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1 RF VIBROMETER NON CONTACT MEASUREMENT OF VIBRATION S USING DOPPLER RADAR By YAN YAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 2
2 201 2 Yan Yan
3 ACKNOWLEDGMENTS I want to thank my mom for her great support all the time in my life. I also want to thank my advisor Dr. Jenshan Lin, and my previous co worker Dr. Changzhi Li for their help and support for my Ph. D.
4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 3 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 15 1.1 Background ................................ ................................ ................................ ....... 15 1.2 The Development of RF Vibrometer ................................ ................................ 16 2 DETECTION THEORY AND IMPLEMENTATION OF RF VIBROMETER .............. 19 2.1 RF Vibrometer Prototype ................................ ................................ .................. 20 2.1. 1 System Architecture and Detection Theory ................................ ............. 20 2.1.2 Limitation of Detection Theory ................................ ................................ 22 2.2 RF Vibrometer Using Multiple Harmonic Pairs ................................ .................. 23 2.2.1 System Architecture and Detection Theory ................................ ............. 23 2.2.2 Experiment Verification ................................ ................................ ............ 25 2. 2.3 RF Vibrometer vs. Laser Displacement Sensor ................................ ....... 28 2.3 RF Vibrometer Using Multiple Carrier Frequencies ................................ .......... 29 2.3.1 Verification of Detection Theory in Simulation ................................ ......... 30 2.3.2 Experiment ................................ ................................ .............................. 31 2.3.3 Performance Analysis ................................ ................................ .............. 35 2.4 Summary ................................ ................................ ................................ .......... 38 3 I/Q MISMATCH EFFECT ON MEASUREMENT OF VIBRATION USING RF VIBROMETER ................................ ................................ ................................ ........ 39 3.1 Theory and Simulation ................................ ................................ ...................... 40 3.1.1 Phase Mismatch Effect ................................ ................................ ............ 40 3.1.2 Amplitude Mismatch Effect ................................ ................................ ...... 43 3.2 Experiment Verification ................................ ................................ ..................... 44 3.2. 1 Verification of Amplitude Mismatch Effect ................................ ............... 45 3.2.2 Verification of Phase Mismatch Effect ................................ ..................... 46 3.3 I/Q Mismatch Effect on Measured Vibration Amplitude ................................ ..... 47 3.4 Summary ................................ ................................ ................................ .......... 48 4 DETECTION RANGE AN D ACCURACY OF RF VIBROMETER ........................... 49
5 4.1 Experiment and Analysis ................................ ................................ .................. 49 4.1.1 Measurement Sensitivity Dependence on Carrier Frequency ................. 49 4.1.2 Sensitivity Limited Detection Range vs. Vibration Amplitude .................. 52 4.2 60 GHz IC Realization of RF Vibrometer ................................ .......................... 55 4.3 Summary ................................ ................................ ................................ .......... 58 5 APPLICATION OF RF VIBROMETER IN VITAL SIGN DETECTION ..................... 59 5.1 System ................................ ................................ ................................ .............. 60 5.1.1 Vibrometer ................................ ................................ ............................... 60 5.1.2 Infant Simulator ................................ ................................ ....................... 61 5.2 Experiment and Analysis ................................ ................................ .................. 62 5.2.1 Baseline State ................................ ................................ ......................... 64 5.2.2 Bradypnea ................................ ................................ ............................... 6 5 5.2.3 Faint Breathing ................................ ................................ ........................ 65 5.2.4 Heart Rate Equals the Harmonic of Respiratory Rate ............................. 66 5.2.5 Tachypnea and Bradycardia ................................ ................................ .... 67 5.3 Summary ................................ ................................ ................................ .......... 69 6 ANALYSIS OF DETECTION METHODS OF RF VIBROMETER FOR COMPLEX MOTION MEASUREMENT ................................ ................................ .. 70 6.1 Modeling of Harmonic Vibrations ................................ ................................ ...... 71 6.2 Harmonic Analysis of Wavelength Division Sensing Technique and Multiple Harmonics Based Detection Method ................................ ................................ ... 73 6.2.1 Harmonic A mplitude Approximation ................................ ........................ 75 6.2.2 Harmonic Analysis of Wavelength Division Sensing Technique .............. 77 6.2.3 Choice of Harmonic Pairs on Detection Accuracy ................................ ... 80 6.2.4 Detection Method Using Multiple Harmonic Pairs at a Fixed Carrier Frequency ................................ ................................ ................................ ..... 82 6.3 Experimental Verification ................................ ................................ .................. 83 6.4 Sensitivity of Harmonic Amplitude Ratio to A dditional Phase Angle ................. 86 6.5 Experimental Implementation of Real time RF Vibrometer ............................... 93 6.6 Summary ................................ ................................ ................................ .......... 96 7 ANALYSIS OF RF VIB ROMETER FOR VITAL SIGN DETECTION ....................... 98 7.1 Analysis of Special Cases ................................ ................................ ................. 98 7.1.1 Respiration Rate and Heartbeat Rate in Harmonic Relation ................... 98 7.1.2 Bradycardia and Tachypnea ................................ ................................ .. 101 7.2 Optimal Carrier Frequency for Infant Vital Sign Monitoring ............................. 102 7.3 Harmonic Cancellation Using Double Sideband System ................................ 109 7.3.1 The Effect of Power Difference between Sidebands ............................. 112 7.3.2 The Relation between Harmonic Order And LO Frequency .................. 115 7.3.3 The Relation between Chest Wall Displacement and RF Frequency .... 116 7.4 Experiment Verification ................................ ................................ ................... 117 7.4.1 2 nd Order Harmonic Cancellation ................................ ........................... 119
6 7.4.2 3 rd Order Harmonic Cancellation ................................ ........................... 120 7.4 Summary ................................ ................................ ................................ ........ 121 8 CONCLUSION ................................ ................................ ................................ ...... 122 LIST OF REFERENCES ................................ ................................ ............................. 124 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 129
7 LIST OF TABLES Table page 2 1 Measurement results (WCC: Waveform correlation coefficient) .......................... 27 2 2 I/Q Mismatch Effect on H 2 /H 10 and m 1 m 2 and m 3 ................................ ............... 37 4 1 Measurement results vs. programmed value ................................ ....................... 51 6 1 Combination of Bessel function index with 3 P +5 L = X and Harmonic Amplitude Expression with 4 M 1 / = A 1 4 M 2 / = A 2 ................................ ................................ 78 6 2 Combination of Bessel function index with 4 p +6 l +8 q = x ................................ ....... 84 6 3 Measured m 1 using H 1 /H 3 and H 3 /H 4 ................................ ................................ ... 95 6 4 Measured m 2 using H 1 /H 3 and H 3 /H 4 ................................ ................................ ... 95 6 5 Measured m 1 using H 2 /H 3 and H 3 /H 4 ................................ ................................ ... 95 6 6 Measured m 2 using H 2 /H 3 and H 3 /H 4 ................................ ................................ ... 96 7 1 m rr and f LO for 2 nd and 3 rd harmonic cancellation ................................ ................ 116 7 2 Double sideband Ka band radar building blocks and their specifications .......... 117
8 LIST OF FIGURES Figure page 2 1 Block diagram and experiment set up of the RF vibrometer prototype. .............. 20 2 2 Block diagram of the RF vibrometer using multiple harmonic pairs. ................... 23 2 3 Time domain and frequency domain baseband signal.. ................................ ..... 26 2 4 Reconstructed move ment pattern and residual error ................................ .......... 27 2 5 Measurement setup of LDS and vibrometer ................................ ....................... 28 2 6 Radar detected baseband spectrum under carrier frequencies of 5 GHz, 6 GHz and 7 GHz. ................................ ................................ ................................ 31 2 7 Block diagram of the wavelength division sensing RF vibrometer. ..................... 32 2 8 Measurement setup of shaker. ................................ ................................ ........... 33 2 9 Time domain and frequency domain baseband signal ................................ ....... 34 2 10 Acceleration signal from accelerometer. ................................ ............................. 35 2 11 Comparison of recovered vibration pattern using wavelength division sensing RF vibrometer, accelerometer and the reference from LVDT. ............................ 36 3 1 The variation of H 1 /H 2 vs. residual phase under different phase mismatch degrees of 5 o 10 o 15 o 20 o with the ideal value as reference. .......................... 42 3 2 The variation of H 1 /H 2 vs. residual phase under different amplitude mismatch of 1 dB, 3 dB, 5 dB, with the ide al value as reference. ................................ ....... 43 3 3 Block diagram of the experimental setup. ................................ ........................... 44 3 4 2 dB and 6 dB. ................................ ................................ ................................ .... 46 3 5 Measured H 1 /H 2 o and 20 o ................................ ................................ ................................ .............. 46 3 6 Detected and simulated displacement of vibrations vs. residual phase under different amplitude imbalance of 2 dB, 6 dB, with 2 mm reference ..................... 47 3 7 Detected and simulated displacement of vibrations vs. residual phase under different phase imbalance of 15 o 20 o with 2 mm reference. .............................. 47 4 1 Baseband spectrum of a single tone vibration pattern. ................................ ....... 50
9 4 2 Harmonic amplitude ratio H 1 /H 2 vs. movement amplitude. ................................ 51 4 3 Detection range vs. movement amplitude. ................................ ......................... 54 4 4 System block diagram of the 60 GHz micro radar including flip chip packaging ................................ ................................ ................................ ........... 55 4 5 Layout of the whole 60 GHz transceiver ................................ ............................. 56 4 6 Detected peak on the CSD spectrum for different vibration displacement at various distances ................................ ................................ ................................ 56 4 7 Detected time domain I/Q signals and CSD baseband spectrum for vital s ign detection ................................ ................................ ................................ ............. 57 5 1 Block diagram of 5.8 GHz vibrometer. ................................ ................................ 61 5 2 Experimental set up of infant simulator monitoring ................................ ............. 62 5 3 Measured heart rate vs. programmed heart rate. ................................ ............... 63 5 4 Measured respiratory rate vs. programmed respiratory rate. .............................. 63 5 5 Programmed Tidal Volume of each event. ................................ ......................... 63 5 6 Measured time domain baseband signal with programmed RR=40, HR=130. ... 64 5 7 Normalized measured baseband spectrum with programmed RR=40, HR=130. ................................ ................................ ................................ ............. 64 5 8 The comparison of normalized spectrums of measured baseband signal of Event 2 and Event 3. ................................ ................................ .......................... 66 5 9 The comparison of simulated absolute spectrums of two cases. Case1: Normal RR at 60, normal HR at 80. Case2: Weak RR at 80, normal HR at 60. 68 6 1 Block diagram and experimental setup of the wavelength division sensing RF vibrometer. From  ................................ ................................ ......................... 76 6 2 Bessel function Jn(a) of n=0, 1, 2, 3 with 0
10 6 6 Variation of H 2 /H 3 vs. ( 1 an d 2 ) ................................ ................................ ...... 87 6 7 Variation of H 1 /H 3 vs. ( 1 and 2 ) ................................ ................................ ...... 87 6 8 Variation of H 3 /H 4 vs. ( 1 and 2 ) ................................ ................................ ...... 87 6 9 Calculated m 1 using H 1 /H 3 and H 3 /H 4 reference value m 1 =2 mm ..................... 90 6 10 Calculated m 2 using H 1 /H 3 and H 3 /H 4 reference value m 2 =1 mm ...................... 90 6 11 Calculated m 1 using H 2 /H 3 and H 3 /H 4, reference value m 1 =2 mm ....................... 91 6 12 Calculated m 2 using H 2 /H 3 and H 3 /H 4 reference value m 2 =1 mm ...................... 91 6 13 Experiment set up of the through wall vibration detection ................................ .. 94 6 14 Real time monitoring of vibrations that are odd functions in time using RF vibrometer ................................ ................................ ................................ .......... 95 7 1 Variation of H 2 /H 1 when m rr changes from 0 to 5 mm with m hb @ 0.08 mm ........ 99 7 2 Variation of H 2 /H 1 when m hb changes from 0 to 0.1 mm with m rr @ 4 mm ........ 100 7 3 Harmonics of the special case with the heartbeat strength fixed ...................... 102 7 4 Baseband spectrum for a normal vital sign state of RR=40 bpm, HR=130 bpm at fc=5.8 GHz ................................ ................................ ........................... 104 7 5 Baseband spectrum for a normal vital sign state of RR=40 bpm, HR=130 bpm at fc=27 GHz ................................ ................................ ............................ 104 7 6 Heartbeat signal vs. the 3 rd harmonic of respiration at different m rr and carrier frequencies ................................ ................................ ................................ ....... 105 7 7 J 0 (x)/J 3 (x) ................................ ................................ ................................ .......... 107 7 8 J 1 (x)/J 0 (x) ................................ ................................ ................................ .......... 108 7 9 Heartbeat signal vs. the 2 nd harmonic of respiration at different m rr and carrier frequencies ................................ ................................ ................................ ....... 108 7 10 Double sideband Ka band quadrature radar ................................ .................... 109 7 11 Bessel function of order n=0 and n=3 ................................ ............................... 111 7 12 Vital sign baseband spectrum at a single carrier frequency of 33 GHz ............ 112 7 13 Vital sign baseband spectrum from two sidebands at 33 GHz and 45 GHz ..... 113
11 7 14 Bessel functions of order n=0 to n=3 ................................ ................................ 115 7 15 Double sideband radar output spectrum ................................ ........................... 118 7 16 Baseband spectrum with single carrier frequency at 26GHz ............................ 119 7 17 2 nd order harmonic cancellation experiment. Upper: time domain I/Q signals. Lower: baseband spectrum ................................ ................................ .............. 120 7 18 3 rd order harmonic cancel lation experiment. Upper: time domain I/Q signals. Lower: baseband spectrum ................................ ................................ .............. 120
12 LIST OF ABBREVIATIONS BPM Beats P er Minute CSD Complex Signal Demodulation HR Heart beat Rate IF Intermediate Frequency LDS Laser Displacement S ensor LDV Laser Doppler vibrometer LVDT Linear Variable Differential Tr ansformer PSD Position Sensitive D etector RF Radio Frequency RR Respiratory Rate SIDS Sudden Infant Death Syndrome TV Tidal Volume WCC Waveform Correlation Coefficient
13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RF VIBROMETER NON CONTACT MEASUREMENT OF VIBRATION S USING DOPPLER RADAR By Yan Yan May 2012 Chair: Jenshan Lin Major: Electrical and Computer Engineering This dissertation begins with the illustration of working principle of RF vibrometer The proposed RF vibrometer can obtain the accurate displacement of vibrations whose movement patterns are non sinusoidal periodic and odd function in time. Two different sets of detection theory are develop ed to fulfil l the function. One is measuring the amplitude ratios of multiple harmonic pairs in baseband spectrum at a certain carrier frequency; the other is detecting the variation of amplitude ratio of a fixed harmonic pair at different carrier frequencies. Both of these two d etection theories are based on non linear D oppler phase modulation effect. After that, the effect of I/Q mismatch on the measured vibration amplitude is analyzed in simulation and verified through experiment. It is proved that there exist optima l residual phases (or optimal detection distances) that can minimize the degradation of detection accuracy caused by amplitude and phase mismatches, respectively. Then, the improvement of RF vibrometer detection accuracy and sensitivity by increasing carr ier frequency is verified through experiment It is demonstrat ed that the minimum vibration amplitude that can be accurately measured will decrease in
14 proportion to the carrier frequency. The relation between sensitivity limited detection range and vibrati on amplitude is also found out through experiment and analyzed theoretically. The sensitivity of harmonic ratio pair s to excess phase angle s of each harmonic components consisting of the vibration is also analyzed. Some insensitive pairs can be used to ex tract characteristics of the vibration system The advantages of the detection method using multiple harmonic pairs compared to the wavelength division sensing technique are also shown through harmonic analysis. T he proposed RF vibrometer is also applied t o monitor the vital signs of an infant simulator The abnormal cases are further analyzed through detail harmonic analysis. The optimal detection frequency for vital sign detection is found to be in the low frequency range. In the end, harmonic cancellation technique by using double sideband signals has also been presented.
15 CHAPTER 1 INTRODUCTION 1.1 Background The development of various instrumentations and techniques for vibration measurement and analysis has become increasingly important nowadays for monitoring modern mechanical equipment. Conventional vibration sensing elements comprise displacement or velocity transducers. One of the most widely used is the acceleromete r . A piezoelectric based accelerometer can produce an electrical output proportional to the vibratory acceleration of the target it attaches to but they are often big  A c apacitance based MEMS accelerometer can be much smaller and low power . A nother contact measurement instrument is linear variable differential transformer (LVDT) [ 4 ] which works as a displacement transducer that can measure the vibratory displacement directly. These contacting mode instruments can provide accurate measurement results but require careful mounting operation in order to reduce detection errors  thus incurring inconvenience in some circumstances in which non contact technique is preferred The laser Doppler vibrometer (LDV) can be used to detect the honeycomb vibrations in beehives or other insect communications and become a useful tool for the research of entomologists . Presently, non contact vibration measurement instruments and techniques are developed increasingly Most of them are laser based, such as laser Doppler vibrometer (LDV) [ 6 ]  laser interferometer [ 9 ]  and laser displacement sensor (LDS) [ 11 ]. The working principle of LDV and laser interferometer is based on the interference of two laser beams. The freque ncy (or phase) difference between a reference beam and a test beam that is modulated by the motion of the vibration target is measured to extract
16 the velocity of the vibration. Another mechanism called triangula tion detection  is used by the LDS. It co mprises a light emitting element and a position sensitive detector (PSD). A lens is used to focus the transmitting laser beam on the moving target. The target reflects back the beam through another lens and focuses on the PSD, forming a beam spot. The beam spot will move as the target moves. The instantaneous displacement can then be determined by detecting the movement of the beam spot. Laser based devices are widely used for their high accuracy, but they are costl y as well. In addition, they are no longer workable in low visibility environment such as dusty or rainy circumstances and cannot detect vibration behind a wall [ 13 ] [ 14 ] Besides this, the narrow detection range [ 11 ] also limits its application in remote wireless sensing. 1.2 The Development of RF Vibrometer Since RF based instruments can be integrated at a much lower cost and also remain workable in low visibility environment, it become s a hot research topic recently. The RF vibrometer prototype is fir stly presented in [ 1 5 ]. It is implemented as a direct conversion Doppler radar with a single channel baseband signal When the displacement of vibration is comparable to the carrier wavelength of the radar system, the nonlinear Doppler phase modulation effect will genera te harmonics other than the frequency components of the vibration itself. It is found that the amplitude ratio between two even order or two odd order harmonics in the baseband spectrum is a function of the vibration displacement Thus, t he displacement of vibrations can be obtained by solving an equation using the measured harmonic amplitude ratio. This prototype vibrometer has the following advantages: (1) It does not need calibration for accurate vibration measurement (2) It can verify itself through the baseband spectrum (3) It features a very simple structure. The calibration free characteristic of RF vibrometer can
17 be very attractive compared to laser sensor which usually inevitably needs calibration operation  Due to the limit ation of the prototype architecture of the radar system, the vibrometer can only measure the vibration that is purely sinusoidal (only one frequency component ). Moreover, the existed residual phase will cause null detection point problem [ 1 6 ]  [ 49 ] whi ch will degrade the detection accuracy severely. In order to eliminate the residual phase problem from essentially and make a more reliable and advanced RF vibrometer, quadrature system architecture and complex signal demodulation technique are utilized. A 27.6 GHz vibrometer that based on the detection approach using multiple harmonic pairs [ 1 8 ] and another one using multiple carrier frequencies technique [ 1 9 ] are developed. They are both demonstrated to be capable of accurately measuring the pattern of a complex vibration that includes three frequency components. The I/Q mismatch effect of the radar system is also studied [ 2 0 ]. When there is phase or amplitude mismatch, the harmonic amplitude ratio will deviate from the real value and degrade the accuracy of calculated displacement of vibrations using the harmonic amplitude ratio It is found that there exists optimal detection distance to resist the error caused by I/Q mismatch. The detection accuracy of the proposed RF vibrometer is dependent o n the carrier frequency. It is found out through experiment that t he minimum displacement amplitude of vibrations that can be accurately measured by the 27.6 GHz vibrometer is 0.5 mm, while the 5.8 GHz vibrometer can only measure vibration s with the peak v alue as small as 2 mm [2 1 ] In addition, the sensitivity limited detection range is found to be proportional to the square root of the displacement of vibrations Both the stud ies on
18 detection accuracy and detection range provide a guideline on the design of RF vibrometer for various applications RF vibrometer can also be used in other application area s besides the measurement of mechanic vibration s A 5.8GHz RF vibrometer is used to monitor the variation of the respiration and heartbeat rate of an infant simulator non contactly [ 2 2 ] It shows the potential application of RF vibrometer for initial clinic diagnose. The comparison between these two detection theories has been presented. The method based on multiple harmonic pairs has proved to be more reliable for accurate vibration detection. In the end, a harmonic cancellation technique using double sideb and demodulation has been presented. Using this technique, the undesired harmonic can be removed from the spectrum. For example, the 3 rd order harmonic of the respiration signal will overwhelm the weak heartbeat signal. Removing it from the spectrum can po tentially improve the vital sign detection accuracy.
19 CHAPTER 2 DETECTION THEORY AND IMPLEMENTATION OF RF VIBROMETER Microwave Doppler radar has been used for displacement related measurement for many years. Most common applications include displacement and low velocity measurement [ 2 3 ], automobile speed sensing [ 2 4 ] position sensing [2 5 ] and precision noise measurement [2 6 ] The working principle of the 35.6 GHz microwave Doppler radar in [ 2 3 ] is based on detecting the instantaneous Doppler frequency shift that is 2 v / to obtain the velocity of a moving target where v is the instantaneous velocity, is the carrier wavelength Therefore, the sampling rate should be fast to guarantee the number of samples is enough at the highest speed moment of the movement Otherwise, it will render a frequency shift that is not accurate and a reconstructed movement pattern with large distortion to the real one. I f we assume the vibration pattern to be x(t) = m si n( t ) m =5 mm, f =10 Hz, the carrier wavelength of the 35.6 GHz system is approximately 8.4 mm T aking the derivative of x ( t ) renders the velocity v ( t ) equal ing to m cos ( t ). Hence, the maximum Doppler frequency shift f dmax happen ing at the fastest speed equals to m f / In order to avoid distortion, the sampling rate should be at least twice of f dmax ( m f / ) which is around 1 50 Hz according to the Nyquist sampling theory It can be expected that if the vibration is fast, the microwave radar requires high s ampling rate ADC and DSP which will increase the cost significantly. T herefore, microwave Doppler radar that based on traditional method of detecting instantaneous Dopple r frequency shift is not suitable to work as vibrom e ter due to its limitation in measuring high speed vibration
20 On the other hand instead of directly measuring the instantaneous Doppler frequency shift, the proposed RF vibrom e ter is based on non linear D oppler phase modulation effect that uses the harmonic amplitude ratios from the fixed baseband spectrum It only requires a sampling rate that is higher than twice of the highest order harmonic that is used to take the amplitude ratio. Therefore, for the assumed scenario the fundamental tone of 10 Hz and the 2 nd order harmonic 20 Hz is what we need to obtain the vibration amplitude. Thus, a sampling rate of 40 Hz is enough, which is much less than the required 1 50 Hz sampling rate of t he detection method in [ 2 3 ]. Moreover since the sampling rate is not related to the movement amplitude, it would always remain the same no matter how large the amplitude is. Based on above analysis, the pr opos ed detection method that based on nonlinear ph ase modulation effect would be favorable in measuring high speed strong vibration without the need of expensive high sampling rate ADC. Hence it can potentially be used as an RF vibrometer at a lower cost compared to the microwave Doppler radar in [ 2 3 ]. 2.1 RF Vibrometer Prototype 2.1 .1 System Architecture and Detection Theory The first RF vibrometer prototype is reported in [ 1 5 ], its block diagram is shown in Figure 2 1. Fig ure 2 1. Block diagram and experiment set up of the RF vibrometer prototype.
21 The LO source is used as the transmitting signal working at 40 GHz and also the reference signal for down conversion in order to utilize range correlation effect that can greatly reduce phase noise [ 2 8 ] The transmitting power is 50uW, and the moving target is placed 1.65 m away from the antenna. The receiving signal is down converted into a single channel baseband signal that can be expressed as: (2 1) w here x(t) represents the displacement of the moving target, is the carrier wavelength, is the total residual phase determined by the distance to the moving target d 0 and the reflection at the surface. The vibration in [ 1 5 ] is assumed to be When the movement amplitude m is much smaller than the carrier wavelength a linear approximation can be applied . However, when the carrier frequency is high such that the movement amplitude is comparable to the short wavelength, a rigorous spectru m analysis based on Fourier series transformation [2 7 ] should be applied. T he baseband signal can then be written as: (2 2) where J n (x) is the n th order Bessel function of first kind. It can be seen from (2 2) that the phase modulated baseband signal is decomposed into a series of harmonics whose frequency is n times the vibration fundamental frequency. Using the relation between the even order and odd order Bessel functions as: (2 3)
22 The baseband signal represented in (2 2) can be further transformed to be: (2 4) (2 4) shows that the relative strength between any two even order (or two odd order) harmonics is a function of the vibration amplitude m For example: (2 5) where H n is the amplitude of the n th harmonic. It can be seen from (2 5) that the residual phase is cancelled by taking the a mplitude ratio Thus, the vibration amplitude m can be extracted from the amplitude ratios between any two even order harmonics or any two odd order harmonics. 2.1 .2 Limitation of Detection Theory It is known that the vibration pattern can be more complex than being a single sine wave pattern It can be non sinusoidal pattern such as triangular wave or square wave that includes not only the funda mental frequency component but also its harmonics. The detection method of the vibrometer pro totype is not feasible anymore in those cases. For example, i f the same detection method is used to detect a vibration that includes the fundamental frequency component and its second harmonic as x ( t ) = m 1 sin ( ) + m 2 sin (2 ), where m 1 and m 2 represent the amplitudes of the fundamental tone and its second harmonic, respectively. Using the same derivation method, the amplitude ratio between H 2 and H 4 is:
23 (2 6 ) I t can be seen from (2 6 ) that at each even order harmonic, both cos and sin terms exist simultaneously. Therefore, the residual phase cannot be cancelled by taking the amplitude ratio between harmonics belong to the same even or odd order group as shown in ( 2 5 ). More advanced detection technique that can be used for general cases is needed. 2 2 RF Vibrometer Using Multiple Harmonic Pairs 2.2 .1 System Architecture and Detection Theory The RF vibrometer prototype cannot measure vibration patterns that include multiple frequency components because it has only a single channel baseband signal, which cannot cancel the residual phase. Quadrature system architecture and complex signal demodulation technique makes it possible to use Doppler radar measure vibration s of more complex patterns, such as non sinusoidal periodic m ovement. The block diagram of the improved radar system is plotted in Figure 2 2 Figure 2 2 Block diagram of the RF vibrometer using multiple harmonic pairs
24 Compared to the prototype architecture, the original 5.8 GHz carrier is up converted to 27.6 GHz s ince higher carrier frequency will make the nonlinear Doppler phase modulation effect more evident and increase the detection accuracy of measuring small movement amplitudes [ 2 9 ] A parallel coupling microstrip bandpass filters with the center frequ ency of 27.6 GHz and stopband attenuation of 20 dB is manufactured [ 30 ]. In addition, instead of using a regular mixer to down convert the received signal into a single channel, a quadrature mixer is used here instead. The expression of a typical non sinu soidal vibration pattern can be written as: (2 7) where m n represents the amplitude of each frequency component. f 1 f 2 f N denote the frequency of each in Hz and it is assumed that they are in ascending order and are arbitrary positive numbers. N indicates the number of the frequency components of the vibration. For the vibration pattern represented in ( 2 7 ), u sing complex signal demodulation technique [ 31 ] [ 32 ] the combined complex baseband signal of the I / Q channels can be written as: ( 2 8 ) where A indicates the amplitude of the signal. Since has a constant envelope of unity, the effect of on signal amplitude is thus eliminated In ( 2 8 ), w hen the term f 1 k + f 2 l f N p in the exponent equals to x it denotes the frequency of the harmonic is x Hz and its strength can be represented as:
25 ( 2 9 ) with the constraint of f 1 k + f 2 l f N p =x It can be figured out that x is an integer multiple of the largest common divisor of all the frequency components of the vibration. (2 9) shows that H x is a function of the amplitudes of N tones composing the movement. Therefore, by measuring the amplitude ratio of N pairs of harmoni cs in the baseband spectrum the amplitude of each frequency component of the vibration can be obtained by solving N equations involving N variables. The frequencies of all the components co mprising the vibration can be i dentified from the baseband spectr um directly. Although there will be harmonics other than the frequency components of the vibration itself due to nonlinear phase modulation effect, as long as the carrier wavelength is much larger (e.g. about 10 times) compared to the vibration amplitude, the nonlinear effect will be weak. The amplitudes of those harmonics will be smaller than those belonging to the vibration itself. Thus, if the vibration contains N frequency components, the frequency of each can be figured out by indentifying the stronges t N harmonics in the baseband spectrum. With the information of the amplitude and frequency of each, the originally unknown vibration pattern can be recovered. 2.2 .2 Experiment Verification The 27.6 GHz vibrometer i s tested in lab environment. A horn antenna with 20 dB gain is used to increase the directivity. The power measured at the antenna input is 20 dBm. With the 3 dB beamwidth of 17.5 o the estimated beam spot size of the antenna at
26 1 m away is about 0.074 m 2 The moving target is attached to a precision linear actuator controlled by a laptop to produce a desired non sinusoidal vibration pattern Limited by the maximum velocity and velocity change rate of the actuator, an ideal non sinusoidal vibration with sh arp transitions such as triangular wave or square wave cannot be generated. Nevertheless, the first three harmonics of a triangular waveform already contain more than 95% of the waveform energy. Thus, in our experiment, a vibration containing three frequen cy compon ent s (unit: mm) shown as ( 2 10 ) i s generated to approximate an ideal triangular wave movement pattern. ( 2 10 ) In the experiment, measurements are conducted from the detection dis tance of 0.5 m to 1.5 m, with an increment of 0.1 m. At each location, the measurement is repeated 10 times. A B Figure 2 3 Time domain and frequency domain baseband signal. A) Measured time domain baseband I/Q signals B) N ormalized spectrum of combined complex baseband signals at 1.5 m.
27 Table 2 1 Measurement results (WCC: Waveform correlation coefficient) Amplitude m 1 (mm) m 2 (mm) m 3 (mm) WCC Worst case 2.61 0.31 0.03 0.9996 Best case 2.54 0.28 0.1 1 Average 2.56 0.31 0.08 0.9999 Reference 2.5 0.277 0.1 1 A B Figure 2 4 Reconstructed movement pattern and residual error. A) Overlap of reconstructed movement patterns using the worst case, best case and average measurement results, with the programmed waveform as reference B) Residual error of each reconstr ucted movement pattern. Figure 2 3 shows the measured time domain and frequency domain baseband signals at the distance of 1.5 m respectively. As described in previous section since
28 the vibration consists of three frequency components three harmonic amplitude ratios are required to build equations to solve the three unknown amplitudes of the vibration In the experiment, H 1 / H 2 H 1 / H 3 H 1 / H 4 are used. Other harmonic amplitude ratios can also be used as long as the strengths of the chosen harmonics are strong enough to be clearly read from the baseband spectrum. Table 2 1 lists the calculated amplitude value of each frequency component consisting of the vibration using the worst case, best case, and average measurement results as compared to the progra mmed value (reference). 2.2 .3 RF Vibrometer vs. Laser Displacement Sensor Fig ure 2 5. Measurement setup of LDS and vibrometer : A) Laser displacement sensor LK G32 B ) RF vibrometer. The a dvan tages of the proposed RF vibrometer would appear through comparison with a laser displacement sensor (L DS) LK G32 manufactured by Keyence Co. The LDS LK G32 achieves its high accuracy by sacrificing the de tection range, which is only 25 mm to 35 mm. Based on triangulation mechanism [ 11 ], those movements falling out of the detection range cannot generate bea m spots small enough for accurate detection. A B 3 0 mm 1.5 m
29 O n the other hand, the RF vibrometer can have a much larger detection range from 0.5 m to 1.5 m. When the moving target is closer than 0.5 m, the baseband signal becomes too large and saturates the baseband amplifier. If the target is more than 1.5 m away, the signal to noise ratio of the receiving signal drops below 10 dB which is required to achi eve a reconstructed movement pattern with WCC better than 0.9995. It is expected that a larger detection range can be achieved with baseband circuit of larger dynamic range and/or higher transmitted power. Figure 2 5 shows the measurement setup of the two sensors. In addition to the advantage of longer detection range the RF vibrometer can also be easily integrated at relatively low cost. It remains workable in low visibility environment and can potentially measure vibrations behind a wall 2 3 RF Vibromet er Using Multiple Carrier Frequencies The vibrometer presented in section 2. 2 is using the detection technique that measures the amplitude ratio of multiple harmonic pairs at a fixed carrier frequency. Another alternative detection approach is measuring the amplitude ratio of a fixed harmonic pair under different carrier frequencie s. It has been noticed that the strength of each harmonic in the baseband spectrum will change as the carrier frequency varies. The amplitude ratio of a fixed harmonic pair will not remain the same under different carrier frequencies. Based on ( 2 9 ), we k now that it is the variation of wavelength at each carrier frequency that makes the harmonic amplitude ratio changes. Therefore, a RF vibrometer is implemented as a tunable carrier frequency Doppler radar sensor to verify this proposed alternative detectio n theory. In this section the detection theory of the multiple carrier frequency vibrometer is presented. It is verified through both simulation and experiment The accuracy of the
30 recovered vibration pattern using the non contact RF vibrometer rivals other contact measurement instruments, such as LVDT and accelerometer. 2 3 .1 Verification of Detection Theory in Simulation The detection theory of the proposed alternative vibrometer is that if the vibration contains N frequency components, by me asuring the amplitude ratio of a specific harmonic pair under N different carrier frequencies, the N unknown amplitude of each frequency component of the vibration can be obtained. The detection theory is verified through simulation first before any exper iment is conducted. In simulation, the vibration pattern is assumed to be (unit: mm): x ( t t t t ) ( 2 11 ) The frequency and amplitude of each sine wave component are chosen arbitrarily to make a general case. Since the vibration contains three frequency components, three carrier frequencies at 5 GHz, 6 GHz, 7 GHz are used to solve the unknown amplitudes of them Figure 2 6 shows the radar detected baseband spectrum under the three carrier frequenc ies. As can be seen that besides the three frequency components of the vibration itself (0.6 Hz, 1 Hz, 1.6 Hz), there are also other intermodulation frequency components due to nonlinear Doppler phase modulation effect. All of the frequencies are integer m ultiples of 0.2 Hz, which is the largest common divisor of 0.6 Hz, 1 Hz and 1.6 Hz as predicted before. The relative strength between harmonics also varies with the carrier frequency. We measured the ratio between H 0.4 from the low frequency range and H 2.2 that belongs to the high frequency range under the three carrier frequencies. 1 2 and 3 are the carrier wavelengths correspond to 5 GHz, 6 GHz and 7 GHz, respectively. Based on ( 2
31 9 ), let u m 1 / 1 v m 2 / 1 w m 3 / 1 a = 1 / 2 b= 1 3 then the three equations are built using the measured values. 5 GHz: ( 2 11 ) 6 GHz: ( 2 1 2) 7 GHz: ( 2 1 3) The root of the equations are m 1 =2.94, m 2 =2.59, m 3 =0.96. All of them have less than 4% error compared to t he real value of m 1 =3, m 2 =2.5, m 3 =1. The small amount of deviation is tolerable considering the existence of some inherent numeric error of the calculation. Hence, the proposed detection theory has been proved feasible. Fig ure 2 6 Radar detected baseband spectrum under carrier frequencies of 5 GHz, 6 GHz and 7 GHz. 2.3 .2 Experiment The block diagram of the RF vibrometer is shown in Figure 2 7 A frequency synthesizer ADF4108 and external VCO with 4 8.5 GHz tuning range form a PLL to generate diffe rent carrier frequencies  [3 8 ] The output power of the PLL is about 8 dBm, through two stage amplifiers and a power splitter, the transmit power at the
32 antenna connector is around 0 dBm. The gain of the receiving chain is 35 dB [3 9 ] A broadband patch antenna with the bandwidth from 3 GHz to 9 GHz is fabricated by utilizing the partial ground technique [ 40 ]. The quadrature baseband signal s are sent to a laptop through a DAQ (Data Acquisition Board) for real time signal processing. Th e experiment setup is shown in Figure 2 8 ( A ). The antenna is placed at 0.4 m above the vibrating target. The vibration is driven by a long stroke shaker from APS Dynamics. A Lab V iew program is used to generate the excitation voltage of the shaker. An LVDT and an accelerometer are attached on the vibrating target as shown in Figure 2 8 ( B ). The real time data from them are sent back to the computer for monitoring. Since the LVDT can accurately measure the vibration displacement directly, it is used to provi de a reference of the actual movement pattern. In the experiment, a vibration containing three sine wave components of different frequencies is generated. Thus, three carrier frequencies are needed to recover the original movement pattern. The output volt age from the charge pump of the frequency synthesizer is approximately 0 4.5 V, which corresponds to 5 7 GHz of the VCO, and 5.5 GHz, 6 GHz, 6.5 GHz are used. Fig ure 2 7 Block diagram of the wavelength division sensing RF vibrometer.
33 A B Fig ure 2 8 Measurement setup of shaker. A ) Setup of the experiment B ) LVDT and accelerometer attached on the moving target. Figure 2 9 shows the measured baseband quadrature signal and the normalized spectrum of the combined complex baseband output at 6 GHz, respec tively. The monitored LVDT waveform shows that the displacement of the vibration is about 5 mm. While the carrier wavelengths in our case are around 50 mm, which are much larger than the vibration amplitude. Hence, as illustrated in section 2 3 the streng th of the harmonics generated due to the nonlinear phase modulation effect will be weaker than that of the frequency components of the vibration itself. As can be seen from Figure 2 9 ( B ), the strongest three harmonics are located at 4 Hz, 6 Hz and 8 Hz, t he three frequency components of the vibration. In consideration of choosing the harmonic pair for solving the amplitude of each frequency component of the vibration, it is suggested to use harmonics involving both low frequency and high frequency componen ts in the baseband spectrum. Using two harmonics that are both located at low frequency or at high frequency range may not
34 contain enough information about the shape of the whole spectrum and may increase error in calculation. Thus, in the experiment, the harmonic pair H 2 and H 10 is chosen. A B Fig ure 2 9 Time domain and frequency domain baseband signal. A ) Baseband I/Q signals at 6GHz B ) Normalized baseband spectrum at 6GHz. At each carrier frequency, 10 measurements are conducted. The average value of measured H 2 /H 10 at 5.5 GHz, 6 GHz and 6.5 GHz are 1.84, 1.89 and 1.95, respectively. Using the equations in section 2 4 1 2 and 3 are the carrier wavelengths corresponding to 5.5 GHz, 6 GHz and 6.5 GHz, respectively. m 1 m 2 and m 3 represent the am plitudes of the frequency components at 4 Hz, 6 Hz and 8 Hz, and u m 1 / 1 v m 2 / 1 w m 3 / 1 a = 1 / 2 b= 1 3 Three equations are constructed as: 5.5 GHz: ( 2 14 ) 6 GHz: ( 2 15 ) 6.5 GHz: ( 2 16 )
35 The solutions are m 1 =2.329, m 2 =1.921, m 3 =0.855 (unit: mm). In addition, f 1 =4 Hz, f 2 =6 Hz, f 3 =8 Hz. Therefore, the recovered vibration pattern using the RF vibrometer has the expression as: x ( t t t t ) ( 2 1 7) 2.3 .3 Performance Analysis As presented earlier, accelerometer is the conventional instrument used to measure vibrations. In our experiment, an accelerometer is also used. Since the accelerometer measures the acceleration of the vibration, we need to integrate the acceleration waveform twice to recover the displacement of the vibration. It is interesting to compare the performance of the proposed RF vibrometer and accelerometer by co mparing their recovered vibration patterns using LVDT output as a reference. Figure 2 10 shows the acceleration signal measured by the accelerometer. Fig ure 2 10 Acceleration signal from accelerometer. Figure 2 11 shows the comparison of the three waveforms: one is the recovered vibration pattern using RF vibrometer, which is represented in ( 2 1 7 ), and the other two are the recovered displacement by double integrating the acceleration signal and the reference signa l coming from LVDT. As can be seen, the recovered vibration pattern using RF vibrometer agrees well with the reference signal. The correlation coefficient between the waveform recovered from RF vibrometer and the accelerometer relative to
36 the reference is 0.9987 and 0.9924, respectively. Hence the RF vibrometer can achieve comparable accuracy as the accelerometer. In order to further analyze the accuracy of the detection method using RF vibrometer, it is useful to know the actual amplitude of each frequency component of the vibration and compare it to the calculated ones shown in ( 2 17 ). The curve fitting toolbox of Mat L ab is used to obtain the actual amplitude of each frequency component of the vibration by fitting the LVDT signal. The result is m 1 =2.54, m 2 =1.896, m 3 =0.97 (unit: mm) The measured amplitudes using RF vibrometer are m 1 =2.329, m 2 =1.921, m 3 =0.855. They have around 10% error compared to the actual values. Fig ure 2 11 Comparison of recovered vibration pattern using wavelength division sensing RF vibrometer accelerometer and the reference from LVDT. It has been proved that the amplitude or phase mismatch between the I/Q channels will cause deviation of the amplitude ratio between harmonics in the baseband, and thus result in error of the final calculated amplitude of each frequency component of the vibration [ 20 ]. The I/Q signal with amplitude and phase mismatch can be written as:
37 ( 2 1 8 ) where x vibration displacement. 20log(1/1 ) is the amplitude imbalance in dB scale, represents the phase imbalance. The data sheet of the quadrature mixer shows that it can have up to 1dB amplitude mismatch and 10 phase mismatch. Since we are using H 2 /H 10 to calculate the amplitude of each frequency component of the vibration, it is important to know how much deviation of the ratio will be introduced by the I/Q imbalance. Table 2 2 I/Q Mismatch Effect on H 2 /H 10 and m 1 m 2 and m 3 20log(1/1 ) 0.3dB 0.5dB 1dB 0dB 5 10 5 10 5 10 0 H 2 /H 10 @5.5G 1.87 1.87 1.83 1.84 1.76 1.76 1.93 H 2 /H 10 @6G 1.93 1.93 1.89 1.89 1.80 1.81 1.99 H 2 /H 10 @6.5G 1.99 2.0 1.95 1.95 1.85 1.86 2.06 m 1 (mm) 2.44 2.44 2.33 2.33 2.1 2.1 2.54 m 2 (mm) 1.9 1.9 1.92 1.92 1.76 1.77 1.9 m 3 (mm) 0.91 0.91 0.85 0.86 0.75 0.76 0.97 Table 2 2 shows H 2 /H 10 and the calculated amplitude of each frequency component under different I/Q mismatch scenarios. The last column provides the ideal values when there is no I/Q mismatch. It can be found that amplitude imbalance will have more evident effect on the harmonic amplitude ratio than phase imbalance. Comparing to the measured value of H 2 /H 10 in experiment, we can notice that 0.5 dB amplitude mismatch and 5 phase mismatch will cause the ratio to deviate from the ideal value and result in the 10% error of the calculated amplitude compared to the ideal values. The detection accuracy can be further improved by either introducing phase shifter and
38 attenuator/gain control to pre compensate the I/Q imbalance or by carrying out detection at the optimal d etection distance to alleviate the effect of I/Q mismatch. 2 .4 Summary The develop e ment of RF vibrometer from the prototype that can only measure purely sinusoidal vibration to the improved ones that can measure complex vibration that includes multiple fre quency components are presented. The use of quadrature system architecture and complex signal demodulation technique eliminates the residual phase problem from essentially which also brings more thorough spectral analysis theory that makes it possible for the RF vibrometer to be capable of measuring complex vibration pattern s One detection technique is using multiple harmonic amplitude ratios under a certain carrier frequency to calculate the amplitude of each frequency components consisting of the vibrat ion. The other is using a tunable carrier frequency radar sensor that measures the variation of amplitude ratio of a fixed harmonic pair under multiple carrier frequencies. Both of these two methods are verified through experiment and proved to be able to obtain accurate reconstructed vibration pattern using the measurement results. The performance of the proposed RF vibrometers is also compared to laser displacement sensor (LDS), accelerometer and LVDT. Besides the capability of achieving comparable detec tion accuracy, t he advantages of long detection range, capability of working in low visibility environment and low cost of integration makes RF vibrometer a potential alternative in application of non contact detection of vibrations.
39 CHAPTER 3 I/Q MISMATCH EFFECT ON MEASUREMENT OF VIBRATION USING RF VIBROMETER It has been proved that using quadrature system architecture and complex signal demodulation technique can eliminate the residual phase problem that causes null detection point in measurement, thus improving the detection accuracy. Although the residual phase problem is no longer a concern when the I/Q signals are perfectly matched it can still introduce error when there is mismatch between the I and Q signals. During the measurement of vibra tion using the RF vibrometer of quadrature architecture it i s found that the amplitude or phase imbalance between the in phase and quadrature channels at the output of l ocal oscillator (LO) ha s evident impact on the baseband spectrum. In addition, it i s a lso noticed that the amplitude ratio of measured harmonic s under certain I/Q imbalance is different at various locations. Since the residual phase is dependent on the nominal distance at each location, it leads to t he exploration of the relation between th e residual phase and the measured amplitude ratio of harmonics under specific I/Q mismatch. Through simulation, the following characteristics are found: first, the residual phase causes periodic variation in the error of measured ratios with the period of Second, the optimal residual phase to minimize the deviation of ratios caused by phase mismatch is in the vicinity of k /2 Third, the optimal residual phase to minimize the deviation caused by amplitude mismatch equals to (2 k +1) / 4. All of these characteristics have been verified by experimental results. The experimental results of detected vibration amplitudes under different I/Q mismatches have also been presented.
40 3 .1 Theory and Simulation The vibrati ng target is assumed to be vibrating at a certain frequency such as x ( t )= msin ( ). The combined complex baseband signal can be represented as: ( 3 1) where A represents the signal amplitude, is the carrier wavelength, is the total residual phase Note that the term can be separated as an independent term with constant envelope of unity Therefore, the effect of on amplitudes of harmonics can be eliminated when I/Q channels are perfectly matched In simulation, the amplitude and frequency of the vibration is set to be 2 mm and 1 Hz, respectively. equals to 51.72 mm for the 5.8 GHz radar system, which is used in the experiment. The amplitude ratio between the fundamental frequency component H 1 and the second harmonic H 2 is 8.11 measured from the simulated baseband spectrum. The calculated vibration amplitude using the ratio value 8.11 is 2 mm. Therefore, the ideal ratio that can render accurate vibration amplitude should be 8.11. However, when there is I / Q mismatch [ 41 ] the effect of residual phase can no longer be eliminated. This causes the deviation of the relative strength of harmonics from its ideal value s thus degrading the measurement accuracy. .1 .1 Phase Mismatch Effect In this section, a phase imbalance of is introduced between the I and Q channel s and the baseband signal can be represented as:
41 ( 3 2) T he expressions of the amplitude s of the fundamental and the second harmonic frequency components can be derived as shown below: ( 3 3) ( 3 4) Therefore, the absolute value of H 1 /H 2 ratio will be : ( 3 5) As can be seen, the ratio is now a function of residual phase It can be seen from Figure 3 1 results in larger deviation. Each curve has crossing points with the line of idea l ratio value, which indicate a series of optimal residual phases corresponding to some specific detection distances that can eliminate the error due to phase mismatch. It can be seen that those points are located around /2. It is also noted that when th e phase mismatch becomes larger, the crossing points would shift to the left side, which means the optimal residual phases will become k ( /2 ), where is a small correction term corresponding to the phase shift. The following is a more detailed analysis.
42 Fig ure 3 1 The variation of H 1 /H 2 vs. residual phase under different phase mismatch degrees of 5 o 10 o 15 o 20 o with the ideal value as reference. 1) When = (2 k ) /2, 2) When = (2 k+ 1) 2, Therefore, when the phase mismatch either the term | | or the term | | will be very close to 1, thus eliminating the error introduced by phase mismatch. By letting the exact optimal residual phase can be found to be opt = Through calculation, it shows that when
43 increases from 0 to 20 opt decreases from 180 to 170 thus verifying the shifting of the curves to the left shown in Figure 3 1 3 .1 .2 Amplitude Mismatch Effect In this section, an amplitude difference is introduced to represent the amplitude imbalance. The combined complex baseband signal can be represented as: ( 3 6) The absolute value of H 1 /H 2 can be represented as: ( 3 7) Figure 3 2 shows the variation of |H 1 /H 2 | vs. residual phase under different amplitude mismatches. It can be seen that the residual phase effect on the ratio also repeats itself every period as the phase mismatch scenario. However, u nlike phase mismatch, a ll the curves of different amplitude mismatch cross the lin e with the value of ideal ratio at the same place s thus having the same optimal residual phase s of (2 k +1) / 4. Fig ure 3 2 The variation of H 1 /H 2 vs. residual phase under different amplitude mismatch of 1 dB, 3 dB, 5 dB, with the ideal value as reference.
44 The optimal residual phase can be figured out by letting the term and opt turns out to be equal to (2 k +1) /4, regardless of Figure 3 2 3 .2 Experiment Verification Fig ure 3 3. Block diagram of the experimental setup. The block diagram of the experiment al setup that is used to verify the theory and simulation is depicted in Figure 3 3 An actuator is controlled by a laptop to produce a vibr ation with amplitude of 2 mm and frequency of 0.5 Hz. A signal generator is used to generate the transmitting signal and the LO reference signal. The LO reference signal was divided into in phase and quadrature phase channels using a 90 power divider. Two identical mixers are used to down convert the I/Q signals to baseband. Since the I/Q mismatch comes from the LO source, not the input RF signals, a 0 power splitter is inserted in the receiving chain to generate two channel signals of the same phase and amplitude to guarantee that the two input RF signal s are matched A variable phase
45 shifter and an attenuator are introduced in one of the LO paths to produce specific amount of amplitude and phase imbalance. The output I/Q signals are fe d into the baseband circuit for further amplification and sent to another laptop through the DAQ for real time signal processing. The residual phase =4 0 / + 0 [ 28 ], where d 0 is the nominal distance from the antenna to the target, and 0 is a constant ph ase shift in the electronic circuit. As a result, the residual phase will change linearly with d 0 Hence, in order to observe the residual phase effect for one period, the variable term 4 0 / Therefore, the total distance variation should be d 0 = into 13 segments of 1 mm each during the measurement. 3 .2 .1 Verification of Amplitude Mismatch Effect Two measurements of different amplitude mismatches are conducted. One has a 2 dB amplitude mismatch and the other has 6 dB mismatch. After inserting the specific attenuator, the variable phase shifter i s adjusted to achieve a 90 phase difference between t he I and Q channels to ensure there is no phase mismatch. Since 0 is unknown, the exact residual phase can not be decided. In experiment, the starting point of measurement is chosen by adjusting the target to a place where the measured H 1 /H 2 has a compar able deviation as that in Figure 3 2 then the two measurements are both started from that place. The results are shown in Figure 3 4 It can be seen that generally, the 6 dB amplitude mismatch causes larger deviation than the 2 dB amplitude mismatch does, and both of these two curves cross the ideal value around /4 and 3 /4, thus verifying the optimal residual phases should be (2 k +1) /4 to minimize the deviation caused by amplitude mismatch.
46 Figure 3 4 Measured H1/H2 vs. Residual phase (0~ ) under the amplitude mismatch of 2 dB and 6 dB. 3 .2 .2 Verification of Phase Mismatch Effect Figure 3 5. Measured H 1 /H 2 o and 20 o Two measurements are conducted under the phase imbalance of 15 and 20 which are estimated from the measurement results, respectively. It can be seen from the results shown in Figure 3 5 that, in general, both of the curves cross the ideal line at k deviation caused by phase mismatch. In addition, the curve with 20 phase mismatch crosses the line of ideal ratio value ahead of the curve with 10 as predicted.
47 3 .3 I/Q Mismatch Effect on Measured Vibration Amplitude Fig ure 3 6 Detected and simulate d displacement of vibrations vs. r esidual phase under different amplitude imbalance of 2 dB, 6 dB with 2 mm reference Figure 3 7 Detected and simulated displacement of vibrations vs. residual phase under different phase imbalance of 15 o 20 o with 2 mm reference. From the measured and simulated diplacement amplitude values under certain amplitude and phase mismatches shown in Figure 3 6 and Figure 3 7, it can be seen that the detected results agrees with the simulated value generally.
48 There are two r easons that cause the deviation appeared in the end of the phase mismatch. First, the phase mismatch may not exactly equal to 15 and 20 these values are estimated from the measured waveform displayed in the oscilloscope. Second, without precision instru ment to measure the distance of 1 mm of each step, the error accumulated in distance measurement translated to the error accumulated in residual phase. Therefore, the difference between the actual and the theoretical residual phase values will become large r as the distance increases, thus explaining the deviation of the measurement results from the theoretical value. Nevertheless, the results indicate that I/Q mismatch effect can be minimized at certain residual phase values. It should be noted that the amp litude and phase mismatch used in the simulation and experiment of this paper is much greater than what a typical quadrature mixer at this frequency can achieve. Normally, the imbalance of an actual mixer is within 0.2 dB amplitude mismatch and 4 phase mi smatch [ 3 7 ]. The estimated maximum error of detected movement amplitude by using such mixer would be around 10%. 3 .4 Summary The optimal residual phase to minimize the error caused by the I/Q mismatch of a quadrature RF vibrometer in detect ing the displacement amplitude of vibration has been studied through simulation s and experiment It can be used as a I/Q mismatch calibration technique for Doppler radar [4 2 ]. Since the residual phase is determined by the detection distance and circuit characteris tics, by either adjusting the detection locations or tuning the phase delay in the circuit at a fixed location can achieve the optimal residual phase. Based on this approach, the measurement error using typical quadrature transceivers can be further reduce d.
49 CHAPTER 4 DETECTION RANGE AND ACCURACY OF RF VIBROMETER It has been known that RF vibrometer uses the amplitude ratio between harmonics in the baseband spectrum to obtain the vibration pattern of the target. Thus, its detection accuracy is dependent on the accuracy of the harmonic amplitude ratio. It is predicted in [ 1 6 ] that the sensitivity can be improved by increasing the ratio of m / ( m is the movement amplitude and is the wavelength of carrier frequency) as it improves the accuracy. The higher the ratio, the more sensitive the radar will be. If the movement amplitude m is small and the carrier frequency is low, the sensitivity is low and the nonlinear Doppler phase m odulation effect is not strong enough to generate evident harmonics for detection. Thus, the measurement accuracy would be degraded. In this chapter, we study the accuracy dependence on the carrier frequency. In some circumstances, such as earthquake sear ching and rescuing [4 3 ] the main concern is detecting the existence of a target, not the exact characteristics of it. I t is worthwhile to investigate how far away the RF vibrometer can detect the existence of a vibration of certain magnitude without conce rns on the accuracy. Hence the maximum distance that the RF vibrometer can detect the existence of a certain vibration is also found out through experiment and analyzed theoretically. 4 1 Experiment and Analysis 4 .1 .1 Measurement Sensitivity Dependence o n Carrier Frequency In order to verify that the sensitivity can be improved by increasing carrier frequency, a 5.8 GHz carrier is up converted to 27.6 GHz. The vibrating target is controlled through program to vibrate at 1Hz with variable amplitude as x(t) =msin(2 t). Typical baseband spectrum for such vibration is depicted in Figure 4 1.
50 Figure 4 1 Baseband spectrum of a single tone vibration pattern. The amplitude ratio between the fundamental frequency component at 1 Hz and the harmonic at 2 Hz represented as ( 4 1) is used to solve the displacement amplitude. ( 4 1) In the experiment, the moving target is placed at 1 m away from the horn antenna. The amplitude of the movement is decreased with the step size of 0.1 mm. At each vibration amplitude, ten measurements are conducted. Table 4 1 lists the measured vibration amplitude for the cases of 0.3 mm, 0.4 mm and 0.5 mm. T he measurement result that has less than 5% error is regarded to be accurate in our case It is found that the 27.6 GHz vibrometer can accurately measure the displacement amplitude as small as 0.5 mm. The maximum error of individual measurement result is 6% (0.53 mm vs. 0.5 mm) and the averaged result using 10 individual results is 0.51 mm, which has only 2% error. When the programmed amplitude decreased to 0.4 mm and 0.3 mm, the measurement accuracy degraded, and the average measurement result is 0.44 mm and 0.33 mm respectively, both have 10% error.
51 Table 4 1 Measurement results vs. programmed value Programmed Measured 0.3 (mm) 0.4 (mm) 0.5 (mm) 1 0.38 0.37 0.48 2 0.31 0.47 0.51 3 0.32 0.45 0.5 4 0.36 0.46 0.53 5 0.32 0.45 0.5 6 0.3 0.46 0.51 7 0.32 0.44 0.53 8 0.34 0.42 0.48 9 0.3 0.45 0.53 10 0.33 0.44 0.52 Averaged value 0.33 0.44 0.51 Fig ure 4 2 Harmonic amplitude ratio H 1 /H 2 vs. movement amplitude. Figure 4 2 shows the harmonic amplitude ratio H 1 /H 2 vs. movement amplitude. It can be seen that as the movement amplitude decreases, H 1 /H 2 increases dramatically, which means the second harmonic becomes much smaller as the movement amplitude decreases. When signal becomes weaker, it is more vulnerable to n oise, thus introducing bigger error. This explains why the accuracy is degraded when the vibration amplitude becomes smaller than 0.5 mm.
52 In order to verify that the 27.6 GHz vibromter has improved sensitivity compared to the 5.8 GHz counterpart the outp ut power of the two systems should be the same and the target should be located at the same distance away from the antenna with the same vibration pattern to ensure the measurement is taken under the same RF signal power, leaving the sensitivity only deter mined by the carrier frequency In experiment, the output power measured at the connector of the horn antenna of the 27.6 G Hz vibrometer is 20 dBm, and that measured at the patch antenna connector of the 5.8 G Hz sensor is 9 dBm This difference is offset by the gain of the two kinds of antennas. The horn antenna has the gain of 20 dB [4 4 ] and the gain of the patch antenna is 9 dB. Therefore, both of these two vibrometers have the equivalent output power of 0 dBm after the anten na. The minimum displacement amplitude that can be accurately measured by the 5.8 G Hz vibrometer is 2 mm, which is approximately 4 times of that of the 27.6 G Hz system. Therefore, it is verified that by increasing the carrier frequency, the measurement se nsitivity can be improved proportionally. In addition since the wavelength of the 27.6 GHz and 5.8 GHz radar is 10.87 mm and 51.7 mm respectively, it can be figured out that the measurement sensitivity of RF vibrometer is approximately 0.05 of the carrier wavelength. 4 .1 .2 Sensitivity Limited Detection Range vs. Vibration Amplitude In the experiment, the displacement amplitude of the vibration is increased from 0.2 mm to 0.5 mm with increment of 0.1 mm. At each amplitude, the moving target is moved far awa y from the sensor gradually. It is known that the fundamental frequency in the baseband spectrum indicates the vibration frequency. Therefore, as long as the fundamental frequency component can be identified from the baseband spectrum, the
53 vibrometer can s till detect the existence of the target. It will finally disappear when the target is too far away from the antenna that the reflected signal is too weak to be detected and the baseband spectrum is overwhelmed by noise. The location from where the fundamen tal frequency component begins to disappear is marked, and the distance from the antenna to that location is the detection range. The radar range equation shown in ( 4 2) indicates that usually, the received power declines as the fourth power of the range [4 5 ] ( 4 2) w here is the carrier wavelength, P t and P r is the transmitting and receiving power, G t and G r are the power gain of transmitting antenna and receiving antenna respectively. is the antenna cross section. However, in our case, the power of the reflected signal will not keep the same as the incident signal. There is a modulation gain due to the nonlinear Doppler phase modulation effect, which is not modeled in the radar range eq uation ( 4 2). The relation between the modulation gain G m and the vibration amplitude is thus need to be figured out. Since the amplitude of the modulated reflecting signal is mainly determined by the fundamental frequency component, which is proportional to J 1 [4 4 ] For the movement amplitude from 0.2 mm to 0.5 mm, the simulation shows that: ( 4 3) Thus, the power of the reflecting signal will increase in a square law relation with m as:
54 ( 4 4) Taking G m into account, the modified effective power of the received signal should be: ( 4 5) Thus, the detection range R has the following express ion: ( 4 6) For a given radar system with a specific sensitivity, P t P r G t and G r are all fixed values. Thus, a critical relation can be obtained. ( 4 7) Figure 4 3. Detection range vs. movement amplitude.
55 Figure 4 3 shows the measured detection range at each different vibration amplitude and the fitting result using the square root relation given in ( 4 7). It can be seen that the measured result agrees well with the theoretic relation. 4. 2 60 GHz IC Realization of RF Vibrometer It has been proved that by increasing the carrier frequency, we can detect smaller movement. The 27. 6 GHz radar can accurately detect the displacement as small as 0.5 mm. Since the heartbeat driven chest wall movement is usually on the scale of 0.1 mm, previous 5.8 GHz or Ka band radar has limited capability of detecting the accurate heartbeat rate due the relatively longer wavelength compared to the small value of heartbeat related chest wall movement. Therefore, a 60 GHz radar sensor is realized using UMC 90nm  The testing results show that it has much higher sensitivity and can detect heartbeat a ccurately while holding the breath. Figure 4 4. System b lock diag ram of the 60 GHz micro radar including flip chip packaging Figure 4 4 shows the block diagram of the 60 GHz IC RF vibrometer. The RF front end from the 64 GHz to 6 GHz has a total gain of 40 dB. Compared to the 6 GHz
56 quadrature radar that we previously used. The 60 GHz radar has another 20 dB loss due to the 10 times smaller wavelength (4 2) and also the antenna at 60 GHz usually has 10 dB less gain compared to the gain at 6 GHz, the total loss by using a 60 GHz provide 40 dB gain to compensate the lo ss. Figure 4 5. Layout of the whole 60 GHz transceiver Figure 4 6. Detected peak on the CSD spectrum for different vibration displacement at various distances Figure 4 5 shows the layout of the whole 60 GHz transceiver, lumped inductors of different shapes are modeled using HFSS. By using lumped inductors instead of
57 transmission line, we can achieve a compact layout of 2.3 cm* 0.96 cm. Figure 4 6 shows the measured peak on the baseband spectrum for different vibration displacements from 0 1mm at different distances (0.3 m, 0.6 m, 0.9 m, 1.2 m, 2.1 m). All of the values are normalized to the maximum value obtai ned at 0.3 m distance. It can be seen from Figure 4 6 that the 60 GHz radar can detect the existence of a small vibration that has a displacement less than 0.1 mm. At a closer location, the signal on the baseband spectrum would become stronger and can pote ntially be used for accurate measurement of small vibrations. Figure 4 7. Detected time domain I/Q signals and CSD baseband spectrum for vital sign detection Figure 4 7 shows the time domain and baseband spectrum of human vital sign detection. An accurat e heartbeat rate of 69 beats/Minute is detected by holding breath in order to avoid the interference caused by harmonics of respiration.
58 4 .3 Summary It is demonstrated that the minimum movement amplitude that can be accurately measured by a 5.8 GHz vibrometer can be improved to be in the sub millimeter range by increasing the carrier frequency to Ka band. It is also verified tha t the minimum value will decrease in proportion to the carrier frequency. The square root relation between the sensitivity l imited detection range and the movement magnitude also provides a guideline on the design of RF vibrometer for various applications. Finally, a 60 GHz RF vibrometer is also implemented using UMC 90nm. The preliminary testing results of the chip proves the potential advantage of using it to measure smaller mechanical vibrations that has displacement on the scale of 0.1 mm and also the capability of accurately detecting human vital signs.
59 CHAPTER 5 APPLICATION OF RF VIBROMETER IN VITAL SIGN DETECTION Since t he chest wall movement can be regarded as a vibration that is consisted of respiration and heartbeat signals, the RF vibrometer can also be used to detect it and extract the information of vital signs There have been reported non invasive systems for sens ing physiological movement and volume changing  : a double sideband Ka band detector has been implemented to be capable of measur ing the heartbeat and respiration rate s from four sides of a human body [ 4 7] [4 8 ] ; r adar s ensor s that can detect human vita l signs at 1m [4 9 ] and 2 m distance [5 0], respectively ; and l ong term overnight monitoring of vital signs has also been demonstrated [ 5 1 ]. Compact system modules have also been developed on the IC level. [ 52 ] [5 5 ]. The sensor module can achieve accurate monitoring results by placing it beneath a sleeping subject, since better detection accuracy has been observed when measuring from the back of the body [ 1 6 ]. The random body movement in one dimension [ 31 ] and two dimension [5 6 ] that c aused the degradation of detection accuracy has been solved by placing two antennas face to face on one side of human body or four antennas around the body, respectively T he introduced random phase error can be cancelled by comple x signal demodulation tec hnique However, all the different testing experiments that mentioned above are c onducted on adults. There has been a lack of experimental data to verify the effectiveness of using RF vibrometer to detect apnea or lack of respiratory effect which leads to the Sudden Infant Death Syndrome (SIDS) on infant subjects [5 7 ] While an adult test subject can be instructed to hold breath to mimic some symptoms, an infant cannot.
60 In this chapter, the verification of non contact vital sign monitoring using a high fid elity infant simulator (METI) [ 5 8 ] i s presented. T he vital signs o f the infant simulator can be varied by computer control to produce various changes in the heart rate and respiratory rate which mimic pathologic conditions. During the experiment, the infan t simulator i s programmed to behave in a baseline state and s everal abnormal states including bradypnea, tachy pnea bradycardia etc The heart rate, respiratory rate and associated tidal volume are change d from the baseline state in a systematic manner. The accuracy of using the non contact RF vibrometer to track the changes in vital si gns in normal and abnormal situations i s analyzed The experimental results show that the 5.8 GHz vibrometer can detect normal vital sign signals accurately and track the change in vital signs during abnormal conditions. However, when vital signs become weak and with a lot of background noise caused by walking and talking of people nearby, it will be hard for the vibrometer to detect the relatively weak vital sign signals f rom high level background noise, unless smaller carrier wavelength is used to improve the sensitivity. Other errors caused by the electronic circuits and signal processing can be eliminated or, at least reduced through the modification of circuits and furt her spectral analysis. 5 .1 System 5.1 .1 Vibrometer The block diagram of the 5.8 GHz vibrometer is shown in Figure 5 1. The 5.8 GHz signal is generated by a signal generator. It is then divided into two equal parts through a 3 dB power splitter. One half of the signal is transmitted out and the other half is sent the quadrature mixer in the receiving chain as the reference signal. When the transmitting signal hits the infant simulator, it is modulated by the chest wall move ment
61 of it. After being amplified, the received signal is down converted into two quadrature signals of I and Q. The baseband signal is further amplified by the baseband circuit and fed to the computer through a DAQ (Data Acquisition Board) for real time s ignal monitoring Figure 5 1. Block diagram of 5.8 GHz vibrometer The baseband signal, either I or Q channel can be expressed as: ( 5 1) where is the carrier wavelength x ( t ) is the infant s chest wall displacement due to the respiration and heartbeat, m r and f r are the amplitude and frequency of respiration, m h and f h are those of heartbeat, ( t ) is the total residual phase that can be eliminated through complex demodulation. It should also be noted that there are two AC coupling capacitances between the mixer and baseband circuit to block the DC components. 5.1 .2 Infant Simulator The infant simulator manufactured by METI is developed for training medical professionals to experience realistic clinical conditions. It provid es an appropriate
62 representation of a three to six month old infant The system uses two umbilicals for control. O ne is fluidic/pneumatic umbilical, the other is electrical umbilical. These two umbilicals are attached to the Power/Communications Unit ( PCU ) interface panel to generate the automatic and realistic physiological response of an infant whose vital signs are controlled by software. The specific software is installed on a Macintosh workstation. 5 .2 Experiment and Analysis The experiment i s carri ed out in the N eonatal I ntensive C are U nit (NICU) at Shands H ospital at the University of Florida. Figure 5 2 shows the setup of the experiment. The vibrometer i s placed underneath the crib where x rays can be taken through a non metal structure The radio wave can also penetrate through and reach the infant simulator. The baseband signal is fed to the laptop through a DAQ and a Lab V iew program i s designed to perform real time monitoring and signal processing. A B Figure 5 2. Experimental set up of infant simulator monitoring A) close shot, B) distant shot Figure 5 3 and Figure 5 4 show the measurement results of heart rate and respiratory rate of all events respectively, both with the programmed values plotted for comparison. Infant Simulator Vibrometer Infant Simulator
63 Figure 5 3 Measured heart rate vs. programmed heart rate. Figure 5 4 Measured respiratory rate vs. programmed respiratory rate. Figure 5 5 Programmed Tidal Volume of each event. Figure 5 5 is the programmed respiratory tidal volume of each event. Bigger TV indicates larger amplitude of respiration. When TV drops to 20 ml, the breathing
64 becomes very weak. The experiment is conducted through 18 continuous events. In each even t, the respiratory rate (RR), heart rate (HR), and tidal volume (TV)  are controlled and changed by the software Typical clinical ill syndromes such as tachypnea (Event 14 and 15) and bradypnea (Event 7 and 9) and other special cases are simulated. T he experimental results proved that the vibrometer can achieve accurate detection results when the infant simulator i s in a baseline or normal physiologic state Although the results have some deviation to the programmed values when detecting the infant un der abnormal conditions, they can reflect the change of vital signs under abnormal conditions and provide approximate data that are useful for initial diagnose of specific syndromes. Analyses of the typical cases are presented as follows. 5.2 .1 Baseline State Fig ure 5 6. Measured time domain baseband signal with programmed RR=40, HR=130. Fig ure 5 7. Normalized measured baseband spectrum with programmed RR=40, HR=130. At the be ginning, the infant simulator i s programmed to have normal vit al signs. Since the average HR and RR of a normal newborn infant are 130 and 40 [ 60 ] these
65 two values are chosen as the baseline state in the program. Figure 5 6 and Figure 5 7 show the time domain and normalized spectrum of measured baseband signal under this situation. It can be seen from Figure 5 7 that there are two strong frequency components located at 40 and 130 respectively. Normally, the heart rate is always faster tha n respiratory rate, and the amplitude of respiration activity is larger than that of heart beat. Therefore, the strongest frequency component located at 40 i s determined to be the respiratory rate and the second strongest peak at 130 represents the heart r ate. 5 .2 .2 Bradypnea In Event 7 and Event 9, the infant simulator i s programmed to have a very low respiratory rate of RR=1 (0.017Hz) and RR=5 (0.04Hz) respectively. Because of the DC blocking capacit or used in the system the frequency components near DC are attenuated and cannot be accurately detected from the spectrum. That is the reason why the system can only achieve accurate results of relatively high rate vital signs and will lose the low rate information near DC. T his problem can potentially be solved by introducing a direct coupling in the circuit without a capacitor so that DC and low frequency component s can pass through and be detected 5.2 .3 Faint Breathing It can be seen from the measurement results that starting from Event 11, the accuracy i s degraded, especially for the respiratory rate. This is attributed to the large decrease of tidal volume that makes the respiration amplitude drop significantly such th at the weak respirat ory signal i s overwhelmed by the background noise. In this situation, higher carrier frequency should be used to increase the detection sensitivity. For the 5.8 GHz vibrometer the carrier wavelength is approximately 5.2 cm,
66 the phase modulation index in ( 5 1) is too small to have an evident effect. Thus, the non linear phase modulation effect is so weak that the harmonic in the baseband spectrum would be overwhelmed by noise. However, i f the frequency is increase d by 10 times, the wavelength will be comparable to the small chest wall movement even when the respiration is weak and thus generate harmonics strong enough for accurate detection. Thus, the accuracy can be improved by using higher carrier frequencies 5. 2 .4 Heart Rate Equals the Harmonic of Respiratory Rate In Event 3, both RR and HR are set at 40. Due to the nonlinear phase modulation effect and the harmonics of movement itself, t here exists t he 2 nd harmonic of RR=40, which is 80. If judging by common sense that heart rate is always higher than respiratory rate, the 2 nd harmonic of respiratory rate would be considered as the heart rate mistakenly. Fig ure 5 8. The comparison of normalized spectrums of measured baseband signal of Event 2 and Event 3 However, looking further into the spectrums of Event 3: RR=40, HR=40 and Event 2: RR=40, HR=80, the subtle difference between these two cases can be found Figure 5 8 shows the comparison of the measure d spectrums of Event 2 and Event 3. It is easy to notice the difference at the location of 80: the amplitude of the 2 nd harmonic of RR = 40 is lower than the amplitude of HR = 80 that really exists in Event 2 Therefore, two approaches can be adopted to avoid this kind of problem. The first method is to use lower carrier frequency so that the nonlinear phase modulation effect
67 is reduced which results in a baseband signal spectrum containing only f h and f r without harmonics that could cause confusion [ 61 ] The second approach is to set a detection threshold. If the amplitude of a frequency component is lower than the threshold, it will be determined as harmonic. If it is above the threshold, it can be regarded as useful signal. 5 .2 .5 Tachypnea and Brady cardia Based on vital sign reference charts [ 60 ], the normal RR for a newborn infant is 30 50 and the normal HR is 100 170. Occasionally the RR of an infant will go faster than the upper limit of 50 with its HR dropping below 100 at the same time. In this situation, the infant would be diagnosed to have both tachypnea and b radycardia. This special case i s simulated in Event 15 where HR= 60 and RR= 80. Because the respiratory TV is weak, the strength of the respir ation frequency component may become comparable to the heartbeat in spectrum. In this situation, it is easy to mistakenly judge that RR= 60, and HR= 80, which is just the opposite result of the actual case. Fortunately, using absolute spectrum can potentiall y solve this problem to identify the vital signs correctly The abovementioned detection method is using the frequency difference between respiration and heartbeat to distinguish these two vital signs. However, the difference of strength s of vital sign si gnals from case to case which can be useful to improve the detection accuracy in special cases, cannot be seen on the normalized spectrum. Thus, the absolute spectrum needs to be used. Simulations have been performed to illustrate the benefit of using abs olute spectrum to disti nguish the vital signs that can not be identified in normalized spectrum.
68 Figure 5 9. The comparison of simulated absolute spectrums of two cases. Case1: Normal RR at 60, normal HR at 80. Case2: Weak RR at 80, normal HR at 60. In simulation, a state with normal respiratory strength is set as follows: the strength of respiration is much stronger than heartbeat and heart rate is faster than respiratory rate (RR = 60, HR = 80, m r = 0.8 mm, m h = 0.2 mm)  In another state, a much weake r respiratory signal at 80 and normal strength heartbeat signal at 60 (RR = 80, HR = 60, m r = 0.4 mm, m h = 0.2 mm) i s used. Figure 5 9 shows the comparison of absolute spectrums of these two s tate s set as above. It can be observed from Figure 5 9 that under normal conditions (the dash line), there is always an evident strong signal on the spectrum, which indicates the strength of normal respirat ory signal. Since the amplitude of respiratory signal is always larger than that of heartbeat, even when breathing b ecomes weaker, its amplitude is still larger than heartbeat. Therefore, the highest peak on the absolute spectrum usually represents the respiratory signal. If the peak of an absolute spectrum drops to a lower level, as shown in Figure 5 9 (solid line), it can be determined that the respiration of the infant becomes weak. If using normalized spectrum, since this variation of signal strength cannot be
69 seen from the spectrum, the ill infant may still be considered to be normal, thus missing the opportunity of instant treatment due to misdiagnosis. Although it can be initially diagnosed from the spectrum shown in solid line in Figure 5 9 that the infant breathing becomes weaker, it still cannot distinguish which signal is respiration and which is heartbeat. Ho wever, it is known that the amplitude of heartbeat has a relatively narrow varying range, which is from 0 mm (no heartbeat) to 0.3 mm (very strong heartbeat ). Using high carrier frequency vibrometer can potentially obtain the accurate vital sign signal amp litude. If the amplitude is larger than 0.3 mm, it can be determined as respiratory signal, not heartbeat. In this approach, the vital signs can be correctly identified. 5 .3 Summary For the first time, the accuracy of using RF vibrometer to monitor baby vital signs is verified through an infant simulator. The experimental results show that the vibrometer can monitor the vital signs accurately when the infant simulator behaves in baseline states, it can also track the variations of vital signs of some typi cal syndromes. Limited by hardware and algorithm, the system could not detect vital signs accurately in some abnormal cases. It is suggested that d irect coupling circuit, carrier frequency tuning technique and further spectral analysis can be used to impr ove the detection accuracy in those special cases In summary t he experimental result s demonstrat e the potential of using RF vibrometer for non contact monitoring of sleeping infants to reduce SIDS.
70 CHAPTER 6 ANALYSIS OF DETECTIO N METHODS OF RF VIBR OMETE R FOR COMPLEX MOTION MEASUREMENT The two detection techniques of using RF vibrometer to measure complex motion have been described in chapter 2. One is using multiple harmonic pairs at a fixed carrier frequency, the other is using a single, fixed harmonic pair at multiple carrier frequencies, which is based on the wavelength division sensing technique. It is important to compare these two methods to know their limitations and advantages, respectively. Since both of the detection theories use the harmonics in the baseband spectrum, and the harmonic is represented by Bessel functions a detail harmonic analysis by investigating the Bessel function coefficients of the harmonic is conducted to analyze the two methods By far the model of the complex motion used in theory and experime nts is assumed to be odd function in time which means there is no excess phase angle in each of them. However, the c omplex movement s in real world include harmonic motions taki ng the ge neral form that usually have random excess phase angles Our detection methods are developed to obtain the magnitude and frequency of each harmonic motion of the movement, which carry useful information about the characteristics of the vibration system. It is important to know if it is still possible to obtain the information of interest, especially the amplitude of each harmonic motion, when there are unknown excess phase angles in each of them. In regards to the signal processing part of the two detectio n methods, previous post signal processing function is integrated to the LabView testing program so that the real time mo vement monitoring function can be realized. The see through wall detection capability is also verified by conducting all the measuremen ts behind a wall with the detection distance of 1.5 m.
71 6.1 Modeling of Harmonic Vibrations The previous paper [19 ] did not explain the physical meaning of the proposed complex periodic motion model. A harmonic vibration of a dynamic system will be generated when the external driving force is complex periodic. The force will lead to a steady state output with a term of each frequency component. If the external driving force is purely sinusoidal, the steady state response of the linear system will be at the same frequency as the excitation. When the excitation force is complex periodic, such as for a square wave, the res ponse will be a multi tone harmonic vibration. A harmonic vibration can be described as: ( 6 1) m n is the amplitude of each harmonic of the vibration, and is the fundamental frequency. Since the phase angle of each motion 1 2 N are determined by the initial conditions, they can assume different values for every independent test. Thus, the phase angles are usually randomly distributed unless the initial conditions of the system are fixed. On the other hand, the ampli tude response is determined by the characteristics of the system itself and the external driving force. For a spring mass damper vibration system, the mass of the object ( m ), the spring coefficient ( k ), the natural frequency ( n ) of the system and the magn itude of the external driving force ( F 0 ) can all be extracted from the amplitude response spectrum. The wavelength division sensing RF vibrometer was designed to measure harmonic vibrations that are odd functions in time, which corresponds to the scenario when all phase angles are zero. The conventional way to obtain the amplitude and phase of each harmonic of a complex
72 rule given below [63 ]. (6 2) (6 3) with (6 4) and (6 5) where is the vibration period, t 1 t 2 t M / M x i is the corresponding value of the displacement at t i The advantage of the numerical method is that it can obtain both the amplitude and phase of each harmonic, which means it can recover the pattern of the vibration. However, this can be guaranteed only when there are sufficient time domain samples Otherwise, the recovered pattern will be distorted. On the other hand, instead of using the time domain data, the reported wavelength division sensing RF vi brometer uses the frequency domain information. In particular, the amplitude ratio between harmonics in the baseband spectrum is used to extract the amplitude of each frequency component of a vibration that is an odd function in time (zero phase angles). I f the vibration contains harmonics that are even functions in time, the movement pattern cannot be recovered since the phase angle of each harmonic cannot be obtained (as will be explained in
73 s ection 6.5 ). However, the phase angles are random values that d o not contain useful information and can be neglected. RF vibrometer can be a helpful diagnostic tool in mechanical testing, as for example technicians use the response spectrum of a machine under several external periodic driving forces of different frequ encies to obtain the natural frequency and evaluate the conditions of the machine by identifying the spectral resonance peak and amplitude variation [64 ]. The condition monitoring and fault diagnosis of electrical motors need the information of amplitude a nd frequency of harmonics of a vibration where RF vibrometer can be used [65 ]. In addition, an RF vibrometer can also be potentially used in clinical diagnosis by monitoring the variation of vital signs. 6.2 Harmonic Analysis of Wavelength Division Sensing Technique and Multiple Harmonics Based Detection Method The wavelength division sensing RF vibrometer features a quadrature direct conversion ar chitecture as depicted in Figure 6 1. The same transmitting signal is also sent to the down conversion mixer a s the LO signal in order to take advantage of the range correlation effect [ 17 ]. A software controlled PLL is used to generate different carrier frequencies. It comprises a PLL frequency synthesizer (ADF4108) and an external VCO. A shaker controlled by a l aptop generates the vibration Two 2.5 cm 3 cm patch antennas are placed 0.4 m above the vibration platform as shown in Figure 6 1. The 10 cm 10 cm marble platform is covered by aluminum foil for better reflection. The antenna ba ndwidth of S11 < 10dB is 3 9 GHz to accommodate the required large frequency tuning range. Two op amps are used to build the 30 dB baseband amplifier. The DAQ model is NI USB 6008 with 12 bit resolution and its highest sampling rate is 10 kS/s. The maximu m vibration frequency that can be detected is limited by the
74 sampling rate of the DAQ and determined by the frequency of the highest order harmonic that is used for calculation. For example, if the fundamental vibration frequency is 500 Hz, and it contains three harmonic motions, thus, three harmonics are required in the spectrum to set up the equations. Assuming the 5 th order harmonic located at 2.5 kHz is used, then the sampling rate should be at least 5 kHz. For the DAQ used in the experiment, the estima ted maximum vibration frequency can be detected is 1 kHz. Depending on the characteristics of vibration, this value may be higher or lower. For a vibration that is odd function in time and contains two harmonics as represented in (6 6 ) (6 6 ) using a complex signal demodulation technique [ 31 ], the combined complex baseband I/Q signals can be written as: ( 6 7) where is the total residual phase and is the carrier wavelength. J n ( a ) represents the first kind Bessel function of the n th order. Since has a constant envelope of unity, the effect of on signal amplitude is thus eliminated, leaving the amplitude of the harmonic determined only by the Bessel fun ction coefficient All the terms in the sum that satisfy f 1 p + f 2 l equaling to x contribute to the harmonic frequency equaling x Hz, and its amplitude equals:
75 (6 8) It can be seen that the amplitude ratio between two harmonics is a function of which can be represented as H x / H y = f ( ). Therefore, in order to obtain m 1 and m 2 the wavelength division sensing technique works in the following steps: (1) Choosing two harmon ics Hx and Hy (2) Measuring H x / H y @ carrier frequency f c1 H x / H y = f 1 ( 1 ) (3) Measuring H x / H y @ carrier frequency f c2 H x / H y = f 2 ( 2 ) (4) m 1 and m 2 can be obtained by solving two equations. There is no explanation about ho w to choose harmonic pairs in [19 ]. They were chosen arbitrarily. It is possible that some harmonic pairs will render more accurate measurement results than others 6. 2 .1 Harmonic Amplitude Approximation As mentioned in [ 19 ], the amplitude of harmonics other than the frequency components of the vibration itself increases if a higher carrier frequency is used. In order to distinguish the frequency components belonging to the vibration from the harmonics that are inter modulation products caused by the nonlinear Doppler phase modulation eff ect, the carrier wavelength is usually at least 10 times larger than the amplitude of each harmonic motion of the vibration ( >10 m n ). As represented in ( 6 8), the strength of each harmonic is determined by the summation of infinite numbers of J p m 1 J l m 2 Thus, it is critical to know the value of Bessel function of different
76 Figure 6 1. Block diagram and experimental setup of the wavelength division sensing RF vibrometer. From [19 ] orders When n m n ting a m n Figure 6 2 shows Bessel functions J n ( a ) for orders n=0 to 3. The values of J n ( a ) can be obtained based on the symmetry of Bessel functions given in ( 6 9). ( 6 9 ) As can be seen from Figure 6 J n ( a ) will be negligible. The original infinite sum can be approximated by the summation of products of Bessel functions of orders of n=0 or n=1.
77 Figure 6 2. Bessel function Jn(a) of n=0, 1, 2, 3 with 0
78 each frequency. For example, for x =4 Hz, the combinations ( p =3, l = 1) and ( p =8, l = 4) can also result in 3 p +5 l =4 This and other such higher order harmonics are not taken into account because of negligible values of the high order Bessel functions. O nly th e dominant combination s for each frequency are shown in Table 6 1 In this case, the product of two corresponding Bessel functions given i n Table 6 1 can approximate every harmonic amplitude. T able 6 1 Combination of Bessel function index with 3 P +5 L = X an d Harmonic Amplitude Expression with 4 M 1 / = A 1 4 M 2 / = A 2 Harmonic Frequency ( x Hz) P L Harmonic Amplitude H x 1 2 1 | J 2 ( a 1 ) J 1 ( a 2 )| 2 1 1 | J 1 ( a 1 ) J 1 ( a 2 )| 3 1 0 | J 1 ( a 1 ) J 0 ( a 2 )| 4 2 2 | J 2 ( a 1 ) J 2 ( a 2 )| 5 0 1 | J 0 ( a 1 ) J 1 ( a 2 )| 6 2 0 | J 2 ( a 1 ) J 0 ( a 2 )| 7 1 2 | J 1 ( a 1 ) J 2 ( a 2 )| 8 1 1 | J 1 ( a 1 ) J 1 ( a 2 )| Fig ure 6 3. Baseband spectrum of the assumed vibration pattern at 5 GHz carrier frequency.
79 Figure 6 3 shows the normalized baseband spectrum of the vibration pattern ( 6 10) at a carrier frequency of 5 GHz. The expressions of harmonic amplitudes shown in Table 6 1 can explain why some of the harmonics are stronger than others in the baseband spectrum. A few frequency components from the spectrum are taken as examples. 1) H 4 : Table 6 1 shows its amplitude is mainly determined by | J 2 ( a 1 ) J 2 ( a 2 )|. As shown in Figure 6 2, J 2 ( a ) is much smaller than J 0 ( a ) or J 1 ( a ), thus it contributes negligibly to the spectrum. 2) H 2 and H 8 : From Table 6 1 we know that: H 2 = | J 1 ( a 1 ) J 1 ( a 2 )| =| J 1 ( a 1 ) J 1 ( a 2 )| ( 6 12) H 8 = | J 1 ( a 1 ) J 1 ( a 2 )| (6 1 3) H 2 and H 8 have the same amplitude expressions, which explains why H 2 and H 8 appear to have equal strength in the spectrum. 3) H 3 and H 5 : H 3 = | J 0 ( a 2 ) J 1 ( a 1 )| (6 1 4) and H 5 = | J 0 ( a 1 ) J 1 ( a 2 )| ( 6 15) Since m 1 > m 2, thus a 1 > a 2 Figure 6 2 shows that J 0 ( a 2 )> J 0 ( a 1 ), and J 1 ( a 1 )> J 1 ( a 2 ). Because both of the two terms of H 3 are bigger than those of H 5 their product would also be larger. This is why H 3 appears larger than H 5 in the spectrum.
80 6.2 3 Choice of Harmonic Pairs on Detection Accuracy The detection accuracy of the wavelength division sensing techniq ue depends on the amplitude ratio of harmonic pairs. The following analysis will show how important it is to choose the appropriate harmonic pairs. 1) H 2 and H 8 : In Section B, it is shown that: ( 6 16) which means that H 2 /H 8 will always be equal to 1 regardless of the carrier frequency. Therefore, the wavelength division sensing technique is not applicable for this situation. 2) H 2 and H 3 From Table 6 1 ( 6 17) It can be seen that the Bessel function involving a 1 which is a function of m 1 is cancelled out, and the ratio is determined only by a 2 ( m 2 ). Despite the fact that we measure the ratio twice at two different carrier frequencies in the wavelengt h division sensing technique, an accurate result of m 1 cannot be achieved here, since we are essentially building two equations to solve only one variable m 2 This outcome is also verified through simulation. In simulation, the spectrum of the vibration at 5 GHz and 6 GHz are obtained, respectively. The ratio H 2 /H 3 at 5 GHz is 0.2141 and at 6 GHz is 0.2595. The calculated m 1 =2.59 mm, m 2 =2 mm. As expected, an accurate result for m 2
81 can be achieved, but not m 1 which has 13.7% error compared to the programme d value of 3 mm. Thus, in order to obtain accurate calculations of both m 1 and m 2 we should avoid using harmonic pairs that contain the same order (absolute value) Bessel function involving the same variable, such as J 1 ( a 1 ) and J 1 ( a 1 ) in this case. 3) H 3 and H 5 Based on the aforementioned analysis, the harmonic pair of H 3 and H 5 will turn out to be an appropriate pair that can render accurate results for both m 1 and m 2 as shown in the following analysis. ( 6 18) Since there is no term being cancelled, the ratio will be a function involving both the variables of a 1 and a 2 Thus, using the wavelength division sensing technique, both m 1 and m 2 can be accurately determined by solving two equations which inc lude both of them. In simulation, the measured H 3 /H 5 at 5 GHz is 1.5487 and at 6 GHz is 1.5703. The calculated m 1 =2.99 mm, m 2 =1.99 mm. As can be seen, by using the harmonic ratio H 3 /H 5 an accurate result of both m 1 and m 2 can be obtained. From Table 6 1 it can be figured out that in addition to the pair H 3 and H 5 the pair H 2 and H 6 and the pair H 6 and H 8 are the appropriate choices as well for achieving accurate results. Theoretically, H 1 and H 3 can also render an accurate result. However, since the lev el of H 1 is relatively low, it can be easily overwhelmed by noise, it is thus not considered suitable. In summary, in order to achieve accurate detection result by using the wavelength division sensing technique, the following rules should be followed.
82 ( 1 ) Avoid using harmonics whose amplitudes are too small, which could be susceptible to noise. ( 2) Avoid using two harmonics that have equal amplitudes, such as H 2 and H 8 ( 3) Avoid using two harmonics that involve the same order (absolute value) Bessel func tions of the same variable. For example, J n ( a m ) and J n ( a m ) or J n ( a m ) and J n ( a m ) are undesirable. 6.2 4 Detection Method Using Multiple Harmonic Pairs at a Fixed Carrier Frequency The analysis in the previous sections shows that the detection accuracy of the wavelength division sensing technique depends greatly on the selection of harmonic pairs. Without checking the harmonic amplitude expressions for the baseband spectrum, one risk s a large error in the final calculated amplitude of each harmonic motion constituting the vibration. Since the carrier frequency needs to be tunable, it requires a frequency synthesizer or wide tuning range VCO and a broadband antenna, all of which will i ncrease the complexity of system design as well as the manufacturing cost. A detection technique that is more reliable with a simpler architecture is desirable. The detection method based on multiple harmonic pairs at a fixed carrier frequency turn out to be more reliable. The principle of the detection technique is described below, assuming the vibration contains N harmonic motions: ( 1) Choosing N different harmonic pairs (H x and H y ), (H y and H z ( 2) Measuring the N harmonic amplitude ratios at a fixed carrier frequency fc H x / H y = f 1 ( 1 ) and H u / H v = f 2 ( 1 ( 3) m 1 m 2 m N can be obtained by solving N equations.
83 Since this method uses multiple harmonic pairs, the probability of all harmonic pairs being inappropriate is small. Therefore, it can be expected that the detection accuracy can be improved, especially when there are more than two harmonics in the vibration pattern. 6.3 Experimental Verification In this section, the experimental results of the RF vibrometer using multiple carrier frequenci es will first be evaluated through harmonic analysis. The improvement in detection accuracy of the method that uses multiple harmonic pair s will then be verified. T he reference vibration pattern in the experiment of vibrometer using multiple carrier freque ncies is: x ( t )=2.54sin(2 4 t )+1.896sin(2 6 t )+0.97sin(2 8 t ) ( 6 1 9) Figure 6 4 is the measured baseband spectrum at 6 GHz. The harmonic amplitude ratio H 2 /H 10 was chosen at that time with no specified reason. The amplitudes of harmonics in the baseband spectrum can be represented as : ( 6 20) Fig ure 6 4. Normalized baseband spectrum of a three tone movement at 6 GHz From [19 ]
84 with the constraint condition 4 p +6 l +8 q = x Since the Bessel function with order higher than 2 has negligible value, we only need to consider p l q belonging to (0, +1, 1). T he list of different combinations of indexes is shown in Table 6 2 m 1 a 1 m 2 a 2 m 3 a 3, ( 6 21) T able 6 2 Combination of Bessel function index with 4 p +6 l +8 q = x x (unit: Hz) p l q 2 0 1 1 1 1 0 4 1 1 0 0 0 1 6 0 1 0 8 0 0 1 10 1 1 0 12 1 0 1 14 0 1 1 It can be seen that the terms involving m 2 are cancelled by taking the ratio between H 2 and H 10 Therefore, measuring the ratio three times at three carrier frequencies cannot guarantee accurate calculation result of m 2 The pair (H 6 and H 12 ) or (H 8 and H 10 ) should be used since the absolute values of the indexes p at J p m 1 l at J l m 2 q at J q m 3 all different from each other, thus ensuring the information involving m 1 m 2 and m 3 are all preserved when taking the ratio. The calculation result of each harmonic motion amplitude by using the measurement data of
85 the ratio H 6 /H 12 and H 8 /H 10 at the three dif ferent carrier frequencies are ( m 1 =2.49, m 2 =1.9, m 3 =0.92), ( m 1 =2.5, m 2 =1.88, m 3 =0.94) respectively. Compared to the result ( m 1 =2.33, m 2 =1.921, m 3 =0.855) from using the ratio H 2 /H 10 using H 6 /H 12 or H 8 /H 10 improves the detection accuracy from 10% in error to 3% with the reference value given in ( 6 19). On the other hand, because of the reduced probability of inadvertently choosing inappropriate harmonic pairs, the detection theory using multiple harmonic pairs tends to ensure accuracy more easily without t he need to carefully inspect the combination of Bessel functions in advance as one must with the previous wavelength division sensing technique. For instance, if we pick arbitrarily from the experimental data at 6 GHz of the three harmonic ratio pairs of H 2 /H 10 H 6 /H 14 H 6 /H 8 we will end up with: ( 6 22 1) ( 6 22 2) ( 6 22 3) It can be seen that each pair alone does not include all the information involving m 1 m 2 and m 3 The ratio H 2 /H 10 loses the information of m 2 H 6 /H 14 is independent of m 1 and m 2 and H 6 /H 8 does not involve m 1 Therefore, none of them alone would be a good choice if the wavelength division sensing technique were used. However, combining them can render accurate calculation results, since the missing information of one pair
86 can be provided by another pair. For example, although H 2 /H 10 does not involve m 2 H 6 /H 8 does; the information of m 1 contained in H 2 /H 10 and m 2 in H 6 /H 8 can provide the lost information for H 6 /H 14. To achieve the value of m 1 m 2 and m 3 we can first use ( 6 22 2) to obtain m 3 then substitute m 3 to ( 6 22 1) and ( 6 22 3), and m 1 and m 2 can be obtained, respectively. The calculation for the measured data is m 1 =2.5, m 2 =1.9, m 3 =0.94, all of which deviate less than 3% error from the reference values. Thus, the proposed detection theory using multiple harmonic pairs at a fixed carrier freque ncy has been verified to be more reliable and accurate than the wavelength division sensing technique. The discussion in the following sections and the code used in a real time monitoring program are all based on the multiple harmonic pairs detection metho d. 6.4 Sensitivity of Harmonic Amplitude Ratio to Additional Phase Angle The new detection method can be used to obtain the movement pattern of an unknown harmonic vibration if it is an odd function in time. In general, harmonic vibration patterns may in clude an additional phase angle of each harmonic as represented in ( 6 1). The corresponding complex baseband signal can be represented as: Fig ure 6 5. Simulated b aseband spectrum of the vibration given in ( 6 27) @ 5.8GHz without phase angle
87 Fig ure 6 6 Variation of H 2 /H 3 vs. ( 1 and 2 ) Figure 6 7. Variation of H 1 /H 3 vs. ( 1 and 2 ) Fig ure 6 8. Variation of H 3 /H 4 vs. ( 1 and 2 )
88 ( 6 23) When there is no 1 2 N the baseband signal has the following expression: ( 6 24) As can be seen in ( 6 24), when there are no phase angles (resulting in an odd function in time), the amplitude of each harmonic is determined by the direct summation of Bessel function coefficients The existence of phase angles makes the harmonic amplitude a summation of complex numbers shown in ( 6 23). It can be expected that the absolute value of the harmonic amplitude will be different from the scenario when there are no phase angles. Since the harmonic amplitude ratio is used to solve each amplitude, it is important to know how sensitive the ratio will be to the phase angle. The following analysis begins with a single tone harmonic vibration scenario and then a detailed analysis and simulation result for a two tone case is provided. To save readers from tedious derivati ons and gain an insight into the issue, the detailed deduction of multi tone vibration case will not be given in this paper. It can be readily obtained by following the analysis for the two tone case. The baseband signal of a single harmonic motion with ph ase angle can be expressed as:
89 ( 6 25) Without loss of generality, the amplitude ratio of H 1 /H 2 will be: ( 6 26) This shows that the phase angle 1 has no effect on the harmonic amplitude ratio, which rema ins the same as when there is no phase angle 1. For a single tone harmonic vibration, the phase angle indicates the time delay. Changes to it shift the whole waveform without changing its shape. Thus, the pattern of an arbitrary sinusoidal harmonic motio n can always be reconstructed. For the two tone case, let us assume a motion as shown in ( 6 27): ( 6 27) Its baseband signal can be written as: ( 6 28) Since the detection technique based on multiple harmonic pairs only needs a single carrier frequency, a 5.8 GHz Doppler radar was built. The simulation is also conducted using this frequency. Figure 6 eband spectrum is
90 Fig ure 6 9. Calculated m 1 using H 1 /H 3 and H 3 /H 4 reference value m 1 =2 mm Figure 6 10. Calculated m 2 using H 1 /H 3 and H 3 /H 4 reference value m 2 =1 mm
91 Figure 6 11. Calculated m 1 using H 2 /H 3 and H 3 /H 4, reference value m 1 =2 mm Figure 6 12. Calculated m 2 using H 2 /H 3 and H 3 /H 4 reference value m 2 =1 mm determined by p+3l. Ignoring the Bessel functions with orders higher than 3, the corresponding expressions of each harmonic amplitude are as below: ( 6 29) ( 6 30) ( 6 31) ( 6 32) Figure 6 6 to Figure 6 8 show the variation of H 2 /H 3 H 1 /H 3, and H 3 /H 4 versus 1 and 2 combinations of 1 and 2. Therefore, accurate phase angles cannot be determined from the value of harmonic amplitude ratio. The ideal values of each of them are H 2 /H 3
92 = 0, H 1 /H 3 =2.037, H 3 /H 4 =4.12 It can be seen that the ratio H 2 /H 3 is much more sensitive to the excess phase angle compared to H 1 /H 3 and H 3 /H 4 whose maximum deviation are 1% and 1.6% respectively By substituting m 1 =2 mm, m 2 = 1 mm and =51.72 mm into the Bessel functions, the numeric value of each harmonic can be shown: ( 6 33) ( 6 34) ( 6 35) ( 6 36) One notices that for H 1 H 3 and H 4 each of them has a dominant term much bigger than the other, and therefore less susceptible to the effect of phase angle. However, H 2 which includes two terms of equal value, will evidently be affected by the phase angle. Any ratios involving H 2 would therefore also be sensitive to the phase angle and should be avoided. Figure 6 9 and Figure 6 10 show the calculated m 1 and m 2 by using H 1 /H 3 and H 3 /H 4 which are the two insensitive harmonic pairs. The maximum deviations for both of them are les s than 2%. Figure 6 11 and Figure 6 12 depict the amplitudes calculated from H 2 /H 3 and H 3 /H 4. Because of the big variation of H 2 /H 3 accurate values of m 1 and m 2 cannot be obtained. Meanwhile, the results also prove that using insensitive harmonic pairs prevents the deviation of the calculated amplitude caused by phase
93 angle and allows one to obtain accurate information of the vibration. 6.5 Experimental Implement ation of Real time RF Vibrometer Previously reported techniques using Doppler radar to measure displacement and velocity [23 ], and to obtain the pattern of periodic movements [ 15 ] [ 19 ], all require time consuming post processing in order to acquire the de sired information. Real time vibration monitoring would speed the adoption of Doppler radar vibration detection in real world applications by reducing the tedium of such measurements. A 5.8 GHz RF vibrometer based on the multiple harmonic pairs is implemen ted in board level. Two patch antennas ( 5 cm 5 cm ) of 9 dB gain are connected to the vibrometer board through SMA connectors. The moving target is driven by a linear actuator that can be program controlled through a laptop. The experimental s et up for vibration detection is shown in Figure 6 13. The thickness of the wall is 15 cm and the detection distance is 1.5 m. The parameters of amplitude, frequency and phase angle of each tone of the vibration can be set in the program. The sampling rate is 20 Hz, and the FFT window size is 512. The monitoring programs in previous research  [19 ] only display in real time the time domain and frequency domain waveforms of the baseband I/Q signals. They do not have a real time display of the vibration pa ttern. In this work, the MATLAB code previously used for post processing is integrated into a LabVIEW program to realize real time movement pattern monitoring. After an initial 30 s settling time (this step can be skipped once the circuit is settled), the data file is continually read into a MATLAB routine integrate d in the program to get the accurate baseband spectrum. A peak search block in LabVIEW is used to collect the peaks on the spectrum and their corresponding frequencies. T hese data are then trans ferred into another block
94 that runs the detection algorithm. When the background calculation is finished, the vibration pattern of the target is shown on the user interface immediately. The whole background signal processing job takes about 2 s to finish. The harmonic frequency and amplitudes that are used to do the calculation and the calculated displacement and frequencies of all the harmonic motions in the vibration are also shown on the monitoring screen after the signal processing is finished. Figure 6 14 shows the real time monitored pattern of two tone and three tone vibrations. The excess phase angles are set to be zero in these cases. The measurement values and the programmed values for each case are noted in the caption. The deviations are all withi n 10%. Thus, the improved monitoring program delivers in real time the movement pattern of an unknown vibration that is an odd function in time (zero phase angles). For a typical commercial quadrature mixer, it has been verified that even if it operates a t the worst condition that has both the maximum amplitude mismatch and maximum phase mismatch, the resulting detection error would be less than 10%. For most quadrature mixers operating in normal conditions, the introduced error from I/Q im balance should b e negligible [20 ]. Figure 6 13. Experiment set up of the through wall vibration detection
95 a b c Figure 6 14. Real time monitoring of vibrations that are odd functions in time using RF vibrometer a) Program value: m 1 =2 mm m 2 =1 mm f 1 =0.2 Hz, f 2 =0.6 Hz, Measurement result: m 1 =2.1 mm m 2 =1.05 mm f 1 =0.2 Hz, f 2 =0.6 Hz b) Program value: m 1 =2 mm m 2 = 1 mm f 1 =0.2 Hz, f 2 =0.6 Hz, Measurement result: m 1 =2.15 mm m 2 = 1.1 mm f 1 =0.2 Hz, f 2 =0.6 Hz c) Program value: m 1 = 1.8 mm m 2 = 1.2 mm m 3 = 0.8 mm, f 1 =0.2 Hz, f 2 =0.6 Hz, f 3 =0.8 Hz, Measurement result: m 1 = 1.77 mm m 2 =1. 2 mm m 3 =0.84 mm, f 1 =0.2 Hz, f 2 =0.6 Hz f 3 =0.8 Hz Table 6 3 Measured m 1 using H 1 /H 3 and H 3 /H 4 m 1 (mm) 1 2 2.0783 2.1752 2.171 2.2014 2.2862 2.2911 2.2869 2.0757 2.0033 1.8986 1.8963 2.3001 2.3053 2.2736 2.0876 2.3017 1.8988 2.087 2.1958 2.2142 1.8723 2.2749 1.9866 1.8782 1.7701 Table 6 4 Measured m 2 using H 1 /H 3 and H 3 /H 4 m 2 (mm) 1 2 1.0548 1.1344 1.05 1.2386 1.086 0.8369 0.9363 0.8347 0.769 1.0381 0.7881 0.8188 1.1396 1.0746 1.2367 0.8387 0.7685 1.2366 0.8379 1.0651 1.1338 1.2443 0.8364 1.0749 0.8334 Table 6 5 Measured m 1 using H 2 /H 3 and H 3 /H 4 m 1 (mm) 1 2 3.6271 3.382 2.2689 4.4606 4.0168 4.1694 4.0179 3.3829 4.503 4.3909 4.295 4.3926 4.5193 3.0913 4.0181 4.461 4.3909 4.0172 4.2948 4.5177 3.0905 3.3806 4.0168 3.6262 2.2671
96 Table 6 6 Measured m 2 using H 2 /H 3 and H 3 /H 4 m 2 (mm) 1 2 0.5811 0.6558 1.135 1.2165 0.4843 0.4531 0.4844 0.6559 1.151 1.3415 1.5663 1.3441 1.1311 0.7604 0.4848 1.2167 1.343 0.4847 1.5637 1.1301 0.7595 0.6561 0.4846 0.5814 1.1349 The sensitivity of the harmonic ratios to the phase angle has also been verified in the experiment. Table 6 3 shows the real time measured m 1 and m 2 using H 1 /H 3 and H 3 /H 4 at different combinations of the additional phase angles 1 and 2 set in the program. Table 6 3 lists the measurement results by using H 2 /H 3 and H 3 /H 4. Compared to the programmed value of m 1 =2 mm and m 2 =1 mm, it can be seen that by using insensitive harmonic ratio pairs, results with much less deviations can be obtained. 6.6 Summary This chapter develops the harmonic analysis of RF vibrometers by investigating the properties of Bessel function coefficients for complex periodic motions. It reveals that the detection accuracy of the previously reported multiple carrier frequency technique is dependent on the choice of harmonic pairs. The alternative detection theory that measures multiple harmonic pairs at a fixed carrier frequency has been proven to be more reliable. It reduces the probability of erroneous results caused by the wrong choice of a single inappropriate harmonic pair using the multiple carrier frequency technique. The analysis provides a guideline to improve the detection accuracy and reliab ility by first inspecting the Bessel function coefficient of each harmonic. The detection technique based on multiple harmonic pairs obtains the pattern of a harmonic vibration that is an odd function in time. When the vibration contains both odd and even function harmonics (non zero phase angles), by picking the insensitive
97 harmonics from the baseband spectrum, the amplitude of each frequency component can still be obtained, from which the characteristics of the vibration can be identified. This work demon strates the first real time, through wall Doppler RF vibrometer.
98 CHAPTER 7 ANALYSIS OF RF VIBROMETER FOR VITAL SIGN DETEC TION In the experiment o f using RF vibrometer monitoring the vital sign of infant simulator the detection accuracy degraded at some abnormal cases. Such as when the respiration rate and heartbeat rate are in harmonic relations, or when the baby experiences both tachypnea and bradycardia. It is to investigate into the baseband spectrum of those special cases to identify the problem s beh ind and propose potential solutions. The optimal carrier frequency for infant vital sign monitoring has also been studied. Lower carrier frequency around a few giga Hz turns out to be more suitable than high frequency, such as Ka band, or even higher. Bess el function analysis also shows that using double sideband signals in an indirect conversion radar system, the undesired harmonics can be removed from the baseband spectrum by choosing certain combination of RF and IF frequecies 7.1 Analysis of Special Cases 7. 1 .1 Respiration Rate and Heartbeat Rate in Harmonic Relation In the experiment of monitoring the vital sign of infant simulator, there are two cases that the RR and HR are in harmonic relations. For example, in case 2, RR=40 bpm HR=80 bpm and case 3, RR=40 bpm HR=40 bpm Since the 2 nd harmonic of RR is 80 bpm for case 3, and people usually assume the HR is higher than RR, the 2 nd harmonic of RR in case 3 was mistakenly judged as HR whereas the real HR was 40 bpm. It is important to look into the spectrum and harmonic expression to explore the possibility to solve this problem. The chest wall motion due to respiration and heartbeat can be modeled as the following expression:
99 (7 1) where m rr and m hb represent the chest w all displacement caused by respiration and heartbeat, respectively. m hb is usually in the scale of 0.01 mm  In simulation, 0.08 mm is used. m rr on the other hand, can vary in the mm range. The values from 2 mm to 5 mm are used in simulation for norma l breathing. f rr and f hb are the respiration rate and heartbeat rate accordingly. In simulation, two different situations are emulated. One is to explore how the respiration affects the harmonics with the heart beat strength maintaining at the same level. m rr is changed from 0 to 5 mm ( peak to peak amplitude is 0 to 1 cm) to emulate the state varying from no breathing to normal breathing, while m hb is fixed at 0.08 mm to indicate chest wall movement due to normal heartbeat. T he other case is to see the effect of how heart beat activity affect harmonics in the baseband spectrum while the breathing strength stays the same. m rr is set to be 4 mm and m hb is changed from 0 to 0. 1 mm to show the effect of no heartbeat changing to a strong one. Figure 7 1. Variation of H 2 /H 1 when m rr changes from 0 to 5 mm with m hb @ 0.08 mm
100 Figure 7 2. Variation of H 2 /H 1 when m hb changes from 0 to 0. 1 mm with m rr @ 4 mm Figure 7 1 and 7 2 show the variation of H 2 /H 1 vs the respiration amplitude and heartbeat amplitude respectively. It can be seen from Figure 7 2 that since the magnitude of chest wall motion due to heartbeat is much smaller compared to respiration, the variation of strength of the heartbeat signal does n ot have strong effect on the harmonic ratio. The real heartbeat signal at 80 bpm and the 2 nd harmonic of a normal respiration signal at 40 bpm have almost the same amplitude with less than 10% variation on the harmonic ratio H 2 /H 1 Human eyes cannot tell t he difference between 0.26 and 0.29 from the baseband spectrum, thus the accurate vital sign rates cannot be determined correctly. On the other hand, if the inf ant experiences weak respiration and normal heartbeat the difference between the 2 nd harmonic o f RR and the real heartbeat signal can be noticed from th e normalized baseband spectrum, as shown in the shadow area in Figure 7 1. Notice that when the infant breaths deeply, which means the chest wall movement is dominated by the respiration, the 2 nd har monic of the RR will finally
101 have the same level as the HR signal at 80 bpm, as can be seen from the area in Figure 7 1 when m rr goes beyond 3 mm. From the above analysis, one can conclude that when the breathing is shallow, and HR and RR ar e in harmonic relation, the marked region in Figure 7 1 can work as an indicator to help identify the HR and RR correctly. If H 2 /H 1 under certain respiration amplitude follows the red line, one can determine that the peak at 80 is the real heartbeat signal not the 2 nd h armonic of RR and vise verse. Likewise, when the patient is breathing normally and H 2 /H 1 goes beyond 0.4, mostly likely, the peak located at 80 would come from a real strong heartbeat signal of 80 bpm, but not the 2 nd harmonic of respiration signal. 7.1 .2 Bradycardia and Tachypnea In the experiment, the infant simulator was programmed to experience both bradycardia and tachypnea at the same time in case 15. HR droppe d to 60 bpm and RR goes beyond to 80 bpm TV also decreased, which means the infant, was having shallow breaths. In the baseband spectrum, there exists not only the vital sign signals but also their harmonics. Such as the 2 nd harmonic of heartbeat signal at 120 bpm, and that of respiration sign al at 160 bpm. In addition to these harmonics, the inter modulation product between heartbeat and respiration signals due to nonlinear phase modulation effect would also come out, e.g. the 20 bpm from RR HR and 140 bpm from RR+HR. Because of these harmonics and inter modulation products, it is easy to mistakenly take them as the real vital signs. Figure 7 3 shows the variation of strength of HR, RR, the inter modulation product located at 20, and the 2 nd harmonic of RR as m rr changes from 0 to 5 mm. Looking further into the figure, when the respiration is weak, below 1 mm (the left hand side area
102 to the dash line) the heartbeat signal at 60 bpm is stronger than the respiration signal at 80 bpm. Thus, people will mistakenly judge that the signal at 60 bpm as the RR and 80 bpm to be the HR, which is just the opposite result to the real case. Figure 7 3. Harmonics of the special case with the heartbeat strength fixed When the respiration magnitude becomes larger, one can see that the har monics at 20 bpm and 160 bpm grow stronger than the heartbeat signal at 60 bpm. Either of these two harmonics can be taken as the HR by mistake. From Figure 7 3, we can see that the respiration signal maintains to be the maximum as long as its magnitude is above 1 mm. Thus, as suming the maximum signal to be the respiration signal, one can obtain the correct RR most of the time. However, due to the nonlinear Doppler phase modulation effect, when m rr becomes larger, the inter modulation products and harmonics will come out and ca use confusion for accurate detection. 7.2 Optimal Carrier Frequency for Infant Vital Sign Monitoring The vital sign detection sensitivity has been studied in   . In general, it has proved that using higher carrier frequency can increase the detection sensitivity
103 proportionally since the modulation index equals to 4 m/ ( m is the movement ampli tude and is the carrier wavelength). Therefore, one usually tends to use higher carrier frequency in order to detect heartbeat signal accurately because it is much smaller than respiration signal. However, when the carrier frequency is higher, the nonlin ear modulation effect of respiration signal also becomes stronger and its harmonics will appear on the spectrum. When the heartbeat frequency is around those harmonics, it will be overwhelmed and we cannot detect the accurate HR in those situations. This i ssue has also been studied in , the respiration amplitude is assumed to be less than 1 mm in , which indicates weak breathing activity. In this sectio n, normal respiration strength which incurs chest wall displacement around 5 mm is studied. The am plitude ratio of heartbeat signal to the harmonics of respiration is analyzed in a more detail method based on Bessel functions. We first look into the baseband spectrum when the infant is at a baseline state that has R R at 40 bpm (0.67 Hz) with associated 2 mm chest wall displacement and a normal heartbeat rate at 130 bpm (2.17 Hz) with rela ted chest wall displacement of 0.08 mm. Figure 7 4 shows the spectrum at the carrier frequency of 5.8 GHz, which is the frequency used in prev ious experiment. Figure 7 5 is the one using a Ka band frequency of 27 GHz with all other assumptions maintain ing the same. It can be seen that by increasing the carrier frequency from 5.8 GHz to 27 GHz, the heartbeat signal at 2.16 Hz cannot be detected. It is overwhelmed by the 3 rd harmonic of respiration signal at 2 Hz. Therefore, using higher frequency is not a better choice. For normal vital sign detection, the 3 rd harmonic of RR will cause the biggest problem for accurate detection of heartbeat since its frequency is close to the HR In
104 order to achieve accurate HR detection, the strength of heartbeat signal needs to be much bigger than the 3 rd harmonic of respiration. Figure 7 4. Baseband spectrum for a normal vital sign state of RR=40 bpm, HR=130 bpm at fc=5.8 GHz Figure 7 5. Baseband spectrum for a normal vital sign state of RR=40 bpm, HR=130 bpm at fc=27 GHz Heartbeat signal
105 Figure 7 6 Heartbeat signal vs. the 3 rd harmonic of respiration at different m rr and carrier frequenci es Figure 7 6 shows the ratio of heartbeat signal strength vs. the 3 rd harmonic of respiration signal under different respiration strength as the carrier frequency changes from 5 GHz to 30 GHz. As can be seen, the ratio quickly drops to close to zero as the carrier frequency increases. In addition, larger m rr will have stron ger 3 rd harmonics. Thus, it results in smaller ratio, which makes the accurate detection of heartbeat signal more difficult. For optimal detection the carrier frequency should be less than 10 GHz. The reason behind this effect can be found by exploring th e Bessel function expressions of each frequency component on the baseband spectrum. respiration signal, heartbeat signal and also the 3 rd harmonic of respiration in Bessel function s. The complex baseband signal for the chest wall movement given in (7 1) can be written as:
106 (7 2) We know from (7 2) that each frequency component on the baseband spectrum is determined by f rr p+f hb l The heartbeat signal is determined by the index of p=0 and l=1, and the 3 rd harmonic of respiration corresponds to p=3 and l=0. Therefore, their amplitudes can be represented as follows, respectively. (7 3) (7 4) (7 5) Letting 4 m rr / =u, 4 m hb / =v (7 5) can be re written as: (7 6) In simulation, m rr is assumed to be changing from 2 mm to 5 mm, and m hb is set to be 0.08 mm. Thus, we have: 1) f c =6 GHz u: 0.5~1.25 v: 0.02 2) f c =27 GHz u: 2.26~5.65 v: 0.09
107 Figure 7 7 and 7 8 plot the corresponding J 0 (x)/J 3 (x) and J 1 (x)/J 0 (x), respectively. As can be seen, for v changes from 0.02 to 0.09, J 1 (v)/J 0 (v) changes from 0.01 to 0.05, which maintains at the sa me scale. However, for the variation of u, the 6 GHz frequency will render J 0 (u)/J 3 (u) at the scale of hundred, while the value corresponding to 27 GHz GHz. The above an alysis shows that if the heartbeat signal locates around the 3 rd harmonic of respiration, one should use lower frequency instead of higher one to achieve better detection accuracy. Figure 7 7 J 0 (x)/J 3 (x) The special case in the experiment that the heartbeat is at the 2 nd harmonic of RR can also follow the same analysis to gain more insights of the case. Figure 7 9 shows the ratio of strength of heartbeat signal verses the 2 nd harmonic of RR at different carrier frequencies. Compared to Figure 7 6 i t shows that the heartbeat signal is much smaller than the 2 nd harmonic of RR, all of the ratio is less than 0.3. At some specific carrier frequencies, there are null points, which mean the heartbeat signal is overwhelmed by the 2 nd harmonic. Because of th e small ratio, it is
108 much more difficult to detect the accurate HR if it is around the 2 nd harmonic of RR. Note that using low carrier frequency is also better than using high frequency. Figure 7 8 J 1 (x)/J 0 (x) Figure 7 9 Heartbeat signal vs. the 2 nd harmonic of respiration at different m rr and carrier frequencies
109 7.3 Harmonic Cancellation Using Double Sideband System For previously used Ka band radar sensor, if there is no bandpass filter in the transmitt ing chain as shown in Figure 7 10 the transmitting signal will contain three signals: two main sideband signals, one is the lower sideband signal at f L =f 2 f 1 the other is the upper sideband signal f U =f 2 +f 1 There is also a leakage signal from LO2. The phases of these three signals are a ll modulated by the movement of the target which is controlled through an actuator. After the first Rx Mixer, the modulated signal at f 2 will be down converted into DC and the other two sideband signals will be converted to f 1 The limited bandwidth of IF amplifier will filter out the DC component. T he two IF signals whose phases are modulated by the movement will be amplified Then, a quadrature IF mixer will down convert the IF signals into baseband for real time monitoring and signal processing. Figu re 7 10 Double sideband Ka band quadrature radar
110 The IF frequency is generated through a signal ge nerator and its output power is 1 0 dBm. Through a 3 dB power splitter, and up conversion mixer and also the cable loss, the measured output power at the antenna connector is around 6 dBm. A 15 dB gain block is inserted between the power splitter output port and the passive mixer to boost the LO drive power around 12 dBm. The mea sured receiving power at the input of the IF Amp is around 30 dBm. In order to obtain a baseband signal around 0 dBm, a 15 dB gain block is inserted to compensate the conversion loss of the passive mixer. The detail specifications of each component is lis ted in Table 7 2. The baseband signal contains the signal down converted from the lower sideband B L (t) and that from the upper sideband B U (t). It can be repres ented as: (7 7) where U and L are the carrier wavelength of upper sideband and lower sideband, respectively. U and L are the corresponding residual phase, which are independent values without correlation. Since the baseband signal is the superposition from the two sidebands, the amp litude of each frequency components on the baseband spectrum can also be represented as the superposition of bessel functions corresponding to two different carrier wavelenghts. Therefore, the heartbeat signal and the 3 rd harmonic of respiration signal ta ke the following form, respectively.
111 (7 8) (7 9) As mentioned earlier, H rr_3 should be made as small as possible in order to detect accurate heartbeat signal. For m hb ~0.05 mm, the term 4 m hb / even at 60 GHz c arrier frequency. From Figure 7 10 we know that J 0 ( 4 m hb / all carrier frequencies. Therefore, to make H rr_3 zero, we need to manipulate the IF and RF frequency in order to make J 3 ( 4 m rr / L ) and J 3 ( 4 m rr / U ) the same magnitude but opposite polarity with each other. Figure 7 11 Bessel function of order n=0 and n=3 The IF (also f 1 ) of the system is 6 GHz. Assume m rr =4 mm, 4 m rr / 4 m rr / U 4 m rr / L =0.167(f U f L )=0.167*2f1=2 (x= 4 m rr / This means that the 2 points located on the curve of J 3 (x) should be separated by 2. For example, the two points of
112 5.5 and 7.5 can be a suitable pair, since J 3 (5.5)=0.2516, J 3 (7.5)= 0.258. Therefore, we have 0.167f L =5.5, 0.167f U =7.5. So f L =33 GHz, f U =45 G Hz and LO2 =39 GHz. It can be expected that the 3 rd harmonic of RR will be reduced to close to zero by using LO1= IF=6 GHz and LO2 =39 GHz. The theoretical prediction has been ver ified in simulation. Figure 7 12 shows the baseband spectrum at carrier frequen cy of 33 GHz when there is no image band. While Figure 7 13 is the spectrum of double sideband, as expected, the 3 rd harmonic at 2 Hz has been reduced to a great extent. 7.3.1 The Effect of Power Difference between Sidebands Since the components such as m ixer, amplifier in the radar system have limited bandwidth and frequency dependent gain, the lower sideband signal at f L and upper sideband signal at f U will experience different gain or attenuation T hus they usually have different powers. The difference between the signal strengths will affect the choice of IF and RF because the cancellation equation will change when there is power mismatch between the two sidebands. It will be explained through the following analysis. Figure 7 12 Vital sign baseband spectrum at a single carrier frequency of 33 GHz
113 Figure 7 13 Vital sign baseband spectrum from two sidebands at 33 GHz and 45 GHz For example, if the upper sideband signal experiences more attenuation tha n the lower sideband signal due the limited bandwidth, the baseband signal can be written as: (7 10) rd harmonic of RR will correspondingly have the following expression: (7 11) For quantitative analysis, if the power of lower sideband signal is 2 dB higher than the upper sideband signal, which means 2 0log(1+
114 on foregoing analysis, in order to cancel H rr 3 from the spectrum, the following e quality condition needs to be met. (7 12) For the same assumed case that m rr =4 mm, the appropriate IF (LO1) and LO (LO2) rr L =x 1 rr U = x 2, we need to find two points x 1 and x 2 from the curve of J 3 (x) that can meet the equality given in (7 12). Many pairs can be found suitable and one of them is: x 1 =5.94, x 2 =6.98, since J 3 (5.94)=0.1327, J 3 (6.98)=0.1676, and 1.26 L =5.94, U =6.98. T his results in f L =35.45 GHz, f U =41.66 GHz, so LO=38.55GHz, IF=3.1GHz. It can be seen that, because of the larger power of the lower sideband signal than that of upper sideband signal, the distance between the two points is decreased from 2 (7.5 5.5) to 1.0 4 (6.98 5.94). Since the distance between the two rr (f U f L rr 2IF/c, the decrease in distance indicates IF frequency becoming lower. This effect can be verified from the foregoing analysis. The IF is reduced from 6 GHz when the two sideband signals have equal powers to 3.1 GHz when the lower sideband signal is 1dB higher than the upper sideband signal. One can easily prove that when the upper sideband signal is larger than the lower sideband signal, the IF also becomes smaller d ue to same mechanism. In experiment, the appropriate IF should be chosen based on the power difference between the two sideband signals.
115 7.3.2 The Relation between Harmonic Order And LO Frequency The principle of the harmonic canceling technique using dou ble sideband transmission is that if we want to cancel the n th order harmonic, two points need to be foun d on the n th order Bessel function They should locate on the two sides of the first zero crossing point of the n th order Bessel function Figure 7 14 Bessel functions of order n=0 to n=3 Figure 7 14 shows that each order Bessel function has zero crossing points, and as the order increases, the zero crossing points become larger. For example, the first zero crossing points of J 0 (x) is 2.37, J 1 (x) is 3.82, J 2 (x) is 5.13, J 3 (x) is 6.38. It should also be noted that each curve has multiple zero crossing points, only the first zero crossing point is used given the following explanation. It is known that the two points ( rr f L /c and rr f U /c) that u sed to cancel the n th harmonic usually locate nearly symmetrically (if the two sidebands have approximately equal power) on the two sides of the zero crossing points of J n (x). Since f LO =( f L + f U )/2, rr f LO /c will be close to the zero crossing points valu es. Taking the 2 nd order Bessel function as an example, its 1 st and 2 nd zero crossing points are 5.13 and 8.38, respectively (m rr is still 4 mm as in previous analysis). Therefore, the corresponding f LO
116 would be 30.6 GHz and 50 GHz for 1 st and 2 nd zero cro ssing points. As can be seen, the LO frequency needs to be increased significantly if higher order zero crossing points were used. Thus, higher order zero crossing points are not appropriate considering the prohibitively high cost of high frequency compone nts that would otherwise be required to use, such as high frequency LO, mixer and antenna. Therefore, the LO frequency is determined by the first zero crossing point of Bessel curves. 7.3.3 The Relation b etween Chest Wall Displacement and RF Frequency As explained in section 7.3.2, the value of the first zero crossing point of the n th Bessel function determines the value of RF frequency for a given chest wall displacement. Since the chest wall movement is dominated by the respiration activity, the displace ment due to heartbeat is usually around 0.05 mm, thus we approximate the chest wall displacement to be m rr The value of the first zero crossing point of each order Bessel function is fixed, and it approximately equals to rr f LO /c. Table 7 1 lists the va lue of m rr and the required LO frequency for 2 nd and 3 rd harmonic cancellation. Table 7 1. m rr and f LO for 2 nd and 3 rd harmonic cancellation Chest wall displacement (mm) 2 nd harmonic 3 rd harmonic f LO (GHz) f LO (GHz) 1 122.5 152.3 2 61.2 76.1 3 40.8 50.7 4 30.6 38 5 24.5 30.5 6 20.4 25.4 7 17.5 21.8 8 15.3 19 As can be seen from Table 7 1, when the chest wall displacement is small, which usually indicates the respiration activity is weak, it requires very high RF to cancel harmonics. Nevertheless, when the respiration signal is weak, its harmonic will also be
117 stronger that results in a larger chest wall displacement, it harm onics, especially the 3 rd harmonic that is very close to the heartbeat rate would become strong and overwhelm the weak hear t into use to remove the undesired harmonics from the baseband spectrum and improve the detection accuracy of heartbeat rate potentially. For normal breathing, the chest wall movement has the displacement around 5 mm. From the data shown in Table 7 1, a ka band RF would be the appropriate choice. When the respiration becomes stronger, a K band or Ku band RF would be suitable. 7.4 Experiment Verification In experiment, a program controlled actuator is used to generate different vibration patterns. For the convenience of verification, one tone movement is assumed. Due to the limitation of the actuator itself, it cannot move in a pure sinusoidal pattern, but more like a triangular waveform. This factor should also be taken into account in the analysis of results. The IF frequency is tuned through a signal generator and t he RF frequency is adjusted by a YTO, which is a current controlled oscillator Table 7 2. Double sideband Ka band radar building blocks and their specifications Blocks Manufacturers Specifications LO1 Agilent Signal Generator 0~40GHz LO2 Avantek 20 40G, Pout: 10dBm Tx_mixer Rx_mixer Miteq RF/LO: 4 40GHz, IF: 0.5 20GHz Conversion loss: 10dB I/Q mixer Hittite RF: 4 8.5GHz, IF: 0 3.5GHz, Conversion loss: 8 dB IF Power Splitter Narda 0.5 18GHz, 3dB RF Power Splitter Narda 10 40GHz, 3dB LNA Miteq 26 40GHz, Gain: 27dB, NF: 3dB IF Amplifier Miteq 0.1 8GHz, Gain: 33dB Tx and Rx antenna AMD 26.5 40GHz, Gain: 20dBi Gain Block Hittite Gain: 15dB, P1dB: 15 dBm
118 Figure 7 15 Double sideband radar output spectrum For the tuning current of 400mA to 860mA, the oscillation frequency will change from 20 GHz to 40 GHz. The specifications of the main building blocks of the Ka band radar are listed in Table 7 2. The output spectrum i s shown in Figure 7 15 It can be seen that besides the two sideband signals, there will also be LO leakage, which is attenuated by roughly 30 dB from 10 dBm output. In addition, as mentioned in section 7. 3. 1, there will be mismatch between the two sideb ands. The power of lower sideband is 1.5 dB higher than the upper sideband. In order to make the nonlinear modulation effect more evident, the actuator is program m ed to move with the peak displacement amplitude larger than 4 mm and the vibration frequency is 0.2 Hz. By tuning the RF and IF frequencies, we can observe that certain harmonics will disappear from the baseband spectrum as expected. LO leakage: 30.7 GHz Pout: 16 dBm fL: 26.6 GHz Pout: 6.8 dBm
119 7.4.1 2 nd Order Harmonic Cancellation nd order harmonic on the baseband spectr um the RF frequency of 31 GHz, and the IF frequency is 4.6 GHz. Also in this case, the vibration amplitude is set to be 4 mm. Figure 7 16 shows the baseband spectrum when t here is only a single carrier frequency at 26 GHz. With displacement amplitude m= 4 mm, IF=4.6 GHz and RF=31 GHz, we have f L =26.6 GHz and f U =34.7 GHz. Then we can know that x 1 =4 m/ L =4.46, x 2 =4 m/ U =5.81. Thus, J 2 (x1)=0.23, J 2 (x2)= 0.2. As can be seen that the combination of LO of 4.6 GHz and RF and 31 GHz will render two points on the 2 nd order Bessel function that have opposite sign and almost equal magnitude that can attenuate the 2 nd harmonic to a great extent shown in Figure 7 17 Note that the 2 nd harmonic cannot be exactly cancelled due to the fact that the magnitude of the two points are not strictly equal to each other and also there will always be mismatch between the two sidebands due to the limited bandwidth of the circuit and the bandwidth of the horn antenna. However, compared to the spectrum when there is only a single carrier frequency (Figure 7 16 ), the double sideband radar system can significantly reduce the power of 2 nd harmonic of vibration. Figure 7 16 Baseband spectrum with single carrier frequency at 26GHz
120 Figure 7 17 2 nd order harmonic cancellation experiment. Upper: time domain I/Q signals. Lower: baseband spectrum 7.4.2 3 rd Order Harmonic Cancellation Figure 7 18. 3 rd order harmonic cancellation experiment. Upper: time domain I/Q signals. Lower: baseband spectrum For the 3 rd order harmonic cancellation experiment, the RF frequency is fixed at around 31 GHz. The peak displacement value is set at 5 mm. It is found that when the
121 IF equals 4 GHz, the 3 rd harmoni c on the baseband spectrum can be removed. Figure 7 18 shows the measured time domain I/Q signals and the corresponding baseband spectrum. Given the displacement amplitude m= 5 mm, IF=4 GHz and RF=30.7 GHz, we have f L =26.6 GHz and f U =34.7 GHz. Then we can know that x 1 =4 m/ L =5.57, x 2 =4 m/ U =7.27. Thus, J 3 (x1)=0.238, J 3 (x2)= 0.223. These two values almost cancel each other, which explain the negligible value of the 3 rd order harmonic at 0.6 Hz. 7.4 Summary In this chapter, the ratio between the respiration harmonics to the heartbeat signal is studied. The heartbeat rate of an adult under normal condition is usually close to the value of 3 rd order harmonic of respiration signal. It is found that using lower carrier frequency around a few giga Hertz would be more suitable than higher carrier frequency such as Ka band for vital sign detection. It is also proven that utilizing double sideband quadrature radar can cancel out undesired harmonics from the baseband spectrum. It is realized by tuning the IF and/or RF frequency to generate two points that have opposite values to each other on the nth order Bessel function, the nth harmonic can be cancelled. It can be a potential helpful technique for accurate vital sign detection by cancelling the undesired harmonic of respiration (such as the 3 rd order harmonic) from the baseband spectrum.
122 CHAPTER 8 CONCLUSION The concept of RF vibrometer, which is a wireless vibration detection technique by using Doppler radar has been proposed for the first time. Two detection theo ries, one is using the amplitude ratio of multiple harmonic pairs at a fixed carrier frequency, and the other one measuring the variation of amplitude ratio of a fixed harmonic pair under multiple carrier frequencies have been presented, implemented and co mpared. Both of these two methods are based on the nonlinear Doppler phase modulation effect. Harmonics and inter modulation products of the frequency components of the vibration itself will come out due to this nonlinear effect. We use the amplitude ratio s among those harmonics to develop the two different detection theories. Both of them can be used to accurately measure the vibration pattern that is odd function in time, such as triangular waveform or square waveform. The method using multiple harmonic pairs has proven to be more reliable and accurate b ecause it can better preserve the information about the unknown amplitude of each frequency components of the vibration. Without the need to switch carrier frequencies, this detection technique features a simpler architecture and also lower manufacturing cost. For the general form of vibration that includes random excess phase inside of each harmonic frequency component current technique of RF vibrometer cannot recover the vibration pattern since the exce ss phase cannot be accurately determined. However, by using insensitive harmonic pair whose amplitude ratio is insensitive to the variation of excess phase, the amplitude and frequency of each frequency component
123 of the vibration can be obtained, from whic h, the characteristics of th e vibration system can be identified. The non ideal factor from the hardware part, such as the I/Q mismatch effect from LO source has also been investigated. We find out that by adjusting the detection distance to the optimal va lue, the detection error caused by amplitude or phase mismatc h can be significantly reduced. It can also be potentially used as a calibration technique to identify I/Q mismatch by looking at the amount of deviation of harmonic amplitude ratio compared to t he ideal value when there is no mismatch. RF vibrometer has also been used to wirelessly detect human vital signs. Preliminary experimental results show the potential of using RF vibrometer for clinical diagnosing. Further study shows that using lower carrier frequency, it would be helpful for accurate detection of heartbeat signal. Another technique to improve the detection accuracy of heartbeat signal is to use double sideband transmission to cancel the 3 rd harmonic of respiration signal that locates around the heartbeat signal. By tuning the IF and RF frequency, the baseband signals from the lower sideband and upper sideband can assume equal magnitude and opposite value around the first zero crossing point of n th order Bessel function to cancel the n t h harmonic. The research of RF vibrometer shows its potential as a low cost alternative of laser based vibration or displacement sensors for wirele ss periodic movement detection especially for those applications in low visibility environment or thru wal l vibration detection.
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129 BIOGRAPHICAL SKETCH M s Yan Yan received the B.S. degree in electr onics and information engineering from Huazhong University of Science and Technology Wuhan China, in June 200 7. She also rec eived the Master of Science in m anagement from University of Florida in August 2010. She received her Ph.D. from the University of Florida in the spring of 2012 Her research interests include RF vibrometers biomedical application of Doppler radar sensors, and RF /Millimeter Wave IC design M s Yan Yan is a student member of the IEEE Microwave Theory and Techniques Society (IEEE MTT S), and the IEEE Engineering in Medicine and Biology Society. She is the third place recipient of the Best Student Paper award in the 20 10 IEEE Radio and Wireless Symposium (RWS)