1998 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL Amir Dezfooliyan, Member, IEEE, and Andrew M. Weiner, Fellow, IEEE

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1 1998 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016 Spatiotemporal Focusing of Phase Compensation and Time Reversal in Ultrawideband Systems With Limited Rate Feedback Amir Dezfooliyan, Member, IEEE, and Andrew M. Weiner, Fellow, IEEE Abstract We investigate the performance of phase compensation (PC) and time reversal pre-equalizers in multipath indoor channels when a quantized version of the channel state information (CSI) is available at the transmitter side. We conduct a comprehensive experimental study to assess their spatial and temporal focusing as a function of the number of quantization levels over the frequency band of 2 12 GHz. To characterize multipath compression performance, root-mean-square (RMS) delay spread and peak-to-average power ratio (PAPR) are calculated for different numbers of quantization levels. Bit error rate (BER) curves have been simulated for data rates in the range of Mb/s based on the measured channel responses. To assess spatial focusing, we investigate the decay of the received response peak power as we move away from the intended receiver. Our study suggests that for the same feedback rate, PC has considerably superior performance in suppressing multipath dispersions and focusing the transmitted energy at the intended receiver. Index Terms Limited-rate feedback, multipath channels, spatiotemporal focusing, transmit beamforming, ultrawideband (UWB). I. INTRODUCTION ULTRAWIDEBAND (UWB) is a radio technology for future wireless communication, radar, and imaging systems [1], [2]. Although this technology offers several unique advantages such as multipath immunity, high data rate, and strong antijamming ability [3], there are a number of practical challenges, which are topics of current research. One key challenge is the increased multipath dispersion, which results because of the fine temporal resolution [4]. Although such challenges have been investigated to some extent, they have not been fully explored in connection with transmit beamforming techniques in realistic multipath environments [5] [11]. Beamforming is a transmission technique that can be employed to combat the multipath dispersion and provide temporal and spatial focus- Manuscript received October 5, 2014; revised January 25, 2015; accepted March 15, Date of publication April 7, 2015; date of current version April 14, This work was supported by the Office of the Assistant Secretary of Defense for Research and Engineering through the National Security Science and Engineering Faculty Fellowship program under Grant N from the Naval Postgraduate School. Any opinion, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsors. The review of this paper was coordinated by Prof. X. Wang. The authors are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN USA ( amw@purdue.edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TVT ing at the target receiver. The temporal compression leads to an improved signal-to-noise ratio (SNR), which reduces the intersymbol interference in high-speed wireless communications [5], [11]. On the other hand, spatial focusing means that the received power decreases away from the target location, leading to lower probabilities of intercept by an eavesdropper or interuser interference in a secure multiuser communication channel [7], [12] [14]. Due to this spatiotemporal focusing, the receiver complexity is shifted to the transmitter side, and a simpler receiver s structure can be employed to capture the received energies. As an example, time reversal (TR) [15] [17] is one of the well-known beamformers in which the flipped version of the channel impulse response is used as a prematched filter. When the time-reversed signal is transmitted back through the same channel, multipath components arrive constructively aligned at the target receiver at a particular time. To perform, however, all these beamforming techniques require the channel state information (CSI) at the transmitter side. Typically, the CSI is estimated at the receiver by exciting the channel with a training signal [3]. Then, the obtained information is quantized and sent back to the transmitter through a reverse link as overhead [18]. This feedback load proportionally grows with the length of the channel impulse and the number of quantization levels used in channel estimation. In UWB channels with a large number of resolvable components, deploying a beamformer with very fine quantization levels implies a large amount of feedback load, which becomes a hurdle in practical systems. In particular, in time-varying systems in which the CSI is valid only over the coherence time, it is necessary to limit the feedback time as much as possible. To alleviate this problem and avoid excessive overhead, one scheme is to quantize the CSI with coarser steps so that a smaller number of bits is required to be fed back to the transmitter side. The effect of quantization error on UWB transmit beamforming has been investigated to some extent by a few researchers [19] [21]. They particularly study the TR beamforming performance when only the temporal phase information of the channel impulse response (the sign of each path gain) is provided at the transmitter side, which is a technique known as 1-bit TR [19] [25]. A majority of these works are theoretical studies based on simplified models that do not consider important propagation phenomena such as the frequency dependence of the MPC and path-loss exponent [19] [21]. For example, in [19], Chang et al. theoretically predict the performance of 1-bit TR compared with the conventional TR technique, assuming IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 1999 that a Rayleigh fading model holds for UWB channels. They simulate the bit error rate (BER) and the output signal-tointerference-plus-noise ratio performances at data rates of 25 and 50 Mb/s. Abbasi-Moghadam and Vakili [21] also evaluate the performance of 1-bit TR based on the Rayleigh channel fading assumption for single-input multiple-output systems. As explained in [26] and [27], Rayleigh fading is not a realistic propagation model for UWB systems with large bandwidth. We have recently conducted a series of experiments to evaluate the performance of TR for biconical omnidirectional and spiral directional antennas over the frequency range of 2 12 GHz, which covers the full UWB band [10]. Our study shows that although TR effectively compensates the phase distortions of broadband spiral antennas, it provides only a limited compression for the delay spread associated with multipath channels [10]. In [11], we introduced phase compensation (PC) beamforming as a solution to suppress multipath dispersion. Our experimental and theoretical results indicate that PC achieves superior temporal focusing compared with TR when the full CSI is available. The lack of comprehensive study on UWB transmit beamforming has motivated us to extend our previous works and investigate the effectiveness of TR and PC under limited-ratefeedback situations. As developing a precise model for UWB systems, which includes frequency dependence of the MPC, path-loss exponent, etc., in rich multipath environments is still a topic of current research [27], our study is based on channel impulse responses measured over the full 2 12-GHz frequency range. The emphasis of this paper is to evaluate the effectiveness of TR and PC in realistic non-line-of-sight (NLOS) environments using digitized versions of the CSI. We conduct a comprehensive experimental study to assess the performance of PC and TR beamforming, from both spatial and temporal focusing perspectives as a function of the number of quantization levels. Although the spatial focusing of TR UWB systems under limited feedback has been investigated, most of the previous works are limited to 1-bit TR. The spatial performance of PC beamforming has not been previously investigated, to the best of our knowledge. To characterize multipath compression performance, rootmean-square (RMS) delay spread and peak-to-average power ratio (PAPR) are calculated for different numbers of quantization levels [10]. Data transmission performance is evaluated based on BER simulations for received SNR values in the range of 5 to 30 db. To investigate spatial focusing, we apply TR/PC techniques on a specific channel and use a robotic antenna positioner to move the receive antenna to investigate how fast the received peak power decays as we move away from the target location. Our study suggests that for the same feedback rate, PC has superior spatial and temporal focusing compared with TR in UWB channels. Although temporal focusing deteriorates under limited-rate systems, spatial focusing remains comparable to that observed under full feedback, particularly for PC. This paper is laid out as follows. Section II formulates the quantized PC and TR techniques. We also explain the characterizationparameters to evaluate spatiotemporal focusing and data transmission performance. Section III describes the experimental setup and our research methodology. We investigate spatiotemporal focusing of PC and TR as a function of quantization levels in Section IV. Finally, we conclude in Section V. II. TIME REVERSAL AND PHASE COMPENSATION BEAMFORMING A. Finite-Rate Feedback TR and PC Here, we present the mathematical formalism of TR and PC in limited-rate-feedback channels. We also employ a continuous-time notation consistent with the model presented in [7]. We denote the impulse response from the transmitter to the receiver at location R by h(t, R). WedefineR = R 0 as the intended receiver location. Ideally, TR is a prematched filter in which the transmitted signal, i.e., x Ideal TR (t, R 0), is a flipped version of the channel impulse response, i.e., X Ideal x Ideal TR (t, R 0 )=h ( t, R 0 ) (1) XTR Ideal (f,r 0 )=H (f,r 0 ). (2) Here, TR (f,r 0) is the Fourier transform of x Ideal TR (t, R 0). The received response in the time domain is the autocorrelation of the system impulse response, and that in the frequency domain is the square magnitude of the channel transfer function, i.e., YTR Ideal (f,r 0 )=H(f,R 0 ).XTR Ideal (f,r 0 )= H(f,R 0 ) 2. (3) In a finite-rate feedback system in which the quantized version of the channel impulse response is provided at the transmitter side, the transmitted signal can be mathematically presented as x TR (t, R 0 )=f Q (h( t, R 0 )). (4) Here, f Q (.) is a midrise uniform quantizer [29]. This quantizer does not have zero as one of the output quantized levels. For input x within a finite range of ( x max,x max ),wedefine the output of the midrise quantizer as f Q (x) =Δ. ( x Δ where Δ=(2x max /L). Here, rounds to the closest integer less than or equal to the element, x is the magnitude of x, Δ is the step size between adjacent equalized levels, and L is the number of quantization levels. L can be defined as 2 m,wherem is the number of bits representing each sample. The number of quantization levels is determined based on the feedback load restriction and length of the channel response. From now on, to facilitate discussion, we label each beamformer with the number of quantization levels used in the channel estimation process. Here, in the extreme case, which is two-level TR (1-bit TR in the previous literature), only the sign of the channel gains is sent back to the transmitter side, and the beamformer signal (x 2L TR (t, R)) can be modeled as ) (5) x 2L TR (t, R 0 ) sign (h( t, R 0 )). (6)

3 2000 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016 Compared with the ideal TR, two-level TR requires a much smaller feedback load and has a constant peak power, which can be important from an implementation point of view [23]. (f,r 0)) and the resulting received response (YPC Ideal(f,R 0)) can be mathematically presented in the frequency domain as The PC transmitted signal (X Ideal PC XPC Ideal (f,r 0 )=exp( j. arg (H sys (f,r 0 ))) (7) YPC Ideal (f,r 0)=H sys (f,r 0 ).XPC Ideal (f,r 0)= H sys (f,r 0 ) (8) where arg(h sys (f,r 0 )) is the spectral phase of the system response, which can vary in the range of [ π, π). InPC,the excitation signal cancels the system spectral phase distortion and leads to a compressed waveform at the target receiver. As PC is a frequency-domain equalizer that depends only on the channel spectral phase, it is more efficient to apply quantization directly to the spectral phase information in a finite-rate feedback system. Here, the transmitted PC signal (X PC (f,r 0 ))in the frequency domain can be represented by X PC (f,r 0 )=exp( j.f Q (arg (H(f,R 0 )))) (9) where f Q (arg(h(f,r 0 ))) is the quantized spectral phase of the system response. In the limit where only two quantization levels are used, the two-level PC (X 2L PC (f,r 0 )) can be mathematically written in the frequency domain as { exp(jπ/2), if 0<arg (H(f,R 0 )) <π X 2L PC (f,r 0 )= exp( jπ/2), if π<arg(h(f,r 0 )) <0. (10) B. Performance Characterization Metrics a) Temporal focusing: RMS delay spread (σ) is an important parameter that is commonly used to characterize delay dispersion of multipath channels [3]. To evaluate temporal focusing of TR and PC, we calculate the relative percentage difference of the RMS delay spreads before and after applying the prefilters, i.e., C rms = σ IR σ TR/PC σ IR 100 (11) where C rms is the temporal compression parameter, and σ IR and σ TR/PC are, respectively, the RMS delay values [3] of the channel impulse response and of the corresponding TR/PC received responses. A positive value of C rms means the RMS delay spread is decreased after implementing the beamformer. On the other hand, a negative value of C rms indicates that the prefilter broadens the received response, which is an undesirable effect. The RMS delay value strongly depends on the received noise level [3]. We choose thresholds of 33 and 37 db, respectively, for PC and TR and set to zero all signals below these levels. This way, we eliminate the noise effect as much as possible but include most of the real received energy. In another approach to evaluate temporal focusing of different pre-equalizers, we calculate the achieved PAPR [3] gain (G ϑ ) by employing the beamformers as G ϑ = ϑ TR/PC ϑ IR (12) where ϑ IR and ϑ TR/PC are, respectively, the PAPR values of the impulse response and of the corresponding TR/PC received response in decibels (db). The PAPR is calculated over a 200-ns time window. In contrast to the RMS delay spread, the PAPR is more robust and is not sensitive to the selected noise threshold. b) BER: To assess the performance of limited-ratefeedback TR and PC in high-speed data transmission, we simulate their BER performance. The simulation is based on transmitting 10 5 random bits using binary phase-shift keying modulation over the measured channel realizations. We use TR and PC prefilters for combating the multipath channel dispersion. At the receiver side, we sample the received signal at the peak of PC/TR and make our decision based on the maximum-likelihood criteria. We assume the receiver to be perfectly synchronized with the transmitter. Simulations are performed as a function of the received SNR (defined as the maximum received peak power to the noise power in decibel scale) over 5 to 30 db in steps of 1 db for data rates ranging from 125 Mb/s to 4 Gb/s. The average BER performances are evaluated by averaging the BER of the 15 channel realizations for NLOS. c) Spatial focusing: To characterize spatial focusing, we excite the channel with a TR/PC beamformer, which is calculated based on the measured impulse response from Tx to the target receiver located at R 0. We then move the receive antenna and measure the received peak power for an array of locations away from the target location. The received response at location R can be mathematically expressed as y TR/PC (t, R) =h(t, R) x TR/PC (t, R 0 ) (13) where is the convolution operation, and y TR/PC (t, R) is the received response at location R. Consistent with the notation used in [7] and [14], we define η M (R) as the peak power of y TR/PC (t, R) 2, i.e., η M (R) =max t { ytr/pc (t, R) 2}. (14) We normalize (14) to the maximum received peak power at the target location (η M (R)/η M (R 0 )) and plot it over a contour to demonstrate the spatial focusing of different beamformers as a function of offset from the intended receiver. To quantify spatial focusing in range and cross-range directions (i.e., axes that are respectively parallel and orthogonal to the transmit receive direction), we find the minimum offsets such that the maximum peak power falls below 3 or 10 db relative to the peak power at the intended receiver. For example, for 3 db, we can define η M (R 0 + G r u r + G c u c )/η M (R 0 ) < 0.5 (15) where u r and u c are the unit vectors in the range and crossrange directions, and G r and G c are the characteristic parameters. To quantify spatial focusing in the range direction, we find

4 DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 2001 Fig. 1. Schematic of the experimental setup. the minimum value of G r that satisfies inequality (15) for any arbitrary value G c. Similarly, for the cross-range direction, we find the minimum value of G c such that inequality (15) holds for any arbitrary value of G c. III. EXPERIMENTAL SYSTEM A. Experimental Setup Fig. 1 shows the main components of the experimental setup. The arbitrary waveform generator (AWG) has a maximum RF bandwidth of 9.6 GHz and a sampling rate of 24 GS/s (Tektronix AWG 7122B). The generated signal is boosted by 10 db by a broadband amplifier with 14-GHz bandwidth. Two omnidirectional antennas (ELECTRO - METRICS EM-6865, 2 18 GHz) with a uniform radiation pattern in the azimuth plane are employed as the transmitter (Tx) and receiver (Rx). The received signal is amplified by 51 db by passing through one low-noise amplifier (31-dB gain, GHz) and two broadband amplifiers. The amplified received response is recorded with a real-time oscilloscope (Tektronix Digital Serial Analyzer 72004B), which has an analog bandwidth of 20 GHz and a maximum real-time sampling rate of 50 GS/s. A personal computer is used to control the AWG and store the recorded signals from the oscilloscope. The wireless local area network (LAN) between the AWG and the personal computer provides a feedback loop to the transmitter side. To investigate the spatial properties of our system, the received antenna can be moved with a robotic antenna positioner over a 2 m 2 m rectangular grid with interelement spacing of 2 cm, whereas the Tx antenna is fixed. This is equivalent to a total of measurements to scan the whole grid. There are two cement walls in the direct path of the Tx Rx antennas, and their direct propagation distance is between 13 and 15 m. More details about our setup are given in [28]. B. Research Methodology Experiments have been carried out in the laboratories in the subbasement of the Material Science and Electrical Engineering building at Purdue University. The experimental procedure of applying TR/PC can be divided into three major steps. First, we measure the system impulse response from the Tx to the Rx by probing the system with spread-spectrum waveforms [28]. In our experiments, AWG generates an upchirp waveform with the time aperture of 85.3 ns over the frequency range spanning Fig. 2. (a) Impulse response of a typical NLOS indoor environment over a 150-ns time window. (b) RF power spectrum and unwrapped spectral phase of this response. Multipath dispersion produces strong spectral amplitude and phase distortion GHz. To extract the system impulse response, the received response after wireless propagation is deconvolved from the transmitted signal [28]. To minimize the noise effect, we define thresholds of 17 db for up to eight-level quantization and 20 db for any higher number of quantization levels with respect to the peak power of the impulse response. This part of the channel impulse response is communicated back to the transmitter with some predefined accuracy through a feedback loop (wireless LAN). For TR, the CSI is communicated on a time-domain basis. For PC, the corresponding quantized data of the spectral phase are sent back to the transmitter side on a frequency-domain basis. In the second step, the TR/PC beamformers are calculated at the transmitter side based on the obtained CSI. The TR beamformer is simply a flipped version of the CSI in the time domain. For PC, we calculate the frequency response of the PC using (9). The time-domain PC waveform is calculated by taking inverse Fourier transform. For two-level and four-level PC, the sharp spectral phase jumps introduce an irregular tail in addition to the main part of the time-domain signal. We only keep 70 ns of the signal, which includes the main part. Finally, these signals are generated by the AWG and transmitted through the antenna. On the receiver side, the received waveforms are recorded using the real-time oscilloscope. IV. MEASUREMENT RESULTS AND ANALYSIS A. Temporal Focusing Fig. 2(a) shows the impulse response of a typical NLOS indoor environment over a 150-ns time window. To better show individual features, the small subfigure shows the first 10 ns of the power delay profile. The impulse response is a superposition of different multipath components that disperse over a 130-ns time window. This is more than 2000 times broader than the 50-ps time resolution of the system with

5 2002 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016 Fig. 3. Received responses when different beamforming techniques are applied over the channel in Fig. 2. The sidelobes of PC are considerably smaller than TR in both full- and limited-feedback situations. bandwidth of 10 GHz. The RF power spectrum and the unwrapped spectral phase of this response are shown in Fig. 2(b). Due to the frequency-dependent nature of propagation loss, the power spectrum decays at higher frequencies. The multipath components interfere with each other in the frequency domain, leading to a strongly frequency-selective response. In addition to the spectral amplitude distortion, we experience a significant frequency-dependent spectral phase distortion. The unwrapped spectral phase nonlinearly varies with frequency, which contributes to the temporal signal dispersion. To suppress the multipath effects, we employ TR and PC beamforming. The quantized channel impulse responses are used to calculate the TR and PC prefilters. The received response is computed as a convolution of the channel impulse response with the calculated TR/PC. Fig. 3 shows the received responses. To make the comparison easier, each plot is individually normalized to one. For full-feedback TR and PC, we quantize the channel impulse response with 2 8 levels (8 bits for each sample of the signal). For a limited-feedback scenario, we consider the first 92 ns of the channel impulse response, which includes the received multipath components within the thresholds of 17 db with respect to the peak power of the impulse response. At a sampling rate of 24 GS/s, this is equivalent to 2208 samples. In these figures, we compare two-level TR (1-bit TR) with four-level PC. In a carrierless system, the channel impulse response is real, and its Fourier transform is a complex antisymmetric function. If the time-domain vector has N real samples, then its fast Fourier transform can be represented by N/2 independent complex samples. For twolevel (1-bit) TR, the feedback load is N. However,forPC,we are only interested in the spectral phase information, which can be represented by N/2 independent real samples. As a result, the feedback load for a two-level TR is equivalent to a four-level (2-bit) PC. In this example, in which we have 2208 samples, the feedback load is 2208 bits in both scenarios. Comparing these figures, we clearly see the superior multipath suppression of PC over TR in both full- and limitedfeedback scenarios. To understand the intuitive reason behind the superior performance of PC, we look back at their mathematical equations. Ideal TR compensates spectral phase distortions, but it squares the spectral magnitude. This spectral shaping aggravates the system spectral amplitude distortion, which broadens the received response in the time domain. PC only compensates the spectral phase distortion and does not increase the spectral amplitude distortion. As a result, PC achieves better temporal compression. A more detailed discussion is presented in [11]. To statically evaluate temporal focusing, we measure 15 channel impulses with low mutual correlation. The receive antenna is moved on a track to scan a rectangular area of 1.2 m 2.4 m, whereas the transmit antenna is fixed. The interelement spacing of the grid is 60 cm to ensure that the channel impulse responses are approximately uncorrelated. Based on the measured impulse responses, we calculate the received responses from TR and PC under full- and limitedfeedback scenarios. Table I summarizes the average and standard deviation of the parameters introduced in Section II-Ba for the received responses from TR and PC. Full-feedback PC reduces the RMS delay spread of the channel by 67.7% and increases the PAPR by 13.5 db. These numbers for fullfeedback TR are only 20.1% and 8.0 db, which prove the superior performance of PC. Under the limited-rate-feedback scenario, while four-level PC provides temporal compression of 32.3%, the two-level TR has a negative value (C rms = 11.4%), indicating that the channel RMS delay spread is increased. Two-level TR provides 6.4 db of PAPR gain, which is 6.2 db less than the 12.6-dB gain achieved by four-level PC. We also observe that the four-level PC outperforms fullquantization TR in terms of both temporal compression and PAPR gain.

6 DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 2003 TABLE I PERFORMANCE OF TR AND PC IN BOTH FULL- AND LIMITED-FEEDBACK SCENARIOS.AVERAGE (AVG) AND STANDARD DEVIATION (STD) VALUES FOR OMNIDIRECTIONAL EXPERIMENTS OVER 15 NLOS LOCATIONS Fig. 4. (a) Average temporal compression and (b) PAPR for TR and PC as a function of quantization levels. We perform a series of numerical calculations to evaluate the performance of PC versus TR as a function of quantization levels. Fig. 4 shows the average temporal compression and PAPR of the 15 channel impulses as a function of quantization levels. As explained, due to the antisymmetric property of the spectral phase, PC requires half-feedback load compared with TR for the same number of quantization levels. PC provides superior gain compared with TR from both temporal compression and PAPR gain perspectives. For instance, the PAPR gain for PC is approximately 6 db higher than the corresponding value for TR with the same number of quantization levels. Both TR and PC reach a plateau approximately after 2 6 quantization levels in which a larger quantization level does not improve the performance. At this point, the limited-rate system achieves performance of a full-feedback TR/PC prefilter. The BER performance for full-feedback TR and PC is studied in [11]. Here, we focus on the BER performance of two-level TR and four-level PC. The simulated BER curves are presented in Fig. 5. For a low-snr regime (< 0 db), the dominant noise level determines the system performances, and both PC and TR have high BERs. BER curves for the TR prefilter reach a plateau for data rates of 500 Mb/s and above, where increasing the SNR cannot improve the performance any further. In this high-snr regime, the system performance is saturated by the intersymbol interference originating from TR sidelobes. For the PC prefilter, we have the performance saturation only for the data rate transmissions higher than 2 Gb/s. The 2-Gb/s curve for PC levels off at BER, which is by far better compared with the level of the Fig. 5. Average BER for NLOS PC and TR. The performance of PC is clearly superior to that of TR for the data rates of 250 Mb/s and above. BER plateau of the 2-Gb/s TR curve. The BER curves show that in limited-rate-feedback systems, PC BER performanceis considerably superior to the TR technique. B. Spatial Focusing To evaluate spatial focusing of TR and PC under both full and limited feedback, experiments were carried out in an NLOS environment (average propagation distance of 15 m). First, we measure the spatial focusing in the absence of any transmit beamforming. We excite the channel with the chirp signal described in Section III and measure the received responses as the receive antenna moves with the step size of 2 cm over a2m 2 m grid under control of an automatic antenna positioner. Then, we extract the channel impulse responses by the deconvolution technique described in [28] and calculate the total signal power. Fig. 6 shows the result normalized to the maximum calculated power. As we expected, there is no systematic spatial focusing that can be employed in the system design.

7 2004 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016 Fig. 6. Spatial focusing in the absence of any transmit beamforming. The result is normalized to the maximum calculated impulse response power. As expected, there is no systematic spatial focusing that can be employed in system design. In the next step, the channel is excited with the TR/PC beamformer calculated based on the measured impulse response from the Tx to the target receiver, which is located at the center of the described automatic antenna positioner. Then, we move the receive antenna with the step size of 2 cm on the square grid and measure the received peak power as we move away from the center location. The experimental results are presented in Figs. 7 and 8. Each figure consists of measurement points. Fig. 7(e) (h) shows zoomed-in versions of Fig. 7(a) (d), respectively. In Fig. 8, we show line-out plots for each of the four cases along the range and cross-range directions passing through the center of the antenna positioner. In contrast to Fig. 6, the peak power is now focused at the target receiver and decays rapidly as we move away. For both TR and PC, the spatial focusing rolls off faster in the cross-range direction. As predicted by simulation in [7], the structure of these peaks strongly depends on the environment geometry. To characterize the spatial focusing, we use (15) in which R 0 is the center position of the antenna positioner. Table II summarizes the values G r and G c for both 3- and 10-dB thresholds. Overall, PC provides a much better spatial focusing compared with TR. For instance, the peak power for full-feedback TR falls below 3 db with respect to the main central peak after 22-cm offset in the range direction, whereas this number is only 5 cm for PC. As shown in Table II, the maximum peak power is at least 10 db lower than the central peak power after 19 cm in the range direction for both full- and limited-feedback PC; however, this never happens within the 100-cm distance of the center for TR. Although the four-level PC provides the best spatial focusing (even better than full-feedback PC), the twolevel TR has the worst focusing performance. This superior performance of PC can be exploited for the future covert highspeed UWB communication channels as an effective way to provide spatiotemporal focusing and reduce intersymbol and interuser interference. V. C ONCLUSION The performance of PC and TR prefilters has been investigated in NLOS environments when the digitized version of Fig. 7. Spatial focusing of TR and PC under both full- and limited-feedback systems in an indoor NLOS environment. In panels (e) (h), we zoom in at the center location to better show details. In contrast to Fig. 6, the peak power is now focused at the target receiver and decays rapidly as we move away. For both TR and PC, the spatial focusing rolls off faster in the cross-range direction. Overall, PC provides a much better spatial focusing compared with TR. the channel impulse response is available at the transmitter. We conducted an experimental study to assess their performance from both spatial and temporal focusing perspectives over the frequency band of 2 12 GHz. To characterize the temporal focusing, RMS delay spread and PAPR parameters are calculated. The BERs of the measured channels are presented for different data rates (from 125 Mb/s to 4 Gb/s) as a function of the received SNR. To characterize spatial focusing, we investigated the decay of the received response peak power as we move away from the intended receiver. Our study suggests that for the same feedback rate, PC has superior spatiotemporal focusing performance compared with TR. For instance, while four-level PC provides an average 12.6-dB PAPR gain, twolevel TR provides only 6.4-dB gain while requiring the same quantity of information feedback as four-level PC. From the spatial focusing perspective, the peak power for two-level TR

8 DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 2005 Fig. 8. Line-out plots for each of the four plots shown in Fig. 7(a) (d) along the range and cross-range axes passing through the center of the antenna positioner. The peak power decays rapidly as we move away from the intended receiver. For both TR and PC, the spatial focusing rolls off faster in the cross-range direction. TABLE II MINIMUM REQUIRED OFFSET IN THE RANGE AND CROSS-RANGE DIRECTIONS SUCH THAT THE MAXIMUM RECEIVED PEAK POWER FALLS BELOW 3 OR 10 db RELATIVE TO THE PEAK POWER AT THE TARGET RECEIVER falls below 3 db with respect to the main central peak after 31-cm offset in the range direction, whereas this number is only 4 cm for four-level PC. ACKNOWLEDGMENT The authors would like to thank Dr. D. E. Leaird for his helpful technical assistance. REFERENCES [1] R. J. M. Cramer, R. A. Scholtz, and M. Z. Win, Evaluation of an ultrawide-band propagation channel, IEEE Trans. Antennas Propag., vol. 50, no. 5, pp , May [2] A. F. Molischet al., A comprehensive standardized model for ultrawideband propagation channels, IEEE Trans. Antennas Propag., vol. 54, no. 11, pp , Nov [3] A. Goldsmith, Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, [4] A. F. Molisch, Ultrawideband propagation channels and their impact on system design, in Proc. IEEE Int. Symp. Microw., Antenna, Propag. EMC Technol. Wireless Commun., 2007, vols I/II, pp. AK41 AK45. [5] I. H. Naqvi et al., Experimental validation of time reversal ultra wideband communication system for high data rates, IET Microw., Antennas Propag., vol. 4, no. 5, pp , May [6] K. Popovski, B. J. Wysocki, and T. A. Wysocki, Modelling and comparative performance analysis of a time-reversed UWB system, EURASIP J. Wireless Commun. Netw., vol. 2007, no. 1, Apr. 2007, Art. ID [7] C. Oestges et al., Time reversal technique for broadband wireless communication systems, presented at the Eur. Microwave Conf., Amsterdam, The Netherlands, Oct [8] D. Abbasi-Moghadam and V. T. Vakili, Characterization of indoor time reversal UWB communication systems: Spatial, temporal and frequency properties, Int. J. Commun. Syst., vol. 24, no. 3, pp , Mar [9] T. Wang and T. Lv, Canceling interferences for high data rate time reversal MIMO UWB system: A precoding approach, EURASIP J. Wireless Commun. Netw., vol. 2011, no. 1, Mar. 2011, Art. ID [10] A. Dezfooliyan and A. M. Weiner, Experimental investigation of UWB impulse response and time reversal technique up to 12 GHz: Omnidirectional and directional antennas, IEEE Trans. Antennas Propag., vol. 60, no. 7, pp , Jul [11] A. Dezfooliyan and A. M. Weiner, Phase compensation communication technique against time reversal for ultra-wideband channels, IET Commun., vol. 7, no. 12, pp , Aug [12] Z. Chenming, N. Guo, and R. C. Qiu, Experimental results on Multiple- Input Single-Output (MISO) time reversal for UWB systems in an office environment, in Proc. IEEE MILCOM, 2006, pp [13] P. Blomgren, P. Kyritsi, A. D. Kim, and G. Papanicolaou, Spatial focusing and intersymbol interference in multiple-input single-output time reversal communication systems, IEEE J. Ocean. Eng., vol. 33, no. 3, pp , Jul [14] C. Oestges, A. D. Kim, G. Papanicolaou, and A. J. Paulraj, Characterization of space time focusing in time-reversed random fields, IEEE Trans. Antennas Propag., vol. 53, no. 1, pp , Jan

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Molisch, Ultra-wide-band propagation channels, Proc. IEEE, vol. 97, no. 2, pp , Feb [27] K. Haneda, A. Richter, and A. F. Molisch, Modeling the frequency dependence of ultra-wideband spatio-temporal indoor radio channels, IEEE Trans. Antennas Propag., vol. 60, no. 6, pp , Jun [28] A. Dezfooliyan and A. M. Weiner, Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding, IEEE Trans. Antennas Propag., vol. 60, no. 10, pp , Oct [29] A. Gersho, Quantization, IEEE Commun. Soc. Mag., vol. 15, no. 5, pp. 16, Sep Andrew M. Weiner (F 95) received the Sc.D. degree in electrical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA, in He is the Scifres Family Distinguished Professor of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. After his Sc.D. studies, he joined Bellcore, which was then a premier telecommunications industry research organization, first as a Member of Technical Staff and later as a Manager of Ultrafast Optics and Optical Signal Processing Research. In 1992, he joined Purdue University, where and has since graduated over 30 Ph.D. students. He also spent sabbaticals with the Max Born Institute for Nonlinear Optics and Ultrashort Pulse Spectroscopy, Berlin, Germany; and with JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO, USA. He is an author of a textbook entitled Ultrafast Optics; has published eight book chapters, over 300 journal articles, and over 500 conference papers; and is an inventor of 16 U.S. patents. His research focuses on ultrafast optics, with a focus on processing of extremely high speed lightwave signals and ultrabroadband radio-frequency signals. He is particularly well known for his pioneering work on programmable generation of arbitrary ultrashort pulse waveforms, which has found application both in fiberoptic networks and in ultrafast optical science laboratories around the world. Dr. Weiner has received numerous awards, including the Hertz Foundation Doctoral Thesis Prize (1984), the Optical Society of America s Adolph Lomb Medal (1990), R. W. Wood Prize (2008), the International Commission on Optics Prize (1997), and the IEEE Photonics Society s William Streifer Scientific Achievement Award (1999) and Quantum Electronics Prize (2011). At Purdue University, he has been recognized with the inaugural Research Excellence Award from the Schools of Engineering (2003), the Provost s Outstanding Graduate Student Mentor Award (2008), the Herbert Newby McCoy Award for outstanding contributions to the natural sciences (2013), and the College of Engineering Mentoring Award (2014). In 2008, he was elected to membership in the National Academy of Engineering. In 2009, he was named a Department of Defense National Security Science and Engineering Faculty Fellow. He recently served a three-year term as Chair of the National Academy s U.S. Frontiers of Engineering Meeting. He currently serves as Editor-in-Chief of Optics Express, an all-electronic open-access journal publishing more than 3000 papers a year, emphasizing innovations in all aspects of optics and photonics. Amir Dezfooliyan (M 14) received the B.Sc. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2009 and the Ph.D. degree in electrical and computer engineering from Purdue University, West Lafayette, IN, USA, in Upon graduation, he joined Tektronix Communications Co., where he is currently the Manager of RF Engineering. He is the author of more than 20 scientific papers on multiple-antenna systems, transmit beamforming, and arbitrary micro/ millimeter-waveform generation. His research interests include optical wireless communications, signal propagation modeling, and ultrafast optics.