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Robust and Low Power Multiplierless Digital Filter Design for Wireless Communication

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Title:
Robust and Low Power Multiplierless Digital Filter Design for Wireless Communication
Creator:
NOH, SIWOO ( Author, Primary )
Copyright Date:
2008

Subjects

Subjects / Keywords:
Architectural design ( jstor )
Bandpass filters ( jstor )
Digital filters ( jstor )
FIR filters ( jstor )
Frequency response ( jstor )
Narrowband ( jstor )
Polynomials ( jstor )
Receivers ( jstor )
Signal processing ( jstor )
Signals ( jstor )

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Source Institution:
University of Florida
Holding Location:
University of Florida
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Copyright Siwoo Noh. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
11/30/2007
Resource Identifier:
1126526893 ( OCLC )

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1 ROBUST AND LOW POWER MULTIPLIERLESS DIGITAL FILTER DESIGN FOR WIRELESS COMMUNICATION By SIWOO NOH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 Copyright 2007 by Siwoo Noh

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3 To my family

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4 ACKNOWLEDGMENTS I would like to sincerely tha nk my advisor, Dr. Fred F. Taylor, for his support, encouragement and patience in gui ding the research. I would also like to thank Dr. John Shea, Dr. Liuqing Yang, and Dr. Tim Olso n for being on my committee and for their helpful advice. Finally, I wish to thank my wife and parents for their support. I thank, my dear princess, Hyunjhee, for providing big mo tivations to finish my study.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............11 CHAPTER 1 INTRODUCTION..................................................................................................................12 1.1 Background................................................................................................................. ......12 1.2 Research Contributions.....................................................................................................13 1.3 Dissertation Organization.................................................................................................14 2 OVERVIEW FILTER DESIGN FOR WIRELESS COMMUNICATIONS.........................16 2.1 Digital Signal Processing for Wireless Communication..................................................16 2.2 Digital Filter Design...................................................................................................... ...16 2.2.1. FIR Filters............................................................................................................. .18 2.2.2 Multi-Rate Signal Processing.................................................................................19 2.2.3 Polyphase Representation.......................................................................................20 2.3. Classic Channelizers...................................................................................................... ..20 2.3.1. Classic Channelizer Architecture..........................................................................20 2.3.2. Cascaded Integrator Comb Theory........................................................................22 2.4. Basic Theory of Multiplier-free Filter.............................................................................24 2.4.1. Multiplier-free Bandpass Filter.............................................................................24 2.4.2. Notch and Integrate Second Order Polynomial Filters..........................................27 3 MULTIPLIER-FREE FILTER...............................................................................................31 3.1 Multiplier-Free Uni-Mode Bandpass Filters....................................................................31 3.2 Multiplier-Free Lowpass Filter.........................................................................................36 3.3 Multiplier-Less Lowpass Filter and Shaping Filters........................................................39 4 NUMERICALLY CONTROL OSCILLATOR-BASED CHANNELIZER..........................45 4.1 Numerically Control Osc illator-Based Channelizers System Specifications...................45 4.2Multiplierless Lowpass Channelizers................................................................................47 4.3 Multiplier-less Cascaded Integrator Co mb and Shaping Filter Based Multi-rate Channelizer.................................................................................................................... .....54 4.3.1 IS-95.................................................................................................................... ...55 4.3.2 WiMAX..................................................................................................................58

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6 4.4. Hybrid less Cascaded Integrator Comb -Based Multirate Channelizer...........................61 4.5. Multiplier-Free Efficient FIR Downconverter for Channelizer.......................................63 4.5.1 Multiplier-Free FIR-based Downconverter............................................................63 4.5.2 Shaped Multiplier-Free FIR Downconverter..........................................................65 5 APPLICATION OF MULTIPLIERFREE FILTER TECHNIQUES...................................67 5.1 Numerically Controlled Os cillator-free Channelizer........................................................67 5.1.1 Numerically Controlled Oscillator -f ree Channelizer with Fractional Resampler........................................................................................................................ .70 5.1.2 Numerically Controlled Oscillator -Fr ee Channelizer with Simple Alternating Sign ( ) Switch............................................................................................................78 5.2 Periodic and Non-Periodic Narr owband Notch Filter Design..........................................88 6 SIMULATION AND PRELIMINARY RESULTS...............................................................93 6.1 Channelizer Complexity...................................................................................................93 6.1.1 Numerically Controlled Osc illator -Based channelizer..........................................94 6.1.2 Numerically Controlled Oscillator -Free and Multiplier-Free Channelizer...........96 6.2 Complexity and Performance of Multiplier-Less Notch Filters.......................................97 7 CONCLUSIONS AND FUTURE WORK.............................................................................99 7.1 Conclusions................................................................................................................ .......99 7.2 Future Work................................................................................................................ ....100 LIST OF REFERENCES.............................................................................................................101 BIOGRAPHICAL SKETCH.......................................................................................................104

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7 LIST OF TABLES Table page 2-1 Sample multiplier-f ree transfer functions, 1 = positive frequency, a = coefficients........26 4-1 Wireless Standards......................................................................................................... ....46 4-2 Passband and passband ripple of wireless standard ..........................................................47 4-3 Wireless standards which need PFIR and CFIR................................................................49 4-4 Wireless standards which need less then two FIR.............................................................54 4-5 Output data of multiplier-less Cascaded Integrator Comb and shaping filter based multirate channelizer..........................................................................................................58 4-6 Output data of multiplier-less Cascaded Integrator Comb and shaping filter based multirate WiMAX Channelizer..........................................................................................60 4-7 Output data of Numerically Cont rolled Oscillator-based channelizer...............................61 5-1 Multiplier-free filter transfer function for N =48................................................................68 5-2 Data of Numerically Controlled Oscill ator-free channelizer with fractional resampler........................................................................................................................ .......71 5-3 Summary of proposed channelizer.....................................................................................80 6-1 Computational complexity comparison fo r the overall NCO based channelizer with two FIR filters................................................................................................................ ....96 6-2 Complexity for IS-95 mobile communication...................................................................97

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8 LIST OF FIGURES Figure page 2-1 Basic CIC-based channelizer.............................................................................................17 2-2 Magnitude frequency response of CIC filter.....................................................................18 2-3 Steep skirt system architecture...........................................................................................19 2-4 CIC-based channelizer [8].................................................................................................21 2-5 NCO Architecture [9]....................................................................................................... .21 2-6 Two-stage CIC filter (down conversion le ft panel, up conversions right panel)...............23 2-7 Sharpened CIC D ecimation filters.....................................................................................24 2-9 Frequency magnitude response of ISOP filter...................................................................30 2-10 Frequency magnitude response of ISOP filter...................................................................30 3-1 The frequency response of all N=48 channe ls of a multiplier-less filter are shown in the top panel. The highlighted filter res ponse is that of an uni -mode filter section.........32 3-2 Two uni-bandpass filters obtained from an N=48 filter....................................................34 3-3 The frequency response of all channels of a multiplier-free un i-bandpass filter. ............35 3-4 Typical lowpass filter specification...................................................................................36 3-5 Architecture and the attendant magnitude frequency response of lowpass filters.............37 3-6 Example of Multiplier-free CIC-based lowpass filter.......................................................38 3-7 Examples of shaping filter’s magnitude frequency response (left) and impulse response (right) with two non-zero coefficients................................................................41 3-8 Multiplier-less lowpass filter having a passband ripple=0.05dB, passband =15.75dB, and stopband 7.18dB..........................................................................................................43 3-9 Multiplier-less lowpass filter: pass band ripple=0.06dB, passband =27.51dB, and stopband 9.12dB................................................................................................................44 4-1 Wireless filter mask requirements.....................................................................................48 4-2 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of GSM decimation filter.......................................................................................................50

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9 4-3 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WCDMA decimation filter................................................................................................51 4-4 Magnitude frequency response of conven tional (A,B,C) and proposed (D,E,F) of IS95 decimation filter........................................................................................................... .52 4-5 Magnitude frequency response of conven tional (A,B,C) and proposed (D,E,F) of IS136 decimation filter..........................................................................................................53 4-6 The architecture of multiplier-less CI C and ISOP based multi-rate channelizer...............55 4-7 Magnitude frequency response of three cl assed of filters, namely a CIC, multiplierfree lowpass filter, ISOP based multiplier-freefilter..........................................................56 4-8 Magnitude frequency response of multip lierless CIC and ISOP based Multirate Channelizer.................................................................................................................... ....57 4-9 Architecture of proposed Wi MAX multirate channelizer.................................................58 4-10 Passband ripple with two shaping filter.............................................................................59 4-11 Continued................................................................................................................. ..........59 4-11 WiMAX decimation filter with first stage.........................................................................60 4-12 The Architecture (left) and magnitude re sponse (right) of CIC decimation filter with M = 10, K = 1, 2, 3, and 4..................................................................................................61 4-13 The Architecture and magnitude res ponse of Hybrid CIC based Multirate Channelizer.................................................................................................................... ....62 4-14 Magnitude frequency response of CIC filters. ................................................................63 4-15 Architecture and magnitude response of the Multiplier-Free FIR down converter with 1, 2, 3=[1 1 1 1] ..................................................................................................64 4-16 Architecture and magnitude freque ncy response of a multiplier-free FIR downconverter with multiplier-free bandpass filter...........................................................66 5-1 The Architecture and magnitude res ponse of multiplier-free bandpass filters..................69 5-2 Architecture of NCO-free channeli zer with fractional re-sampler....................................71 5-3 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANa decimation filter..................................................................................................72 5-4 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANb decimation filter..................................................................................................73

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10 5-5 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANg decimation filter..................................................................................................74 5-6 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WCDMA decimation filter................................................................................................75 5-7 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WiMAX decimation filter..................................................................................................76 5-8 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of GSM decimation filter.......................................................................................................77 5-9 Bandpass filter based channelizer options.........................................................................78 5-10 Proposed channelizer...................................................................................................... ...79 5-11 NCO-free channelizer simulation......................................................................................81 5-12 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANa decimation filter..................................................................................................82 5-13 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANb decimation filter..................................................................................................83 5-14 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WLANg decimation filter..................................................................................................84 5-15 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WiMAX decimation filter..................................................................................................85 5-16 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of WCDMA decimation filter................................................................................................86 5-17 Magnitude frequency response of conve ntional (A,B,C) and proposed (D,E,F) of GSM decimation filter.......................................................................................................87 5-18 Final architecture of multiplier-less notch filter................................................................90 5-19 Magnitude and phase response of a multi-mode notch filter.............................................90 5-20 Magnitude and phase response of a uni-mode non-periodic notch filter...........................91 5-21 Magnitude frequency response of a typical multiplier-free notch filter for various parameterizations.............................................................................................................. .92 6-1 NCO Architecture........................................................................................................... ...95

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11 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ROBUST AND LOW POWER MULTIPLIERLESS DIGITAL FILTER DESIGN FOR WIRELESS COMMUNICATION By Siwoo Noh May 2007 Chair: Fred A. Taylor Major Department: Electrical and Computer Engineering Over the last several decade s, digital signal processing (DSP) has emerged as a key enabling technology in such fields as wire less communications (e.g., software-defined radio(SDR), multimedia, controls, and speech processing to name a few. In wireless communications, DSP is used at many levels, begi nning at the analog-to-digital converter (ADC) for receivers and ending at the digital-to-ana log converter (DAC) for transmitters. Performance and economic forces demand that the interface be tween the analog and di gital signal processing domains be relentlessly moved toward the antenn a (i.e., increased digital content). A crucial element in the “digitization” of modern wire less systems is called a channelizer, or digital up/down converter (DUC/DDC). Our study exam ined in new and novel DUC/DDC technology.

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12 CHAPTER 1 INTRODUCTION 1.1 Background Over the last several decade s, digital signal processing (DSP) has emerged as a key enabling technology in the fields as wireless communications, multi media, controls, and speech and image processing to name a few. In wirele ss communications technology, DSP is used at a number of levels, beginning with an analog-to-d igital converter (ADC) fo r receivers and ending with a digital-to-analog converter (DAC) for transmitters. Performance requirements and economic forces are demanding that the digita l content of both receivers and transmitters (transceivers) be increased. The fusion of di gital technology, DSP, and communications theory is the enabling force behind the rise software-def ined radios (SDR) [1], and SDR inspired multichannel wireless systems. A critical element found in a modern wireless system is called a channelizer, or digital up/down converter (DUC/DDC). A channelizer is intrinsically a multi-rate device that resides between the radio’s RF/IF secti on and the back-end base band processor. The function of the receiver’s channelizer is to aff ect a sample rate change, from high front-end sample rate to much lower backend sample rate. In the process the ch annelizer is to isolate a particular subband of frequencies found within the input RF/IF signal. The transmitter’s channelizer reverses this process. Digital channelizers have become an essential infrastructure technology in the field wireless communications. Principal commerci al manufactures of this technology are Texas Instruments [1] [2], Analog Devices [3], National [4], Intersil [5] who produce millions of these devices annually. The research conducted in the field of channe lizer theory and design includes a rigorous survey of the current state-of-t he-art, investigation of low-complexity alternates to today’s

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13 baseline channelizers, simulations studies, and a critical analysis of the outcomes. The intellectual foundation for the new channelizers is found in the nu mber theoretic properties of ternary valued polynomials. This theory lead s to a means of implementing DSP algorithms, which historically have a high multiplier demand, as multiplier-free operations. It will be shown that the researched channelizer s possess many of the desirable attributes of the traditional channelizer without the disadvant ages, which include high-power c onsumption and limited speed. 1.2 Research Contributions A conventional channelizer is based on a co re technology called a cascaded integratorcomb (CIC) filter [7], introduced by Hogenauer [6] in 1981. The multi-rate signal processing systems CIC filter, by itself, is insufficient to perform channelization. Additional elements are needed, including digital mixers (modulators), nu merically controlled oscillators (NCO) and signal conditioning filters. The CIC-enabled channelizer accepts da ta at the ADC, which theoretically could be in the 24 GHz range [13]. Performance lim itations of today’s channelizer limit its speed to be hundreds of MHz. The research performe d indicates that much higher speeds and lower power levels are possible and thereby attendant benefit of wireless communications. The first contribution of this dissertation research is the development of multiplier-free channelizer framework that can operate at hi gh sampling rate and isolate desired signal subbands. In some instances the subband signal decomposition results in a signal contiguous spectrum and is called an uni-band process. In other instances the system responds to multiple non-contiguous frequency bands which will be calle d multi-band. The research also investigates the design of channelizers with a nd without the presence of an NCO with the later promising a reduced complexity design.

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14 The second contribution is an inte gration strategy that leads to a complete channelizer that can meet a wide range of design requirements. This activity results in a number of design strategies that are used to real ize channelizer designs that meet or exceed published requirements found in the communications industry. Each de sign strategy is evaluated and compared and found to have its own set of advantage and disadvantages. The third contribution is a theory of design fo r a linear phase multiplier-less notch filter for high speed wireless comm unication applications. 1.3 Dissertation Organization The major objectives of the proposed research is to explore and evalua te alternative means of implementing high-speed and low-complexity channelizers suitable for use in high-speed lowpower, mobile wireless applica tions. The claimed innovation is based on a theory for new ternary valued bandpass filters [8]. These filt ers are shown to achieve or exceed CIC-class performance without inheriting the tr aditional problems with this cl ass of filter. The dissertation study includes developing channelizer filters that have high-speed and low-complexity measures, superior to those of a conventional channeli zer, while meeting industry-standard frequency domain behavioral requirements. Research is also conducted in th e area of digital filter banks and notch filters for use in wireless communication applications . The study is premised on the theory of frequency-masking FIR filters, compliment notch f ilter, and a new method of impl ementing multiplier-free filters. Specific goals include eliminating NCO and/or conventional CIC subsystems, thereby gaining a reduction in design complexity. The dissertation consists of se ven chapters, the first being an introduction to the problem. Chapter 2 provides a general overview of multi-ra te signal processing, digital filter design, and a new low-complexity filter design theory. Chapter 3 develops multiplier-free uni-bandpass filter

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15 and multiplier-less shaping filter, both base d on ternary value filter design methodology introduced in Chapter 2. Chapter 4 presents ei ght recognized wireless communications standards and specification that define de sign targets. Four different methods of designing NCO based channelizers, with respect to published standards, are the focus of Chapter 4. Chapter 5 designs and compares NCO-free channelizer designs with respect to the published standards. The new linear phase type 1 multiplier-less notch filter is designed for periodic and non-periodic noise cases. Chapter 6 presents a preliminary performa nce assessment of the new solutions introduced in Chapters 4 and 5. Chapter 7 presents conclu sions and suggestions for future studies.

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16 CHAPTER 2 OVERVIEW FILTER DESIGN FOR WIRELESS COMMUNICATIONS 2.1 Digital Signal Processing for Wireless Communication The current communication demand on quality of services (QOS), added functionality, higher performance, unification of interfaces, and communication security place additional stringent requirements on the design of the system s. Ideally what is desired is a compact, lowpower, high-speed digital processing subsystem th at can define a digital bridge between the RF/IF section of a radio and the baseband processing units. In addition, the added digital technology should be programmable to the degr ee needed to allow the system to be reconfigurable in order to m eet changing environments and requirements. The object of the dissertation research is to develop such a communication technology and the underlying theory of operation of such a technology. The outco me will incrementally advance the wireless communications industry towards the universal go al of making wirele ss communication more affordable and reliable. In Chapter 2 the foundation for the research is developed. 2.2 Digital Filter Design A crucial element in a modern wireless syst em is the channelizer. A channelizer is intrinsically a multi-rate device that resides between the radio’s RF/IF section and back-end processors. The function of the channelizer is to isolate a pr e-specified subband of frequencies and affect a sample rate change. Th e change in sample rate, denoted D=fin/fout, is called the decimation rate if fin>fout and interpolation rate if fin
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17 Analog Device [3], TI (Gray) [2], Intersil [5], a nd National [4] to name but a few. A channelizer typically accepts data at input sample rates in the 100 Sa/second ra nge. The output sample rate is dictated by the expected bandwidth of the output process (broadba nd vs. narrowband). Modern channelizers normally consist of thr ee major subsystems (Figure 2-1). They are Numerically controlled oscillator (NCO) and mixer. Used to hete rodyne a selected subband of frequencies down to baseband. NCO a nd mixer subsystem’s are clocked at a high sample rate fs normally established by the front-end ADC. Cascade integrator-comb (CIC) or Hogenauer filter [6] which, for a receiver is a lowpass filter operating at a high sample rate fs, exporting lowpass filtered data at reduced sample rate fs=fs/D ( D 10 for broadband, D >>10 for narrowband applications). The magnitude frequency response of a CIC filter section is that of a moving average (MA) filter which has a sin(x)/x shape in the frequency domain (see Figure 2-2). CIC filter are fabricated using only adders and shift-registers and are technically multiplier-free. FIR shaping filters. FIR filters are used to shape the passband and stopband spectrum found at the output of the CIC section. The limitations of this type of channe lizer are also well known and include Large internal dynamic range and data-path requirements (often exceed 60-bits). Requires high-speed NCO and mixer whic h can exact a high complexity penalty. Figure 2-1. Basic CICbased channelizer.

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18 Figure 2-2. Magnitude frequenc y response of CIC filter. 2.2.1. FIR Filters Fixed-coefficient digital filters are normally classified as being of finite impulse response (FIR) or infinite impulse respons e (IIR). For communications app lications FIR are generally the digital filter type of choice. Within the fam ily of FIR filters, fixed sample rate windowed or equiripple designs are predominant. These basic structures are fully supported with software design tools (e.g., MATLAB). The most popular FIR form, namely equiripple, is specified in terms acceptable passband deviation (p), passband frequency (p), acceptable stopband deviation (a), stopband frequency (a), and a sample rate (s). From these parameters an of estimated order can be derived by Equation 2-1. 1 14 15 ) ( log 1010 p a FIRN (2-1)

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19 Where is the normalized transition bandwidth and is given by =(a s)/s. It can therefore be deduced that steep-skit or narrow-band ( ~0.0) equiripple FIR filters are of high order. As a “rule of thumb,” when the normali zed transition band has a value less then 0.04, then an equiripple FIR filter solution size is virtually impossible to build. Since steep skirt filters are needed, in many instances, to meet wireless standa rds, alternative techniques need to be found. 2.2.2 Multi-Rate Signal Processing The design of high-performance, frequency selec tive, fixed sample rate filters can present a design challenge. The alternative is a multi-rate f ilter. Multi-rate digital DSP systems operate at multiple sample rates relaxing the design cons traints in many cases. An example is the frequency masking filter method which can achieve steep skirt st atus with a set of relatively low order FIR filters [7]. The frequency masking filte rs, shown in Figure 2-3, is based on the fusion of Type I linear phase FIRs and their complement filters. Figure 2-3. Steep skirt system architecture In Figure 2-3, the highpass complement filter H2( z ), such that H1( z )+ H2( z )=1.0, is constructed using a subtractor and shift register. The filters H3( z ) and H4( z ) are used to suppress unwanted passbands arising from H1( z ) and H2( z ). The final stage H5( z ) performs output housekeeping duties. ) ( ) ( 1 1Nz H z H ) ( ) ( 3 3Mz H z H ) ( ) ( 4 4Mz H z H 2 / ) 1 ( N L z ) (5z H H 2 ( zN ) -

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20 2.2.3 Polyphase Representation Polyphase signal and system represen tation techniques are defined in the z -domain. They are used to represent an arbitrary time series x [ k ], sampled at a rate of sf samples per second, having a discrete-time signal model is given by Equation 2-2. k kz k x z X ] [ ) ( (2-2) The z-transform of the decomposed time series can be defined in term of polyphase form as Equation 2-3. k k iz i kM x z P ) ( ) ( M =decimation rate, (2-3) The z-domain polyphase signal and sy stem representation of the orig inal time-series is given by Equation 2-4. ) ( ) (1 0 M M i i iz P z z X (2-4) The resulting representation is called an M -component polyphase decomposition of a time series x [ k ] [7]. 2.3. Classic Channelizers The conventional channelizer’s performance advantage is gained from the fact its core technology, the CIC section, is mu ltiplier-free. As a result, such a system can operate at a high real-time data typically in the hundreds of MHz ra nge. A single channel, in its common form, is illustrated in Figure 2-4. 2.3.1. Classic Channelizer Architecture Channelizers are a core communication technology. They perform two roles, one of sample rate conversion and the other be ing frequency (subband) selection. The receive-side channelizer

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21 Figure 2-4. CIC-based channelizer [8]. shown in Figure 2-4, possesses two (quadrature) signal paths, an NCO and mixer to create heterodyned I and Q-ch annel signals, two Nth order decimating CIC filters, two compensation FIRs (CFIR) filters that remove the sin(x)/x roll-off introduced by the CIC filter, and two programmable FIR (PFIR) filters that provide general frequency-domain housekeeping services. A typical NCO architecture is shown in Figure 25. It consists of a phase accumulator and collection of sine and cosine lookup tables (LUT) that synthesize a sinewave and/or cosinewave envelope in real-time. Figure 2-5. NCO Architecture [9]. Additional decimation may occur at the output of the CFIR and PFIR filters [1] [9]. The complex down converter is designed to translate the spectrum of a sampled bandpass signal from an RF or IF range down to baseband usi ng the NCO/mixer (heterodyning).the lowpass I-channel Output NCO In p u t C I C l owpass fil ter C FIR D PFIR E C I C l owp a ss filt er C FIR D PFIR E Q-channel Out p u t f s f s /R f s /RDE f s /RD Phase Register Phase Accumulator + Sine Generator Cosine Generator

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22 channelizer that extracts the low frequency subband using a CIC filter whose output is then processed by the shaping filters. The output sample rate is decimated by N = D E , where f0= fs/ N . 2.3.2. Cascaded Integrator Comb Theory The two basic building blocks of a CIC filter are an integrator and a comb filter. An integrator implements the accumulation operation is given by Equation 2-5. ] [ ] 1 [ ] [ n x n y n y (2-5) And has a transfer function form as Equation 2-3. ) 1 ( 11 z HI (2-6) With magnitudes and phase frequency re sponses are given by Equation 2-7. cos 1 sin tan ) ( arg ) cos 1 ( 2 1 ) (1 2 jw I jw Ie H e H (2-7) The integrator’s magnitude frequency response is that of a lowpass moving average filter having a -20 dB per decade (-6 dB per octave) roll off, and infinite DC gain due to a pole located at z = 1. A comb filter running at a decimated sample rate fs/ R is filter described by Equation 28. RM n x n x n y ] [ ] [ (2-8) Where M is a design parameter and is called the differential delay. The parameter M can be any positive integer, but it is nor mally to 1 or 2. The corresponding transfer function, relative to a sample rate fs, is given by Equation 2-9. ) 1 (RM Iz H (2-9) The frequency response is given by Equation 2-10.

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23 2 ) ( arg )) cos( 1 ( 2 ) (2 RM e H RM e Hjw C jw C (2-10) An N -stage CIC filter, sampled at fs and decimated by R, is shown in Figure 2-6. Figure 2-6. Two-stage CIC filter (down conversi on left panel, up conversions right panel). The transfer function for a CIC filter is therefore given by Equation 2-11. N RM k k N N RM N C N Iz z z z H z H z H 1 0 1) 1 ( ) 1 ( )) ( ( )) ( ( ) ( (2-11) A CIC filter has a linear phase response and therefore having a constant group delay. The magnitude frequency response at the output of the filter can be shown to be in Equation 2-12. NR f Mf f H sin sin ) ( (2-12) The CIC filter, by itself, can not meet typical passband and stopband attenuation requirements. The output of a CIC filter needs to be post-proces sed by additional filters, albeit at a slowed sample rate. One possible improvement is to co nfigure the CIC sections using a sharpened filter methodology [10]. A sharpened CIC filter is given by Equation 2-13. ) ( 2 3 ) ( ) (2z H z H z Hs (2-13) where each H ( z ) is a CIC filter shown in Figure 2-7. The resulting filter has improved transition band and stopband performance with an attendant increase in complexity. I I C C R C C I I R CIC Decimating Stage 2 CIC ing Interpolat Stage 2

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24 Figure 2-7. Sharpened CI C Decimation filters. 2.4. Basic Theory of Multiplier-free Filter 2.4.1. Multiplier-free Bandpass Filter In this section a new linear phase innovation called a multiplier-free bandpass filter is introduced. The filter coefficients are only ternary valued {1 0 -1}, and therefore the filter is devoid of multipliers. In concept, a bandpass fi lter with a CIC-structure could be achieved by replacing the pole-zero cancellation, that normally occurs at DC (i.e., z=1.0), with pole-zero cancellation at another point on the unit circle (z=ej ). Unfortunately, moving the pole-zero cancellation point to another loca tion on the unit circle would require a filter take the form of Equation 2-14. N N RMz z z z H ) 1 /( ) 1 ( ) (2 1 (2-14) This filter model can exact a high multiplier penalty, plus introduce stability questions. If a bandpass filter could be define in the context the multiplier-free solution, as found in CIC filters, then a potentially viable filter technology will result. This w ill require that the masking filter (poles) of the multiplier-free filter (i .e.,{1,0,-1}) be exactly located at a point on the periphery of the unit circle1 , 0 , N n W zn N). To illustrate, consider a 4th order polynomial denoted ) (12Z that produces four of the 12 roots of ) 1 (12 z (see Table 2-1). It ca n be noted that the CIC CIC 3 2 CIC +

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25 multiplier-free band pass filter has a transfer function of H12= (1-z-RD)/) (12Z = (1-z-RD) / (1z2+z4), where R is the interpolation rate and D is the comb delay (in this case RD =12). In general, the pole locations of a polynomial i (z) are given by Equation 2-15. M M iz a z a a z .... ) (1 1 0 (2-15) It will be generated by Equation 2-16. j i z z z D z N zi j j ); ( / ) 1 ( ) ( / ) ( ) ( (2-16) Where i divides j . Note that ) ( zj has poles residing on the peri phery of the unit circle at locations z = ej2k /S, for k an integer. The resulting bandpa ss filter has only ternary valued coefficients. In general, an N -stage filter can be defined by Equation 2-17. N j N S iz z H ) /( ) 1 ( ) ( (2-17) Where S = RD . Since filter coefficients in both the feedforward and feedback paths are ternary valued, exact pole-zero cancellation can be achieved. Referring to Figure 2-8, one notes that the magnitude freq uency response has a sin(x)/x envelop is centered about fs/12, for RD =12, 24 and 48. Notice that RD effectively defines the frequency selectivity (“ Q ”) of the filter. To illustrate, z12-1 admits a factorization z12-1 = 1 2 3 4 6 12, where 1, 2, 3, 4, 6, and 12 generate the 0, 6, 3 and 9, 4 and 8, 2 and 10, and 1, 5, 7 and 11 harmonics respectively of an equivalent 12-point FFT. Like CIC-based lowpass filters, the sensitiv ity and frequency selectivity of the CICenabled multiplier-free bandpass filters are established by S , which defines the number of unit circle zeros of multiplicity N . The depth of the stopband and st eepness of the filter skirt are primarily influenced by the order parameter N .

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26 Table 2-1. Sample multiplier-free transfer functions. i a =[a0, a1, a2, ak] 1 Positive roots 1 [ 1 -1] 0 1 2 [ 1 1 ] 2 /2 1 3 [ 1 1 1 ] 2 /3 1 4 [ 1 0 1] 2 /4 1 5 [ 1 1 1 1 1 ] 2 /5, 4 /5 2 6 [ 1 -1 1 ] 2 /6 1 7 [ 1 1 1 1 1 1 1 ] 2 /7, 4 /7, /7 3 8 [ 1 0 0 0 1 ] 2 /8, 6 /8 2 9 [ 1 0 0 1 0 0 1 ] 2 /9, 4 /9, 8 /9 3 10 [ 1 -1 1 -1 1 ] 2 /10, 6 /10 2 11 [ 1 1 1 1 1 1 1 1 1 1 1] 2 /11,4 /11, 6 /11, 8 /11, 10 /11 5 12 [ 1 0 -1 0 1 ] 2 /12 , 10 /12 2 15 [1 -1 0 1 -1 1 0 -1 1] 2 /15, 4 /15, 8 /15, 14 /15 4 20 [1,0,-1,0,1,0,-1,01 ] 2 /20, 6 /20, 14 /20, 18 /20 4 30 [1 1 0 -1 -1 -1 0 1 1 ] 2 /30, 14 /30, 22 /30, 26 /30 4 60 [1 0 1 0 0 0 -1 0 -1 0 -1 0 0 0 1 0 1 ] 2 /60,14 /60, 22 /60, 26 /30 34 /60, 38 /60, 46 /60, 58 /30 8 Note: 1 = positive frequency, a = coefficients.

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27 Figure 2-8. Frequency magnitude response of multiplier-free filter [8]. 2.4.2. Notch and Integrate Second Order Polynomial Filters Notch or narrowband band rejection filters are use to suppress or incise narrowband noise and interfering signals. To maintain high sust ained real-time signal processing rates, a linear phase jam suppressing notch filter should also be multiplier-free. This essentially eliminates from consideration conventional FIR or IIR filters. One approach to this problem is to design complementary filters which are based on multiplier-free narrow passband filers [11]. There are four basic forms that a complementary filter can assume and they are 1. delay-complementary filter, 2. power-complementary filter, 3. power-symmetric filters, and 4. conjugate quadratic filter. The delay-complementary hold the greatest promise in delivering low-complexity bandstop filter solution. A set of L transfer functions, Hi( z ), 0 i L -1, are defined to said to be delay-complementary versions of each other if the sum of their transfer functions is equal to some integer multiple of unit delays that is given by Equation 2-18. (2-18) 0 , ) (1 0 on L i iz z H

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28 Where n0 is a nonnegative integer, A delay-complementary pair ( H0(z), H1(z)) can be readily designed if one of the pairs is a known to be Type 1 FIR. The delay complement of H0( z ) is given by H1(z) = z-k H0(z). As a result, H1(z) has a complementary magnitude frequency response characteristic to that of H0(z) [7] [33]. Another important digital filter used in classical channelizatio n is the interpolating second order polynomial filter (ISOP) which is used to improve the passband performance of a CIC filter. The system function of the ISOP filter P ( z ) is defined as Equation 2-19. ) 1 ( 2 1 ) (2 1 I Iz cz c z P (2-19) Where I is a positive integer and c is a real number. P ( z ) is an interpolated version of the second order polynomial form as Equation 2-20. ) 1 ( 2 1 ) (2 1 1 z cz c z S (2-20) Property: When “ c ” is real, the magnitude frequency respon se of the polynomial is expressed as form as Equation 2-21. ) cos( 2 2 1 ) (1 c c e Sj (2-21) S ( z ) is monotonically increasing in (0, ] if c < -2. The filter’s scale factor is 1/| c +2|, the dc gain is 1, and the slope of the magnitude response varies depending on the parameter “ c ”. The filter-sharpening characteristic of the ISOP f ilter stems from the filter’s magnitude frequency response which given by Equation 2-22 [27]. ) cos( 2 2 1 ) (1I c c e Pj (2-22)

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29 The magnitude frequency response is monotonically increasing in (0, / I ] and is periodic with periodI / 2 , where I is an interpolation factor. The ISOP filter can compensate for the passband droop of the CIC filter which is monotonically decreasing. To compensate for passband droop, the width of region (0, /I] should coincide with the input bandwidth with 2 fc. This means that I =1/2 fc. In designing an ISOP filter, it is sufficient to consider only those I values satisfying Equation 2-23. cf I 2 1 1 (2-23) Figure 2-9 and 2-10 shows the example of two di fferent ISOP filters. Figure 2-9 has sinewave shape of frequency magnitude response and Fi gure 2-10 has cosinwave shape of frequency magnitude response. The period and magnitude freq uency response of both filters can change by altering “ c1 ” and “ I ”. Multiplier-less bandpass filter, therefore, can enable new and unique channelizers. These opportunities need to be quantified and evaluated.

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30 0.5 1 1.5 2 2.5 3 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Figure 2-9. Frequency magnitude response of ISOP filter. 0 0.5 1 1.5 2 2.5 3 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 Figure 2-10. Frequency magnitude response of ISOP filter.

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31 CHAPTER 3 MULTIPLIER-FREE FILTER 3.1 Multiplier-Free Uni-Mode Bandpass Filters In Chapter 2, a new linear phase innovation, namely a multiplier-free bandpass filter having only ternary valued coefficients {1 0 -1}, was introduced. Th e production rules for the multiplier-free bandpass filter was defined in terms of ternary valued polynomial j(z). The roots of j(z) defines the points of admissible pole -zero cancellation on the periphery of the unit circle in the z-domain. The points of pole-zer o cancellation locate the ce nter frequency of the bandpass filter’s subband or subbands. The densit y of the frequency coverage is controlled by the filter order parameter N. Since the resulting filter is multiplier-free has the potential of operating at high-speeds with low complexity as is the case for a lowpass CIC filter, except the new filter is bandpass. A bandpass filter having a single passband shall be referred as an uni-mode filter. A bandpass filter having a multiple passband s shall be referred as a multi-mode filter. To illustrate, the frequency response of all N=48 ch annels of a multiplier-free filter are shown in Figure 3-1. The highlighted filter response is th at of a multi-mode filter section. For N=60, all N=60 channels of a multiplier-fre e filter are also shown in Figure 3-1. The highlighted filter response is that of a dual passband multi-mode filter section. Uni-mode bandpass filters are highly desirable in general filtering applications. However, there is only a limited number of uni-mode multiplier-free bandpass filters available for a specific choice of N or S ( Table 2-1). A new strategy is presented that is based on a concept called multiplier-free masking filter j( z ). This method can converts a multi -mode multiplier-free bandpass filter Hi( z ) into an unimode filter.

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32 0 0.5 1 1.5 2 2.5 3 -50 -40 -30 -20 -10 0 A 0 0.5 1 1.5 2 2.5 3 -70 -60 -50 -40 -30 -20 -10 0 B Figure 3-1. The frequency response of all N=48 channels of a multiplier-less filter are shown in the top panel. The highlighted filter response is that of an uni-mode filter section. A) 48 channels of multiplierfree bandpass filters. B) 60 ch annels of multiplier-free bandpass filters.

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33 The unwanted passbands are selectively cancell ed by cascading the multi-mode filter with a multiplier-free filter structures j( z ) (Table 2-1) that places additional zeros at or near undesired bandpass center frequency locations. The FIR filter j( z ) shall be referred to as a masking filter . One or more masking filters maybe needed to convert a multi-mode bandpass filter into a unimode bandpass filter. A single stage of a masked filter is given by Equation 3-1 and shown in Figure 3.2. z z z z z z z H Hi N j NM N j i bandpass ) ( ) 1 ( ) ( (3-1) An Rth stage of extension of the uni-mode bandpass found in Equation 3.1 is given by Equation 3-2. R i R N j R NMz z z z H )) ( ( ) 1 ( (3-2) The adjacent stopband attenuation can be estima ted to be R times of first stage of adjacent stopband attenuation. The magnitude frequency response of two uni -mode bandpass filters are shown in Figure 3-2. One is naturally uni-mode and the other be gins with a multi-mode filter with the unwanted passbands masked by a masking filter. The to p figure (Figure 3-2A) has a classic sin(x)/x magnitude dispersion while the bottom response (F igure 3-2B) shows the effect of approximate pole-zero cancellation as typically found in masking operations. The frequency response of all the filter sections of an order 48 and 60 order multiplier-free uni-bandpass filters are shown in Figure 3-3.

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34 0.5 1 1.5 2 2.5 3 -20 -10 0 10 20 30 A 0.5 1 1.5 2 2.5 3 -50 -40 -30 -20 -10 0 10 20 30 40 50 B Figure3-2. Two uni-bandpass filters obtained from an N=48 filter. A) An uni-mode filter. B) An uni-mode filter obtained by masking filter.

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35 0 0.5 1 1.5 2 2.5 3 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 A 0 0.5 1 1.5 2 2.5 3 -120 -100 -80 -60 -40 -20 0 B Figure 3-3. The frequency response of all channels of a multiplier-free unibandpass filter. A) 48 channels of multiplier-free uni-bandpass filters. B) 60 channels of multiplier-free unibandpass filters.

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36 3.2 Multiplier-Free Lowpass Filter The required performance level of a communica tions system is often defined in terms of the system’s required filter frequency response. Figure 3-4 shows the to lerance specifications of the ideal lowpass filter, where passD and stopD which refer to the allo wable passband ripple and stopband ripple respectively. passW and stopW are normalized passband and stopband frequencies respectively. Figure 3-4. Typical lowpa ss filter specification. Consider a special case form as Equation 3-3. stop passD D (3-3) stop passW W . This condition defines a half-band filter, a filter class that has been intensively studied in the literature. The magnitude frequency response of a half-band filter is symmetrically distributed about the normalized passband frequency /2 (1/2 the Nyquist frequency). An Nth order halfband filter has essentially N/2 filter coefficients. In other wo rds, half-band filter requires about half multiplications per filter cycle when compared to a common Nth order FIR filter. Since the cutoff frequency of the ha lf-band filter is around /2, the filter’s output is often decimated by a

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37 factor of 2. Reducing the system’s sample ra te relaxes the design requirements of system. However, in addition to halfband filtering, mo re general filtering capabilities will be required to meet modern communication system requirements. The concept of multiplier-free lowpass and ba ndpass were introduced in Chapter 2. To illustrate, consider the filter shown in Figure 3-5A whose magnitude frequency magnitude response is equivalent to a form of FFT. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -50 -40 -30 -20 -10 0 A B Figure 3-5. Architecture and the attendant magnitude frequency re sponse of lowpass filters. A) Multiplier-free CIC based 4 channel filter banks and its magnitude response. B) Architecture of multiplier-free lowpass filter with sharp transaction. ) 1 ( 16 z1 632 ) 1 ( 112 z1 64

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38 A 0 0.5 1 1.5 2 2.5 3 3.5 -30 -25 -20 -15 -10 -5 0 5 10 15 B 0 0.5 1 1.5 2 2.5 3 3.5 -40 -30 -20 -10 0 10 20 C 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -15 -10 -5 0 5 10 15 20 25 D 0 0.5 1 1.5 2 2.5 3 -20 -10 0 10 20 30 E 0.5 1 1.5 2 2.5 3 -10 0 10 20 30 40 50 Figure3-6. Example of Multiplier-free CIC-based lowpass filter. A) Dpass=10.89dB, Dstop=-25Db, Wpass=2.7, Wstop=3.12. B) Dpass =15.29dB, Dstop =1.86Db, Wpass =1.49, Wstop =1.85. C) Dpass =26.73dB, Dstop =15.12Db, Wpass =1.18, Wstop =1.4. D) Dpass =26.97dB, Dstop =16.35Db, Wpass =0.08, Wstop =0.95. E) Dpass =44.45dB, Dstop =29.95, Wpass =0.319, Wstop =0.38.

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39 Figure 3-6 illustrates example of the magn itude frequency response of lowpass filters derived from a multiplier-less architecture. Each filter section has a different stopband and passband frequency. The large passband ripple and transaction bandwidth can be mitigated with a shaping filter which was introduced in Chapte r 2 and multiplier-free lowpass filter with sharp transition band as shown in Figure 3-5B. 3.3 Multiplier-Less Lowpass Filter and Shaping Filters The advantages of multiplier-less lowpass filter are its low complexity and high speed. The disadvantage of multiplier-less lowpass filte r is its high passband ripple. The problems can be mitigated with a shaping (multi-order polyno mial) filter which requires only two non-zero coefficients. A shaping filter when used with CIC decimation filter can improve the passband ripple. A shaping (multi-order polyno mial) filter is given by Equation 3-6. ) 1 ( 1 1 ) (K J Iz cz cz c z P (3-6) Where I, J, and K are positive integers and c is a real number. P (z) is a multi-order polynomial. When “c” is real, the magnitude re sponse of the polynomial is monotonically increasing in , 0 if c1 < -2. The scale factor is 1/|c1|, the dc gain is 1, and the slope of the magnitude response varies depending on the parameter “c1”. The shaping filter can compensate for the passband ripple droop such as that found in multiplier-less lowpass filters. To compensate for passband ripple droop, the width of the monotonically increasing regionI / , 0 should coincide with the input bandwidth withcf 2. In designing shaping filter, it would be sufficient to consider only those I values satisfying Equation 3-7. cf I 2 1 1 (3-7)

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40 Examples of frequency and impulse response of shaping filters are pr esented in Figure 3-7. The combination of multiplier-less lowpass filter and shaping filter can generate desired filter responses shown in Figures 3-8 and 3-9. It can be seen that the filters have a small passband ripple and sharp transition band.

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41 A 0.5 1 1.5 2 2.5 3 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 B 0 0.5 1 1.5 2 2.5 3 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C 0 0.5 1 1.5 2 2.5 3 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 35 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Figure3-7. Examples of shaping filter’s magn itude frequency response (left) and impulse response (right) with two non-zero coeffici ents A) Sine-shape shaping filter. B) Cosine-shape shaping filter. C) Decreasing sine-shape shaping filter. D) Decreasing sine-shape shaping filter. E) Frequency reject shaping filter. F) Frequency reject shaping filter.

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42 D 0 0.5 1 1.5 2 2.5 3 -35 -30 -25 -20 -15 -10 -5 0 5 0 2 4 6 8 10 12 14 16 18 20 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 E 0.5 1 1.5 2 2.5 3 -25 -20 -15 -10 -5 0 5 0 2 4 6 8 10 12 14 16 18 20 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 F 0.5 1 1.5 2 2.5 3 -0.5 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 35 40 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Figure3-7. Continued

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43 A 0.5 1 1.5 2 2.5 3 4 6 8 10 12 14 16 18 X: 0.9633 Y: 15.22 X: 2.577 Y: 7.117 B 0 0.5 1 1.5 2 2.5 3 -30 -25 -20 -15 -10 -5 0 5 10 15 X: 1.068 Y: 15.72 X: 2.602 Y: 7.18 C Figure3-8. Multiplier-less lowp ass filter having a passband ripple=0.05dB, passband =15.75dB, and stopband 7.18dB. A) Architecture of mu ltiplier-less lowpass filter. B) Magnitude frequency response of multiplierless lowpass filter and shaping filter. C) Magnitude frequency response of the combination of multiplier-less lowpass and shaping filter ) 1 ( 11 z1 6 ISOP

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44 0 0.5 1 1.5 2 2.5 3 3.5 -40 -30 -20 -10 0 10 20 30 40 A 0 0.5 1 1.5 2 -40 -30 -20 -10 0 10 20 30 X: 1.006 Y: 27.81 X: 1.829 Y: 9.421 B Figure3-9. Multiplier-less lowp ass filter: passband ripple=0.06dB, passband =27.51dB, and stopband 9.12dB. A) Magnitude response of multiplier-less lowpass filter and shaping filter. B) Magnitude response of the combination of multiplier-less lowpass and shaping filter.

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45 CHAPTER 4 NUMERICALLY CONTROL OSCILLATOR-BASED CHANNELIZER A new technique is presented for reducing power consumption and complexity of a digital channelizer. In this Chapter, new and novel NC O based channelizer architectures are compared to conventional designs based on cascaded integrator-comb (CIC) filters. 4.1 Numerically Control Oscillator-Based Channelizers System Specifications The performance of a receiver is measured by its ability to select a desired channel or subband in the presence of strong adjacent channels activity and noise. These parameters affect the receiver’s selectivity, detectable signal, and sensitivity. Wireless communication systems are designed with respect to published standards. Each standard defines the sensitivity and selectivity requirements that a receiver must meet in order to maintain a certain bit error rate (BER). This section reviews many of these st andards. In particular IS-95, IS-136 DAMPS, GSM, WCDMA, 802.11a, 802.11b, 802.11g an d WiMAX wireless standards are studies along with their implementation by Texas Instruments [1] and NOVA Engineering [9]. The IS-95 is the first CDMA-based digital cellula r standard pioneered by Qualcomm. IS-95 is also known as TIA-EIA-95. D-AMPS (Digital-Advan ced Mobile Phone Service) is a digital version of AMPS (Advanced Mobile Phone Service), the original analog standard for cellular telephone phone service. These standards provide a framework in which channelization can be researched in the context of system performance and complexity. Currently channelizer architectures contain an NCO, digital mixer, CIC filter, and spectral shaping filters. The signal sample rates vary depe nding of the channelizer subsystem, application, and whether the device is an up or down converter. The target standards are described as Table 41 [2]-[5], which vary in terms of channel bandwidths, number of channels, and so forth.

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46 Table 4-1. Wireless Standards. Standards Frequency Range (GHz) Channel spacing [MHz] Sub carriers Symbol rate /chip rate Modulation GSM D L 0.935-0.96 U L 0.89-0.915 0.2 1 270.833 Ksymbol/s 0.3 GMSK WCDMA D L 2.11-2.17 U L 1.92-1.98 5 1 3.84 Mchip/s QPSK, 16QAM WLANa 5.15-5.35 20 52 12 Msymbol/s BPSK, 16QAM QPSK, 6 4QAM WLANb 2.4-2.4835 25 1 11 Mchip/s DBPSK, DQPSK CCK WLANg 2.4-2.4835 25 52 12 Msymbol/s BPSK, 16QAM QPSK,64QAM CCK WiMAX 10-66 20 256 16.704 Msymbol/s BPSK, 16QAM QPSK, 64QAM, 256QAM IS-95 D L 0.869~0.894 U L 0.824~0.849 1.250 20 1.22 Msymbol/s OQPSK QPSK IS-136 D L 0.869~0.894 U L 0.824~0.849 0.048 3 48.6 Ksymbol/s DQPSK Note: DL= Down Link, UL=Up Link. The dynamic range (DR) requirements of a dig ital processing system can be specified in absolute or dB units. The DR requirements of an ADC, for example, are defined by the linear range of the physical conversion device. These fact ors play a very important role in the study of communication systems where signal levels can vary widely. If the signal is too large, it will overflow the system’s DR range introducing large and aggressive run-time overflow errors.

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47 These concerns apply to channelizer as well, requ iring that the systems be developed to operate without introducing run-time DR overflow. Filter tolerable passband and passband ripple are two more elements in the design equation. For the reported study, 80% of the baseband is defined to be the passband. The passband ripple deviations per published standard are reported in Table 4-2. Table 4-2. Passband and passband ripple of wireless standard. Standards IS-95 IS-136 GSM WCDMA WLANa WLANb WLANg WiMAX Passband [MHz] 0.63 0.012 0.08 2 8 10 10 8 Passband Ripple [dB] 0.7 0.5 0.1 0.5 0.5 0.5 0.5 0.5 Note: Rate of passband and transaction-band is 4:1. The magnitude frequency responses of a colle ction of wireless sta ndards are shown in Figure 4-1. The channelizer must meet the stan dards passband requirements as well as serve as an anti-aliasing filter, removing and suppressing out-of-band signals and noise. It can be seen that the largest stopband signa l level leaving the channelizer is attenuated by 65dB, 55dB, 42dB, 44dB, 44dB, 50dB, 90dB, and 39dB for GSM, WCDMA, WLANa, WLANb, WLANg, IS-95, IS-136 and WiMAX respectively. Adjacent interference and the neighboring signal have more relation with filter design then coherence interference, since it can be minimized through careful filtering and channel assignments. In sum, each standard has its ow n requirement, the communication only occurs properly when the interference limited in a certain range. 4.2Multiplierless Lowpass Channelizers In this chapter, multiplier-less, linear-phase, lowpass filters are introduced. These filters can replace existing and more complex GSM, WCDM A, IS-95, and IS-136 compensation filters.

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48 A B C D Figure 4-1. Wireless filter mask requirements. A) GSM(left) and WCDMA(right). B) IS-95(left) and IS-136(right). C) WLANa(left) a nd WLANb(right). D) WLANg(left) and WiMAX(right).

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49 The reported multiplier-less linear-phase lowpas s filter will be shown to share some of the architectural details found in a conventional CIC filter. Table 4-3. Wireless standards which need PFIR and CFIR. Non-ternary value coefficient (Total number of coefficients) Standards Modulator wordwidth OSR Filter Structure Decimation rate Present practices New method CIC 64 0(4) 0(4) PFIR 2 21(21) 2(10) GSM 1 bit 128 CFIR 1 63(63) 63(63) CIC 5 0(5) 0(5) PFIR 2 11 0 PFIR 2 15 2(10) WCDMA 1bit 20 CFIR 1 101 101(101) CIC 24 0(4) 0(4) PFIR 2 21 2(10) IS-95 1bit 48 CFIR 1 63 63(63) CIC 320 0(4) 0(4) PFIR 2 21 2(10)_ IS-136 1bit 640 CFIR 1 63 63(63) Note: OSR = Over Sample Rate. The four multiplier-less CIC-base d lowpass filters, found in Table 4-3, meet or exceed the appropriate published standards. Figure 4-2 through 4-5, Frequency magnitude response of GSM, WCDMA, IS-95, and IS136 decimation filter. A (Frequency magnitude response of CIC and lowpass filter), B (Frequency magnitude response of Decimation filter), and C (Frequency magnitude response of passband ripple) are from a conventional design and D (Frequency magnitude response of CIC and lowpass filter), E (Frequency magnitude response of Decimation filter), and F (Frequency magnitude response of passband ripp le) are from the proposed method.

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50 A 0 0.5 1 1.5 2 2.5 x 106 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 0 0.5 1 1.5 2 2.5 x 106 -300 -250 -200 -150 -100 -50 0 D B 0 1 2 3 4 5 6 7 8 9 x 105 -150 -100 -50 0 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 9 x 105 -100 -80 -60 -40 -20 0 FrequencydBIF receiverE C 1 2 3 4 5 6 7 8 x 104 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 X: 6.348e+004 Y: 0 X: 3.809e+004 Y: -0.1065 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 9 10 x 104 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 X: 1.27e+004 Y: -0.001799 FrequencydBIF receiver X: 7.194e+004 Y: -0.1091F Figure 4-2. Magnitude frequency response of conventional (A,B,C) and proposed (D,E,F) of GSM decimation filter. A) CI C and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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51 A 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 107 -150 -100 -50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 x 107 -200 -150 -100 -50 0 D B 1 2 3 4 5 6 7 8 9 10 x 106 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 2 4 6 8 10 x 106 -150 -100 -50 0 FrequencydBIF receiverE C 0 0.5 1 1.5 2 x 106 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 FrequencydBIF receiver 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 106 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 FrequencydBIF receiverF Figure 4-3. Magnitude frequency response of conventional (A,B,C) and proposed (D,E,F) of WCDMA decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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52 A 1 2 3 4 5 6 7 x 106 -140 -120 -100 -80 -60 -40 -20 0 1 2 3 4 5 6 7 x 106 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 D B 0 0.5 1 1.5 2 2.5 x 106 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 x 106 -150 -100 -50 0 FrequencydBIF receiverE C 0 1 2 3 4 5 6 x 105 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 FrequencydBIF receiver 0 1 2 3 4 5 6 7 x 105 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 FrequencydBIF receiverF Figure 4-4. Magnitude frequency response of co nventional (A,B,C) and pr oposed (D,E,F) of IS95 decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation fi lter. F) Passband ripples.

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53 A 0 0.5 1 1.5 2 2.5 3 3.5 x 105 -140 -120 -100 -80 -60 -40 -20 0 0 0.5 1 1.5 2 2.5 x 105 -100 -80 -60 -40 -20 0 D B 0 1 2 3 4 5 6 x 104 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 1 2 3 4 5 6 x 104 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 FrequencydBIF receiverE C 0 2000 4000 6000 8000 10000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 FrequencydBIF receiver 0 2000 4000 6000 8000 10000 12000 -4 -3 -2 -1 0 1 FrequencydBIF receiverF Figure 4-5. Magnitude frequency response of co nventional (A,B,C) and pr oposed (D,E,F) of IS136 decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation fi lter. F) Passband ripples.

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54 4.3 Multiplier-less Cascaded Integrator Comb and Shaping Filter Based Multi-rate Channelizer In this section, multiplier-less CIC and shaping filter based multi-rate channelizers are introduced and applied to the design the ch annelizer meeting the WLANa, WLANb, WLANg, WiMAX, IS-136 and 1S-95 standards. This met hod uses a low complexity shaping filter to correct for envelop distortion introduced by a CIC lowpass filter. The advantage of multiplierless CIC and ISOP based channelizer is its overall low complexity. Table 4-4. Wireless standards which need less then two FIR. Non-ternary value coefficients (total number of coefficients) Standards Modulator wordwidth in bits OSR Filter Structure Decimation rate Present practice New method CIC 5 10 N/A WLANa 3 5 FIR 1 51 N/A CIC 4 10 N/A WLANb 4 4 FIR 1 51 N/A CIC 4 10 N/A WLANg 4 4 FIR 1 51 N/A CIC 5 10 0(5) WiMAX 4 5 FIR 1 51 5(13) CIC 0(4) 0(4) PFIR 21(21) 0(0) IS-95 1 48 CFIR 63(63) 5(13) CIC 0(4) 0(4) PFIR 21 0(0) IS-136 1 320 CFIR 63 5(13) Note: OSR = Over Sample Rate, PFIR = Pr ogrammable FIR, CFIR = Compensation FIR Existing WiMAX, IS-95 and IS-136 designs can operate with up to 0.5 dB passband ripple deviation. Table 4-4 reports the minimum total nu mber of non-ternary value coefficients for the proposed method and conventional method per specification. The proposed methods decimation filter provides greater flexibility, cost effectiven ess, as well as providing a means for system upgrades and multi-leveled software.

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55 4.3.1 Multiplier-less Cascaded Integrator Co mb and Shaping Filter Based Multi-rate Channelizer for IS-95 The target sample rate for an IS-95 filter is 49.152Msps, is 40 times the chip rate of a signal rated at 1.2288 Mchips/s. The passband and stop band specifications of the decimation filter are determined based on those of a commercially available analog intermediate frequency filter used for IS-95 system applications as summarized in Table 4.1 [8]. A= 4 1) 1 ( 1 z B=4 1) 1 ( z, M=60; N=1; J=6, I=3 D= ) 1 1 ( 2 1 12 J Jz z c c P= ) 2 1 ( 2 2 12 I Iz z c c B1=4 2 1 4) 1 ( * z z z , Lists the transfer functions and the downsampling rate Figure 4-6. The architecture of multiplier-le ss CIC and ISOP based multi-rate channelizer. A CIC filter, multiplier-free bandpass filter, a nd shaping filter architectures are shown in Figure 4-6. Existing implementation methods have filters following the ISOP stages that include a multistage halfband decimation filter, programmable FIR filter, and an interpolation filter [10]. Traditional architecture has a high complexity penalty due to a high coefficient count. The proposed alternative method has a much lower complexity as shown in Table 4-4. Figure 4-7 exhibits the magnitude frequency respons es of three classes of filters. They are a CIC filter, multiplier-fr ee bandpass filter, CIC, and decimating lowpass filter . The IS-95 spectral mask requirements are easily met as clea rly demonstrated the Table 4-5. The passband P A A B M B B1 D NN 1234 2

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56 and stopband details are shown in Figure 4-8. The peak to peak ri pple requirement of being less than 0.7 dB is also easily met. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -60 -50 -40 -30 -20 -10 0 10 20 30 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -200 -150 -100 -50 0 50 100 A B 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -300 -250 -200 -150 -100 -50 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -150 -100 -50 0 50 100 150 200 250 C D Figure 4-7. Magnitude frequency response of thr ee classed of filters, namely a CIC, multiplierfree lowpass filter, ISOP based multiplier-freefilter. A) CIC filter. B) Multiplier-free lowpass filter. C) CIC and decimating lowp ass filter. D) Convolution of CIC and decimating lowpass filter.

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57 0 1 2 3 4 5 6 7 8 9 10 x 107 -150 -100 -50 0 50 100 150 200 250 A 0 1 2 3 4 5 6 7 8 9 x 104 160 165 170 175 180 185 190 195 200 205 X: 6.27e+004 Y: 204 X: 9.12e+004 Y: 157.5 0 1 2 3 4 5 6 7 x 104 204 204.2 204.4 204.6 204.8 205 205.2 X: 1.045e+004 Y: 204.3 X: 4.085e+004 Y: 204.7 B C Figure 4-8. Magnitude frequency response of multiplierless CIC and ISOP based Multirate Channelizer. A) Magnitude frequency res ponse of decimating lowpass filter. B) Passband and stopband. C) Passband ripple. The design could be further refine d to provide a smaller transition width at the expense of larger peak to peak passband ripple and/or lesse r adjacent band rejection depends on other specifications.

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58 Table 4-5. Output data of multiplier-less CIC an d shaping filter based multi-rate channelizer. Simulation performance based on MATLAB simulation of IS-95 Sampling frequency 49.125Msps Passband edge 633 kHz from the carrier Passband ripple 0.35dB 35 dB attenuation at 750 kHz from the carrier Stopband 50 dB attenuation at 900 kHz from the carrier 4.3.2 Multiplier-Less Cascaded Integrator Co mb and Shaping Filter Based Multi-rate Channelizer for WiMAX The target sample rate for WiMAX filter is 167. 04Msps, which is 10 times the chip rate of 16.704 Mchips/s. The passband and stopband specif ications of the decimation filter are determined based on those found in commercially available analog IF filters used for WiMAX system design and summarized in Table 4-1 [8]. A CIC, 1st shaping filter, lowpass filter a nd 2nd shaping filter architecture is shown in Figure 4-9. The optimal non-zero coe fficients of the first shaping filter and second shaping filter are determined by minimizing the passband ri pple value as shown in Figure 4-10. Figure 4-9. Architecture of propos ed WiMAX multirate channelizer. CIC 1st shapping lowpass 2nd shapping

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59 0 5 10 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Min error:0.1275dB Figure 4-10. Passband ripple with two shaping filter. 0 0.5 1 1.5 2 2.5 3 3.5 -40 -30 -20 -10 0 10 20 A 0 0.5 1 1.5 2 2.5 3 x 107 40 45 50 55 60 65 70 75 80 B Figure 4-11. Continued.

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60 1 2 3 4 5 6 7 8 x 107 -60 -40 -20 0 20 40 60 80 X: 8.185e+006 Y: 77.63 X: 1.002e+007 Y: 64.13 C 0 2 4 6 8 10 12 14 16 18 20 x 106 62 64 66 68 70 72 74 76 78 80 X: 8.185e+006 Y: 77.63 X: 2.339e+006 Y: 77.85 D Figure 4-11. WiMAX decimation filt er with first stage. A) Magn itude response of lowpass and 1st shaping filter. B) Magnitude response of lowpass and 2nd shaping filter. C) Magnitude response of decimation filter. D) Magnitude response of decimation filter on passband range. Table 4-6. Output data of Multiplierless CI C and shaping filter based Multirate WiMAX Channelizer. Simulation performance based on Matlab si mulation of WiMAX with three stage Used sampling frequency Input:167.04Msps, output: 16.704Msps Passband edge 8 MHz from the carrier Passband ripple 0.3825dB 46.44 dB attenuation at 10 MHz from the carrier Stopband 88.68 dB attenuation at 25 MHz from the carrier Figure 4-11A and B display the magnitude frequency responses of multiplier-less lowpass filter and two shaping filter. The pa ssband and stopband details are shown in Figure 4-11C and D. The peak to peak ripple requirement being less than 0.5 dB is easily met (see in Table 4-6).

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61 The other three channelizers, namely WLAN a, WLANb and WLANg, can be designed with multiplier-less CIC and shaping filter based on a multi-rate method, but they have problem with meeting passband and stopband specifications. 4.4. Hybrid less Cascaded Integrator Comb -Based Multirate Channelizer CIC decimation filter performance can be compromised when aggressive decimation creates a potential aliasing problem. It should be noted that a CIC f ilter has an adjacent band stopband attenuation of only 13dB. In this section, a new CIC-based decimation filter is proposed as a useful altern ative to the CIC filter. 0 0.5 1 1.5 2 2.5 3 -200 -150 -100 -50 0 Figure 4-12. The Architecture (left) and magnitude response (right) of CIC decimation filter with M = 10, K = 1, 2, 3, and 4. Table 4-7. Output data of NCO based channelizer. Stopband attenuation 3dB bandwidth Number of comb filter Number of integrator First stage conventional CIC filter -13.24dB 0.083 1 1 First stage High performance CIC based filter -27.11dB 0.080 2 1 Second stage conventional CIC filter -26.48dB 0.071 2 2 Second stage High performance CIC based filter -54.22dB 0.078 4 2 Note: CIC is cascade integrator and comb filter M kz ) 1 ( 11 kz ) 1 (1

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62 A B C Figure4-13. The Architecture and magnitude response of Hy brid CIC based Multirate Channelizer. A) The Architect ure of Hybrid Channelizer . B) Second stage of CIC filter vs. first stage of Hybrid CIC filter. C) Fifth stage of CIC filter Vs fifth stage of Hybrid CIC filter. Figure 4-12 shows the architect ure and magnitude frequency response of a conventional CIC decimation filter with fixed decimation rate M and order parameter k . The adjacent stopband attenuation can be estimated to be k13.3 dB. An effect of increasing the CIC order is M N ) 1 ( 11 z ) 1 (1 zj

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63 a reduction of the 3dB bandwidth. It is proposed to exploit this arch itecture in the form of a new hybrid design that includes the use of mu lti-rate, multiplier-le ss bandpass filters. Figure 4-13 and Table 4-7 s how the hybrid architecture’s magnitude frequency response and performance data. It is easy to verify that the hybrid desi gn has superior performance and requires fewer number of integrator. 4.5. Multiplier-Free Efficient FIR Downconverter for Channelizer 4.5.1 Multiplier-Free FIR-based Downconverter In previous the section, a hybrid CIC filter was introduced. An Nth-order CIC filter is equivalent to a moving-average FIR of length RM and has a transfer fu nction given by Equation 4-1. N M R k k N M R Nz z z z H 1 . 0 . 1) 1 .( 1 1 ) ( (4-1) The length of the CIC’s impulse response increases linearly on N . 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -60 -50 -40 -30 -20 -10 0 X: 0.405 Y: -13.2 13.2dB 0 0.5 1 1.5 2 2.5 3 -200 -150 -100 -50 0 A B Figure 4-14. Magnitude frequenc y response of CIC filters. A) R =1, M =1,2,3,4,5,6 . B) N =1,2,3, 4.

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64 A 0 0.5 1 1.5 2 2.5 3 -40 -35 -30 -25 -20 -15 -10 -5 0 B 0 0.5 1 1.5 2 2.5 3 -30 -25 -20 -15 -10 -5 0 C 0 0.5 1 1.5 2 2.5 3 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 D 0 0.5 1 1.5 2 2.5 3 -50 -40 -30 -20 -10 0 CIC LOWPASS PARALEL FIR E Figure 4-15. Architecture and magnitude response of the Multiplier-Free FIR down converter with 1, 2, 3=[1 1 1 1] . A) The Architecture of Multiplier-Free FIR downconverter. B) Frequency magnitude response of 1. C) Frequency magnitude response of decimating 1 by NM. D) Frequency magnit ude response of all three filters. E) Overall frequency magn itude response of CIC and proposed. M N 12 3

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65 Figure 4-14A displays the magnitude frequenc y response of CIC filters with decimation factors of M =1, 2, 3, 4, 5, 6. In Figure 4-14B th e magnitude frequency response of CIC filters with the number of stages being N =1, 2, 3, 4. It can be seen the nulls of the CIC filter are set by the zero locations whose density is determined by M . It is also evident that the dept h of the stopbands is determined by N . Shaping the response of a CIC section with FIR filter will increase th e complexity of the system. The frequency masking technique can be applying to reduce the complexity of the FIR filter as mentioned in chapter 2. Figure 4-15 displays the magnitude frequency response of multiplier-free efficient FIR using a frequency masking technique. 4.5.2 Shaped Multiplier-Free FIR Downconverter The performance of the sharped multiplier-free FIR filter is shown in Figure 4-16. In this instantiation, the decimated filter has two main advantages which are better passband control and stopband attenuation when compared to a conventional CIC decimation filter.

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66 A B 0 0.5 1 1.5 2 2.5 3 -50 -40 -30 -20 -10 0 C 0 0.5 1 1.5 2 2.5 3 -100 -80 -60 -40 -20 0 D Figure 4-16. Architecture and magnitude fr equency response of a multiplier-free FIR downconverter with multiplier-free bandpass fi lter. A) The Architecture of shaped multiplier-free FIR downconverter. B) Magn itude frequency response of all three filters. C) Overall magnitude frequenc y response of shaped multiplier-free FIR downconverter. D) First stage and second stag e CIC filter Vs first stage of Shaped Multiplier-Free FIR. M N 4 3* 5 2* 6 1*

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67 CHAPTER 5 APPLICATION OF MULTIPLIERFREE FILTER TECHNIQUES The conventional channelizer, or digital down co nverter (DDC), is intrinsically a multi-rate lowpass filter. DDC’s require the presence of a pre-processing digital mixer, direct digital synthesizer (DDS) or numerically controlled oscillator or NCO to heterodyne a selected subband down to DC. The need for a complex NCO and mixer can be mitigated if the lowpass filters, found in conventional channelizer, ar e replaced by a bandpass filter. In this chapter, multiplier-free bandpass filter are applied to the problem of channelizing without the need of an NCO and mixer. In addi tion, two important classes of filters, called notch filter and filterbank, are also studied. 5.1 Numerically Controlled Oscillator-free Channelizer High-end digital filtering algorithms are notor iously multiply-accumulate (MAC) intensive and therefore present a number of implem entation challenges. Currently commercial channelizers from Intel, National, Texas Instrume nts, Intersil, and others, require the presence complicated NCO/mixers to perform their frequency selective tasks. Potentially superior channelizers can be implemented if the NCO/mixe r requirement can be relaxed or removed. This motivates the study of an alte rnative channelizer design strategy. In Chapter 2 a multiplier-free band-selectable filter generator was argued to have the form as Equation 5-1. j i z z z D z N zi j j ); ( / ) 1 ( ) ( / ) ( ) ( (5-1) Whose roots on the unit circle in the z-plane. The result is multiplier-free bandpass filter has a transfer function as Equation 5-2. N j N s iz z H ) ( ) 1 ( ) ( (5-2)

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68 With these simple multiplier-free filters, freque ncy selective filtering can be performed that can isolate a particular subband, or collection of subbands, and translate the selected subbands down to baseband for continued back-end proce ssing and information extraction. There are several design control parameters that can be used to adjust the sensitivity and frequency selectivity of the multiplier-free bandpass filter s. The foundational number theoretic concept is illustrated in the following Table 5-1. The filter coefficients are found to be ternary valued and the filter’s center frequencies on fi = fs/48 centers defining 24 positive and 24 negative subbands. The 48 subbands are spread acr oss ten distinct filters. Table 5-1. Multiplier-free filter transfer function for N =48. No i(z) H(z) H Freq. ( fs=48) G 1 1-z-1 1-z-48/1-z-1 1 0 1 2 1+z-1 1-z-48/1+z-1 1 -24 1 3 1+z-2 1-z-48/1+z-2 2 +/-12 2 4 1-z-1+z-2 1-z-48/1-z-1+z-2 2 +/-8 3 5 1+z-1+z-2 1-z-48/1+z-1+z-2 2 +/-16 3 6 1+z-4 1-z-48/1+z-4 4 +/-6, +/-18 4 7 1-z-2+z-4 1-z-48/1-z-2+z-4 4 +/-4, +/-20 3 2 8 1+z-8 1-z-48/1+z-8 8 +/-3, +/-9, +/-15, +/-21 8 9 1-z-4+z-8 1-z-48/1-z-4+z-8 8 +/-2, +/-10, +/-14, +/-22 3 2 10 1-z-8+z-16 1-z-48/1-z-8+z-16 16 +/-1, +/-5, +/-7, +/-11, +/-13, +/-17, +/-19, +/-23 3 8 Note: H =number of harmonics (Eul er’s Totient function); G =maximum gain The filter architecture showed in Figure 5-1A consists of multiplier-free number theoretic filter sections from Chapter 3, along with decimators and post-pr ocessing filters. The frequency response of the filters are shown in Table 5-1 are displayed in Figure 5-1B for 24 channels, Figure 5-1C with 48 channels and Figure 5-1D with 60 channels. The first filter in Figure 5-1 A performs frequency selective ba ndpass filtering, the second suppre sses possible aliasing signal sources, and the third (a comb filter) defines the overall filter’s stopband performance. Because the low-complexity filter elements are multiplier-free.

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69 A B 0 0.5 1 1.5 2 2.5 3 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 C 0 0.5 1 1.5 2 2.5 3 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 D 0 0.5 1 1.5 2 2.5 3 -40 -35 -30 -25 -20 -15 -10 -5 0 Figure5-1. The Architecture a nd magnitude response of multiplie r-free bandpass filters. A) The architecture of multiplier-fr ee bandpass filter based channe lizer. B) The magnitude frequency response of all 24 multiplier-fr ee bandpass filters. C) The magnitude frequency response of all 48 multiplier-fr ee bandpass filters. D) The magnitude frequency response of all 60 mu ltiplier-free bandpass filters. M 1/ i 1-z-1 FIR shaping filter Multiplier-free j N

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70 The filter consisting only of shift-registers and adders, the resulting filter has a high sustained bandwidth potential. Choosing this design strategy is synergistic with ASIC and FPGA implementation requirements [38] [39]. The targeted (eight) standards are described as Ta ble 5-2. The receiver’s profile influences the final receiver architecture defi nition and design. The channel bandwidth and frequency range establish the number of communi cation channels and input sampli ng rate. Figure 5-1B, C, and D display three different multiplier-free bandpass f ilters with 24, 48 and 60 channels for the 8 wireless standards which are mentioned in Chapter 4. In this chapter, two different methods of de signing NCO-free channeli zers are presented. The design strategies establish meaningful comple xity trade-offs. The sampling frequency of the demodulation part must be the multiple of symbol rate of the certain standard. The sampling frequency is software configurable with complexi ty related to the implemented sample rate. If the re-sampling rate is integer valued, the re-sampl er is a simple signal decimator. Otherwise the re-sampler is a generalized sample-rate converter. The first method presented is an NCO-free chan nelizer with fractional re-sampler. The resampler matched the output sampling rate to that specified by the system’s standard. The second method uses an alternating sign (i.e., ) switch channelizer. 5.1.1 Numerically Controlled Oscillator -free Channelizer with Fractional Re-sampler Multi-stage decimated systems generally plac e the subsystem of lowest complexity up front. This is the strategy used in designi ng an NCO-free channelizer with a fractional resampler and the multiplier-free bandpass filter. The architecture and data of NCO-free channelizer with fractional re-sampler is displayed in Figure 5-2 and Table 5-2.

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71 Figure5-2. Architecture of NCO-free ch annelizer with fractional re-sampler. Table 5-2. Data of NCO-free channe lizer with fractional re-sampler. Standards Frequency range (GHz) Channel spacing (MHz) Channel number OSR Input sampling frequency (MHz) Resampling rate Symbol rate(S) (MHz) WLANa 5.15~5.35 20 10 12 240 3/5 12 WLANb 2.4~2.4835 20 4 12 240 11/20 11 WLANg 2.4~2.4835 25 3 6 150 12/25 12 GSM 0.935~0.96 0.2 60 60 120 0.270833/0.2 0.270833 WCDMA 2.11~2.17 5 24 24 120 3.84/5 3.84 WiMAX 10~66 20 12 12 240 16.704/20 16.704 IS-95 0.824~0.849 1.250 20 48 58.982 0.615/1.250 0.615 IS-136 0.824~0.849 0.060 2560 320 62.208 0.0486/0.060 0.0486 Note: OSR = Over Sample Rate. Figure 5-3 through 5-8, Fr equency magnitude response of WLANa,WLANb, WLANg, CDMA, WiMAX, and GSM decima tion filter. A (Frequency magn itude response of CIC and lowpass filter), B (Frequency magnitude res ponse of Decimation filter), and C (Frequency magnitude response of passband ripple) are from a conventional design and D (Frequency magnitude response of CIC and lowpass filter), E (Frequency magnitude response of Decimation filter), and F (Frequency magnitude response of passband ripple) are from the proposed method. The filter structure and length found in Table 5-2, provides evidence of the complexity advantage of the new method. Multiplierfree bandpass filter CFIR and/or PFIR S OSR

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72 A 0 0.5 1 1.5 2 x 108 -300 -250 -200 -150 -100 -50 0 0 0.5 1 1.5 2 2.5 x 108 -250 -200 -150 -100 -50 0 50 100 150 D B 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverE C 0 1 2 3 4 5 6 7 8 9 x 106 -2 -1.5 -1 -0.5 0 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 9 x 106 -2 -1.5 -1 -0.5 0 0.5 1 1.5 FrequencydBIF receiverF Figure 5-3. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of WLANa decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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73 A 0 0.5 1 1.5 2 x 108 -350 -300 -250 -200 -150 -100 -50 0 0 0.5 1 1.5 2 2.5 x 108 -250 -200 -150 -100 -50 0 50 100 150 D B 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -150 -100 -50 0 FrequencydBIF receiver 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverE C 0 2 4 6 8 10 x 106 -2 -1.5 -1 -0.5 0 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 9 10 x 106 -2.5 -2 -1.5 -1 -0.5 FrequencydBIF receiverF Figure 5-4. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of WLANb decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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74 A 0 2 4 6 8 10 12 14 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 0 5 10 15 x 107 -300 -250 -200 -150 -100 -50 0 50 100 B 0 1 2 3 4 5 6 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 1 2 3 4 5 6 x 107 -200 -150 -100 -50 0 FrequencydBIF receiver C 1 2 3 4 5 6 7 8 9 10 11 x 106 -2 -1.5 -1 -0.5 0 0.5 FrequencydBIF receiver 0 2 4 6 8 10 x 106 -2 -1.5 -1 -0.5 0 0.5 FrequencydBIF receiver Figure 5-5. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of WLANg decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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75 A 0 1 2 3 4 5 6 7 x 107 -150 -100 -50 0 2 4 6 8 10 12 14 x 107 -100 -50 0 50 100 D B 2 4 6 8 10 12 14 16 18 x 106 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 0.5 1 1.5 2 x 107 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverE C 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 106 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 FrequencydBIF receiver 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 106 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 FrequencydBIF receiverF Figure 5-6. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of WCDMA decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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76 A 0 2 4 6 8 10 12 14 16 18 x 107 -350 -300 -250 -200 -150 -100 -50 0 0 0.5 1 1.5 2 2.5 x 108 -250 -200 -150 -100 -50 0 50 100 150 D B 0 1 2 3 4 5 6 7 x 107 -150 -100 -50 0 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -140 -120 -100 -80 -60 -40 -20 0 20 FrequencydBIF receiverE C 0 1 2 3 4 5 6 7 8 x 106 -2 -1.5 -1 -0.5 0 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 9 x 106 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 FrequencydBIF receiverF Figure 5-7. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of WiMAX decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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77 A 0 0.5 1 1.5 2 2.5 3 x 106 -160 -140 -120 -100 -80 -60 -40 -20 0 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 x 107 -200 -150 -100 -50 0 D B 1 2 3 4 5 6 7 8 9 10 x 105 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0 1 2 3 4 5 6 7 8 x 105 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverE C 1 2 3 4 5 6 7 8 9 x 104 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 FrequencydBIF receiver 1 2 3 4 5 6 7 8 9 x 104 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 FrequencydBIF receiverF Figure 5-8. Magnitude frequenc y response of conventional (A,B ,C) and proposed (D,E,F) of GSM decimation filter. A) CI C and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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78 5.1.2 Numerically Controlled Oscillator -Free Cha nnelizer with Simple Alternating Sign () Switch. The multiplier-free bandpass filter can opera te at much higher input ADC speed than conventional multiplier-bound bandpass channelizers. In fact, the reported bandpass filter has the complexity of a basic CIC filter. In rem oving the NCO dependence, the resulting NCO-free channelizer requires the use of a fractional re -sampler where the re-samplier’s complexity depends on the standards requirements. This si tuation can be relaxed by mixing the output of a bandpass filter with a sinusoid having a center fre quency located at the center of the subband to be channelized, say 0. This is essentially the center opti on shown in Figure 5-9. Decimating the multiplier-less bandpass filter, as shown on the right panel of Figur e 5-9, is not a viable option since all the active subbands w ill be aliased down of baseband thereby rendering the filter useless. Instead, a low complexity replacement fo r a NCO, or DDS sinusoid generator, and mixer is proposed that defines a solu tion which is center of the pane l in Figure 5-9. In order to eliminate the need for a multiplier-based NCO/mi xer at the output of the bandpass filter shown in the middle panel of Figure 5-9, a Nyquist ra te modulation signal can be used which, for a given sample rate, is defined by Equation 5-3. s[k]={1, -1, 1, -1, } (5-3) Figure 5-9. Bandpass filter based channelizer options. The Fourier transform of s [ k ] is known to have a strong component at the designated frequency0 as well as attendant harmonics located on k0 centers. The binary–valued mixing NCO Bandpass filter fs fs/R R NCO Bandpass filter fs fs/R R Bandpass filter fs fs/R R

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79 signal s [ k ] is trivially generated and used to modula te the bandpass filter’s output at the bandpass filter’s sample rate. It should be appreciated that the mixer multiplier is now, in fact, a simple “”time-series. It can be assumed that the fr equency band distributed about the fundamental frequency is desired, but th e bands about the harmonics (= k0) will produce unwanted out-ofband signals. The removal of these unwanted out-of-band signal components traditionally requires the use of a lowpass filt er to pass the desired heterodyne d subband and block all others subbands. This approach is viable only if the lowp ass excision filter is of low complexity and can operate at the bandpass filter sample rate. Such a f ilter exists and has existed for decades and it is the CIC filter. The result is the solution proposed in Figure 5-10. It is worth noting that the reason that the binary-valued m odulation signal was not directly applied to the ADC output is due to the fact that sidebands of s [ k ] could modulate undesired si gnal components into the passband(s) of the multip lier-free bandpass filter. Figure 5-10. Proposed channelizer. The proposed channelizer was simulated us ing MATLAB. The resu lts are reported in Figure 5-11. The uni-channel multiplier-free bandpass filter was chosen to be a 1st order ( N =1) uni-band filter (Figure 5-1, Table 5-1). The out-ofband attenuation of the system is more than 70dB down from the passband with 5th order ( N =5) uni-band filter. The stopband attenuation can be further improved by increasi ng the order of the bandpass or lowpass multiplier-free filter selectivity. The spectral housekeeping final stage filters, denoted CFIR and PFIR, are added to Multi-free Bandpass Filter Multi-free Lowpass Filter x [ k ] s [ k ] y[ k ] z [ k ] PFIR CFIR

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80 the final design to provide additiona l spectral shaping. It should be appreciated that the spectral shaping filters operates at a de cimated sample rate. The architecture and data of NCO-free channelizer, using a simp le alternating sign “” switch, are reported in Fi gure 5-10 and Table 5-3. Table 5-3. Summary of proposed channelizer. standards Frequency range (GHz) Channel spacing (MHz) Channel number OSR Input sampling frequency (MHz) Resampling rate Symbol rate(S) (MHz) WLANa 5.15~5.35 20 10 12 240 1 12 WLANb 2.4~2.4835 20 4 12 240 1 11 WLANg 2.4~2.4835 25 3 6 150 1 12 GSM 0.935~0.96 0.2 60 60 120 1 0.270833 WCDMA 2.11~2.17 5 24 24 120 1 3.84 WiMAX 10~66 20 12 12 240 1 16.704 IS-95 0.824~0.849 1.25 60 60 73 1 1.22 IS-136 0.824~0.849 0.06 60 60 2.88 1 0.048 Note: OSR = Over Sample Rate. Conventional NCO-based channelizers ar e compared with the proposed NCO-free channelizer using a simp le alternating sign () switch as presented in Table 5-3 in Figures 5-12 through 5-17. Frequency magnitude respons e of WLANa,WLANb, WLANg, CDMA, WiMAX, and GSM decimation filter. A (Frequency magnit ude response of CIC and lowpass filter), B (Frequency magnitude response of Decimation f ilter), and C (Frequency magnitude response of passband ripple) are from a conventional design and D (Frequency magnit ude response of CIC and lowpass filter), E (Frequency magnitude response of Decimation filter), and F (Frequency magnitude response of passband ripple) are from the proposed method. Th e filter structure and length found in Table 5-3, provides evidence of the complexity advantage of the new method.

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81 A 0.5 1 1.5 2 2.5 3 -150 -100 -50 0 50 100 B 0 0.5 1 1.5 2 2.5 3 -150 -100 -50 0 50 100 150 C 0.5 1 1.5 2 2.5 3 -50 0 50 100 150 200 250 Figure 5-11. NCO-free channelizer simulation. A) Multiplier-free uni-bandpass filter. B) Uniband bandpass filter and modulator output . C) Lowpass CIC output filter.

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82 A 0 0.5 1 1.5 2 x 108 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 0 0.5 1 1.5 2 x 108 -160 -140 -120 -100 -80 -60 -40 -20 0 20 D B 0 0.5 1 1.5 2 2.5 x 108 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 x 108 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -160 -140 -120 -100 -80 -60 -40 -20 0 20 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverF Figure 5-12. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of WLANa decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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83 A 0 0.5 1 1.5 2 2.5 x 108 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 0 0.5 1 1.5 2 2.5 x 108 -350 -300 -250 -200 -150 -100 -50 0 D B 0 0.5 1 1.5 2 2.5 x 108 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 x 108 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiver 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverF Figure 5-13. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of WLANb decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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84 A 0 2 4 6 8 10 12 14 x 107 -300 -250 -200 -150 -100 -50 0 0 5 10 15 x 107 -350 -300 -250 -200 -150 -100 -50 0 D B 0 5 10 15 x 107 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 5 10 15 x 107 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C 0 1 2 3 4 5 6 x 107 -150 -100 -50 0 FrequencydBIF receiver 0 1 2 3 4 5 6 x 107 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverF Figure 5-14. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of WLANg decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples

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85 A 0 2 4 6 8 10 12 14 16 x 107 -250 -200 -150 -100 -50 0 0 0.5 1 1.5 2 x 108 -250 -200 -150 -100 -50 0 D B 0 2 4 6 8 10 12 14 16 x 107 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 0.5 1 1.5 2 x 108 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C -1 -0.5 0 0.5 1 1.5 2 x 107 -80 -70 -60 -50 -40 -30 -20 -10 FrequencydBIF receiver 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 107 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 FrequencydBIF receiverF Figure 5-15. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of WiMAX decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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86 A 0 1 2 3 4 5 6 7 8 x 107 -350 -300 -250 -200 -150 -100 -50 0 0 2 4 6 8 10 12 14 16 x 107 -300 -250 -200 -150 -100 -50 0 50 D B 0 1 2 3 4 5 6 7 8 x 107 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 5 10 15 x 107 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C 2 4 6 8 10 12 14 16 18 x 106 -150 -100 -50 0 FrequencydBIF receiver 0.5 1 1.5 2 2.5 x 107 -250 -200 -150 -100 -50 0 FrequencydBIF receiverF Figure 5-16. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of WCDMA decimation filter. A) CIC and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Deci mation filter. F) Passband ripples.

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87 A 1 2 3 4 5 6 7 8 9 10 x 105 -120 -100 -80 -60 -40 -20 0 20 1.05 1.1 1.15 1.2 1.25 x 107 -120 -100 -80 -60 -40 -20 0 D B 0 0.5 1 1.5 2 2.5 3 3.5 x 107 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiver 0 0.5 1 1.5 2 2.5 3 3.5 x 107 -400 -350 -300 -250 -200 -150 -100 -50 0 FrequencydBIF receiverE C 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 105 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 FrequencydBIF receiver 0 1 2 3 4 5 x 105 -100 -80 -60 -40 -20 0 FrequencydBIF receiverF Figure 5-17. Magnitude frequency response of conventional (A,B,C) a nd proposed (D,E,F) of GSM decimation filter. A) CI C and FIR. B) Decimation filter. C) Passband ripples. D) CIC and FIR. E) Decimation filter. F) Passband ripples.

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88 5.2 Periodic and Non-Periodic Narrowband Notch Filter Design Intentional or unintentional jamming of a mu lti-carrier digital receiver is an on-going problem. Intentional narrowband jamming is part icularly insidious due to its simplicity. Narrowband jamming signals can be easily implemented that can overwhelm the receiver’s ADC, rendering the system virtually useless. For example, a basic GPS system can be completely disrupted by a single frequency sm all 4 W Coke can-sized GPS jammer available on the Internet. This problem can be mitigated w ith the use of a narrowb and notch filter that selectively incises the interfering signal for the information process. While the design of notch filters is considered pedestrian in many circles, performing signal incision at high data rates and low-complexity presents a unique challenge to th e system designer. To illustrate, the digital portion of a modern multi-carri er communication receiver can operate at ADC speeds well beyond 100 MHz. It has been established that mapping a received signal from a selected subband to DC is generally accomplished by a digital down converter (DDC) or channelizer . Commercial channelilzers can opera te at high real-time speeds due to the fact that they are based on a multiplier-free Hogenauer CIC architecture. To maintain these high sustained real-time signal processing rates, any linear-phase jam s uppressing notch filter must also be multiplierfree. This essentially eliminates from considera tion conventional FIR or IIR digital filters. The section presents an alternative design methodol ogy that can result in multiplier-less narrowband incision (notch) filter. The conversion of a mu ltiplier-less bandpass to a multiplier-less bandstop filters is based on established filter theory that states that if H ( z ) is an 2 L +1-order ( L = group delay) Type I linear phase FIR, having a frequency response H (ej ), then a delay-complement version of H ( z ) is a Type I linear phase FIR and is given by Equation 5-4. Hc(ej ) = z-L H(ej ) (5-4)

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89 Several modifications to this basi c process will need to be considered before notch filter can be produced. In some case the multiplier-less bandpa ss filter has multiple passbands (multi-mode). These filters need to be mapped into uni-mode filers before conversion to an uni-mode notch filter. In addition, the bandpass filter being tr ansformed needs to be both linear-phase and Type 1. This is not assured in that in some instan ces multiplier-less bandpass f ilter models are Type 2, 3, or 4. These filters need to be converted into Type I filters prior to the application of delaycomplement mapping. It has also been disc overed that multi-mode bandpass filters can be converted into uni-mode filters through the a pplication of a mutiplie r-less masking filter j( z ), as suggested in Chapter 3 a nd shown in Equation 5-5. z z z z Hi N j NM bandpass ) ( ) 1 ( (5-5) Where j( z ) as suggested place zeros in close proximity to the unwanted passbands. Furthermore, it has been determined that a mu lti-mode non-Type I FIR can be converted into a Type 1 FIR filter using the following rules as Equation 5-6 and 5-7. R i R NMz z z H ) 1 ( ; for multi-mode notch application (5-6) R i R N j R NMz z z z H )) ( ( ) 1 (; for uni-mode notch application (5-7) Where NM is an odd integer. Without such modificat ion, the delay-complement version of filter would produce unacceptable outcome because the multiplier-less bandpass filter, mentioned in Chapter 2, would not be a Type 1 filter. Figur e 5-18 illustrates the final architecture of a multiplier-less notch filter as a delay-complement version of H (z).

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90 Figure 5-18. Final architecture of multiplier-less notch filter. A multiplier-free notch filter was designed a nd its performance studied using a MATLAB simulation. The results are report ed in Figure 5-19 and Figure 520 for periodic and non periodic filtering cases. The periodic filtering case is multi-mode notch filter having magnitude frequency response nulls periodically distributed within the filter’s baseband. The design object is the synthesize an Rth order multi-mode notch filter Hc( z ) from a multi-mode bandpass filter H (z) = ((1+ z-12) /(1+ z-4))R. The result is shown in Figure 5-19, where the term (1+ z-12) positions the zeros for Type I operation. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -15000 -10000 -5000 0 Normalized Frequency ( rad/sample)Phase (degrees) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -40 -20 0 20 Normalized Frequency ( rad/sample)M agnitude (dB) Figure 5-19. Magnitude and phase response of a multi-mode notch filter. R j R NMz z H) /( ) 1 ( ) ( Lz

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91 The non-periodic filtering case is uni-mode not ch filter. The object is to design a 4th order uni-mode notch filter Hc( z ) from a base multi-mode bandpass filter H ( z )= ((1+ z-12) (1+ z-1+ z2)/(1+ z-4))4. The outcome is shown in Figure 5-20, where the term (1+ z-12) again positions the zeros for Type I operation and (1+ z-1+ z-2) is the masking FIR. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -4000 -3000 -2000 -1000 0 Normalized Frequency ( rad/sample)P h a se (d e g re e s) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -100 -50 0 Normalized Frequency ( rad/sample)M a g n itu d e (d B ) Figure 5-20. Magnitude and phase response of a uni-mode non-periodic notch filter. The multiplier-free notch filters control parameters are S=NM and R that define the number of zeros distributed uniformly on unit circle with multiplicity R. The depths of the stopband, and the steepness of the fi lter skirt, are primarily infl uenced by the order parameter R as was found in the multiplier-free bandpass filter case. The multiplier-f ree filter’s bandwidth primarily depends on by S=MN, more then R. The main difference in performance between multiplier-free notch filter and multiplier-free bandpa ss filters is their pole zero locations. These choices are motivated in Figure 5-21. In summary, a design paradigm is presented that results in the definition of a multiplierfree narrowband linear-phase Type I notch (incision) filter, suitable for use in multi-carrier multichannel communication applications. The filte rs can operate at high speeds with lowcomplexity. In some cases the filter is reali zed by adding a simple delay path to a basic multiplier-less Type I passband filter.

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92 A B Figure 5-21. Magnitude frequency response of a typical multiplier-free no tch filter for various parameterizations. A) Magnitude frequency response of notch filter of order R=12 and 24. B) Magnitude frequency response of notch filter of for NM=1 and 4.

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93 CHAPTER 6 SIMULATION AND PRELIMINARY RESULTS It is claimed that a new robust and low power digital filter can be designed and applied to the wireless communication based upon multi-rate signal processing theory, frequency masking FIR filter methods, comb and ISOP filters, an d multiplier-free bandpass filter methods. These designs can be classified into three broad classes; 1. NCO based channelizers, 2. NCO-free multiplier-free based channelizers, and 3. Multiplier-less notch filters. In this section the studies reported in the previous chapters are interpreted in the context of design complexity and architectur e that are compared to solu tions found in commercial products. 6.1 Channelizer Complexity Quantifying the complexity of NCO based ch annelizer and NCO-free channelizer is, in general challenging. Eliminating NCO/mixers fo rm a channelizer has se veral consequences. First it will allow the channelizer to operate at sample rates we ll above those currently found in commercial practice. This is generally considered to be desirable. The NCO/mixer-free designs, however, will require a revaluation of both the front-end (ADC) and back-end (DSP microprocessor) designs. Comparisons can be ba sed on speed, complexity (gate count), power dissipation, and cost, to name but a few metrics. In order quan tify these attributes, on a designby-design basis, they need to be instantiated in some technological context. Technology families, such as custom ASIC, structured ASIC, FPGA need to be specified and, within each family, a design rendered using electronic design and anal ysis (EDA) tools. Unfortunately these tools carry a high price-tag (in excess of $1M) per seat. These activities require resources that are not

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94 available at most academic centers, including the University of Florida. Instead, some logical conclusions will be drawn on the basis of what is known or reasonably assumed. If all the detailed design parameters where know n, then a mathematical metric could be developed to account for these differences in design and it could take the following form: X = number of multiplies; Y = number of adds; W = normalized wordwidth; W=wordwidth/16-bits, S = normalized speed; S= fclk/fs; Mg=normalized multiplier gate count; Mg= multiplier gate count/TI TMS 320C67xx; Ag=normalized adder gate count; Ag= adder gate count/TI TMS 320C67xx; Ms=normalized multiplier speed; Ms= multiplier speed/TI TMS 320C67xx; As=normalized adder gate count; As= adder speed/TI TMS 320C67xx; Wg = non-negative complexity weight. Ws = non-negative speed weight FOM = Figure of Merit: WXY(Wg Mg Ag )(Ws Ms As ) 6.1.1 Numerically Controlled Oscillator -based channelizer A commercial digital channelizer consists of an NCO/mixer, decimation filter (viz; CIC), and some signal conditioning devices (viz; FIRs). For NCO/mixer is used to translate an IF signal down to baseband as is the case with commercial systems. Once at baseband signal, the

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95 signal is passed through an Nth order decimating CIC filter to extract a specific range of the baseband for back-end processing. Signal conditio ning is performed using a CFIR FIR filter to remove the sin(x)/x roll-off of the CIC filter and PFIR FIR filters provide spectral housekeeping services. Additional decimation may occur at th e output of the CFIR and PFIR filters. One of the reported new design strategies uses NCOs, but is different from the commercial implementations. This class of architecture was developed in Chapter 3. The objective is to create channelizer of low complexity and high performance relative to existing commercial designs. Figure 6-1. NCO Architecture. A basic NCO is reported in Figure 6-1. This device produces a modula tion signal that is used as part of a heterodyning pr ocess. It should be noted that if an NCO operates a high input sample rates (e.g., 300 M-2 Gsps), it can create power dissipation and logi c design problems. Since all NCO-based channelizer c ontain NCOs similar to that de scribed in Figure 6-1, their complexity will not be factored into the design study. Designs, therefore, will be compared on the basis of their down-conversi on filter requirements. For comparative purposes, this means comparing the designs reported in Chapter 4, specifically form Table 4-3 and Table 4-4, with respect to the eight wireless standards previously introduced. Phase Register Phase Accumulator + Sine Generator Cosine Generator

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96 Table 6-1. Computational complexity comparis on for the overall NCO based channelizer with two FIR filters. Item multiplications additions Conventional channeliz er architecture 84 92 Sharpened Conventional channelizer architecture 86 108 Multiplier-less lowpass based channelizer 65 81 Multiplier-less CIC and ISOP based channelizer architecture 4 29 Hbrid CIC based channelizer architecture 84 100 Multiplier-free FIR channelizer architecture 84 110 Shaped multiplier-free FIR channelizer architecture 84 144 In some cases, a relatively low-order cha nnelizer design resulted that meets a published standard, in other cases higher-order filters ar e required. For the IS-95 and WiMAX case, the multiplier-less CIC and shaping filter based ch annelizer strategy has a small multiplier budget compared to other FIR based channelizers. These relationships, however, are application dependent. Select another standard and the list may become re-ordered. 6.1.2 Numerically Controlled Oscillator -Free and Multiplier-Free Channelizer A receiver needs to run at the input ADC rate (e.g., 2 GHz), while the back-end processing performed at a far lower decimated rate. This is not a challenge to the multiplier-less CIC filter but does have an impact on the input mixer/NCO desi gn. If this condition could be relaxed, then a less complex channelizer can be realized with an attendant area and power advantage. There are two different methods of NCO-free channelizer presented in Chapter 5 which considers only NCO-free channelizers with fract ional re-samplers and NCO-fr ee channelizer with simple alternating sign ( ) switch. They are based on a theory for NCO-free channelizers that also

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97 promote a general theory of band-selectable (bandpass) channelizer based on basic number theory. NCO-free channelizers with fractional re-samplers need re-sampling blocks after the decimation filter for different design reasons. Given a certain m odulator, the sampling frequency can made reconfigurable which results in extra switch circuit design and consumes chip area but leads to more flexibility regarding the follo wing modules design. Concerning the re-sampling block, the complexity depends on the re-sam pling rate. The sampling frequency in the demodulation part must be the multiple of symbol rate of each standard . The re-sampling rate and input sampling rate are review ed in Table 5-2 and Table 5-3. NCO-free channelizer with simple alte rnating sign only needs a simple sign ( ) switch instead of an NCO. Their modulation can theref ore run in high speed. The complexity of all channelizers which mentioned in Chapte r 4 and Chapter 5 are in Table 6-2. Table 6-2. Complexity for IS-95 mobile communication. Architecture NCO Multiplier Adder CIC Conventional channelizer yes 84 92 5 stage Sharpened Conventional channelizer yes 86 108 5 stage Multiplierless CIC and ISOP based channelizer( not proved for GSM) yes 4 36 5 stage Hybird CIC based channelizer yes 84 94 3 stage Mmultiplier-free FIR channelizer yes 84 139 no Shaped multiplier-free FIR channelizer yes 84 118 no NCO-free channelizer with fractional re-sampler Resampler 84 108 5 stage NCO-free channelizer with simple alterna ting sign ( ) switch sign ( ) switch 84 108 5 stage Note: NCO = Numerically Controlled Oscill ator, CIC = Cascaded IntegratorComb. 6.2 Complexity and Performance of Multiplier-Less Notch Filters In some instances, intentiona l and unintentional narrowband noise can have a disruptive effect on wireless communications. A multiplier-free suppressing notch filter can provide a degree of immunity from such occurrences. A de sign paradigm that resu lts in the creation of multiplier-less narrowband linear phase Type I (notch) filter suitable for use in multi-carrier

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98 communication applications is presented in Chapter 5. The resulting filters are highly selective, can operate and very high speeds, are of low co mplexity, and are also linear phase. The design procedure presented can be easily implemented to achieve either uni-band or multi-band notch filtering.

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99 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Conclusions The new channelizer technology reported in this dissertation will benefit the wireless industry. The result is a more capable, lower cost, lower power, and infrastructure technology. The channelizer technology presente d is also shown to be robust by demonstrating an ability to meet or exceed contemporary communication standards. Given the specification for each wireless standards, and corresponding modulation requirements, a decimation filter having a low power budget and low complexity can be determined using the principles presented in Ch apter 4. Different tec hniques of implementing decimation filter in Chapter 4 were compared to conventional decimation filter design strategies. The similarities and differences between the presented methods of implementing decimation filters, along with performance and complexity envelope, can be used to perform comparative designs studies resulting in best overall solution. Very low complexity decimation filters based on a new theory of multiplier-less lowpass filters can achieve very impressive performance when compared to conventional designs. The issue of designing channelizers with and wi thout NCO’s was also addressed. NCO is currently a design liability in conventional channeliz er construction. In Ch apter 5, two different channelizer structures was intr oduces. The first was NCO-free ch annelizer based on the use of multiplier-free bandpass filters to isolate the desi red signal and bring IF signal down to baseband signal using decimation. If the output sample rate is not found within a wireless specification, then a fractional resampler is added to the desi gn. The other NCO-free technique uses a simple alternating sign (“ ”) switch to perform modulation. The Fourier transform of the alternating sign signal is known to have a strong fundamental component at a designated center frequency as

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100 well as attendant harmonics. The fundamental frequency is desired but the harmonics will produce unwanted out-of-band signals at multiples of harmonic of center frequency. These were removed by using a multiplier-less CIC lowpass f ilter. Like an NCO operation, the alternating sign strategy brings a bandpassed signal down to baseband without need of a re-sampler. The other filter class developed in this disserta tion was that of a multiplier-less notch filter which can maintain these high sustained re al-time signal processing rates. 7.2 Future Work Compared to conventional NCO-based channeli zers, the proposed channielizer design holds the promise of lower complexity. This can be translated into low-pow er and/or high-speed. Future work should focus on quantifying this ad vantage in a physical instantiation. Using commercial grade EDA tools, it is recommended that one or more of the proposed channelizer designs be implemented as a structured ASIC or FPGA. The design outcome can then be benchmarked against a commercial unit and pe rformance advantages directly measured. Another area that may prove productive is developing auto-configur ation software or MATLAB attachments that will optimize a design outcome based on a set of specifications.

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101 LIST OF REFERENCES [1] Texas instruments, (Aug. 2001) Multi-Stand ard Quad DDC Chip – Data Sheet: GC 4016., REV 1.0. [2] Texas instruments, IF Analog-to-Digital Converter with Digital Down converter: [Online] Available: www.ti.com [3] Analog Devices, Diversity IF-to-Baseba nd GSM/EDGE Narrow-Band Receiver, AD6650: [Online] Available: http://www.analog.com. [4] National Semiconductor, (Feb.2000) CL C5902 Dual Digital Tuner/AGC: [Online] Available: .http://cache.na tional.com/ds/CL/CLC5902.pdf. [5] Intersil, Implementation of a High Rate Radio Receiver (HSP43124, HSP43168, HSP43216, HSP50110, HSPCLC5902): [Online] Available: www.intersil.com [6] E. B. Hogenauer, “An Economical Class of Digital Filters for Decimation and Interpolation,” IEEE Transactions on Acous tics, Speech and Signal Processing, vol.2, ASSP-29(2), pp. 155-162, 1981. [7] F. Taylor and J. Mellott, Hands-on Digital Signal Proce ssing. McGraw-Hill, New York: 1998. [8] S. Noh, O. Kwon, and F. Taylor, “Multip lier-free Bandpass Filter Channelizer”, ICASSP, vol.4, pp IV-509, 2006. [9] NOVA Engineering, (Dec. 2001) Digital IF Receiver Megafunction: Narrowband and Wideband Digital receiver ver. 1.1. [10] H. J.Oh, S. Kim, and G. Choi, “On the Us e of Interpolated Second-Order Polynomials for Efficient Filter Design in Programmable Downconversion,” IEEE Jounal, on Selected Areas in Communication, vol. 17, no. 4, Apr 1999. [11] S. Noh and F. Taylor, “Digital Notch Filters, A Number Theoretic Approach”, ASILOMAR, Pacific Grove, CA, Oct. 29-Nov. 1, 2006. [12] National Semiconductor Demodulating with the LMX2240 150 MHz IF Receiver: Application Note1020, wireless communica tion, [Online]Available: http://www.sssmag.com/pdf/ifrx.pdf. [13] G. M. Barbosa and J. Carlos, 4 GH z Digital Frequency Discriminator (DFD) Design for Microwave Receivers”, Araujo dos Santos. [14] W. A. Abu-Al-Asua, Efficient Wideband Digital Front-End Transc eivers for Software Radio System, School of Elect rical and Computer Engineering, Georgia Institute of Technology.

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102 [15] R. A. Losada, Practical FIR Filter Design in MATLAB: the mathworks, inc, [16] N. J. Fliege, Multirate Digital Signal Processing: John W iley & Sons Ltd. Chichester, 1994. [17] Graychip, Inc, (Aug. 2001) GC 4016 MULTI-STANDARD QUAD DDC CHIP DATA SHEET: Revision 1.0. [18] S. Norsworthy ,”Delta-Sig ma Data Converters,” 1997. [19] N. Tan, “A Novel Bit-Serial Design of Comb Filters for Oversampling Converters,” Proceedings of IEEE International Symposium on Circuits and Systems, pp. 259-262, May. 1994. [20] I. Fujumori, “A 5V Single-Chip DeltaSigma Audio A/D Convert er with 111dB DynamicRange,” IEEE Journal of Solid-State Circuits, pp. 329-336, Mar. 1997. [21] K. Sienski et al. “Hardware Efficient FIR Filter Structures From Linear Program Constraints, IEEE International Confer ence Proceedings on Acoustics, Speech, and Signal Processing, pp. 1280-2, May. 1996. [22] A. Santraine, S, Leprince, and F Ta ylor, Senior Member, “Multiplier-Free Bandpass Channelizer for Undersampled Applications,” IEEE Signal Processing Letters ,vol. 11.no. 11, Nov. 2004. [23] D. Chester, “Digital IF f ilter technology for 3G systems,” IEEE Commun. Mag. , vol. 7, pp. 102, Feb. 1999. [24] F. J. Harris, Fellow, IEEE, C. Dick, Member, IEEE, and M. Rice, Senior Member, “Digital Receiver and Transmitters Using Polyphase Filter Banks for Wireless Communication”, IEEE Transacti on, vol.51, no.4, Apr. 2003. [25] M. Kimn and S. Lee,”Design of Du al-Mode Down Converter for WCDMA and cdma 2000”, ETRI Journal, vol 26, Dec. 2004. [26] M. Jian, W. H. Yung, and B. Songrong, “An Efficient IF Arch itecture for Dual-Mode GSM/W-CDMA Receiver of a Software Radio,” IEEE Int’l Workshop on Mobile MultimediaCommunications, vol. 87932, pp. 21-24, Nov. 1999. [27] H. J. Oh, S. Kim, G. Choi, Member, IEEE, and Y. H. Lee, Senior Member, IEEE, “On the Use of Interpolated Second-Order Polynom ials for Efficient Filter Design in Programmable Downconversion. [28] B. Wild and K. Ramchandran, “Detecti ng Primary Receivers for Radio Aplications”, 14244-0013-9/05, IEEE, 2005. [29] D. Chester, “Digital IF F ilter Technology for 3G Systems,” IEEE Communications Magazine , Feb. 1999.

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103 [30] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englew ood Cliffs, NJ: PrenticeHall, 1993. [31] W. Lawton, “Analysis of Ternary-Valu ed CIC Filter Based OFDM Channelizers in Modern Wireless Communications Systems,” MS Thesis, University of Florida, 2005 [32] P. P. Vaidyanathan and B.Yoon, “GENE AND EXON PREDIC TION USING ALLPASSBASED FILTERS”, California Institute of Technology Pasadena, CA 91125, USA. [33] J. Bell, “Tunable Multi Notch Digital Filters”: A MATLAB demonstration using real data, CSIRO ATNF, [Online] Available: http://www.atnf.csiro.au/projects/sk a/techdocs/notch_multi_tune.pdf [34] B. Carter, Filters for Data Transmi ssion: Texas Instruments, Application Report (SLOA063), Jul. 2001. [35] T. Hinamoto, N. Ikeda, S. Nishimura, and A. Doi, “DESIGN OF TWO-DIMENTIONAL ADAPTIVE DIGITAL NOTCH FILTERS,” Processing of ICSP 2000. [36] S. C. Dutta Roy, S. B. Jain, and B. Kumar, “Design of digital FIR notch filters,” IEE Proc. Vision Image and Signal Processing, vol.141, no. 5, Oct. 1994. [37] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englew ood Cliffs, NJ: PrenticeHall, 1993. [38] R. Rao, M.Tisserand, M. Severa, and J. Villasenor,”FPGA Polyphase Filter Bank Study &Implimentation,”. [Online] Available: http://slaac.east.isi.edu/prese ntations/retreat _9909/polyphase.pdf [39] High Performance FPGA: Lattice Semiconduc tor Corporation, FPGA Devices. [Online]. Available: http://www.latticesemi.com. [40] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englew ood Cliffs, NJ: PrenticeHall, 1993.

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104 BIOGRAPHICAL SKETCH Siwoo Noh was born in Namwon, Korea. The olde st of three children, he grew up mostly in Junju, Korea, graduating from Sangsan High Sc hool in 1991. He earned his B.S. in electrical engineering in Korea and his M.S. in electrical and computer engi neering from the University of Florida. He was in the High Speed Digital Architecture Laboratory (HSDAL) in the Electrical and Computer Engineering Department at the University of Florida during his PhD study. His present research interests are in the areas of signal processing, digital filter design, and wireless communication filter design. While a Ph.D. stude nt, Siwoo interned with Samsung Electronics. After graduation, he will return there for full-tim e employment as a digital filter design engineer for wireless system.