AN ABSTRACT OF A THESIS THEORY AND APPLICATION OF TIME REVERSAL TECHNIQUE TO ULTRA WIDEBAND WIRELESS COMMUNICATIONS. Abiodun E.

Transcription

1 AN ABSTRACT OF A THESIS THEORY AND APPLICATION OF TIME REVERSAL TECHNIQUE TO ULTRA WIDEBAND WIRELESS COMMUNICATIONS Abiodun E. Akogun Master of Science in Electrical Engineering Inter symbol interference (ISI) is a major obstacle for achieving low bit error rates in wireless communications. Orthogonal frequency division multiplexing (OFDM) and equalization techniques such as zero forcing (ZF) and minimum mean square error (MMSE) have been employed in combating ISI in typical wireless channels. In this research, a technique called time reversal was investigated as a possible means for achieving higher data rate for a given bit error rate (BER) in ultra wideband (UWB) communications. In this thesis work, time-reversal (TiR) technique was studied in detail and its application to UWB was fully evaluated. Different metrics for characterizing the spacetime focusing properties of time reversal in UWB were proposed and evaluated. The technique employed used a time-domain sounding of the UWB channel to extract the channel impulse response (CIR). UWB channels are measured by sounding the channel with a sub-nanosecond pulse. CLEAN algorithm was then used to extract the CIR from the received waveform. From the observed channel impulse response, the leverages and applications of TiR in UWB were then demonstrated. In TiR, a signal is pre-filtered in such a way that it focuses in space and time at a particular receiver. This can be achieved by using a time-reversed complex conjugate of the CIR at the receiver as a transmitter pre-filter. This results in space-time focusing in TiR. Spatial focusing reduces co-channel interference in a multi-user system. Due to temporal focusing, the effective delay spread of the UWB channel is dramatically reduced and thus the complexity of the receiver is reduced. Using defined metrics for characterizing the amount of temporal focusing in UWB, it was observed that TiR works finer in a non-line-of-sight (NLOS) environment as compared with line of sight (LOS). In order to illustrate the principle of secured communications in UWB using TiR, the spatial focusing gain was studied and at a distance of approximately 6m from an intended receiver, this gain was at least 10dB. Also, to illustrate the advantage of TiR in UWB, the energy loss as a result of spatial focusing was studied against the energy loss without TiR and this gave relative information on the energy gain observed using TiR in UWB environments. Lastly, TiR was combined with equalization techniques as a means of compensation for the residual ISI in UWB channels after applying TiR, and a relative improvement was observed.

2 THEORY AND APPICATION OF TIME REVERSAL TECHNIQUE TO ULTRA WIDEBAND WIRELESS COMMUNICATIONS A Thesis Presented to The Faculty of the Graduate School Tennessee Technological University by Abiodun Emmanuel Akogun In Partial Fulfillment Of the Requirements for the Degree MASTER OF SCIENCE Electrical Engineering August 2005

3 CERTIFICATE OF APPROVAL OF THESIS THEORY AND APPLICATION OF TIME REVERSAL TECHNIQUE TO ULTRA WIDEBAND WIRELESS COMMUNICATIONS by Abiodun Emmanuel Akogun Graduate Advisory Committee: R. C. Qiu, Chairperson date P. K. Rajan date X. B. He date N. Ghani date Approved for the Faculty: Francis Otuonye Associate Vice President for Research and Graduate Studies Date ii

4 STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirements for a Master of Science degree at Tennessee Technological University, I agree that the University Library shall make it available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgement of the source is made. Permission for extensive quotation from or reproduction of this thesis may be granted by my major professor when the proposed use of the material is for scholarly purposes. Any copying or use of the material in this thesis for financial gain shall not be allowed without my written permission. Signature Date iii

5 DEDICATION This thesis is dedicated to my dad (Johnson) and my mum (Olufunmilayo) iv

6 ACKNOWLEDGEMENTS I would like to express my sincere appreciation to my advisor, the chairperson of my committee, Dr. R.C. Qiu, for his excellent guidance and patience throughout my thesis work. He has been a great mentor, an excellent teacher, and a very senior colleague and has made a very immense contribution towards the accomplishment of this task. I would also like to thank Dr. P. K. Rajan, Dr. N. Ghani, and Dr. X. B. He for serving as my committee members, reviewing my thesis work, and for patiently answering questions and concerns as regards this work. Also, a very special thanks goes to Dr. Nan Guo for all the long technical discussions and contributions he has made during the course of this work. I will also like to thank Mr. J. Zhang of the Wireless Networking Systems Laboratory for his help with the simulation work in this thesis. I also need to thank Mr. C. Zhou of the Wireless Networking Systems Laboratory for his contributions in some measurement work. All members of the Wireless Networking Systems Laboratory have been very helpful in my accomplishment of this task and I would like to express my special appreciation to every member of the group. Again, I would like to thank all my friends, colleagues, and my family members who have always been a source of encouragement throughout my life. Last but very important I would like to thank the Graduate School for financial support provided during my program of study. I would also like to thank the Center for Manufacturing Research for summer financial support during my program of study. Finally, I would like to express my profound gratitude to the almighty God who has constantly given me life and has kept me through up to this moment in life. v

7 TABLE OF CONTENTS Page LIST OF FIGURES. viii LIST OF TABLES... x CHAPTER 1. INTRODUCTION Motivation and Scope of Research Literature Survey of Time Reversal Technique Research Approach Organization of the Thesis ULTRA WIDEBAND COMMUNICATION (UWB) A Brief History of UWB Technology Definition UWB Signal Sources UWB Modulation Techniques Pulse Position Modulation (PPM) Pulse Amplitude Modulation (PAM) On-Off Keying (OOK) Binary Phase Shift Keying (BPSK) UWB Demodulation/Detection UWB Multiple Access Techniques Direct Sequence, DS-UWB UWB DS-CDMA Basic Signal Model Time Hopping UWB Basic signal model for TH-WB Applications Through-wall Penetration UWB Radar Precision Location Sensor Networks (IEEE a) Summary UWB CHANNEL MODELING AND CHARACTERIZATION Linear Filter-Based Small Scale Channel Modeling UWB Deterministic Channel Modeling UWB Channel Measurement and Modeling UWB Channel Measurement and Modeling Background Measurement Apparatus and Setup Deconvolution Techniques The Clean Algorithm Limitations of the CLEAN Algorithm vi

8 CHAPTER Page 3.6 Summary TIME-REVERSAL COMMUNICATIONS Introduction An Overview of Time-Reversal in UWB Time-Reversal Theory Time Reversal and UWB Systems Performance Rake Receivers ISI Issues in UWB Equalization Techniques Infinite length equalizers Finite length equalizers Zero forcing equalizers Minimum mean square error (MMSE) equalizer TiR System Structure Summary SIMULATION RESULTS Monte Carlo Simulation BER Simulation Results CM3 Simulation Results CM4 Simulation Results Foundry Simulation Result BER Results for Clement Hall 400 Hallway Results Illustrating Temporal Compression Results For Spatial Focusing Gain Results for Time Reversal Loss Versus Distance Summary CONCLUSIONS AND FUTURE WORK Conclusions Recommendations for Future Work APPENDICES A: IEEE CHANNEL MODEL P A..99 A. 1 Multipath Channel Model A. 2 Channel characteristics desired to model 101 B: MATLAB CODE LIST.105 B. 1 List of Signal Processing/Simulation files..106 VITA vii

9 LIST OF FIGURES Page Figure 2.1 Comparison of UWB with traditional wireless technologies Figure 2.2 Spectral Mask for Indoor Applications Figure 2.3 Spectral Mask for outdoor Applications Figure 2.4 UWB Pulses Figure 2.5 Spectrum of UWB pulses Figure 2.6 UWB Modulation schemes (a) OOK, (b) PAM, (c) PPM Figure 2.7 BER Plot for UWB modulation schemes [19] Figure 3.1 Classical ground bounce two-ray model Figure 3.3 Pulser output with a differentiator Figure 3.4 Time Domain UWB Channel Sounding Figure 3.5 UWB channel measurement setup Figure 3.6 Received waveforms at distances 4m (LOS), 7m (NLOS), and 10m (NLOS) from the transmitter Figure 3.7 Received waveforms for LOS cases Figure 3.8 Received waveform showing two back-to-back multipath profiles Figure 3.9 Clement Hall 400 Hallway Figure 4.1 TiR experiment Figure 4.2 Temporal compression illustrated using measured data Figure 4.3 Temporal compression illustrated using IEEE a CM3 channel.. 51 Figure 4.4 Demonstrating spatial focusing in TiR Figure 4.5 Rake receiver structure Figure 4.6 UWB Channel with equalizer Figure 4.7 Discrete UWB channel with equalizer Figure 4.8 UWB systems with TiR Figure 5.1 Simulation setup Figure 5.2 TiR BER simulation result using CM Figure 5.3 TiR BER simulation using CM Figure 5.4 Foundry BER simulation results Figure 5.5 CMR Foundry Figure 5.6 BER simulation result for Clement Hall 400 Hallway Figure 5.7 Temporal compression in CM1 channel Figure 5.8 Temporal compression in CM3 channel Figure 5.9 Temporal compression in CM4 channel Figure 5.11 Temporal compression in CMR Foundry LOS Figure 5.13 Clement Hall 400 Hallway LOS results showing temporal compression. 79 Figure 5.14 Clement Hall 400 Hallway NLOS showing temporal compression Figure 5.15 WNS lab result LOS results showing temporal compression Figure 5.16 WNS laboratory NLOS result results showing temporal compression Figure 5.17 Demonstrating spatial focusing gain in Clement Hall 400 Hallway Figure 5.18 Demonstrating spatial focusing gain in CMR foundry Figure 5.19 Foundry energy loss (TiR versus No TiR) viii

10 Page Figure 5.20 Hallway energy loss (TiR versus No TiR) Figure A.1 CM 1: LOS (0-4m) Figure A.2 CM 2: NLOS (0-4m) Figure A.3 CM 3: NLOS (4-10m) Figure A.4 CM 4 : Extreme NLOS ix

11 LIST OF TABLES Page Table 5.1 Temporal peak to channel energy ratio Table A.1 Channel model components and parameters Table A.2 Typical Channel Characteristics and Model parameters x

12 CHAPTER 1 INTRODUCTION 1.1 Motivation and Scope of Research Ultra-wideband (UWB) has become a suitable candidate for high data rate, shortrange wireless communications [1]. According to Shannon s law, the potential data rate on a given radio frequency (RF) link is proportional to the channel bandwidth and the logarithm of the signal-to-noise ratio. Existing narrowband and spread spectrum technologies are regulated to operate in the unlicensed frequency bands that are provided at 900MHz, 2.4GHz, and 5.1GHz occupying only a narrow band of frequencies relative to that allowed for UWB. UWB is a usage of recently legalized spectrum with a bandwidth of more than 7GHz wide and hence a higher data rate compared to narrowband and spread spectrum systems. In 2002, the United States Federal Communication Commission (FCC) allocated the 3.1 GHz to 10.6GHz spectrum for UWB devices and after this, there has been sparkled interest in UWB research activities in both academia and the industry. To allow for such large operation bandwidth, the FCC has put in place strict power limitations on UWB radios. With strict power limitations, it is therefore possible to implement cost effective CMOS implementations of UWB radios. UWB radios therefore have several advantages, which include low power consumption, low cost, and very high data rate within a short range. Due to the large operation bandwidth, the resolution in time domain is small for UWB radios. UWB involves transmitting ultra-short pulses. The 1

13 advantage of using short pulses is fine timing resolution thus more multipath channels can be resolved [2]. The channel distorts these pulses so that per-path distortion is encountered in UWB systems. References [3] and [4] address the designing of a reception scheme as a key issue for UWB systems. Despite the potential advantages of UWB, several drawbacks have been noted as regards the application of UWB radios. Inter symbol interference (ISI) is a key impediment for reliable high data rate transmission in wireless channels. Orthogonal frequency division multiplexing (OFDM) and equalization techniques have been employed in wireless systems as a means of compensation for ISI. OFDM uses a large number of sub-bands chosen in such a way that each sub-band exhibits flat fading and thus OFDM has the key property of mitigating ISI. Equalization is also an effective means of combating ISI in frequency selective channels. The device, which equalizes the dispersive effect of a channel with memory, is called an equalizer [5]. An approach called time reversal (TiR) has been successfully applied to underwater acoustic channels and narrowband channels as another means of combating ISI in such frequency dispersive channels. When TiR is applied to a dispersive channel, a reduction is observed in the effective channel length. With a reduction in the effective channel length, the effect of ISI in the channel is reduced. This shows that TiR is an effective technique in reducing ISI in frequency dispersive channels. The objective of this project is to study critically the theory behind TiR and to demonstrate several applications of TiR in a UWB channel using both statistical and experimental data collected from different UWB environments. TiR has only recently been applied to UWB [1, 6]. Two key applications that come with this technique are 2

14 spatial focusing and temporal compression. These two key applications are addressed in details and metrics to characterize these two applications are defined in relation to UWB. Spatial focusing is a concept that addresses security concerns in UWB channels. Due to a focus of power at the intended UWB receiver, the probability of a nearby receiver decoding the information on an intended receiver is greatly reduced. In TiR channels, the effective channel impulse response is compressed with a temporal focus of the channel energy being visible around the center of the compressed channel impulse response. Metrics to characterize this temporal compression in UWB channels are defined in this thesis work. Also, the use of TiR technique to compensate for ISI and thus improve UWB receiver performance is addressed is this research work. 1.2 Literature Survey of Time Reversal Technique The concept of time reversal is not new in the world of telecommunications. References [1, 6] show the first application of TiR to UWB. In [1], the concept is combined with a minimum mean square error (MMSE) equalizer to improve receiver performance in UWB. The channel data used are collected using a frequency domain channel sounding technique and the number of taps of the TiR channel is varied to study receiver performance in UWB. In [6], the space-time focusing properties of TiR in UWB are demonstrated also using a frequency domain channel sounder with measurement results from Intel Corporation. In [7], the concept is applied to electromagnetic waves and the concept of spatial focusing and temporal compression is demonstrated using a 1 µs electromagnetic pulse at a central frequency of 2.45GHz. This is the first experimental 3

15 demonstration of TiR space-time focusing with electromagnetic waves. The spatial and temporal focusing that comes with this technique has been demonstrated in ultra-sound by Fink [8, 9]. In underwater acoustics, [10-13] details the application of the technique and the issues of spatial and temporal compression are also addressed. Reference [14] demonstrates the first application of TiR to wireless radio and proposes to convert an available broadband multiple input multiple output (MIMO) channel sounder into a device that can demonstrate the concept of TiR. In [15], the concept of multiple input single output (MISO) is applied in conjunction with TiR as a possible means to reduce the delay spread in a fixed wireless access channel and a delay spread reduction of a factor of three was observed. In [16] the concept is applied to time reversed random fields and the space-time focusing issues are addressed in relation to this field. Reference [17] demonstrates the space-time focusing properties in TiR using a time domain channel sounding technique and at a distance of 6m from the intended receiver, the spatial focusing gain observed is at least 10dB. In [18], the basic principles of applying TiR to underwater acoustic field are explained in details. Reference [19] applies the concept of time reversal with a transmitted reference system and the new receiver structure called time reversal and transmitted reference (TiR-TR) shows a relative improvement of about 9dB performance gain at a data rate of 19Mbps for a BER of In [20], the concept of TiR is applied with MISO in an underwater acoustic channel and a zero forcing preequalization is also applied in the channel to demonstrate the space-time focusing features of TiR. Reference [20] shows that pre-equalization does not alter significantly the spatial focusing properties of time reversal. 4

16 MIMO is a way of exploiting the rich scattering properties in frequency dispersive narrowband channels. In [21], using outdoor measurements that mimic a typical 3G WCDMA system, the feasibility of applying TiR with MIMO in single user wireless systems is studied showing TiR-MIMO as a promising technique for wireless channels. It also studied the feasibility of applying TiR with multi user MISO systems. 1.3 Research Approach The methods employed in literature to demonstrate the application of TiR have all employed a frequency domain channel sounder approach. With this approach, the real time behavior of UWB channels cannot be observed. From the mathematical knowledge of Fourier transforms, it is possible to transform a frequency domain signal into its corresponding time domain equivalent. This shows that a time domain approach is also possible to demonstrate the concept of TiR in UWB since a frequency domain approach has already been used. The received waveform in wireless channels is a convolution of the channel impulse response with the transmitted waveform. In order to extract the channel impulse response from the received waveform, deconvolution techniques are employed. UWB channel data are collected for different UWB environments. From the collected data, a signal processing algorithm, the CLEAN algorithm, is used to extract the channel impulse response. The CLEAN algorithm is a deconvolution technique to extract the observed channel impulse response from the received waveform. From the observed channel impulse response, the space-time focusing properties of TiR in UWB are demonstrated 5

17 using defined metrics. Also, using IEEE channel models for a and a, the concept of TiR is also illustrated. The use of TiR to compensate for ISI is also demonstrated using IEEE a channel models and results from the collected data for typical UWB environments. Bit error rate (BER) is used as the performance metric. It is observed that with the use of TiR, ISI is greatly reduced and the equalization task in the effective TiR channel is also greatly reduced. Equalization if needed for a TiR channel has the complexity of the equalizer being tremendously reduced. 1.4 Organization of the Thesis Chapter 2 details the concept behind UWB communication; a brief history of UWB, UWB signal sources and the associated spectrum, UWB modulation techniques, and the applications of UWB are discussed. Chapter 3 presents the concept involved in time-domain sounding of UWB channels. The principles involved in the use of the CLEAN algorithm as the signalprocessing algorithm used in this thesis are also addressed in this chapter. Chapter 4 focuses on the theory and applications of TiR in UWB. This chapter presents an overview of TiR and the proposed metrics for characterizing TiR in UWB are discussed here. It also focuses on evaluating the performance of TiR channels in UWB environments. It gives an overview of receiver types and signal models for frequency selective channels. It also addresses the use of TiR to improve receiver performance in UWB. 6

18 Chapter 5 presents the results on the applications of TiR in UWB channels. It gives the relative improvement observed using TiR in BER simulation for UWB channels. It also gives a comparison between the line-of sight (LOS) and non line of sight (NLOS) UWB TIR channels. Chapter 6 gives the conclusion from this thesis work. Recommendations for future work are also presented in this chapter. Appendix A briefly introduces IEEE a and a channels. A Listing of the Matlab code is given in Appendix B. 7

19 CHAPTER 2 ULTRA WIDEBAND COMMUNICATION (UWB) Ultra wideband (UWB) technology is well known for its use in ground penetrating radar. UWB has also been of interest in communications and radar applications requiring low probability of intercept and detection (LPI/D), high data throughput, precision ranging and localization, and multipath immunity. In this chapter, the basic concept behind UWB is presented. After a very brief history of UWB, the shapes and spectra of UWB pulses are discussed; UWB modulation techniques and applications of UWB are then discussed. 2.1 A Brief History of UWB Technology The origin of ultra wideband stems from work in time-domain electromagnetic in 1962 [22]. The idea was to characterize linear, time invariant systems (LTI) using the impulse response of such systems instead of using the conventional swept frequency response. The output y (t) of an LTI system to an input excitation x (t) can be determined using the well known convolution integral [23]: y ( t) = x( τ ) h( t τ ) dτ (2.1) where h (t) is the impulse response of the system. However, the impulse response of microwave networks could not be directly observed and measured until the advent of the sampling oscilloscope by Hewlett Packard 8

20 in 1962 and the development of techniques for sub-nanosecond (base band) pulse generation, providing suitable approximations to an impulse excitation. Once these techniques were applied to the design of wideband, radiating antennae elements (Ross, 1968), it became obvious that they could also be applied to short pulse radar and communications systems. Throughout the late 1980 s, this technology was alternately called base band, carrier-free, or impulse. The term ultra-wideband was not applied until 1989 by the U.S Department of Defense (D.O.D). By that time, UWB had already experienced 30 years in its development. Although, UWB is old, its application in communications is new. 2.2 Definition UWB characterizes transmission systems with instantaneous spectral occupancy in excess of 500MHz or a fractional bandwidth of more than 20%. Fractional bandwidth ( B f ) is defined as B B f = (2.2) f c where B = f f denotes the 10dB bandwidth and H H L c 2 f = ( f f L) is the center frequency with f H being the 10dB emission point upper frequency and f L is the 10dB emission point lower frequency. The huge bandwidth implies that UWB can provide high throughput required to address the market for wireless personal area networks (WPAN). In order to co-exist with existing traditional wireless technologies such as spread spectrum and narrowband 9

21 systems, the United States Federal Communication Commission (FCC) imposes strict limitations on the power spectral density from UWB systems. Figure 2.1 shows a brief comparison of UWB with existing wireless technologies in terms of bandwidth and the emitted power expected from the devices. Figures 2.2 and 2.3 show the spectral density mask for indoor and outdoor operations. UWB signals may be transmitted between 3.1 GHz and 10.6 GHz at power levels up to 41dBm/MHz. The primary difference between indoor and outdoor operations is the higher degree of attenuation required for out of band region for outdoors operation. This further protects GPS receivers, centered at 1.6 GHz. 2.3 UWB Signal Sources UWB signals can be realized using sub-nanosecond pulses. Narrower pulses in time domain correspond to an electromagnetic radiation of wide spectrum in frequency domain. The frequency domain spectral content of a UWB signal depends on the pulse waveform shape and the pulse width. The most common signals used to drive UWB antennas include a Gaussian pulse, Gaussian monocycle, Gaussian doublet, Raleigh monocycle and rectangular waveforms. Rectangular waveforms have large DC components, which is not a desirable property. A generic Gaussian pulse can be represented as [24]: t µ p g ( t) = exp (2.3) σ 2π 2 σ 10

22 Figure 2.1 Comparison of UWB with traditional wireless technologies Figure 2.2 Spectral Mask for Indoor Applications 11

23 Figure 2.3 Spectral Mask for outdoor Applications where t is the time in seconds µ is the parameter that defines the center of the pulse σ is the parameter that defines the width of the pulse. A Raleigh monocycle is obtained by differentiating the Gaussian pulse once [25]. The second derivative of the Gaussian pulse gives a Gaussian monocycle while the Gaussian doublet consists of two; amplitude reversed Gaussian pulse having a time gap of T w between the pulses. Figures 2.4 and 2.5 show different UWB pulses and their associated spectra. 12

24 2.4 UWB Modulation Techniques In order to transmit information, it is necessary to modulate the pulse train. For coherent detection several modulation schemes were initially employed for UWB communication. The most common modulation schemes found in the literature include Pulse Position Modulation (PPM), Pulse Amplitude Modulation (PAM), On-Off keying (OOK), and Binary-phase shift keying (BPSK). BPSK has a 3dB performance improvement over OOK and PPM. 1 UWB pulses Amplitude Gaussian monocycle(2nd order differential) Rayleigh monocycle(1st order differential) Gaussian pulse Time(ns) x 10-9 Figure 2.4 UWB Pulses 13

25 Figure 2.5 Spectrum of UWB pulses Pulse Position Modulation (PPM) In PPM, the position of each pulse is varied in relation to the position of a recurrent reference pulse according to the information data. A digital zero could be coded by transmitting a pulse some picoseconds earlier than a reference position while a digital one could be coded by transmitting at the same amount of time later as shown in Figure 2.6. Many positions can be used to increase the number of symbols and hence we can have an M-ary PPM. PPM has the advantage of requiring constant transmitter power since the pulses are of constant amplitude and duration. The periodicity of the pulse repetition period (PRP) makes energy spikes to appear in the spectrum. In order to 14

26 smoothen the spectrum, pseudorandom sequence of delays could be added to the pulse train. This is called time hopping. Binary PPM technique is given by where b { 0,1} n n= 1 ( t ) s( t) = p nt f δ b n (2.4) data bits δ p(t) is the time shift is the UWB pulse shape T f is the frame time Pulse Amplitude Modulation (PAM) In PAM, the information data are carried on a train of pulses with the information being encoded in the amplitude of the pulses. Values are defined by changing the powers of the pulses. An 8-ary PAM for example uses eight levels of the pulse amplitude to yield four bits. The classic binary amplitude modulation (PAM) can be represented using for example two antipodal Gaussian pulses [26] as shown in Figure On-Off Keying (OOK) In On-Off keying, the presence of a pulse indicates a value of one while the absence of a pulse indicates a value of zero. The following equation represents OOK modulated UWB transmitted signal and the waveform is shown in Figure

27 Figure 2.6 UWB Modulation schemes (a) OOK, (b) PAM, (c) PPM n nt f n= s ( t) = b p( t ) (2.5) where s (t) is the UWB signal b { 0,1} n data bits p(t) is the UWB pulse shape T f is the frame time. 16

28 The main advantage of OOK over other modulation schemes is simplicity in its implementation Binary Phase Shift Keying (BPSK) In BPSK, a positive pulse is transmitted for a 1 and a negative pulse is transmitted for a 0 as shown in Figure 2.6. BPSK can be mathematically represented by n nt f n= s ( t) = b p( t ) (2.6) where b { 1, 1} n data bits. 2.5 UWB Demodulation/Detection The major criteria to evaluate the efficiency of a particular modulation scheme are its BER performance, spectral shape, data rate, and transceiver complexity [27]. As seen previously, modulation transmits the required data information. The main function of a demodulator is to extract the original data information modulated on the monocycle train from the distorted waveforms with the highest level of accuracy. A receiver generally consists of a detection and decision device. The detector in ultra wideband systems is different from that of existing narrowband systems since ultra wideband operates in a carrier-less fashion. Typical UWB receiver implementations include autocorrelation 17

29 receivers and correlation or rake receivers. In the UWB correlator receiver, the first operation to be carried out is the match filtering of the waveform. In order to do this, the incoming signal is matched with a waveform template and the result is integrated. This correlation operation between the received signal and the waveform template has to be performed for each possible pulse position and the correlation results are then sent to the base band for further processing. The UWB correlator (matched) receiver already discussed is an optimum receiver for the AWGN channel. For such a receiver, the received signal r (t) in the absence of multiple access interference can be modeled as follows: r ( t) = s ( t) + n( t) (2.7) where s (t) is the transmitted monocycle, n (t) is the zero mean white Gaussian noise with power spectral density No/2. For binary modulation, the BER can be calculated using the Euclidean distance d min between the two symbols. P b = Q 2 d min (2.8) 2N o The Euclidean distance between the two symbols can be evaluated for various modulation options as d min = 2E s for orthogonal PPM, d 2 min = E s for BPSK d = a min E s for OOK, d = a a ) for PAM min ( 1 2 E s where 18

30 E s is the average energy per symbol (Joules) a Q is the average transmitted pulse energy is the Q function [28] which is the tail of the standard. Gaussian density function (mean µ =0 and variance σ=1) and is defined by Q( x) = x 1 e 2π 2 z / 2 dz. (2.9) The advantage of BPSK over OOK and PPM is the improvement in BER performance, since it is 3dB more power efficient for the same probability of error. Figure 2.7 shows the BER plots for different modulation schemes. Figure 2.7 BER Plot for UWB modulation schemes [19] 19

31 2.6 UWB Multiple Access Techniques Based on spreading, the two common multiple access schemes employed with UWB are Time-Hopping UWB (TH-UWB) and Direct Sequence UWB (DS-UWB). In TH-UWB, unique time hopping codes are used to position each of the UWB pulses within a given time frame of a particular bit. In DS-UWB, no time gapping is left between transmitted pulses. A multiple access scheme can either be synchronous or asynchronous depending on whether the bits transmitted are in the same time interval or not. Construction of asynchronous multi-user orthogonal codes is impossible as different users arrive the receiver location with random time delays. TH/SS have spike problems when compared with DS-SS. The co-existence of UWB systems using TH-SS and DS-SS is important since UWB will co-exist with narrowband/wideband systems in the same frequency spectrum. Narrowband/wideband systems include Global system for Mobile Communications (GSM 900) and Universal Mobile for terminal service (UMTS)/wideband code division multiple access (WCDMA) and the Global Positioning system (GPS). In the GPS L1 and L2 channels, DS-SS introduces less interference than TH-SS UWB. Both TH-SS UWB and DS-SS UWB generate similar level of interference in GSM900 and UMTS/WCDMA bands. In the presence of degradation due to jamming from narrowband systems, TH-SS UWB outperforms DS-SS UWB at a low interference level and both TH-SS UWB and DS-SS UWB have similar performance at a high jamming power level. 20

32 2.6.1 Direct Sequence, DS-UWB The DS-UWB is similar to conventional CDMA carrier-based radios. The spreading sequence is multiplied by an impulse sequence. The modulation technique employed is the same as that employed in CDMA UWB DS-CDMA Basic Signal Model where The transmitted signal for a UWB DS-CDMA using PPM is defined as k N 1 r k i= n= 0 k k s ( t) = p bi a n z( t it nt δ d ) (2.10) r c n z(t) k is the transmitted monocycle waveform, is the k th user, k b i are the modulated symbols for the th k user, k a n are the spreading chips, T r T c is the bit period, is the chip period, T r N r = is the spread spectrum processing gain, Tc δ is the extra delay of monocycle for symbol 0, d n is the information data sequence, and p k is the transmitted power. 21

33 Correspondingly, for PAM the transmitted signal is given as s N r k k k t p k 1 ( ) = bi a n z( t it r nt c) d n. (2.11) i= n= 0 The information data sequence d n =1 for symbol 1 in PAM and is represented as where d n =0 for symbol 1 and =1 for symbol 0 in PPM while d n =-1 for symbol 0 in PAM. The received UWB signal r ( t) = s( t) + m( t) + I ( t) + n( t) (2.12) s (t) is the transmitted signal, m (t) is the multiple access interference, I (t) is the narrowband interference, n (t) is a white Gaussian noise process with two sided power spectral density N o /2, and the receiver is a correlator receiver Time Hopping UWB Time Hopping is part of the original proposal for UWB communications. Modulation of TH-SS UWB radio is achieved through shifting of pulses. The key motivations for using TH-SS impulse radio are the ability to highly resolve multipath and the availability of technology to implement and generate UWB signals with low complexity [29]. In both TH-SS and DS-SS one information bit is spread over various monocycles and the required processing gain is achieved in reception. 22

34 Basic signal model for TH-UWB. The transmitted signal from a user in TH-SS using PPM is given by where ( k ) s ( t) = w( t jt c j T δd ) (2.13) k j s k (t) is the k th transmitted signal, w (t) is the transmitted monocycle waveform, T f is the pulse repetition time or frame time, f c n j δ is the jth monocycle that sits at the beginning of each frame, is the time shift that applies to the monocycle and such operation is defined when 1 is transmitted, T c is the additional time delay that associates with the time hopping code, (k ) c j are time hopping code (periodic pseudorandom codes), and d n is the information data sequence. For TH-PAM, the transmitted signal is represented as ( k ) s k ( t) w( t jt f c j T c) j = d. (2.14) n The signal at the receiver is represented as where Nu r( t) = A s ( t τ ) + n( t) (2.15) k= 1 k k k A k models the attenuation at the transmitter signal, n (t) is the additive white Gaussian noise, and 23

35 τ k represents the asynchronisms between the clock of the transmitter and the receiver. The correlator template signal is given by y (t)=w (t)-w(t-δ ) (2.16) where y (t) is the pulse shape defined as the difference between the two pulses shifted by the modulation parameter δ. This will then be correlated with the received signal for the required statistical decision test. 2.7 Applications Typical applications of the UWB technology include through wall penetration, precise location, UWB radar, and UWB sensor networks (IEEE a). UWB is applicable in the above scenarios due to its popularity for multipath immunity, high data throughput, better wall penetration, low power consumption, and low probability of intercept and detection Through-wall Penetration A high resolution is required to track the motion of persons or objects that are placed on the other side of a wall. At longer ranges, precision time gating is required to track multiple targets [30]. An UWB system is a very reliable solution in providing this kind of through-wall penetration and resolution capabilities. 24

36 2.7.2 UWB Radar An advantage of using UWB in radar applications is that due to UWB s inherent time resolution property, it reduces post detection signal processing required in narrowband radars [30, 31]. UWB underground penetrating radars can be used to check if any underground cables or pipes are present before digging. UWB ground penetrating radars can also be used in numerous applications like target specific application, geophysical location, and in civil engineering applications Precision Location The use of differential GPS for outdoor applications can be used to improve errors in modern day GPS and can also be used for precise estimation of location within 1-2 meters. Using UWB in addition with these technologies is a good solution for extending the location finding capabilities to the indoor Sensor Networks (IEEE a) Sensor networks are applicable for surveillance, automobiles, and medical situations. The use of a wired network for these kinds of applications is expensive and cumbersome. In these kinds of applications, UWB is a viable solution as a wireless communication link. With UWB, the network is invisible and unnoticeable to others. Sometimes, a UWB signal can even be used as a sensor. 25

37 2.8 Summary This chapter focused on the fundamentals of UWB communications. UWB pulse shapes and their associated spectra were discussed. The different modulation schemes that can be used for UWB were also discussed. BPSK has a 3dB performance improvement when compared to OOK and PPM. A discussion of UWB multiple access techniques were also presented. TH-SS UWB and DS-SS UWB were discussed as two popular methods of multiple accesses in UWB based on spreading. Finally, some applications of UWB were also discussed. 26

38 CHAPTER 3 UWB CHANNEL MODELING AND CHARACTERIZATION This chapter provides the foundation on which the thesis is based. It describes the concept behind the modeling and characterization of UWB channels. It presents some of the results obtained from the small-scale characterization of UWB channels. These results are based on several measurement efforts conducted in different indoor environments. The first half of the chapter addresses the issue of UWB channel modeling from a deterministic and a statistical point of view. The second half of the chapter considers the overall indoor channel impulse response, based on finite impulse response (FIR) calculated using the CLEAN algorithm. The results obtained from the first half are important towards validating some assumptions used in the second half. The observed channel impulse responses from the second half of this chapter serve as the data on which the applications of TiR are demonstrated in the later chapters of this thesis. 3.1 Linear Filter-Based Small Scale Channel Modeling Accurate channel models are important in designing communication systems. With adequate knowledge of the features that are unique to the channel, communication engineers are able to predict the system performance for specific modulation schemes. Propagation channels set fundamental limits on the performance of UWB communication systems. Due to reflection, refraction, and diffraction, wireless signals usually experience multipath propagation. In narrowband systems, this leads to 27

39 multipath fading. Various theoretical and empirical models have been employed in studying the statistics of multipath fading in indoor environments. Turin s point- scattering model is widely used for amongst these models. In Turin s model, the channel is represented as where L h(τ,t) = α l( t) δ [ τ τ l( t) ] l= 1 j l(t) e θ (3.1) δ L represents the dirac function, is the number of resolvable multipaths, α l(t) are the multipath amplitudes, τ is the delay variable, τ l(t) are the multipath arrival times, and θ l (t) are the path phase values. Distributions used to describe amplitude values are: Rayleigh, Rician, Nakagami (m-distribution), Weibull, and Suzuki. Distributions used to describe the arrival times are modified 2-state Poisson model ( -K model), modified Poisson (Weibull Intervals), and double Poisson (Saleh-Valenzuela). The initial phase is a uniformly distributed random variable [0,2π]. Phase distribution can be incremented by a random Gaussian variable and deterministic values calculated from the environment. Certain parameters are useful as single number descriptions of the channel to estimate the performance and the potential for inter symbol interference (ISI). The parameters include the mean excess delay, RMS delay spread, and maximum excess delay and they describe the time dispersive properties of the channel. These time 28

40 dispersive properties of the channel are measured relative to the time of arrival of the first component. The mean excess delay (X db) of a power delay profile is the time required for the energy to fall X db below the maximum [32]. The mean excess delay is the first moment of the power delay profile k a k k τ = 2 a. (3.2) k 2 τ k The RMS delay spread is the square root of the second central moment of the power delay profile [32] where ( τ ) 2 2 σ τ = τ (3.3) a k 2 k τ k 2 τ =. (3.4) 2 a k 2 k The ratio of the mean excess delay to the RMS delay spread can be used as a measure of the time dispersion for UWB signals. Channel models for UWB can either be physical models taking into account the exact physics of the propagation environment or statistical models taking empirical approach, measuring propagation characteristics of the environment and then developing models based on measured statistics. In order to estimate the parameters associated with a given channel impulse response, a channel sounder is used. A channel sounder is a device that allows estimation of the parameters associated with the impulse 29

41 response of a radio channel namely: the number of multipath components and their associated amplitudes, phases, and delays. 3.2 UWB Deterministic Channel Modeling In UWB systems, the transmitted pulses have width much smaller than the channel propagation delays and hence do not overlap. At the receiver, due to the wideband nature of UWB signals, conventional models for characterizing narrowband channels such as the Turin s model are inadequate for UWB transmission. The Turin s point scattering models does not take into account the frequency dependency of the individual path rays and hence it does not take into account the issue of waveform distortion. In practice, when a waveform propagates through a medium, there are three propagation mechanisms of interests: line of sight (LOS), reflection, and diffraction [33]. Diffraction causes the strength of the diffraction field to be frequency dependent α with a term ω in the diffraction field expression. Including the frequency dependent parameter to Turin s model allows us to represent the wideband channel as where The parameter L l= 1 jθ l( t) [ τ τ ( t) ] e h( τ, t) = α ( t) h ( τ ) δ (3.5) h l l l l (τ ) is the per-path impulse response and denotes convolution operation. h l ( τ ) explains most of the practical diffraction phenomena occurring in buildings, windows, cylinders, furniture, bottles, etc. In studying channel effects, the 30

42 effect of propagation phenomena on the received signal can be categorized as largescale effects and small-scale effects. Large-scale effects are important for predicting service availability and coverage while small-scale effects are those that vary over a short time and are important in designing modulation schemes for UWB systems. UWB channel modeling with emphasis on pulse waveform distortion or frequency dependency in frequency domain was first studied in [33]. The physical foundation of pulse waveform distortion is based on Sommerfield s exact solutions of Maxwell s equations. The study of time-domain or transient wave electromagnetics was initiated by Sommerfield in 1902 on the diffraction of a pulse or a transient wave by a wedge or half plane [34]. The frequency dependency of the path rays can be used to trace, detect, and characterize a ray and is also useful in channel modeling. A ray coming from the line of sight path or a reflected ray has no frequency dependency while a ray from a diffracted path has frequency dependency. Ray tracing of the individual path rays can be used in studying the propagation features of a UWB channel. The concept of pulse waveform distortion or frequency dependency and its impact on UWB transceiver design are studied extensively in [35-37]. The UWB propagation mechanisms include the geometric optical (GO) rays and the diffracted rays. The geometric theory of diffraction (GTD) framework can be used to model the diffracted rays. Mathematically, E = E + E (3.6) t GO GTD where E t represents the total electric field, 31

43 E GO represents the field component of the geometric optic rays, and E GTD represents the diffracted rays. In the deterministic modeling of UWB channels, a two-ray model shown in Figure 3.1 is the mostly used model for studying geometric optic (GO) rays 3.3 UWB Channel Measurement and Modeling UWB Channel Measurement and Modeling Background A limited number of measurement campaigns have been carried out by UWB researchers to characterize UWB channels. Most proposed UWB channel models are extensions of existing wideband channel models. There are many unresolved issues in literature on the characterization of UWB channels and hence there is still a need for more measurements to formulate a comprehensive model before designing UWB simulators. Some proposed UWB channel models are based on empirical UWB results while some are based on extrapolation from wideband measurement and models. The characterization of a UWB channel can be carried out using two different approaches: time domain approach and the frequency domain approach. The major piece of equipment used in the frequency domain approach is a vector network analyzer (VNA). The results obtained in frequency domain approach can then be converted into time domain via inverse Fourier transform. The advantage of frequency domain approach is that the sensitivity of narrowband measurement equipments such as the VNA is much larger than that of oscilloscopes used in time domain measurements. However, extra data processing is required for frequency domain measurements to get the time domain 32

44 Figure 3.1 Classical ground bounce two-ray model channel impulse response of the UWB channel. This thesis has employed the time domain approach for collecting the UWB channel data. In this approach, a short duration pulse p(t) is transmitted as an excitation signal for the propagation channel. This pulse approximates a delta function but in reality, it is not and hence there is a need for a signal-processing algorithm to extract the actual channel impulse response. Mathematically, y( t) = h( t) p( t) (3.7) when p( t) = δ ( t), y ( t) = h( t) p( t) = h( t) = CIR. However, in reality, p( t) δ ( t), and hence the need for deconvloution techniques to extract the CIR from the measured y (t). 33

45 3.3.2 Measurement Apparatus and Setup The equipment used for collecting the UWB channel data involves a UWB pulser that generates a Gaussian like pulse with root mean square (rms) pulse width of approximately 250 ps as shown in Figure 3.2: a power amplifier with a gain of 34 db, a noise figure of 4.0dB, and a third order intercept point of 4.0dBm (for pulse amplification): a Digital Sampling Oscilloscope (DSO) Tektronix TDS 8000E3 (with a bandwidth of up to 20GHz), serving as the receiver: a wideband low noise amplifier (LNA) with 23dB gain: a noise figure of 6.00dB: and a third order intercept point of 30dBm. It is possible to obtain other types of UWB pulses from the pulser for use in sounding the UWB channel. Figure 3.3 shows another possible pulse obtained from the pulser employing a differentiator to the pulser output to differentiate the Gaussian like pulse and hence obtained a derivative of the Gaussian like pulse for use in sounding the UWB channel. The pulser needs a triggering signal for operation. A 2MHz square waveclocking signal obtained from an Agilent 33220A function generator is used as the triggering signal. To maintain synchronization, the same signal is employed in triggering the DSO. To ensure some safety margin on DSO, some attenuator pads are placed at the input to the DSO. The block diagram for the UWB channel sounding set up is shown in Figure 3.4. Figure 3.5 shows a typical setup of the UWB channel sounder in the Wireless Networking Systems Laboratory of Tennessee Technological University. With the 2 MHz square signal acting as a trigger, pulses are transmitted every 500 ns interval. This 34

46 Figure 3.2 Output pulse from the pulse generator used in UWB channel sounding Figure 3.3 Pulser output with a differentiator 35

47 pulse repetition is slow enough to capture multipaths in the UWB channel. The DSO has the capability to average received waveforms for noise reduction. About 64 or 32 sequentially measured profiles are averaged during the course of the UWB channel sounding. The DSO is set in such a way that every 50 ns window measurement contains 4000 samples throughout the experiment. This implies a time of 12.5ps between samples and a sampling rate of 80 GHz. Hence, according to sampling theorem, waveforms with bandwidth of up to 40 GHz can be reconstructed from samples collected by the DSO [39]-[42]. Antennas are omni-directional, linear in polarization, and span a bandwidth of GHz with a feed impedance of 50 ohms. The height of both transmit and receive antenna is about 1.25 m above the floor. The antennas are fixed such that they make an angle of 0 degrees with the vertical. This is because 0 degrees have been tested to give the best received signal energy compared with other angles between zero degrees Figure 3.4 Time Domain UWB Channel Sounding 36

48 Figure 3.5 UWB channel measurement setup and 90 degrees. The measurements are actually conducted at three different locations: Hallway of Clement Hall 400 at Tennessee Technological University Campus, Center for Manufacturing Research foundry, and the Wireless Networking Systems Laboratory. For the purpose of illustrating the concept of UWB channel modeling being discussed in this chapter, some of the results obtained from Clement Hall 400 are being discussed. The results obtained from other measurement environments are presented in later chapters and are used for the purpose of demonstrating the applications of TiR in UWB. The Hallway of Clement Hall measures approximately 37m x 1.84m x 2.68m. The distance between the transmit antenna and received antenna is varied and the results are recorded for two different scenarios: line-of-sight (LOS) and non-line-of-sight (NLOS). Figures 3.6 and 3.7 show the results obtained. In order to verify that the multipath profiles for the first probing pulse have decayed enough before the response of 37

49 the next pulse arrives at the receiving antenna, a single multipath profile of 1000ns duration is made and the result obtained is shown in Figure 3.8. As shown in Figure 3.8, two back-to-back multipath profiles with 500ns duration each are captured and the first multipath profile has decayed enough before the response of the second multipath profile. Figure 3.9 shows the hallway of Clement Hall received waveform LOS 4m reference 0.25 received waveform NLOS 7m Amplitude(V) Amplitude(V) Time index (ns) Time index (ns) 0.1 received waveform NLOS 10m 0.08 Amplitude(V) Time index (ns) Figure 3.6 Received waveforms at distances 4m (LOS), 7m (NLOS), and 10m (NLOS) from the transmitter 38

50 received waveform LOS 4m reference received waveform LOS 7m Amplitude(V) Amplitude(V) Time index (ns) rec eived waveform LO S 10m Tim e index (ns) Amplitude(V) Time index (ns) Figure 3.7 Received waveforms for LOS cases 0.5 received waveform showing two back to back multipath profiles Amplitude(volts) Time index (ns) Figure 3.8 Received waveform showing two back-to-back multipath profiles 39

51 Figure 3.9 Clement Hall 400 Hallway 3.4 Deconvolution Techniques Deconvolution is the process of separating two signals that have been combined by convolution. Several deconvolution techniques exist in literature often for specific type of signal or for use with specific application. Deconvolution can be performed either in frequency or time domain. In the frequency domain, the most straightforward technique used is called inverse filtering. In time domain, the CLEAN algorithm is a common technique used. The CLEAN algorithm is chosen as the method of determining the CIR in this work. This is because the frequency domain techniques treat the CIR as band limited while the indoor propagation channel is not expected to be band limited 40

52 relative to the bandwidth of the sounding pulse used. Since this work focuses on the time domain characterization of the channel, the CLEAN algorithm is used as the primary deconvolution technique in this work. The discrete nature of the CLEAN algorithm makes the resulting impulse response more reasonable to characterize in time domain. The CLEAN algorithm is discussed in details in the next section. 3.5 The CLEAN Algorithm The approach to data analysis uses the CLEAN algorithm to extract the channel impulse response from the observed data. Initially used in radio astronomy [43], it has also been applied in the UWB communication channel characterization problems [44], [45]. The CLEAN algorithm is used here because of its ability to produce discrete CIR in time domain. The CLEAN algorithm assumes the channel to be a train of pulses, with the well-known assumed tapped delay line channel model [46]. In order to use the CLEAN algorithm to estimate the channel impulse response, it is assumed that there is no significant pulse distortion caused to any of the multipaths 1. The received signal at a given receiver location is expressed as y( t) = x( t) h( t) (3.8) where x (t) and y (t) are known and h (t) is the signal to be determined. The received signal from a given measurement location can be represented as r( t) p ( t) h ( t) h ( t) h ( t) = (3.9) sig txant ch rxant 1 If pulse distortion does exist, we can use a FIR filter to represent the pulse distortion. 41

53 where p sig (t) is the transmitted signal, h txant (t) is the transmit antenna impulse response, and h rxant (t) is the receive antenna impulse response. It is required to extract the channel impulse response h ch (t) from the received waveform. To deconvolve the response of the antennas from the channel impulse response, a reference LOS pulse was used for each measurement data. The reference LOS pulse is measured at a distance of 1m in free space in an environment with no reflectors and diffractions. The received LOS pulse is then deconvolved from each measured data to obtain the desired channel impulse response. The reference LOS pulse used is shown in Figure In order to perform the CLEAN algorithm, the autocorrelation of x (t) and cross correlation of x (t) and y (t) in (3.8) are computed. a xx ( t) = x( τ ) x( t + τ ) dτ (3.10) a xy ( t) = x( τ ) y( t + τ ) dτ (3.11) The peaks of the autocorrelation and cross correlation shown in (3.10) and (3.11) are found, recorded, and subtracted from the cross correlation function using the relations below h t) = h ( t) + A δ ( t τ ) (3.12) i ( i 1 i i h o d ( t) = 0 i( i 1 i xx i t) = d ( t) A a ( t τ ) (3.13) 42

54 Amplitude(V) Tim e(ns) Figure 3.10 Received waveform at a distance of 1 m from the transmitter d ( t) a ( t) o = xy where d i 1( i = i 1 t t τ ) arg max d ( ) (3.14) A = ( τ ). i d i 1 i A threshold is usually established to stop the algorithm. A threshold V is defined such that if Ai V max a xy ( t), the algorithm is ended. Some researchers have suggested using energy capture ratio as the stopping criteria [47]. The CLEAN algorithm was stopped after the remaining undetected paths were below 15dB of the peak path strength. The 15dB threshold is sufficient to illustrate the concept of TiR in UWB channels. This is because a 15dB threshold is sufficient enough to capture the majority of the signal power without capturing substantial noise in the CIR. When building a channel model, the statistics of the received signal are of importance. The CLEAN algorithm does a good job representing the received signal [48]. 43

55 The CLEAN algorithm is also robust to noise present in measured data where frequency domain deconvolution techniques fail [49] Limitations of the CLEAN Algorithm The CLEAN algorithm has some limitations when employed in determining a CIR. Below are some of the limitations of the algorithm. The CLEAN algorithm does not give a good estimate of the CIR when the paths are very close and unresolveable. When different pulse shapes are associated with different paths, we only use the LOS pulse as a template. In this case, The CLEAN algorithm cannot give a good estimate of the CIR. Multiple taps are needed to represent distortion. The CLEAN algorithm is only fairly accurate in representing a signal at moderately low SNR. 3.6 Summary This chapter served as the foundation for this thesis work and it presented the whole ideas on which research work is based. The concept of UWB channel modeling was discussed and the UWB channel sounder employed in extracting the channel impulse response was explained in details. The measurement setup and the measurement procedure were discussed and the concept behind the CLEAN algorithm, which will be used in the later chapters to extract the channel impulse response from the received 44

56 waveforms, was discussed in this chapter. The extracted UWB channel information will then be used in the later chapters as the channel data on which the principle and applications of TiR are demonstrated. 45

57 CHAPTER 4 TIME-REVERSAL COMMUNICATIONS 4.1 Introduction In this chapter, the theory and the applications of time reversal in UWB are discussed. Metrics are defined to characterize two key applications in TiR, namely: spatial focusing and temporal compression. The concept of ISI in UWB systems is discussed and the use of TiR to improve receiver performance in UWB ISI channels is discussed. The chapter also studies some equalization techniques used in compensating for ISI in UWB channels. 4.2 An Overview of Time-Reversal in UWB Time-reversal (TiR) also known as phase conjugation in frequency domain is a simple method of preparing a message such that it appears at a particular time at a particular location in space and no where else. In TiR, a signal is prefiltered such that it focuses in space and time at an intended receiver [17]. This can be achieved by using a time-reversed complex conjugate of the channel impulse response at the receiver as a transmitter prefilter. Several advantages come with this technique. Spatial focusing reduces co-channel interference in a multi-user system. Due to temporal focusing, the effective delay spread of the channel is dramatically reduced and thus ISI is also reduced dramatically. This leads to a reduction in the equalization task at the receiver. For 46

58 example, the complexity of a maximum likelihood sequence estimator (MLSE) is proportional to m L, where m is the size of the input alphabet and L is the length of the channel impulse response in units of T with T being the symbol separation [50]. Temporal focusing in TiR reduces the equalization task by reducing the effective channel length. In a TiR experiment, the intended receiver sends a training sequence to the intended transmitter(s). The transmitter(s) time-reverses the estimated channel impulse response (CIR), convolves it with the signal message that is now sent to the receiver. The emitted time reversed waves propagates through the channel retracing their former paths and this leads to a focus of power in space and time at the receiver. The concept of TiR experiment is illustrated in Figure 4.1. The concept has already been successfully applied in underwater acoustic channels and in ultrasound applications. It has also been applied to narrowband systems and has only recently been applied to UWB systems. Being newly applied to UWB systems, further studies are necessary to demonstrate more feasibilities of applying TiR to UWB and hence the reason for this research work. 4.3 Time-Reversal Theory Consider a single user downlink scenario transmit-receive pair in a UWB channel. In TiR, the transmitter uses the time-reversed complex conjugate of the CIR as a transmitter prefilter. Let h ( r o,τ ) denote the impulse response at the intended receiver, where r o is the receiver location and τ is the delay variable. If the transmitter uses ( r o, τ ) h as a transmit prefilter, the effective channel at a given location r is given by 47

59 10 8 Amplit ude(v olts) differentiated gaussian output Time(ps) R hh ( r, τ ) h( τ ) ( r, τ ) = h r, (4.1) o where denotes convolution with respect to the delay variable and r and r 0 means the positions. In order to demonstrate the leverages of TiR, the UWB channel is sounded with a sub-nanosecond pulse and the channel impulse response between the transmitter and the receiver is measured. The measurement is repeated by holding the transmitter fixed and varying the receiver position at different distances from the intended receiver, which is located 4m away from the transmitter. The receiver location is varied for both LOS and NLOS cases and the concept of spatial focusing in TiR is demonstrated. Using the channel information from typical LOS and NLOS cases, temporal compression in TiR is demonstrated. The CIR is compressed and a temporal focus of the energy is visible at the center of the compressed CIR. To characterize the amount of temporal focusing, a ratio called the temporal peak to total energy ratio, which characterizes the percentage energy capture, by the peak of the effective CIR is defined as Transmitter Intended receiver Input data Modulation filter Channel pre-filter Channel h ( τ ) h(τ ) + Matched filter Detector Output data Gaussian Noise Figure 4.1 TiR experiment 48

60 hh E TR p ϑ = (4.2) hh ET where hh E p is the energy in the main peak of the received impulse response, hh E T is the total energy in the received impulse response for the timereversed channel. This ratio is expected to be as high as possible to illustrate good temporal compression and is expected to approximate a fixed value. In order to illustrate spatial focusing in TiR, a ratio called the spatial focusing gain is defined. The energy of R hh ( r, τ ) at any point r in space at a given time τ o is given by () r 2 ε = R r, τ ) (4.3) hh hh( o whereτ o is defined such that R ( r, τ ) = max { R ( r, τ ) }. The spatial focusing hh o o τ hh o gain η hh(r) is the ratio of the energy at r o to the energy at a given location away from r o. ( r ) ε o η r hh hh( ) = (4.4) ε hh () r This ratio gives relative information about security in TiR. A large value of this ratio indicates a better spatial focusing gain and hence a low probability of intercept by a receiver located near the intended receiver. η hh(r) can be computed with respect to time delays other than τ o but τ o is chosen here, because at τ o, the effective time reversed channel captures the largest amount of energy in the channel. Figures 4.2 and 4.3 illustrate the concept of temporal compression in TiR using measured data from Clement 49

61 Hall 400 of Tennessee Technological University campus and IEEE a data respectively while Figure 4.4 illustrates spatial focusing. In Figures 4.2 and 4.3, the temporal compression is visible at the center of the channel impulse response and the amount of temporal compression is defined using Equation 4.1. In Figure 4.4, R o is the intended receiver while receivers R 1 and R 2 are users intending to steal the information from R o. From mathematical properties, it is known that after normalizing the correlation functions with respect to energy, autocorrelation is always stronger than cross-correlation. This implies that the receiver power peaks at R o and is more compared to R 1 and R 2. An intruder at R 2 who tries to steal user information at R o experiences some loss in received power and hence his inability to decode the message signal. The results obtained by this concept are given in details in the next chapter. In order to illustrate the relative gain in UWB channels using TiR, the energy loss due to prefilter is studied against energy loss without a prefilter. The relative information obtained gives the amount of channel energy gain observed using TiR in UWB environments and this is shown in the next chapter. 4.4 Time Reversal and UWB Systems Performance Due to multipath propagation effects, the transmitted UWB waveform arrives at the receiver distorted. The distorted waveforms arriving at the receivers are further corrupted by multiple access interference and background noise. The function of a UWB 50

62 receiver is to extract the information bit sequence from the distorted and corrupted received waveforms with a very high level of accuracy. The basic UWB receiver consists 0.5 received waveform hallwaylos 10m 0.15 HallwayLOS 10m Estimated channel impulse response Amplitude Time index (ns) Amplitude Excess delay (ns) 0.3 Autocorrelation of channel impulse response(nlos) Amplitude Excess delay (ns) Figure 4.2 Temporal compression illustrated using measured data 0.4 CM3 Channel impulse response 0.2 Amplitude excess delay(ns) CM3 TiR channel 4 3 Amplitude excess delay(ns) Figure 4.3 Temporal compression illustrated using IEEE a CM3 channel 51

63 R2 R hh( 2 r 2, τ ) = h ( r o, τ ) h( r, τ ). Tx h(τ ) R hh ( r, τ ) = h ( r, τ ) h( r, τ ). o o o Ro R hh( 1 r 1, τ ) = h ( r o, τ ) h( r, τ ). R1 Figure 4.4 Demonstrating spatial focusing in TiR of a detector and a decision device. The detector is different from conventional narrowband schemes because UWB can be carrier-less. The most common implementations of UWB receivers are threshold detectors, autocorrelation receivers, and correlation or rake receivers. Threshold detectors are simple to implement and are also suitable for UWB radar systems [51]. In threshold detectors, a threshold is usually set for establishing the presence of a radar target. An autocorrelation receiver correlates the received waveform with a previously received waveform [52-56]. This receiver can capture the entire received waveform energy for a slowly varying channel without requiring channel estimation because the transmitter transmits a pilot (reference waveform) to generate side information about the channel. Some research on UWB receivers has been on the rake receiver [57-66]. 52

64 4.4.1 Rake Receivers Rake receivers are used in time-hopping impulse radio systems and direct sequence spread spectrum systems (DS-SS) for matched filtering of the received signal. In theory, the receiver structure consists of a matched filter that is matched to the transmitted waveform that represents one symbol, and a tapped delay line that matches the channel impulse response. It is also possible to implement this structure as a number of correlators that are sampled at the delays related to specific number of multipath components; each of those correlators can be called Rake finger. A Rake receiver structure is shown in Figure 4.5. In UWB systems, frequency dependency is taking into consideration [3,34], the receiver uses several rake fingers for each multipath component (MPC) spaced at the nyquist sampling distance in order to collect the energy in the MPC. The number of rake fingers in this case becomes very large [67]. Due to this problem of energy capture, several simplified Rake structures have been proposed: selective Rake (Srake) and partial rake (Prake). The Srake receiver collect energy from L strongest MPCs while the Prake collects energy from the L first MPCs. The Srake structure has been adopted in this research work. Srake outperforms Prake because Srake collects more channel energy than the Prake [68]. 53

65 Figure 4.5 Rake receiver structure In Figure 4.5, the Rake structure consists of a parallel bank of L correlators followed by a combiner that determines the variable to be used for the decision on the symbol. Different approaches can be used to determine the rake weights: however, maximal ratio combiner (MRC) is a traditional approach. Reference [69] proposes an approach called minimum mean square error (MMSE) Rake combiner and it outperforms MRC-Rake. As shown in [69], MMSE Rake receiver reduces the error floor observed when MRC-Rake is receiver is employed in UWB systems ISI Issues in UWB Inter symbol interference occurs when the effects of a transmitted pulse is not allowed to die away completely before transmitting another pulse. If symbol duration is given as T b and the channel delay spread is given as T d, ISI occurs in a UWB channel if T b < T d. The received signal at the receiver in a frequency selective discrete ISI channel can be represented as 54

66 N = 1 = + l I l I n n 0, n l y x w (4.5) + l n l where y l represent the l th approximated bit at the receiver, I l represent the desired information symbol at the l th sampling time, N 1 = n 0, n l I nx l n represent the ISI term, and w l represent the additive Gaussian noise variable at the k th sampling instant. The ISI term makes it more likely for the decision device to have more decision errors, as compared to a case without ISI because with ISI it is more likely to mix up desired symbols with undesired symbols. In order to minimize the probability of error, the optimum receiver in a mean-square error sense consists of a matched filter, an equalizer, and a maximum likelihood detector. The maximum likelihood sequence estimator (MLSE) is the optimum equalizer for use in wireless channel. The MLSE searches for the information sequence that after convolution is closest in Euclidean distance to the received signal sequence [70]. However, it has a complexity that grows exponential with the channel length and it is thus not suitable for use in channels with large delay spread such as UWB. Two sub-optimum equalization techniques for use in frequency selective channels are the Zero forcing (ZF) and minimum mean square error (MMSE) and are discussed in the next section. 55

67 4.4.3 Equalization Techniques This section briefly discusses ISI compensation technique in UWB channels using equalizers. First, the case where the equalizer has infinite number of taps is discussed and then the case in which the equalizer spans finite time duration is discussed. where Infinite length equalizers. A block diagram of a UWB channel with an equalizer is shown in Figure 4.6. For a given UWB wireless channel of length L, the output of the channel can be written as y [ m] = ( x h)[ m] + w[ m] (4.6) x [m] is the input signal m=0,1 N-1, y [m] is the output signal m=0,1,..n+l-2, and h includes the effects of the pulse-shaping at the transmitter, the physical channel impulse response and the matched filer In matrix notation, (4.6) can be rewritten as a Toeplitz-type system [71]: 56

68 Input data Pulse shaper UWB Channel + Matched Filter Equalizer AWGN Noise Output data Decision device Figure 4.6 UWB Channel with equalizer y Hx+ w = (4.7) where y(0) x(0) w(0)... y =., x =.,w =.... y( N + L 2) x( N 1) w( N 1) (4.8) and H = h(0) 0... h( L 1) h( 0).. h( L 1). (4.9) 57

69 The MMSE estimate of x, xˆ in Equation 4.6 gives the desired received information bit at the output of the detector. In order to compute the bit error rate for the system, x is compared with xˆ. The basic idea of the MMSE estimator is to choose as the estimate the function of the data that gives the smallest expected value of the square of the estimation error [72]. It can be assumed that E (w) = 0 in Equation 4.7 without loss of generality. Assuming xˆ to be a linear function of y, i.e. xˆ = By, where B is to be determined. From (4.7): Since E (w) = 0, y Hx+ w =. K = E[ ww ] T σ 2 I = (4.10) where w is zero mean circularly symmetric complex Gaussian (ZMCSCG) noise with variance N o. To find xˆ, let S be defined as S T ( y Hxˆ) ( y Hxˆ) (4.11) S xˆ = 0 = 2[ H T H ]ˆ x 2H T y (4.12) xˆ = ( H H ) T 1 H T y. (4.13) Equation (4.13) is not optimal [73]. To make it optimal, the covariance of the noise w in Equation (4.10) is added and hence the MMSE estimate of x is represented as T 1 T xˆ = ( H H ) H y + N I (4.14) where I represent a (1xN) identity matrix. o 58

70 As observed in [74], the difference between an MMSE equalizer and a zero forcing equalizer is the absence of the noise term in the ZF equalizer. Hence, (4.13) represents the estimated data sequence for a zero forcing equalizer of infinite length Finite length equalizers. This section describes the cases in which the equalizer spans finite time duration Zero forcing equalizer. The output of the equalizer in z-domain is given by Y (z) =R (z) B (z) (4.15) where Y (z) is the z-transform of the equalizer output, R (z) is the z-transform of the effective channel output, and B (z) is the z-transform of the equalizer coefficient. In the absence of the additive noise introduced by the physical channel, the output of the effective channel is given by R (z) =X (z) H (z). (4.16) Substituting 4.16 in 4.15, the output signal of the equalized system, can be expressed as Y (z) =X (z) H (z) B (z). (4.17) Figure 4.7 illustrates the equivalent discrete time representation of the equalized system. Let C (z) denote the transfer function of the equalized system. 59

71 Figure 4.7 Discrete UWB channel with equalizer Then Y ( z) C ( z) = = H ( z) B( z). (4.18) X ( z) In time-domain, this corresponds to k = N k k = N c = b h = b h. (4.19) n n n n k For ISI free transmission, C (z) =1. (4.20) In time domain, condition (4.20) means that 1, n = 0 c n =. (4.21) 0, n 0 With a finite number of taps (2N+1) in the equalizer, (4.21) becomes 1, n = 0 c( n) =. (4.22) 0, n = ± 1, ± 2,... ± N Equation (4.22) can be guaranteed by choosing the equalizer coefficients to satisfy the following equation 60

72 61 [ ] [ ] T T N o N o N N N N N o N N N N N o b b b b b h h h h h h h h h h h h h h h = + + (4.23) where T denotes the transpose operation. Equation (4.23) represents a finite length zero forcing equalizer Minimum mean square error (MMSE) equalizer. In reality the noise component due to the physical channel cannot be ignored. In the presence of additive Gaussian noise at the receiver input, the output of the equalizer at the n th sampling instant is given by = = N N k k n k n r b ŷ. (4.24) The mean square error (MSE) for the equalizer having 2N+1 taps, denoted by J (N) is = = = 2 2 ˆ ) ( N N k k n k n n n r b x E y E x N J (4.25) minimizing ) (N J with respect to the equalizer coefficients ( k b ) is obtained by the following differentiation: 0 ) ( = b k N J. (4.26) Equation 4.26 leads to the necessary condition for the minimum MSE given by r R xr b R = (4.27)

73 or 1 b = R r R xr (4.28) where b denotes the 2N+1 tap coefficient R = ( R ( N),... R (0),... R ( N )) T xr xr xr xr R r = R r (0)... R r ( N) r R r ( 2N + 1)... R r ( N + 1) R r ( 2N) N... R r ( N) 2 r R (2N) r.. R(1) R (0) TiR System Structure Figure 4.8 gives a typical UWB channel with TiR. The major difference between a system with TiR and a system with no TiR is the presence of the transmitter prefilter ( h ( t) in Figure 4.8. The effective TiR channel impulse response is given by where h TR ( t) = φ ( t) h ( t) h( t) φ ( t) (4.29) φ (t) is the pulse shaping filter, h ( t) is the transmitter prefilter, 62

74 Input data Modulation filter Channel pre-filter Channel h ( τ ) h(τ ) + Matched filter Detector Output data Gaussian Noise Figure 4.8 UWB systems with TiR h (t) is the channel impulse response, and φ ( t) is the filter matched to the transmitted pulse. For a system with TiR, the equations for infinite length equalizers (MMSE and ZF) and finite length equalizers (MMSE and ZF) still hold with the effective channel response h (t) in the previous equations being replaced by a new channel impulse response defined in Equation For an infinite length equalizer, the received signal is therefore given by In matrix notation, this becomes y[ m] = ( x htr )[ m] + w[ m]. (4.30) y = H TR x + w. (4.31) And the equation for an infinite length MMSE estimator is given by T T 1 xˆ = ( H TR H ) H TR y + N I. (4.32) TR o 4.5 Summary In this chapter, a detailed study of TiR in UWB is presented. The theory behind TiR is studied. The various applications of TiR in UWB are presented and ISI issues in UWB are also presented. The various techniques for compensating ISI in UWB channels 63

75 are studied and the idea of combining these techniques with TiR to combat ISI in UWB channels is also presented. 64

76 CHAPTER 5 SIMULATION RESULTS The previous chapters provided a detailed study of UWB systems. The motivations for applying TiR to UWB systems have been discussed in earlier chapters. The signal-processing algorithm (CLEAN algorithm) used in this thesis to obtain the channel information has also been discussed in Chapter 3. The extracted channel information is the data on which the applications of TiR in UWB are demonstrated. In this chapter, a simulation technique called Monte Carlo simulation is employed to analyze the performance of UWB systems using the extracted channel impulse response. MATLAB software package was used for simulating the complete UWB system from the transmitter to the receiver. BER curves are generated for different cases using TiR and equalizers as a means of compensation for ISI in the UWB channels. Also, in this chapter, results for temporal compression, spatial focusing and TiR losses in UWB channels are presented. 5.1 Monte Carlo Simulation Monte Carlo (MC) simulation technique [75,76] is the most widely used simulation technique for evaluating the performance of communication systems and it is based on a game of chance. In the context of BER estimation for digital communication systems, the MC simulation technique involves the following steps: 65

77 (1) Decide on the minimum target BER to be estimated. (In this thesis work, it is 3 10.) (2) Set the number of bits per simulation run to be at least 10 times the inverse of the minimum target BER to be estimated. (Here, it is 10 4 bits.) (3) Set up the base band modulators, demodulators, transmit/receive filters, and channel simulators. (Here, the channel information is known from the CLEAN algorithm.) (4) Run the BER simulation until 100 errors are counted and estimate the BER. (5) Iterate the simulation for some specified number of iterations and compute the average of the BERs obtained in these iterations (Here, the number of simulation runs was chosen to be 40.) The block diagram for the simulation setup is illustrated in Figure 5.1. A 5 th order Gaussian pulse width a pulse width T b of 0.625ns is used as the pulseshaping filter and is represented by φ 3 5 t t t t σ ( t) k e = + (5.1) σ σ σ where σ = is a parameter that controls the width of the pulse. The spread waveform can be obtained from the pulse-shaping filter by 7 p( t) = s φ ( t ). (5.2) k = 0 k kt b The spreading sequence, { } = { 1, + 1, + 1, 1, + 1, + 1, 1, 1} The symbol duration is thus given by s. (5.3) k T = 8T 5nsec. (5.4) s b= 66

78 Figure 5.1 Simulation setup If b k is a sequence to be transmitted, the modulated signal is given as ( t) b k p( t kt s s = ). (5.5) If the UWB CIR is represented as h (t), then the output of the channel is x ( t) = h( t) s( t) + w( t). (5.6) After matched filtering, the output of the matched filter can be expressed as y( t) = x( t) p( t). (5.7) The outputs of the matched filter are then combined using MMSE rake combiner discussed in Chapter 4. A MMSE equalizer is then employed for further receiver performance improvement. The choice of modulation used is BPSK, i.e. b = { +1, 1} channel data information for several cases is used: IEEE a (CM3 and CM4) models and the extracted channel data using CLEAN algorithm from the received waveform for several UWB channel environments. The major aim here is to demonstrate improvement in receiver performance using TiR in UWB channels. k, a 67

79 5.2 BER Simulation Results Performance of TiR systems already discussed is evaluated via simulations in this section. In order to verify the simulation, the setup is evaluated for an AWGN channel and the result obtained is compared with the channel situation in which there is no ISI. These results are expected to be as close as possible. In each BER simulation, different scenarios of UWB receivers are considered. The following cases are considered in the simulation: A Rake receiver with an estimate of the largest 20 channel fingers, MMSE equalizer (with 5 taps), MMSE-TiR, TiR-Rake, No ISI, and AWGN channel. The MMSE-TiR combines MMSE equalization with TiR while TiR-Rake employs TiR channel with a rake receiver also estimating the largest 20 channel taps. The No-ISI case is that in which the bit duration (T b ) is chosen such that T b> T rms, where rms T is the rms delay spread of the channel. 68

80 5.2.1 CM3 Simulation Results The BER simulation results obtained using CM3 channel data is shown in Figure 5.2. As expected, using an MMSE equalizer to compensate for ISI, a relative improvement is observed. The major comparison lies in the TiR channel versus the Rake receiver. Using the TiR channel information as the channel impulse response and estimating the 20 largest channel taps, at a BER of 3 10, TiR-Rake channel has around 1.8dB performance improvement compared to a channel with rake receivers for CM3 channel. Also employing a 5-tap MMSE equalizer to the TiR channel shows a very slight performance improvement (around 0.3 db). After TiR, a very minimum number of taps for the equalizer is employed. This demonstrates that with TiR, the equalization task if needed is reduced to a minimum to achieve a reasonable BER. This is better illustrated using the CM4 channel because the CM4 represents an extreme case of NLOS of site and hence we expect a very intense ISI channel for this case. As a reference, the No-ISI case is compared with a standard AWGN curve and a close result shown in Figure 5.2 is obtained as expected CM4 Simulation Results Using CM4 channel data, the simulation results obtained are shown in Figure 5.3. Using a 5-tap MMSE equalizer as a means of compensation for the ISI, a 1 db improvement in BER is observed at around With 31 channel taps, a performance improvement of about 2.2 db is observed. Using TiR-Rake, i.e. TiR and a rake receiver 69

81 CM3 channel 5-taps MMSE Rake MMSE-TiR TiR-Rake AWGN No ISI 10-2 BER Eb/No(dB) Figure 5.2 TiR BER simulation result using CM3 with no equalization, a gain of around 4dB is observed. This shows that a relative improvement in terms of cost for the equalization task. A TiR channel with no equalization outperforms a channel with 31 taps equalizer. To further improve the performance of the UWB channel, an equalizer is combined with the TiR channel and a gain of 0.5 db is observed compared to the TiR-Rake channel. As a reference, the No- ISI case is compared with a standard AWGN curve and a close result shown in Figure 5.3 is obtained as expected. 70

82 CM4 Channel MMSETiR-Rake TiR-Rake 31taps-MMSE Rake 5tap-MMSE AWGN No ISI BER Eb/No(dB) Figure 5.3 TiR BER simulation using CM Foundry Simulation Result The CM3 and CM4 channel information used above are statistical data obtained from IEEE. The trends in results observed using statistical data are demonstrated here using measured data from UWB channel environments. The results discussed here are those obtained from the Foundry of the Center for Manufacturing Research at Tennessee Technological University Campus. This environment mimics a typical industrial environment with a lot of metals and hence the ISI is expected to be severe especially in the NLOS situations, a situation similar to IEEE a CM4 channel model. The method used in collecting the UWB channel information is as discussed in the previous 71

83 chapters. The BER simulation results obtained using the measured data from the foundry is shown in Figure 5.4 while Figure 5.5 shows a pictorial view of the foundry. As expected, the results show a similar trend as those obtained using statistical channel information from IEEE a CM3 and CM4 channels. At a BER of 3 10, the TiR-Rake outperforms the equalizer with 31 taps by a 2.7 db gain. This shows a reduction in the receiver complexity due to time reversal. The receiver performance after TiR could further be improved by using additional channel equalizer and hence the use of MMSE-TiR receiver. A 5-tap MMSE TiR receiver outperforms the TiR-Rake by around.33db in this case. This shows that after TiR, a minimal amount of equalization will be needed for further improvement in receiver performance BER Results for Clement Hall 400 Hallway Simulation is also carried out using the channel data information obtained from the Hallway of Clement Hall 400 of Tennessee Technological University Campus. The hallway environment is the first environment studied for the various applications of TiR in UWB. The results obtained from the hallway gave further insight for demonstrating TiR in UWB using other channel environments. The hallway mimics a typical indoor environment where ISI is present but not as severe as industrial environments. The BER simulation result obtained here is shown in Figure

84 Foundry Channel MMSE-TiR TiR-Rake 5taps-MMSE Rake 31taps-MMSE AWGN No ISI BER Eb/No(dB) Figure 5.4 Foundry BER simulation results Figure 5.5 CMR Foundry 73

85 Hallway MMSE-TIR TIR-Rake 5taps-MMSE Rake AWGN No ISI 10-2 BER Eb/No(dB) Figure 5.6 BER simulation result for Clement Hall 400 Hallway As shown in Figure 5.6, the ISI condition here is not that severe. This is seen by an energy bit per noise (Eb/No) of around 13.7dB at a BER of However, the TiR Rake receiver still outperforms the Rake receiver by a 1 db gain in Eb/No for a BER of The trend in receiver performance previously obtained is also shown in here as the MMSE-TiR shows the best performance as expected. 5.3 Results Illustrating Temporal Compression In this section, temporal compression is demonstrated using both statistical and measured channel data in order to study the performance trend in UWB channels. CM1, CM3, and CM4 channel information are used where CM1 is a typical LOS situation; CM3 and CM4 are NLOS situations. Also, measured data for Clement Hall 400 Hallway, 74

86 Wireless Networking Systems (WNS) Laboratory at Tennessee Technological University, and the Center for Manufacturing Research foundry are used. After TiR, the effective channel impulse response shows temporal compression that is visible at the center of the observed channel impulse response. The amount of temporal compression is characterized using defined metrics already discussed in Chapter 4. Table 5.1 shows the percentage energy captured by the peak for the effective TiR channel impulse response for the various situations studied here. The results here show that NLOS cases capture more energy at the peak compared to LOS cases. The results here also do not show any trend in the peak energy captured for extreme NLOS situations Table 5.1 Temporal peak to channel energy ratio Environment TR ϑ Hallway LOS 59.96% Hallway NLOS 65.73% Foundry LOS Foundry NLOS CM % CM % CM % Lab LOS 43.53% Lab NLOS 48.8% 75

87 with more discrete channel taps when compared with NLOS cases with less discrete channel taps (e.g. foundry data compared with hallway). For the Foundry and Hallway data, the transmitter and receive antennas are separated by a distance of 10m while in the WNS laboratory, they are separated by a distance of 6m. Other details about the measurement set up are as discussed in Chapter 3. Figures 5.7 to 5.16 show the results obtained using temporal compression in all channel cases shown in Table CM1 Channel impulse response Amplitude excess delay(ns) CM1 TiR channel 4 3 Amplitude excess delay(ns) Figure 5.7 Temporal compression in CM1 channel 76

88 0.4 CM3 Channel impulse response 0.2 Amplitude excess delay(ns) CM3 TiR channel 4 3 Amplitude excess delay(ns) Figure 5.8 Temporal compression in CM3 channel 0.2 CM4 Channel impulse response 0.1 Amplitude excess delay(ns) CM4 TiR channel Amplitude excess delay(ns) Figure 5.9 Temporal compression in CM4 channel 77

89 0.18 Impulse response realizations Time (ns) 1.4 Autocorrelation of Impulse response Time(ns) Figure 5.10 Temporal compression in IEEE a Outdoor channel 0.5 received waveform foundrylos 10m 0.15 Estimated channel impulse response foundrylos10m Amplitude Time index (ns) Amplitude excess delay (ns) 0.35 Autocorrelation of channel impulse response foundrylos10m Amplitude Excess delay (ns) Figure 5.11 Temporal compression in CMR Foundry LOS 78

90 0.16 received waveform foundrynlos 10m 0.1 Estimated channel impulse response foundry NLOS10m Amplitude Time index (ns) Amplitude Excess delay (ns) 0.3 Autocorrelation of channel impulse response foundynlos 10m Amplitude Excess delay (ns) Figure 5.12 CMR Foundry NLOS result showing temporal compression 0.5 received waveform hallwaylos 10m 0.15 HallwayLOS 10m Estimated channel impulse response Amplitude Time index (ns) Amplitude Excess delay (ns) 0.3 Autocorrelation of channel impulse response(los) Amplitude Excess delay (ns) Figure 5.13 Clement Hall 400 Hallway LOS results showing temporal compression 79

91 0.25 received waveform hallwaynlos 10m 0.08 Estimated channel impulse response hallway NLOS10m Amplitude Time index (ns) Amplitude Excess delay (ns) 0.12 Autocorrelation of channel impulse response NLOS10m Amplitude Excess delay (ns) Figure 5.14 Clement Hall 400 Hallway NLOS showing temporal compression 0.5 LOS received waveform WNS lab 0.25 WNS lab LOS Estimated channel impulse response Amplitude Time index (ns) Amplitude Excess delay (ns) 0.6 Autocorrelation of channel impulse response(wns lab LOS) Amplitude Excess delay (ns) Figure 5.15 WNS lab result LOS results showing temporal compression 80

92 0.3 received waveform WNS lab NLOS 0.1 Estimated channel impulse response WNS lab NLOS Amplitude Amplitude Time index (ns) Excess delay (ns) 0.3 Autocorrelation of channel impulse response WNS lab NLOS Amplitude Excess delay (ns) Figure 5.16 WNS laboratory NLOS result results showing temporal compression 5.4 Results For Spatial Focusing Gain One of the key advantages and applications of TiR is the concept of security in UWB systems. Secured communications means the inability of a nearby receiver to successfully decode the information in the TiR channel and this is of particular interest to DoD applications. To demonstrate this concept in UWB using TiR, the channel impulse response is measured and obtained between the transmit antenna and the intended receiver. The receiver antenna is then moved to various locations and the channel impulse response is also obtained using CLEAN algorithm. The aim of this demonstration is to observe the approximate distance at which the spatial focusing gain η hh(r) discussed in the previous chapter is at least 10dB for typical UWB environments. The Foundry channel data and the Hallway channel data are used for the purpose of this demonstration. 81

93 Both LOS and NLOS cases are studied in both environments and the results here show that at a transmitter-receiver antenna separation of 6m is sufficient to obtain a spatial focusing gain η hh(r) of at least 10dB. Figures 5.17 and 5.18 show the results obtained for both the Hallway and Foundry channels LOS and NLOS gain vs distance LOS NLOS space-time focusing gain(db) distance from intended receiver(m) Figure 5.17 Demonstrating spatial focusing gain in Clement Hall 400 Hallway 82

94 14 12 Spatial focusing gain in foundry LOS NLOS spatial focusing gain(db) distance from intended receiver(m) Figure 5.18 Demonstrating spatial focusing gain in CMR foundry 5.5 Results for Time Reversal Loss Versus Distance Lastly, as suggested by Dr. Nan Guo of the Wireless Networking Systems Laboratory [77], in order to have information about the gain or loss in channel energy due to TiR, the energy loss due to TiR can be studied against the channel energy loss for each distance without TiR. A distance of 7m from the intended receiver is chosen as a reference distance for studying the energy loss due to TiR. Two cases were studied: NLOS channel scenario in the Foundry and NLOS channel scenario in the Hallway of Clement Hall 400. Figures 5.19 and 5.20 show the results obtained. A similar study is carried out via simulation by Mr. Chenming (Jim) Zhou [78] also of the Wireless Networking System Laboratory. His simulation models a typical Hallway and the results 83

95 5 0 foundry energyloss energyloss with prefilter energyloss without prefilter -5 energyloss(db) distance(m) Figure 5.19 Foundry energy loss (TiR versus No TiR) 5 0 Hallway energyloss energyloss with prefilter energyloss without prefilter -5 energyloss(db) distance(m) Figure 5.20 Hallway energy loss (TiR versus No TiR) 84

96 obtained is shown to have a similar trend as the experimental result. The experiments result however shows a slightly better performance. For the Foundry environment, the energy loss at a distance of 4m from the transmitter, taking the 7m distance as a reference is shown to be around 3dB. Also, at a distance of 4m, the energy loss by the TiR channel is shown to be around -19dB. The channel energy gain due to TiR is approximately 22dB in this case. This shows that a channel with TiR at this distance will have a 22dB gain in channel energy when compared to that with no TiR. This also demonstrates that TiR energy has more channel gain compared to non-tir channel and hence the reason for a better receiver performance also illustrated in the BER studies previously discussed. The results for other distances are as shown in Figure At a distance of about 1m from the reference location (7m), the TiR channel shows a loss of around db. For the Hallway, a gain of around 21dB is observed at a distance of 4m and other gains due to TiR in the channel are as shown in Figure Summary In this chapter, the performance analysis of UWB systems with TiR has been analyzed and performance improvement was achieved using TiR for UWB channels when compared to channels without TiR. Also, the concept of temporal compression was discussed. Using defined metrics, temporal compression was characterized and the results shown here show temporal compression to work finer for NLOS channels in UWB. 85

97 To demonstrate the concept of secured communications in UWB using TiR, the spatial focusing gain was studied for UWB channels and at a distance of at least 6m,a gain of 10dB was observed. This shows TiR to be a valuable concept in UWB systems and this is of particular interest to the D.O.D. Lastly, knowledge of the amount of channel energy gain using TiR was demonstrated by studying the channel energy loss due to TiR with the channel energy loss by distance. Using a 4m distance from the transmitter as an example, a gain of at least 19dB was observed for both UWB channels studied here. These results show TiR to be a promising technique in UWB. The results also show that TiR, which has successfully been demonstrated in narrowband systems and underwater acoustic channels could be applied to UWB systems. 86

98 CHAPTER 6 CONCLUSIONS AND FUTURE WORK The objective of this thesis was to study and investigate the theory and applications of time reversal in UWB using measurement and statistical data. Various applications of TiR to UWB have been studied and analyzed using different UWB channel data. BER performance using TiR was studied and evaluated and results show TiR to be a promising technique for improving the performance of UWB systems when ISI is present. TiR was also combined with conventional equalization techniques. Temporal compression and spatial focusing in TiR were also studied in details and knowledge of the amount of channel gain observed using TiR in UWB channels was studied. 6.1 Conclusions Performance results showed that the application of a transmitter prefilter ( h ( t)) in a UWB channel with impulse response h (t) results in performance improvement and this technique shows a promising technique for reducing the effect of ISI in UWB channels. Different UWB channel situations were studied and different scenarios at the receiver were used. All channel cases studied here show that TiR reduces the cost of equalization in UWB channels and hence one of the basic aims in any system designs: cost versus performance has been met using TiR. 87

99 Two key applications of time reversal are temporal compression and spatial focusing. These two concepts have been studied in details and results here obtained show that TiR should work fine in NLOS UWB channels when compared with LOS channels. This is because in the presence of ISI, there are more multipath and hence temporal compression works finer because the more the number of multipaths, the better the concept of TiR. For spatial focusing, the aim of the study was to get a minimum distance at which the spatial focusing gain is at least 10dB. A distance of 6m was sufficient for the cases studied in this thesis. Lastly, it is essential to have knowledge of the gain in channel energy by TiR. This was studied comparing the energy losses due to TiR to that with no TiR and plots showing this information were given. Using a typical 4m distance here, it was observed that TiR results in a gain of at least 19dB for all channel situations studied here. This gives an insight why TiR results in better performance in UWB system performance. 6.2 Recommendations for Future Work This thesis gives a study of the applications of TiR in UWB systems and has opened a lot of areas for future work, which could be done to better understand the theory and applications of TiR in UWB systems. Some of the areas are as follows: 1. TiR uses a prefilter at the transmitter which is a time reversed complex conjugate the of the channel impulse response. Other possible prefilter techniques need to be studied and see if possible improvement in performance could be observed e.g. [77]. 88

100 2. Performance of TiR in outdoor channels could also be evaluated (IEEE channel model IEEE a). 3. Single user case has been addressed in work. The performance of UWB systems with TiR for multi-user scenario should be studied when the receiver is not only corrupted by ISI but also multi-user interference (MUI). 4. Hardware implementations issues related to the prefilter in TiR UWB systems should be addressed in future work. 89

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109 APPENDICES 98

110 APPENDIX A: IEEE CHANNEL MODEL P A 99

111 A.1 Multipath Channel Model Clustering phenomenon was observed in several channel measurements.based on this clustering, IEEE proposed a UWB multipath channel model called IEEE P a [45] derived from the model by Saleh-Valenzuela with some slight modifications. Instead of a Rayleigh distribution for the multipath gain magnitude, a log-normal distribution is employed. Log-normal means that the logarithm of the random variable has a normal distribution. Additionally, for each cluster as well as each ray within the cluster independent fading is assumed. Taking these modifications into considerations, the multipath channel model can be represented by the following discrete time channel response: L k = K i i h ( t) X α i k, lδ ( t T l τ k, l ) i = i l= 0 k = 0 (A.1) where : X i represent the log normal fading α i k, l are the multipath gain coefficients i T l is the decay of the l th cluster τ i k, l is the delay of the k th multipath component relative to the th l cluster arrival time T l i refers to the th i c realization The proposed IEEE model uses the parameters in table A.1: 100

112 Table A.1 Channel model components and parameters A.2 Channel characteristics desired to model The parameters discussed in Table A.1 are calculated by matching important characteristics of the channel. Channel characteristics that were used to derive the model parameters were chosen to be the following: Mean excess delay RMS delay spread Number of multipath components (defined as the number of multipath arrivals that are within 10 db of the peak multipath arrival) Power decay profile The first three characteristics above were used to match the parameters as it was found that it was difficult to match to power decay profile. Channel parameters were found using measurement data based on couple of channel characteristics for different channel models and are shown in Table A

113 Table A.2 Typical Channel Characteristics and Model parameters 1 Based on LOS (0-4 m) channel measurements reported by Pandegrass. 2 Based on NLOS (0-4 m) channel measurements reported by Pandegrass. 3 Based on NLOS (4-10 m) channel measurements reported by Pandegrass and Forester. 4 Represents an extreme NLOS multipath channel to fit a 25 ns RMS delay spread. 5 Sampling time for these characteristic is 167 ps. One hundred actual realizations for each channel model were derived from the model above and the channel that was obtained is as shown in Figure A.1-A.4. Channel shown in Figure A.1 is one realization of channel CM 1. This channel model is of a line of sight (LOS) case with the transmitter and the receiver antenna being separated by a distance in the range (0-4 m). Figure A.2 shows single realization of the channel model CM 2. This channel is a model for a non line of sight (NLOS) case with antenna separation being in the range (0-4 m). FigureA.3 and A.4 represent channel models CM 3 and CM 4 for NLOS case with antenna separation being in the range (4-10 m) and an extreme case respectively. 102