsymbolhasadatarateproportionaltoMtimestheoriginalinputdatasymbols.Activeusersareseparatedbytheirspecicspreadingcodeckofthekthuser,usuallychosenfromanorthogonalset.Let'sassumetheLsub-carriersofagivengroupareuniformlydistributedoverthesignalbandwidthtobetterexploitfrequencydiversity.Letimndenoteasub-carrierindexofthemthsymbolofauserwithimn=m+(n1)N=Land1nL. Figure 6-1 showstheblockdiagramofaDLTDDMC-CDMAsystemunderinvestigation.Thedatasymbolvectorakoftheuserkisfedintotheserial-to-parallel 115

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. ... ... S/P S/P S/P + ChipMapping OFDM+GI(pthAnt) OFDM+GI(1stAnt) OFDM+GI(PthAnt) ... ... . GI+FFT(jthMT) ChipDe-mapping ^amj Figure6-1. ArchitectureofMC-CDMAtransceiverwithmultipletransmitterantennae,precodingandreceiver-basedequalization

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ThecontributionofallKusersaresummedtogetherineachsub-carrierindeximn(1nG)toformthefollowingmultiusersignalatthepthantenna Then,eachsmpisuniformlymappedonLsub-carriersusingthechipmapper.AfteranOFDMmodulationforeachantenna,NG-pointcyclicprex(CP)(orguardinterval(GI))isaddedinthetransmittedsignalstoavoidinterferencebetweenadjacentOFDMblocks. ThetransmittedsignalsbytheBSantennaearraypropagatethroughmultipathchannelsandexperiencefrequencyselectivefading.ThejthMTwithasingleantennarecombinessignalsfromPantennaebranchesattheBS.ThereceivedsignalaftertheOFDMdemodulationandCPremovalofthejthMTisgivenby whereHj;p=diagfHj;p(im1);;Hj;p(imL)gisadiagonalmatrixofsizeLL,representingchannelfrequencyresponsebetweenpthtransmitterantennaandjthMToverLsub-carriers,andHj;p(imn)denotescomplexatfadingchannelofthenthsub-carrieronthepthantenna,nj=[nj(1);;nj(G)]Tisthermalnoisewithzeromeanandcovariancematrix2nIL. 117

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^amj=qTjXmj=amjqTjPXp=1Hj;pwj;p!| {z }Desiredsignal+KXk=1;k6=jamkqTkPXp=1Hj;pwk;p!| {z }MAI+qTjnj| {z }Noise(6{3) whereqk=[qk(1);;qk(L)]TisavectorofsizeLthataccountforbothdespreadingandchannelequalizationoperations.Asmentioned,theperformanceoftheMC-CDMAispredeterminedbythe2ndtermin( 6{3 ).Severalreceiverchannelequalizationmethodsforsingleuserdetectionwillbediscussedinthesequel. where()denotesthecomplexconjugateandGj=diagfgj(1);;gj(L)gisadiagonalmatrixofsizeLL,representingcoecientsofthefrequencydomainchannelequalization.Ifweuseonlytheprecodingatthetransmitterantennae,wecanusethepuredespreading(PD)inordertokeeptheMTsatverylowcomplexity.Then,thedespreadingandchannelequalizationvectorqkisthesameastheuser'sdespreadingcodeasfollows: Inmaximalratiocombining(MRC),astrongersignalisassignedahigherweightbythediversitycombinersthanaweakersignal,sinceitscontributionismorereliable. 118

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Theequalgaincombining(EGC)attemptstocorrectthechannel-inducedphaserotations,leavingthefadedmagnitudesuncorrected. Ifwecanceltheeectofthechanneltransferfunctionbyestimatingitandreversingitseects,theorthogonalityofthedierentuserscanbemaintainediforthogonalcodesareused.Thisistheaimoftheorthogonalityrestoringcombining(ORC)orzeroforcing(ZF)equalization. TomitigatethenoiseenhancementofORC,particularlyatlowerSNRvalues,theminimummeansquareerror(MMSE)equalizationcanbeused. 6.2 .Ifwedon'tusetheprecodingatthetransmitterantennae,wecanusethepurespreading(PS).Theweightedoutputwj;pofthejthuserofthepthantennain( 6{3 )forthePSisthesameasthejthuserspreadingcode.Thatis: 119

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6{3 )istheinterferenceofthejthMTonthekthMT.Thatis: Thejointprecodingandspreadingweightvectorwj;pofthejthMTatthepthtransmitantennaisthenobtainedbyconstrainingthedesiredsignalpartofitsowndecisionvariabletoagivenconstantwhilecanceling(orzero-forcing)theMAIcontributionatallotherMTs.Thisleadstothefollowingsetofconditions: wherejisapositiverealvaluethatischosentomeetsomeconstraints.Notethatthemultiuserchannelin( 6{3 )isdecoupledintoKsingleuserparallelAWGNchannelin( 6{12 )withtransmissiongainsgivenbyaspecicvaluej,computedtomeetsomedesigncriterion.Bydoingso,thepurposeoftheprecodingistoeliminatetheMAIcausedbythejthusertootherK1MTsandtomitigatethechanneldistortionsofthejthuserdatasymbolajatthejthMT.Tocomputetheweightvectorwj;p,wehavetosolveKlinearequationsgivenby: whereQisacomplexchannelandusercodematrixofsizeKPGandbjisavectorofsizeKgivenby: 120

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6{5 )attheMTin( 6{14 )insteadofthejointprecodingandequalizationinSection 6.3 ,thecomplexchannelandusercodematrixin( 6{14 )become: where()Hdenotescomplexconjugatetranspose.WewanttominimizethetransmitterpowersubjecttoKconstraintgivenby( 6{13 ).Thustheprecodingoptimizationproblemcanbewrittenas: min|{z}wjwHjwjsubjecttoQwj=jbj(6{16) ThisoptimizationcanbesolvedbytheLagrangemultipliersmethod.Theminimum-normsolutionbecomes: whereQQHisacomplexsquareandHermitianmatrixofsizeKK,andwjrepresentstheweightvectorwithoutpowerscalingandthetransmittedpowerbecomes: 6{17 )to( 6{3 ),thedecisionvariableofthejthMTbecomes: 121

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6{17 )isnormalizedto1foraparticularcase.ThisimpliesthatthereceivedpowerisconstrainedtooneateachMT,butthereisnoconstraintonthetransmittedpowerattheBS.OncetheMAIiscompletelyeliminatedbyusingweightvectorsin( 6{17 ),dierentstrategiescanbeusedtoconstrainthetransmitpowersubjecttoagivenconstraint[ 22 ].Thereareseveralpowerconstraintstrategiesintheliterature[ 22 25 26 46 ]forMC-CDMAsuchasmaximizationofthesumcapacity,minimizationoftheaverageerrorprobability,andlinearpowerallocationapproaches.However,weonlyconsiderlinearpowerallocationapproachesforthesakeofsimplicity. Theaimoflinearpowerallocationapproachesistondsimpleexpressionsfortheconstraintsjthatcanbeeasilyimplementedinpracticalmobileterminals.OveralltransmittedpowerofallKactiveusersis Theconstraintjcanbeobtainedsimplyfrom( 6{20 ), Inthiscase,thetotaltransmittedpowerisnormalizedtoKandthesameconstraintisusedforallKactiveusersasproposedin[ 43 ].Anotherapproach,calledtotalinterferenceremoval(TIR),istoconstrainthetransmittedpowertoagivenconstantinordertonormalizetheweightvectorwaccordingto[ 22 24 25 65 ], Inthiscase,thetransmittedpowerisconstrainedtoone,i.e.,2jkwjk2=1,forallKactiveusers,andjisgivenby: 122

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22 26 ],amodication,calledm-TIR(modied-TIR),ofthepowerconstraintgivenby( 6{23 )wasproposed.TheideaistominimizethesumoftheinverseofSNR,notSNRundertheconstraintgivenby( 6{13 )whichthetotaltransmitterpowerisconstrainedtoK.Thus,thefollowingcostfunctionwasintroducedin[ 22 26 ]. Thejforeachuserjbythem-TIRisgivenby: Intuitively,theconstraintsgivenby( 6{25 )and( 6{21 )onlygivebetterperformancethantheonegivenby( 6{23 )forthecasewherewedonothaveenoughdegreeoffreedomtominimizethetransmitpower[ 22 ]. 6{19 )isgivenby: from( 6{19 )withQ(x)=1=p 6{23 ),theBERoftheuserjcanbewrittenasfollows: 123

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whereR1j;jdenotesthe(k;k)elementoftheinverseofthescattermatrixR=QQH.LetQ=UVHdenotethesingularvaluedecompositionofKLM-sizedQwhereUistheKKunitaryleftsingularvectormatrix,isKLMdiagonalsingularvaluematrixwithnonnegativerealnumbersonthediagonal,andVHdenotestheconjugatetransposeofV,anLMLMunitaryrightsingularvector.Then,thescattermatrixRcanbefactoredinto whereisthediagonalmatrix,theentriesofwhichareeigenvaluesjforj=1;;K.SinceR1=U1UHandR1j;j=1j;j=1j,j=p 6{23 )becomes: Ifweusethegainjin( 6{25 )and( 6{21 ),theBERofthejthuserbecomes 2nPKk=1kwkk2!#=Ej"Qs 2nPKk=11k!#(6{31) 124

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2nkwjkPKk=1kwkk!#=Ej24Q0@vuut NotethattheBERperformanceofthejthuserin( 6{27 ),( 6{31 ),and( 6{32 )dependsontheeigenvaluesofthescattermatrixR=QQH.ThenumericalaverageBERbecomes: 6.4 withtheSUDinSection 6.3 fortheMC-CDMAsysteminSection 6.2 ,weusesystemparametersbasedonthe802.11aphysicallayerstandard.WeassumethatthedistancebetweentransmitantennaeisfaraparttoconsiderPindependentchannelsforeachuser. Themainsimulationparametersusedinthissimulationarethenumberofsub-carrier(Nc)setto64;OFDMsymboldurationis3.2s;systembandwidthis20MHz;numberofdatasymbol(M)perframeis8;lengthofspreadcode(L)orspreadingfactor(SF)is8;cyclicprexcontains16samplesor0.8s;numberofactiveusersis1,4,or8(KL);modulationisBPSK;andchannelismodeledasRayleighfadingwithAWGNchannel.WeuseWalsh-HadamardspreadingsequencesforaDLsynchronizedtransmission.Thechannelisatatleastbetweentwosub-carriersandiskeptxedoveranOFDMsymbolduration,butitvariesfromOFDMsymboltosymbol.Asmentioned,weassumeaperfectCSIknowledgefortheunlinkchannelattheBSandfortheDLattheMT(ifthesingle 125

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Itisinterestingtoobservetheeectsofnumberofactiveusers(KL)andthenumberoftransmitterantennae,P,ontheBERperformancewhenthePSin( 6{10 )andMRCin( 6{6 )areusedatboththeBSandMTs,respectively.WereferthisapproachasthePS/MRCandthesamenotationwillbeusedinthesequel.TheeectofMRCisequivalenttothatofthematchedltering,wherethelteringismatchedtothechanneltransferfunction.Matchedlteringconstitutestheoptimalltering,whichmaximizestheSNRattheoutputofthedecisiondevice.TheachievableBER,Pe,ofthesingleuserperformanceofMRCoverRayleighfadingchannelhavingD-independentpropagationpaths(ordiversityorder)isgivenby: 2(1)DD1Xk=0D1+kk1 2(1+)k(6{34) whereisdenedas andbistheaverageenergyperbit,Eb,dividedbythenoisepowerspectraldensity,N0[ 23 ].Thesignal-to-interference-noiseratio(SINR)in( 6{3 )ofPS/MRCwithP=1is b;SINR=Eb 6-2 .Theanalysiscurvesaredrawnby( 6{34 )with( 6{35 )and( 6{36 )forK=1andK=8.Asthenumberofactiveuserswasincreased,theBERincreasedsignicantlyduetotheincreasedamountofthe2ndtermin( 6{3 ).Figure 6-3 showseectsofarraygainontheBERperformanceofthePS/MRCwithP=1,2,and4transmitantennaeforsingleuser(K=1).Asthenumberoftransmitantennaewasincreased,theBERdecreasedduetothearraygain. 126

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AverageBERofsynchronousMC-CDMAdownlinkusingPS/MRCforsingleuser(K=1)andfullload(K=8)withP=1overRayleighfadingchannel Figure6-3. EectofarraygainontheaverageBERusingPS/MRCforsingleuser(K=1)withP=1;2;4overRayleighfadingchannel 127

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6.4.1 ,themultiuserchannelisdecoupledintoKsingleuserparallelAWGNchannelswithtransmissiongaingivenbyaspecicconstantjin( 6{23 ),whichisconstrainedtooneforallKactiveusersby( 6{22 ).SincetheMRCisemployed,thegainjistochoosetheweightstobefadedtoeachsub-carrier.Therefore,wecanusethesingleuserperformancein( 6{34 )withthediversityorderD.Sinceweuseboththespacediversityandfrequencydiversityatthesametimeinthejointprecoding,thediversityorderisafunctionofthesediversities.Figure 6-4 showstheaverageperformanceoftheTIR/MRCapproach.AnalysiscurvesinFigure 6-4 aredrawnby( 6{34 )withthediversityorder,DTIR=MRC=DPS=MRC+P1,andaveragesignal-to-noiseratiob;TIR=MRC=PEb=N0.ThisanalyticalperformancecanprovideanecientpredictionofvariouscombinationsofthejointprecodingschemesinSection 6.4 Figures 6-6 to 6-9 aresimulationresultsofvariouscombinationsofjointprecodingandsingleuserequalizationwithrespecttotheTIR/MRCscheme.Theperformanceresultsofdierentspace-frequencyprecodingapproachesarederivedfortheMC-CDMAintermsoftheaverageBERasafunctionofSNR. WecanseethattheBERperformanceisenhancedasthenumberoftransmitantennaeincreasedduetoarraygain.Theperformancewithm-TIRin( 6{25 )andSINRin( 6{21 )is,ingeneral,betterthanthatofTIRin( 6{23 ),sincetheseschemescanredistributethetransmissionpoweramongactiveusersaccordingtotheCSI.However,theperformancewithORCinFigure 6-8 indicatesthattheORCwithunequalpowerconstraintscandegradetheperformancewithrespecttoequalpowerconstraint. FromFigure 6-5 andFigure 6-7 ,theperformanceoftheprecodingwiththePDandEGCisbasicallythesame;onlyminordierencesintermsofgainsisobserved.TheuseofanequalizerattheMTsbringssomebenets,sincetheburdenofmitigatingchannelimpairmentscanbedistributedamongtheBSandMTswhentheBSisequippedwithonlyoneortwotransmitantennae.Thismayincurincreasingcomputationalcomplexity 128

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Figure6-4. AverageBERofsynchronousMC-CDMAdownlinkusingTIR/MRCforK=8activeuserswithP=1;2;4overRayleighfadingchannel Figure6-5. PerformancecomparisonofsynchronousMC-CDMAdownlinkusingPDforK=8activeuserswithP=1;2;4overRayleighfadingchannel 129

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PerformancecomparisonofsynchronousMC-CDMAdownlinkusingMRCforK=8activeuserswithP=1;2;4overRayleighfadingchannel Figure6-7. PerformancecomparisonofsynchronousMC-CDMAdownlinkusingEGCforK=8activeuserswithP=1;2;4overRayleighfadingchannel 130

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PerformancecomparisonofsynchronousMC-CDMAdownlinkusingORCforK=8activeuserswithP=1;2;4overRayleighfadingchannel Figure6-9. PerformancecomparisonofsynchronousMC-CDMAdownlinkusingMMSEforK=8activeuserswithP=1;2;4overRayleighfadingchannel 131

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132

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13 66 ]. Acosteectivetransmissiontechniquethatcanusescarcespectralresourceisinneedforwirelessservices.Multi-carriercodedivisionmultipleaccess(MC-CDMA)hasbeendevelopedasacandidateair-interface,especiallyfordownlink(DL),toprovidehighbitrates.However,theperformanceofMC-CDMAisessentiallylimitedbymultipleaccessinterference(MAI),andlowcomputationalcomplexityorresourceusagesaredesiredatmobileterminals(MTs)[ 21 { 23 ].Especiallyforthemilitarycommunicationsystem,itisveryimportanttobeabletooperateinthepresenceofbothjammingandunintentionalinterference. TomitigatetheMAI,theuseofpre-lteringwithMC-CDMAsystemshasalsobeenconsideredrecently.Pre-lteringapproachesdesignedinfrequencyandspaceforDLtimedivisionduplex(TDD)MC-CDMAsystemshavebeenproposedin[ 22 24 { 27 ].However,notmuchworkhasbeendonetomitigatejammingfortheMC-CDMA.TheMC-CDMAhasanti-jammingcapabilityduetousageofspreadsequence,notinterferenceavoidancecapability. Transformdomaincommunicationsystem(TDCS)canprovidetheinterferenceavoidancecapabilityforsingle-carrier(SC)communicationsystem[ 9 11 ].IntheTDCS,aninterferenceavoidingwaveformisadaptivelygeneratedbothatthetransmitterandreceiversideinfrequencydomainviaaspectralenvironmentestimationandspectralnotchingprocess.Severalapproacheshavebeenproposedtomitigatenarrowbandinterference(NBI)andtoenhanceperformanceofthesingle-inputsingle-output(SISO) 133

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9 10 19 34 ]. Formultiple-inputmultiple-output(MIMO),especiallyvertical-BellLaboratorieslayeredspace-time(V-BLAST)system,thefundamentalconceptoftransformdomainprocessing(TDP)andzero-forcing(ZF)V-BLASTwascombinedtomitigateNBIin[ 12 ].However,theapproachusedin[ 12 ]didnotworkwellfornon-stationaryinterferencesbecauseofthenoiseenhancementoftheZFdetector.In[ 35 ],authorsextendourpreviousapproachin[ 34 ]toV-BLASTtoprovidenon-stationaryaswellasstationaryinterferenceavoidancecapabilitiestotheV-BLASTsystem. AperformancecomparisonoftheSC-TDCSand(multi-carrier)OFDMbasedcognitiveradioforMIMOsystemusingV-BLASTreceiverarchitecturetoreconstructthetransmitteddatainRayleighfadingchannelwaspresentedin[ 32 ].Amodicationofboththetransmitterandthereceiverblockdiagramaccordingto[ 11 ]hadbeenmadeintheirsystem.CRwithOFDMconsistentlyoutperformstheCRwithTDCSarchitecturebymorethan56dBsignal-to-noiseratio(SNR)perbitgaineitherforasingletransmitandreceiveantennaorMIMOsystemwithabalanceddesignoftransmitandreceiveantennae1withantipodalmodulationschemeandfrequencydomainzero-forcingequalizer.Sincethezero-forcingequalizerremovedthefrequencyselectivityofthechanneltransferfunction,thereisnoroomforimprovementwiththeaidofthefrequencydomaindiversity.Therefore,weneedtoenhancethebiterrorrate(BER)performanceoftheTDCSunderRayleighfadingwiththehelpofthefrequencydomaindiversitycombiningtechniques. OFDM-basedtransformdomaincommunicationsysteminCRforcontrolmessagetransmissionwasproposedin[ 29 ].However,onlyaSISOantennacongurationwasconsideredandtheperformanceundertheintentionalinterferencewasnotinvestigated. 32 ]. 134

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28 ]andthatperformanceundermultipathfadingwasstudiedin[ 29 ]. Thepurposeofthischapteristoproposeamulti-carrierTDCS(MC-TDCS).TheconceptofTDPprocessingandmulti-carriermodulation(MCM)arecombinedtogetherinMC-TDCStoavoidintentionalinterferenceandtocombatmultipathfading.WealsostudytheperformanceundermultiuserandincorporateaprecodingattransmitterantennaarraytomitigatetheMAIatthetransmitter,notatthereceiver. Thecontributionsofthischapterare:(i)theperformanceimprovementofTDCSundermultipathfadingwiththehelpoffrequencydomaindiversity,(ii)themitigationofjammingandprovisionoftheinterferenceavoidancecapability,(iii)thetransmitterantennaarrayprecoding(orpre-ltering)tomitigatetheMAIinterference,and(iv)analyticalperformanceevaluationoftheproposedMC-TDCS.Therefore,theproposedMC-TDCSwillbeaviableoptionfortheTDCSovermultipathfadingwithAWGN. Theremainderofthischapterisorganizedasfollows:Section 7.2 elaboratesonasystemmodeloftheproposedMC-TDCSanddescribesamathematicalmodeloftheproposedsystem.Then,varioussingleuserequalizerperformanceforthesingleuserdetectionisinvestigatedinSection 7.3 .Section 7.4 describeshowtomitigatetheMAIwithhelpsofthetransmitterdiversityandtheprecodingatthetransmitter.TheperformanceunderNBIisvalidatedinSection 7.5 .Finally,Section 7.6 summarizesthischapter. 7-1 showstheproposedDLMC-TDCStransmitterofthebasestation(BS)andthereceiverofthek0thusermobileterminal(MT).TheBSandMTsjointlyuseapre-lteringandfrequencydomainequalizer,respectively.MC-TDCSisamulti-carriertransmissionwhereitsbandwidthcanbedividedintosmaller 135

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. ... ... S/P S/P S/P + ChipMapper OFDM+GI(pthAnt) OFDM+GI(1stAnt) OFDM+GI(PthAnt) ... ... . GI+FFT(k0thMT) ChipDe-mapper ^amk0 Buer Precodinguk CSI ScaleC SpectrumMagnitude EstimateSpectrum RandomPhase LFSR TransmitterandreceiverarchitectureofMC-TDCSwithmultipletransmitterantennae,pre-lteringandreceiver-basedequalization

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9 11 ],wecanapplytheminfrequencydomain,mappingadierentchipofafundamentalmodulationsignaturewaveform(FMW)toanindividualOFDMsub-carrieradaptively. Thetotalnumberofsub-carriersNcisdividedintoMsmallergroupsofLelementsofthesub-carrierswhereM=Nc=LintheDLMC-TDCSnetworks.ThereforeeachuserktransmitsMdatasymbolsperOFDMsymbol.HenceeachOFDMsymbolhasadatarateproportionaltoMtimestheoriginalinputdatasymbols.WeassumethattheBShasPtransmitterantennaeandusesthesub-carriersofagivengrouptocommunicateKactiveusers(KL).ActiveusersareseparatedbytheirspecicFWMBkofthekthuser,adaptivelygeneratedbyspectrummagnitudeAk,andrandomphasevectork.Let'sassumetheMsub-carriersofagivengroupareuniformlydistributedoverthesignalbandwidthtobetterexploitfrequencydiversity.Letimndenoteasub-carrierindexofthemthsymbolofthekthuserwithimn=m+(n1)N=Land1nL.Afterestimationofthespectralenvironment,asub-bandexceedsthatofthenoiselevelbyafactorofathresholdlevel,interferenceisclaimedtobepresentandthesub-bandisnotchedout,assigningmagnitudevalue`0'.Otherwise,thesub-bandsareretainedandsettothevalueof`1'.Thatis: ThespectrummagnitudevectorAk=[Ak(1)Ak(L)]Tofthekthuserisanelement-by-elementproductofarandomphasevectork=[k(1)k(L)]Hoftheuserkwherek;p(n)isgeneratedbyr-bitoutputsofalinearfeedbackshiftregister(LFSR)and()T(H)denotesthe(conjugate)transpose.Ifr=3,forexample,k(n)hasavalueamong 137

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7-2 showsthepseudo-randomphasevectorforrbitoutputsofaLFSR.2 Re[ejk] Im[ejk] 2rpoints Re[ejk] Im[ejk] 2rpoints Pseudo-randomphasevectorforr,whererdenotesthenumberofrandomsequencebitsgeneratedbyLFSR Then,theunscaledBbbecomes: wheredenotestheHadamardproduct(orentry-wiseproduct).Theenergy-scaledFMWBkofthekthuseris: PLn=1jAk(n)k(n)j2(7{3) Thedatasymbolvectorakoftheuserkisfedintotheserial-to-parallelblockandthemthsymbolofthekthuser,amk,isspreadbyLchipsusingtheFMWsequenceBk=[Bk(1);;Bk(L)]Hofthekthuser.TheresultingamkBkisweightedbyapre-lteringcoecientuk;pofthekthuseratthepthantennaandisfedtoeachantenna.Theweightedoutputwk;p=[wk;p(1);;wk;p(L)]Hofthekthuserofthepthantennais 138

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Then,eachsmpisuniformlymappedonLsub-carriersusingthechipmapper3.AfteranOFDMmodulatorforeachantenna,aNG-pointcyclicprex(CP)(orguardinterval(GI))isaddedinthetransmittedsignalstoavoidinterferencebetweenadjacentOFDMblocks. ThetransmittedsignalsbytheBSarraypropagatethroughmultipathchannelsandexperiencefrequency-selectivefading.WeassumeeachMThasasingleantennaandlethk;p=[hk;p(0);;hk;p(Lk;p1)]Tbethediscretechannelstateinformation(CSI)betweenthepthtransmissionantennaandthekthMT.WeassumetheCSIsarepracticallyconstantovertheDLtimeslotandperfectCSIisassumedattheBSforsimplicity. ThetransmittedsignalsfromthePtransmissionantennaearerecombinedbythereceiverantennaandarepassedtoanOFDMdemodulator.ThedemodulatoroutputsXk0=[Xk0(1);;Xk0(L)]HcorrespondtotheLsub-carriersoftheconsideredgroupofthek0thuserMT.Ifweassumeidealfrequencyandtimingsynchronization,wehave whereHk0;pisadiagonalmatrix 139

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N;n=1;;L&m=1;;M(7{7) andnk0=[nk0(1);;nk0(L)]Tisthermalnoisewithzeromeanandcovariancematrix2nIL. Thedecisionvariableattheinputofthedemodulatorforthedesiredk0thuserisgivenby ^amk0=qTk0Xmk0=amk0qTk0PXp=1Hk0;pwk0;p!| {z }Desiredsignal+KXk=1;k6=k0amkqTkPXp=1Hk0;pwk;p!| {z }MAI+qTk0nk0| {z }Noise=++(7{8) whereqk=[qk(1);;qk(L)]TisavectorofsizeLthataccountforthebothdespreadingandchannelequalizationoperations.Ifweonlyusethepre-lteringatthetransmitterantennae,wecanusethepuredespreading(PD)inordertokeeptheMTsatverylowcomplexity.Thedespreadingandchannelequalizationvectorqkisthesameastheuser'sFMWBkforthePD.Severalchannelequalizationmethodsforsingleuserdetectionwillbediscussedinthesequel. 7{8 )predeterminetheperformanceofthesingleuserdetectionconsideredinthissection.Forsingleuserdetection,theequalizercoecientsaregivenby: wheredenotesthecomplexconjugateandGk=diagfgk(1);;gk(L)gisadiagonalmatrixofsizeLLrepresentingcoecientsofthechannelequalizer,whilethejoint 140

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7{8 )becomes: ^amk0=qTk0Xmk0=(Gk0Bk0)TXmk0=amk0(Gk0Bk0)TPXp=1Hk0;pBk0!| {z }Desiredsignal+KXk=1;k6=k0amk(GkBk)TPXp=1Hk;pBk!| {z }MAI+(Gk0Bk0)Tnk0| {z }Noise=amk0BHk0Gk0PXp=1Hk0;pBk0!| {z }Desiredsignal+KXk=1;k6=k0amkBHkGkPXp=1Hk;pBk!| {z }MAI+BHk0Gk0nk0| {z }Noise=s+s+s(7{10) wherethesubscriptsdenotestheSUD. Thecorrespondinguser'sreceivedsignalcomponent,s,isgivenby 141

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Finally,thenoiseterm,s,isobtainedby TheeectofthematchedlteringisequivalenttothatoftheMRC.Matchedlteringconstitutestheoptimalltering,whichmaximizestheSNRattheoutputofthedecisiondevice.ThesingleuserperformanceofMRCoverRayleighfadingchannelhavingLk;pindependentpropagationpathsforP=1isgivenby: Pe=1 2(1)Lk;pLk;p1Xk=0Lk;p1+kk1 2(1+)k(7{15) whereisdenedas andbistheaverageenergyperbit,Eb,dividedbythenoisepowerspectraldensity,N0[ 23 ].AsimulationresultisshowninFigure 7-3 forNc=1024sub-carriers,L=256codelengths,andP=1singleantennawhilevaryingthenumberofindependentmultipathLk;ppathsoverEb=N0=0;;14dB.NotethatthesimulatedBERperformanceoftheMC-TDCSisthesameastheanalyticalBERperformancein( 7{15 ). ItisinterestingtoobservetheeectsofthenumberofusersandthenumberoftransmitterantennaeontheBERperformance,whenMRCisused.TheBERperformanceoftheproposedMC-TDCSisessentiallylimitedbytheMAI,s,in( 7{10 )dueto 142

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BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuserandsingletransmitantennaoverLk;p-pathRayleighfading multipathfading.WestudytheperformanceoftheDL(fromBStoMT)MC-TDCSwithpurespreading(PS)atBS,whiletheMTsusetheMRCcombiner. TheprobabilityofbiterrorofthemultiuserSC-TDCSinAWGNchannel[ 28 ]isgivenby: whereKdenotesthenumberofusers,whileNcdenotesthecodelengthoftheFWM(orbasisfunction)oftheTDCS.NotethattheMAIinterferenceNIincreasesasthenumberofusersKincreases( 7{17 ).Nowweneedtoconsiderthestatisticalpropertiesofsandsin( 7{12 )and( 7{13 ).Assumingstatisticallyindependentdatasymbolsamkwithzeromeanunitvariance,from( 7{10 )wecanseethattheSINRatthek0thMTisgivenby: SINRk0=E[2s] 143

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ThentheaveragesignalpowerE[s2]becomes whereEbisthesignalenergyperbitduringthebitinterval.Ifweassumethattheabsolutevalueofthesub-carrierchanneltransferfunction,Hp;k(imn),obeysanindependentidenticallydistributed(iid)RayleighprocesswithEjHk;p(imn)j2=22k;p=1andBk(imn)Bk(imn)hasanequalprobability.Then, 144

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Therefore,theSINRin( 7{18 )becomes: SINRk0=E[2] Eb(K1)P+L2n=EbPL EbP(K1)+L2n=PL P(K1)+L2n Thisanalysisin( 7{22 )issupportedbytheFigure 7-4 .Asthenumberoftransmitterantennaeincrease,theBERperformanceisenhanced.SinceK=1,SNRk0=PEb=N0accordingto( 7{22 ).WhenP=2,thereisabout3dBenhancementintheBER.Inso-calledhalf(K=L=2)andfully(K=L)loadedconditions,themultipleaccessinterference(MAI)dominatesthesystemperformanceasopposedtothenoiseandthenumberoftransmitterantennae.ThecorrespondingsimulationresultsaregiveninFigure 7-5 and 7-6 forP=2andP=4,respectively. Figure7-4. BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuser(K=1)andmultipleantennaeoverLk;p=2-pathRayleighfading 145

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BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithtwotransmitterantennae(P=2)overLk;p=2-pathRayleighfading Figure7-6. BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithfourtransmitterantennae(P=4)overLk;p=2-pathRayleighfading 146

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Then,thecorrespondingthreecomponentss,s,ands,aregivenas: ThesimulationresultisshowninFigure 7-7 .NotethatoverallEGCBERperformanceoftheMC-TDCSisworsethantheMRCinSection 7.3.1 147

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BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCwithsingleuser(K=1)overLk;p-pathRayleighfading Thecorrespondingtwocomponentsare: Ontheotherhand,theMUIassociatedwithMRCisgivenby 148

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SimulationresultisshowninFigure 7-8 .SincetheORCschemeusingperfectchannelestimationhadalreadyremovedthefrequencyselectivityofthechanneltransferfunction,leavingnoroomforimprovementwiththeaidofthefrequencydomaindiversity.Thesourceoftheperformancedegradationisthenoiseenhancement,particularlyatlowerSNRvalues. Figure7-8. BERperformanceofthesynchronousMC-TDCSdownlinkusingORCwithsingleuseroverL-pathRayleighfadingwhereListhediversityorder 149

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SimulationresultisshowninFigure 7-9 .TheoverallBERperformanceofMMSEisalmostbetterthanthatofEGC,butisworsethanMRC. Figure7-9. BERperformanceofthesynchronousMC-TDCSdownlinkusingMMSEwithsingleuser(K=1)overLk;p-pathRayleighfadingwhereLk;pisthediversityorder 7.3 ,theperformanceoftheproposedMC-TDCSisessentiallylimitedbytheMAI,causedbythelossoftheorthogonalityamongusersinmultipathenvironments.Infact,while 150

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Theideabehindpre-equalization(orpre-ltering)istovarythegainassignedtoeachsub-carriersothatthetheinterferenceisreducedandalowcomplexdetectionschemecanbeemployedatthereceiver.Inordertoworkproperly,thepre-equalizationtechniquesrequireCSIatthetransmitter.Theuseofthepre-lteringhasseveraladvantages:(i)reducingtheMAIatMTsbythepre-lteringattheBSsothatthereceivedsignalatthedecisionpointisfreefrominterference,(ii)movingmostsignalprocessingtasksfromMTstoBS,and(iii)keepingtheMTsataverylowcomplexitylevel.Thereareseveralpre-lteringmethodsproposedintheliterature[ 22 24 { 27 ]forMISODLMC-CDMA.Thepre-lteringmethodsarebasedonminimizationofthetransmittedpowersubjecttoMAIelimination.Inthesequel,wewillelaborateonthejointpre-lteringandspreadingapproachin[ 22 ]intheproposedMC-TDCS. 7{8 )istheinterferenceofthek0thMTonthekthMT.Thatis: Thejointpre-lteringandspreadingweightvectorofthek0thMTisthenobtainedbyconstraintthedesiredsignalpartofitsowndecisionvariabletoagivenconstantwhilecanceling(orzero-forcing)theMAIcontributionatallotherMTs.Thisleadstothefollowingsetofconditions: 151

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7{8 )isdecoupledintoKsingleuserparallelAWGNchannelin( 7{36 )withtransmissiongainsgivenbythespecicvaluek0.Tocomputetheweightvectorwk;p,wehavetosolveKlinearequationgivenby: whereQisacomplexchannelandusercodematrixofsizeKPLandbkisavectorofsizeKgivenby: Ifweusethepuredespreading(PD)attheMTin( 7{38 )insteadofthejointpre-lteringanddespreading,thecomplexchannelandusercodematrixbecomes: WewanttominimizethetransmitterpowersubjecttoKconstraint.Thusthepre-lteringoptimizationproblemcanbewrittenas: min|{z}wkwHkwksubjecttoQwk=kbk(7{40) 152

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BERperformanceofafull-loadedMC-TDCSwithTIR/PDscheme ThisoptimizationcanbesolvedbytheLagrangemultipliersmethod.Theminimum-normsolutionbecomes: whereQQHisacomplexsquareandHermitianmatrixofsizeKK,andwkrepresentstheweightvectorwithoutpowerscaling. 6.4.2 6.4.3 153

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AnalysiscurvesofMC-CDMAinFigure 7-10 aredrawnby( 6{34 )withthediversityorder,DTIR=MRC=DPS=MRC+P1,andaveragesignal-to-noiseratiob;TIR=MRC=PEb=N0.ComparingFigure 7-4 ,Figure 7-5 ,andFigure 7-10 ,wecanseethatthepre-lteringenhancestheaverageBERperformanceasthenumberoftransmitterantennaeincreased.SincetheFMWsofMC-TDCSarenotorthogonaleachother,theperformanceoftheMC-TDCSispoorerthanthatofMC-CDMAforP=2.However,asthenumberoftransmitterantennaeincreases,theperformanceoftwosystemsisalmostthesameforP=4.Therefore,theMC-TDCScanmitigatetheMAIbythespace-frequencyprecodingscheme. 7{11 )andthesingleuserperformancein( 7{15 )inthesequel. PSDN=N0+NJ(7{42) whereN0isthenoisePSDofcomplexAWGNandNJisthePSDofcomplexBNJ.Therefore,bin( 7{16 )becomestheaverageenergyperbit,Eb,dividedbythetotalnoisepowerspectraldensity,N0+NJ.SimulationresultsareshowninFigure 7-11 andFigure 7-12 forMRCandEGCwithSNR=10dB,respectively.NotethatthesimulatedBERperformanceoftheMC-TDCSisthesameastheanalyticalBERperformancein( 7{15 ) 154

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7{42 ),whiletheoverallEGCBERperformanceoftheMC-TDCSisworsethanMRCunderBNJ. Figure7-11. BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderBNJoverL-pathRayleighfadingwhereListhediversityorder Figure7-12. BERperformanceofthesynchronousMC-TDCSdownlinkusingEGCunderBNJoverL-pathRayleighfadingwhereListhediversityorder 155

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7-13 forMRC.MC-TDCSavoidstheinterferedregionsbythespectralshaping.Therefore,itsperformancewiththespectralshapingisalmostthesameasthatoftheno-jammingcaseinFigure 7-3 BL=2 CL=3 DL=4 BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunder10%PBJoverL-pathRayleighfadingwhereListhediversityorder 156

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whereJisarandomphase,whichisuniformlydistributedover[0;2].AJandfJareamplitudeandfrequency,respectively.Notethatsingle-tonejamming(STJ)isaspecialcaseofmulti-tonejammingwithq=1.TheMTJisawide-sensestationaryjamming,sincethemeanE[j(t)]=0andtheautocorrelationE[j(t)j(t+)]=R()whereE[]denotestheexpectation. SimulationresultforSTJandMTJisshowninFigure 7-14 andFigure 7-15 withMRC,respectively.TheproposedMC-TDCSmitigatesSTJandMTJwithspectralshapinginfrequencydomain. 157

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BL=2 CL=3 DL=4 BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderSTJoverL-pathRayleighfadingwhereListhediversityorder 158

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BL=2 CL=3 DL=4 BERperformanceofthesynchronousMC-TDCSdownlinkusingMRCunderMTJoverL-pathRayleighfadingwhereListhediversityorder 159

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InChapter 1 ,weintroducedandmotivatedtheproblem.InChapter 2 ,weleveragedoninvestigatingtheperformanceofvariouswirelesscommunicationsystemsatphysicallayerunderinterference,sinceinterferencecandisruptcommunicationsbydecreasingthesignal-to-noise(SNR)ratio.Bydoingso,wecanpredicttheperformanceofwirelesscommunicationsystemsunderinterferenceaswellasmotivateustomitigateinterferenceforareliablecommunication. InChapter 3 ,weconsideredhowtocrackanadversary'scommunication,whichusesDS-SS.Toeavesdroponasecureadversary'scommunication,oneneedsto(a)identifythestartpositionofadatasymbolinthespreadsignalforsymbolsynchronizationpurpose,(b)removethepseudo-random(PN)sequence,(c)estimatethePNsequence,and(d)estimatethegeneratorpolynomial.WeaddressedthesefourproblemswitheectivemethodsinChapter 3 .Toidentifythestartpositionofadatasymbol,wedevelopedamethodthatusesthespectralnormofthesamplecovariancematrix.Aftersymbolsynchronization,amethodbasedonthecross-correlationwasusedtoestimatedatasymbolsuptoanunknownmultiplicativefactor.InadditiontoobtainingthePNsequenceandthedatasymbols,wealsoproposedazigzagestimatortoidentifythecodegeneratorpolynomialandproposedamethodtoidentifythepolarityintheinterceptedsignal.Wealsoanalyzedtheprobabilityoferrorofthezigzagestimator.Ourvalidationbysimulationandtheoreticalanalysisshowtheeectivenessofourproposedmethod. 160

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4 ,weproposedanenhancedtransformdomaincommunicationsystem(ETDCS)whichcansecureasingle-carriersingle-inputsingle-output(SC-SISO)systemagainststationaryandnon-stationaryinterference.TheproposedETDCSwithCapon'sMethod(CM)canproperlyestimatedintentionalinterferenceconsideredinSection 2.2.1 .Analyticalbiterrorrate(BER)studyandsimulationresultsveriedthattheETDCSoersasignicantinterferenceavoidancecapabilityforboththestationaryandnon-stationaryinterference. Inchapter 5 ,weconsideredtheproblemofmitigatingthenarrowbandinterference(NBI)forvertical-BellLaboratorieslayeredspace-time(V-BLAST)system.TheproposedV-BLASTsystemcombinedadvantagesofthetransformdomainprocessing(TDP)basedonCMmethodinChapter 4 andV-BLASTdetectionbasedonminimummeansquareerror(MMSE)underintentionalinterference.Thesecombinationsmitigatedbothstationaryandnon-stationaryinterferenceeectively.TheperformanceoftheproposedV-BLASTwasveriedbysimulationresults. InChapter 6 ,westudiedananalyticalBERperformanceofadownlink(DL)timedivisionduplex(TDD)multi-carriercodedivisionmultipleaccess(MC-CDMA)withaprecodingtransmitterantennaarrayatthebasestation(BS).WeanalyzedtheaverageBERperformanceofvariouslinearspace-frequencyprecodingapproacheswithlinearpowerallocationstrategiesattheBS.Theperformanceofprecodingschemesisafunctionofeigenvaluesofachannelscattermatrixbasedonthechannelstateinformationandspreadingsequencesofallactiveusers.ItwasveryclearthattheprecodingschemesallowasignicantperformanceimprovementoveronetransmitantennaattheBSexploitingspace-frequencydiversity.Byconductingthesestudies,wecanpredictandcomparetheperformanceofvariousprecodingtechniques. InChapter 7 ,weproposedamulti-carrierTDCS(MC-TDCS)whichcanprotectaMCmulti-inputsingle-output(MC-MISO)communicationsystemagainstjammingandmultipleaccessinterference(MAI).TheproposedMISOMC-TDCScombinedtheTDP 161

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Insummary,thisresearchstudiedphysicallayermeasuresinwirelesscommunicationsecurity.Althoughtherearestillmanyissuestoberesolved,webelievethatourapproachesinbothprotectingwirelesscommunicationsystemsunderinterferenceandcrackingthefoe'ssecureDS-SScommunicationsystemwillprovidephysicallayermeansforsecurityofwirelesscommunicationsystems. 3 .Wewillextendourresearchtostudyanothertypeofspread-spectrum,namely,frequency-hoppingspread-spectrum(FH-SS). TheFH-SSisamethodoftransmittingradiosignalsbyrapidlyswitchingacarrieramongmanyfrequencychannels,usingaPNsequenceknowntobothtransmitterandreceiver.WewilldesignandimplementaneavesdropperwhichcaninterceptasecureFH-SSsignal.WewillalsoleverageonreverseengineeringaPNsequenceoftheinterceptedsignalswithoutaprioriknowledgeabouttransmitterandreceiver. 2 ,andweleveragedoncountermeasuresforSC-SISO, 162

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4 ,Chapter 5 ,Chapter 6 ,andChapter 7 ,respectively. Wewilluseantennaarrayprocessingtomitigateinterference,sinceitcanprovideinterferenceavoidancecapabilityduetoitscapabilityofnullifyinginterferencesignalscomingfromacertaindirection.Inthisresearch,wewillusedetectionandestimationtheorytodetectjamming/interferenceandestimatetheangleofarrivaloftheinterferingsignal;wewilldesignandimplementantennaarrayprocessingtechniquestocounterthedetectedinterference;wewillevaluatetheperformanceoftheproposedcountermeasureunderdierenttypesofjammingandinterferencesignals;wewillalsoanalyzethecostoftheproposedcountermeasure. 163

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C.Bouder,S.Azou,andG.Burel,\Arobustsynchronizationprocedureforblindestimationofthesymbolperiodandthetimingosetinspreadspectrumtransmissions,"in2002IEEESeventhInternationalSymposiumonSpreadSpectrumTechniquesandApplications,vol.1,2002. [54] L.Jiang,H.Ji,andL.Li,\ABlindEstimationAlgorithmforPNSequenceinDS-SSSignals,"in8thInternationalConferenceonSignalProcessing,vol.3,16-202006,pp.{. [55] G.BurelandC.Bouder,\Blindestimationofthepseudo-randomsequenceofadirectsequencespreadspectrumsignal,"inMILCOM2000.21stCenturyMilitaryCommunicationsConferenceProceedings,vol.2,2000. [56] G.Stewart,\Perturbationtheoryforthesingularvaluedecomposition,"ComputerScienceTechnicalReportSeries;Vol.CS-TR-2539,p.13,1990. [57] P.Peebles,Probability,randomvariables,andrandomsignalprinciples.McGraw-HillCollege,1993. [58] S.Verdu,Multiuserdetection.CambridgeUnivPr,1998. [59] J.Capon,\High-resolutionfrequency-wavenumberspectrumanalysis,"ProceedingsoftheIEEE,vol.57,no.8,pp.1408{1418,1969. [60] H.Simon,Adaptiveltertheory(4thEdition).PrenticeHall,NewJersey,2001. [61] P.StoicaandR.Moses,Spectralanalysisofsignals.PearsonPrenticeHall,2005. [62] J.Benesty,J.Chen,andY.Huang,\AgeneralizedMVDRspectrum,"IEEESignalProcessingLetters,vol.12,no.12,pp.827{830,2005. [63] ||,\EstimationofthecoherencefunctionwiththeMVDRapproach,"in2006IEEEInternationalConferenceonAcoustics,SpeechandSignalProcessing,2006.ICASSP2006Proceedings,vol.3,2006. [64] G.Dillard,M.Reuter,J.Zeiddler,B.Zeidler,S.Center,andC.SanDiego,\Cycliccodeshiftkeying:alowprobabilityofinterceptcommunicationtechnique,"IEEETransactionsonAerospaceandElectronicSystems,vol.39,no.3,pp.786{798,2003. [65] M.Brandt-Pearce,\Transmitter-basedmultiuserinterferencerejectionforthedown-linkofawirelessCDMAsysteminamultipathenvironment,"IEEEJournalonSelectedAreasinCommunications,vol.18,no.3,pp.407{417,2000. [66] M.RahmanandH.Imai,\Securityinwirelesscommunication,"Wirelesspersonalcommunications,vol.22,no.2,pp.213{228,2002. 168

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YounghoJoreceivedaBachelorofScienceinphysicsfromtheKoreaMilitaryAcademy,Seoul,Korea,in1996,andaMasterofScienceinelectricalandcomputerengineeringfromtheUniversityofFlorida,Gainesville,Florida,in2000.From2000to2004,hewasafacultymemberoftheDepartmentofElectronicsEngineering,KoreaMilitaryAcademy.SinceAugust2006,hehasbeenadoctoralstudentoftheDepartmentofElectricalandComputerEngineeringattheUniversityofFlorida.Hisresearchinterestsareintheareasofwirelesscommunicationsecurity,spread-spectrumcommunication,multi-carriermodulation,multi-inputmulti-output,andsignalprocessing. 169