1998 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016

Spatiotemporal Focusing of Phase Compensation andTime Reversal in Ultrawideband Systems With

Limited Rate FeedbackAmir Dezfooliyan, Member, IEEE, and Andrew M. Weiner, Fellow, IEEE

Abstract—We investigate the performance of phase compensa-tion (PC) and time reversal pre-equalizers in multipath indoorchannels when a quantized version of the channel state informa-tion (CSI) is available at the transmitter side. We conduct a com-prehensive experimental study to assess their spatial and temporalfocusing as a function of the number of quantization levels overthe frequency band of 2–12 GHz. To characterize multipath com-pression performance, root-mean-square (RMS) delay spread andpeak-to-average power ratio (PAPR) are calculated for differentnumbers of quantization levels. Bit error rate (BER) curves havebeen simulated for data rates in the range of 125–4000 Mb/s basedon the measured channel responses. To assess spatial focusing,we investigate the decay of the received response peak power aswe move away from the intended receiver. Our study suggeststhat for the same feedback rate, PC has considerably superiorperformance in suppressing multipath dispersions and focusingthe transmitted energy at the intended receiver.

Index Terms—Limited-rate feedback, multipath channels,spatiotemporal focusing, transmit beamforming, ultrawideband(UWB).

I. INTRODUCTION

U LTRAWIDEBAND (UWB) is a radio technology for fu-ture wireless communication, radar, and imaging systems

[1], [2]. Although this technology offers several unique advan-tages such as multipath immunity, high data rate, and strongantijamming ability [3], there are a number of practical chal-lenges, which are topics of current research. One key challengeis the increased multipath dispersion, which results becauseof the fine temporal resolution [4]. Although such challengeshave been investigated to some extent, they have not been fullyexplored in connection with transmit beamforming techniquesin realistic multipath environments [5]–[11]. Beamforming isa transmission technique that can be employed to combat themultipath dispersion and provide temporal and spatial focus-

Manuscript received October 5, 2014; revised January 25, 2015; acceptedMarch 15, 2015. Date of publication April 7, 2015; date of current versionApril 14, 2016. This work was supported by the Office of the Assistant Sec-retary of Defense for Research and Engineering through the National SecurityScience and Engineering Faculty Fellowship program under Grant N00244-09-1-0068 from the Naval Postgraduate School. Any opinion, findings, andconclusions or recommendations expressed in this publication are those of theauthors and do not necessarily reflect the views of the sponsors. The review ofthis paper was coordinated by Prof. X. Wang.

The authors are with the School of Electrical and Computer Engineering,Purdue University, West Lafayette, IN 47907 USA (e-mail: amw@purdue.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2015.2420633

ing at the target receiver. The temporal compression leads toan improved signal-to-noise ratio (SNR), which reduces theintersymbol interference in high-speed wireless communica-tions [5], [11]. On the other hand, spatial focusing means thatthe received power decreases away from the target location,leading to lower probabilities of intercept by an eavesdropperor interuser interference in a secure multiuser communicationchannel [7], [12]–[14]. Due to this spatiotemporal focusing, thereceiver complexity is shifted to the transmitter side, and a sim-pler receiver’s structure can be employed to capture the receivedenergies. As an example, time reversal (TR) [15]–[17] is one ofthe well-known beamformers in which the flipped version of thechannel impulse response is used as a prematched filter. Whenthe time-reversed signal is transmitted back through the samechannel, multipath components arrive constructively aligned atthe target receiver at a particular time.

To perform, however, all these beamforming techniques re-quire the channel state information (CSI) at the transmitter side.Typically, the CSI is estimated at the receiver by exciting thechannel with a training signal [3]. Then, the obtained infor-mation is quantized and sent back to the transmitter through areverse link as overhead [18]. This feedback load proportionallygrows with the length of the channel impulse and the number ofquantization levels used in channel estimation. In UWB chan-nels with a large number of resolvable components, deployinga beamformer with very fine quantization levels implies a largeamount of feedback load, which becomes a hurdle in practicalsystems. In particular, in time-varying systems in which the CSIis valid only over the coherence time, it is necessary to limit thefeedback time as much as possible. To alleviate this problemand avoid excessive overhead, one scheme is to quantize theCSI with coarser steps so that a smaller number of bits isrequired to be fed back to the transmitter side.

The effect of quantization error on UWB transmit beamform-ing has been investigated to some extent by a few researchers[19]–[21]. They particularly study the TR beamforming perfor-mance when only the temporal phase information of the chan-nel impulse response (the sign of each path gain) is provided atthe transmitter side, which is a technique known as 1-bit TR[19]–[25]. A majority of these works are theoretical studiesbased on simplified models that do not consider importantpropagation phenomena such as the frequency dependence ofthe MPC and path-loss exponent [19]–[21]. For example, in[19], Chang et al. theoretically predict the performance of 1-bitTR compared with the conventional TR technique, assuming

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DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 1999

that a Rayleigh fading model holds for UWB channels. Theysimulate the bit error rate (BER) and the output signal-to-interference-plus-noise ratio performances at data rates of 25and 50 Mb/s. Abbasi-Moghadam and Vakili [21] also evaluatethe performance of 1-bit TR based on the Rayleigh channelfading assumption for single-input–multiple-output systems.As explained in [26] and [27], Rayleigh fading is not a realisticpropagation model for UWB systems with large bandwidth.

We have recently conducted a series of experiments toevaluate the performance of TR for biconical omnidirectionaland spiral directional antennas over the frequency range of2–12 GHz, which covers the full UWB band [10]. Our studyshows that although TR effectively compensates the phasedistortions of broadband spiral antennas, it provides only alimited compression for the delay spread associated with multi-path channels [10]. In [11], we introduced phase compensation(PC) beamforming as a solution to suppress multipath disper-sion. Our experimental and theoretical results indicate that PCachieves superior temporal focusing compared with TR whenthe full CSI is available.

The lack of comprehensive study on UWB transmit beam-forming has motivated us to extend our previous works andinvestigate the effectiveness of TR and PC under limited-rate-feedback situations. As developing a precise model for UWBsystems, which includes frequency dependence of the MPC,path-loss exponent, etc., in rich multipath environments is stilla topic of current research [27], our study is based on channelimpulse responses measured over the full 2–12-GHz frequencyrange. The emphasis of this paper is to evaluate the effec-tiveness of TR and PC in realistic non-line-of-sight (NLOS)environments using digitized versions of the CSI. We conducta comprehensive experimental study to assess the performanceof PC and TR beamforming, from both spatial and temporal fo-cusing perspectives as a function of the number of quantizationlevels. Although the spatial focusing of TR UWB systems underlimited feedback has been investigated, most of the previousworks are limited to 1-bit TR. The spatial performance of PCbeamforming has not been previously investigated, to the bestof our knowledge.

To characterize multipath compression performance, root-mean-square (RMS) delay spread and peak-to-average powerratio (PAPR) are calculated for different numbers of quanti-zation levels [10]. Data transmission performance is evaluatedbased on BER simulations for received SNR values in the rangeof−5 to 30 dB. To investigate spatial focusing, we apply TR/PCtechniques on a specific channel and use a robotic antenna po-sitioner to move the receive antenna to investigate how fast thereceived peak power decays as we move away from the targetlocation. Our study suggests that for the same feedback rate, PChas superior spatial and temporal focusing compared with TR inUWB channels. Although temporal focusing deteriorates underlimited-rate systems, spatial focusing remains comparable tothat observed under full feedback, particularly for PC.

This paper is laid out as follows. Section II formulatesthe quantized PC and TR techniques. We also explain thecharacterization parameters to evaluate spatiotemporal focusingand data transmission performance. Section III describes theexperimental setup and our research methodology. We inves-

tigate spatiotemporal focusing of PC and TR as a functionof quantization levels in Section IV. Finally, we conclude inSection V.

II. TIME REVERSAL AND PHASE

COMPENSATION BEAMFORMING

A. Finite-Rate Feedback TR and PC

Here, we present the mathematical formalism of TR andPC in limited-rate-feedback channels. We also employ acontinuous-time notation consistent with the model presentedin [7]. We denote the impulse response from the transmitter tothe receiver at location R by h(t, R). We define R = R0 as theintended receiver location. Ideally, TR is a prematched filterin which the transmitted signal, i.e., xIdeal

TR (t, R0), is a flippedversion of the channel impulse response, i.e.,

xIdealTR (t, R0) = h∗(−t, R0) (1)

XIdealTR (f,R0) =H∗(f,R0). (2)

Here, XIdealTR (f,R0) is the Fourier transform of

xIdealTR (t, R0). The received response in the time domain

is the autocorrelation of the system impulse response, and thatin the frequency domain is the square magnitude of the channeltransfer function, i.e.,

Y IdealTR (f,R0)=H(f,R0).X

IdealTR (f,R0) = |H(f,R0)|2 .

(3)

In a finite-rate feedback system in which the quantizedversion of the channel impulse response is provided at thetransmitter side, the transmitted signal can be mathematicallypresented as

xTR(t, R0) = fQ (h(−t, R0)) . (4)

Here, fQ(.) is a midrise uniform quantizer [29]. This quan-tizer does not have zero as one of the output quantized levels.For input x within a finite range of (−xmax, xmax), we definethe output of the midrise quantizer as

fQ(x) = Δ.

(⌊ x

Δ

⌋+

12

)(5)

where Δ = (2xmax/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 betweenadjacent equalized levels, and L is the number of quantizationlevels. L can be defined as 2m, where m is the number of bitsrepresenting each sample. The number of quantization levels isdetermined based on the feedback load restriction and lengthof the channel response. From now on, to facilitate discussion,we label each beamformer with the number of quantizationlevels used in the channel estimation process. Here, in theextreme case, which is two-level TR (1-bit TR in the previousliterature), only the sign of the channel gains is sent back tothe transmitter side, and the beamformer signal (x2L−TR(t, R))can be modeled as

x2L−TR(t, R0) ∝ sign (h(−t, R0)) . (6)

2000 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016

Compared with the ideal TR, two-level TR requires a muchsmaller feedback load and has a constant peak power, whichcan be important from an implementation point of view [23].

The PC transmitted signal (XIdealPC (f,R0)) and the resulting

received response (Y IdealPC (f,R0)) can be mathematically pre-

sented in the frequency domain as

XIdealPC (f,R0) = exp (−j. arg (Hsys(f,R0))) (7)

Y IdealPC (f,R0) =Hsys(f,R0).X

IdealPC (f,R0) = |Hsys(f,R0)|

(8)

where arg(Hsys(f,R0)) is the spectral phase of the systemresponse, which can vary in the range of [−π, π). In PC, theexcitation signal cancels the system spectral phase distortionand leads to a compressed waveform at the target receiver. AsPC is a frequency-domain equalizer that depends only on thechannel spectral phase, it is more efficient to apply quantizationdirectly to the spectral phase information in a finite-rate feed-back system. Here, the transmitted PC signal (XPC(f,R0)) inthe frequency domain can be represented by

XPC(f,R0) = exp (−j.fQ (arg (H(f,R0)))) (9)

where fQ(arg(H(f,R0))) is the quantized spectral phase ofthe system response. In the limit where only two quantizationlevels are used, the two-level PC (X2L−PC(f,R0)) can bemathematically written in the frequency domain as

X2L−PC(f,R0)=

{exp(jπ/2), if 0<arg (H(f,R0)) < π

exp(−jπ/2), if −π<arg(H(f,R0))<0.(10)

B. Performance Characterization Metrics

a) Temporal focusing: RMS delay spread (σ) is an im-portant parameter that is commonly used to characterize delaydispersion of multipath channels [3]. To evaluate temporalfocusing of TR and PC, we calculate the relative percentagedifference of the RMS delay spreads before and after applyingthe prefilters, i.e.,

Crms =σIR − σTR/PC

σIR× 100 (11)

where Crms is the temporal compression parameter, and σIR

and σTR/PC are, respectively, the RMS delay values [3] ofthe channel impulse response and of the corresponding TR/PCreceived responses. A positive value of Crms means the RMSdelay spread is decreased after implementing the beamformer.On the other hand, a negative value of Crms indicates thatthe prefilter broadens the received response, which is an un-desirable effect. The RMS delay value strongly depends onthe received noise level [3]. We choose thresholds of −33 and−37 dB, respectively, for PC and TR and set to zero all signalsbelow these levels. This way, we eliminate the noise effect asmuch as possible but include most of the real received energy.

In another approach to evaluate temporal focusing of differ-ent pre-equalizers, we calculate the achieved PAPR [3] gain(Gϑ) by employing the beamformers as

Gϑ = ϑTR/PC − ϑIR (12)

where ϑIR and ϑTR/PC are, respectively, the PAPR values ofthe impulse response and of the corresponding TR/PC receivedresponse in decibels (dB). The PAPR is calculated over a 200-nstime window. In contrast to the RMS delay spread, the PAPR ismore robust and is not sensitive to the selected noise threshold.

b) BER: To assess the performance of limited-rate-feedback TR and PC in high-speed data transmission, wesimulate their BER performance. The simulation is based ontransmitting 105 random bits using binary phase-shift keyingmodulation over the measured channel realizations. We useTR and PC prefilters for combating the multipath channeldispersion. At the receiver side, we sample the received signalat the peak of PC/TR and make our decision based on themaximum-likelihood criteria. We assume the receiver to beperfectly synchronized with the transmitter. Simulations areperformed as a function of the received SNR (defined as themaximum received peak power to the noise power in decibelscale) over −5 to 30 dB in steps of 1 dB for data rates rangingfrom 125 Mb/s to 4 Gb/s. The average BER performances areevaluated by averaging the BER of the 15 channel realizationsfor NLOS.

c) Spatial focusing: To characterize spatial focusing,we excite the channel with a TR/PC beamformer, which iscalculated based on the measured impulse response from Txto the target receiver located at R0. We then move the receiveantenna and measure the received peak power for an array oflocations away from the target location. The received responseat location R can be mathematically expressed as

yTR/PC(t, R) = h(t, R) ∗ xTR/PC(t, R0) (13)

where ∗ is the convolution operation, and yTR/PC(t, R) is thereceived response at location R. Consistent with the notationused in [7] and [14], we define ηM (R) as the peak power of|yTR/PC(t, R)|2, i.e.,

ηM (R) = maxt

{∣∣yTR/PC(t, R)∣∣2} . (14)

We normalize (14) to the maximum received peak power atthe target location (ηM (R)/ηM (R0)) and plot it over a contourto demonstrate the spatial focusing of different beamformers asa function of offset from the intended receiver. To quantify spa-tial focusing in range and cross-range directions (i.e., axes thatare respectively parallel and orthogonal to the transmit–receivedirection), we find the minimum offsets such that the maximumpeak power falls below 3 or 10 dB relative to the peak power atthe intended receiver. For example, for 3 dB, we can define

ηM (R0 +Grur +Gcuc)/ηM (R0) < 0.5 (15)

where ur and uc are the unit vectors in the range and cross-range directions, and Gr and Gc are the characteristic parame-ters. To quantify spatial focusing in the range direction, we find

DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 2001

Fig. 1. Schematic of the experimental setup.

the minimum value of Gr that satisfies inequality (15) for anyarbitrary value Gc. Similarly, for the cross-range direction, wefind the minimum value of Gc such that inequality (15) holdsfor any arbitrary value of Gc.

III. EXPERIMENTAL SYSTEM

A. Experimental Setup

Fig. 1 shows the main components of the experimental setup.The arbitrary waveform generator (AWG) has a maximumRF bandwidth of 9.6 GHz and a sampling rate of 24 GS/s(Tektronix AWG 7122B). The generated signal is boosted by10 dB by a broadband amplifier with 14-GHz bandwidth. Twoomnidirectional antennas (ELECTRO - METRICS EM-6865,2–18 GHz) with a uniform radiation pattern in the azimuthplane are employed as the transmitter (Tx) and receiver (Rx).The received signal is amplified by 51 dB by passing throughone low-noise amplifier (31-dB gain, 0.1–20 GHz) and twobroadband amplifiers. The amplified received response isrecorded with a real-time oscilloscope (Tektronix Digital SerialAnalyzer 72004B), which has an analog bandwidth of 20 GHzand a maximum real-time sampling rate of 50 GS/s. A personalcomputer is used to control the AWG and store the recordedsignals from the oscilloscope. The wireless local area network(LAN) between the AWG and the personal computer providesa feedback loop to the transmitter side.

To investigate the spatial properties of our system, the re-ceived antenna can be moved with a robotic antenna positionerover a 2 m × 2 m rectangular grid with interelement spacing of2 cm, whereas the Tx antenna is fixed. This is equivalent to atotal of 10 201 measurements to scan the whole grid. There aretwo cement walls in the direct path of the Tx–Rx antennas, andtheir direct propagation distance is between 13 and 15 m. Moredetails about our setup are given in [28].

B. Research Methodology

Experiments have been carried out in the laboratories in thesubbasement of the Material Science and Electrical Engineer-ing building at Purdue University. The experimental procedureof applying TR/PC can be divided into three major steps. First,we measure the system impulse response from the Tx to the Rxby probing the system with spread-spectrum waveforms [28]. Inour experiments, AWG generates an upchirp waveform with thetime aperture of ∼85.3 ns over the frequency range spanning

Fig. 2. (a) Impulse response of a typical NLOS indoor environment over a150-ns time window. (b) RF power spectrum and unwrapped spectral phaseof this response. Multipath dispersion produces strong spectral amplitude andphase distortion.

∼0–12 GHz. To extract the system impulse response, the re-ceived response after wireless propagation is deconvolved fromthe transmitted signal [28]. To minimize the noise effect, wedefine thresholds of −17 dB for up to eight-level quantizationand −20 dB for any higher number of quantization levels withrespect to the peak power of the impulse response. This partof the channel impulse response is communicated back to thetransmitter with some predefined accuracy through a feedbackloop (wireless LAN). For TR, the CSI is communicated on atime-domain basis. For PC, the corresponding quantized dataof the spectral phase are sent back to the transmitter side on afrequency-domain basis.

In the second step, the TR/PC beamformers are calculated atthe transmitter side based on the obtained CSI. The TR beam-former 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 takinginverse Fourier transform. For two-level and four-level PC, thesharp spectral phase jumps introduce an irregular tail in additionto the main part of the time-domain signal. We only keep 70 nsof the signal, which includes the main part. Finally, thesesignals are generated by the AWG and transmitted throughthe antenna. On the receiver side, the received waveforms arerecorded using the real-time oscilloscope.

IV. MEASUREMENT RESULTS AND ANALYSIS

A. Temporal Focusing

Fig. 2(a) shows the impulse response of a typical NLOSindoor environment over a 150-ns time window. To bettershow individual features, the small subfigure shows the first10 ns of the power delay profile. The impulse response is asuperposition of different multipath components that disperseover a ∼130-ns time window. This is more than 2000 timesbroader than the ∼50-ps time resolution of the system with

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 TRin both full- and limited-feedback situations.

bandwidth of ∼10 GHz. The RF power spectrum and theunwrapped spectral phase of this response are shown inFig. 2(b). Due to the frequency-dependent nature of propaga-tion loss, the power spectrum decays at higher frequencies.The multipath components interfere with each other in thefrequency domain, leading to a strongly frequency-selectiveresponse. In addition to the spectral amplitude distortion, we ex-perience a significant frequency-dependent spectral phase dis-tortion. The unwrapped spectral phase nonlinearly varies withfrequency, which contributes to the temporal signal dispersion.

To suppress the multipath effects, we employ TR and PCbeamforming. The quantized channel impulse responses areused to calculate the TR and PC prefilters. The received re-sponse is computed as a convolution of the channel impulseresponse with the calculated TR/PC. Fig. 3 shows the receivedresponses. To make the comparison easier, each plot is indi-vidually normalized to one. For full-feedback TR and PC, wequantize the channel impulse response with 28 levels (8 bitsfor 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 thethresholds of −17 dB with respect to the peak power of the im-pulse response. At a sampling rate of 24 GS/s, this is equivalentto 2208 samples. In these figures, we compare two-level TR(1-bit TR) with four-level PC. In a carrierless system, thechannel impulse response is real, and its Fourier transform isa complex antisymmetric function. If the time-domain vectorhas N real samples, then its fast Fourier transform can berepresented by N/2 independent complex samples. For two-level (1-bit) TR, the feedback load is N . However, for PC, weare only interested in the spectral phase information, which canbe 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, thefeedback load is 2208 bits in both scenarios.

Comparing these figures, we clearly see the superior mul-tipath suppression of PC over TR in both full- and limited-feedback scenarios. To understand the intuitive reason behindthe superior performance of PC, we look back at their math-ematical equations. Ideal TR compensates spectral phase dis-tortions, but it squares the spectral magnitude. This spectralshaping aggravates the system spectral amplitude distortion,which broadens the received response in the time domain.PC only compensates the spectral phase distortion and doesnot increase the spectral amplitude distortion. As a result,PC achieves better temporal compression. A more detaileddiscussion is presented in [11].

To statically evaluate temporal focusing, we measure15 channel impulses with low mutual correlation. The receiveantenna is moved on a track to scan a rectangular area of1.2 m × 2.4 m, whereas the transmit antenna is fixed. Theinterelement spacing of the grid is 60 cm to ensure that thechannel impulse responses are approximately uncorrelated.Based on the measured impulse responses, we calculate thereceived responses from TR and PC under full- and limited-feedback scenarios. Table I summarizes the average and stan-dard deviation of the parameters introduced in Section II-Bafor the received responses from TR and PC. Full-feedbackPC reduces the RMS delay spread of the channel by 67.7%and increases the PAPR by 13.5 dB. These numbers for full-feedback TR are only 20.1% and 8.0 dB, which prove thesuperior performance of PC. Under the limited-rate-feedbackscenario, while four-level PC provides temporal compressionof 32.3%, the two-level TR has a negative value (Crms =−11.4%), indicating that the channel RMS delay spread isincreased. Two-level TR provides 6.4 dB of PAPR gain, whichis 6.2 dB less than the 12.6-dB gain achieved by four-levelPC. We also observe that the four-level PC outperforms full-quantization TR in terms of both temporal compression andPAPR gain.

DEZFOOLIYAN AND WEINER: SPATIOTEMPORAL FOCUSING OF PC AND TR IN UWB SYSTEMS 2003

TABLE IPERFORMANCE 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 afunction of quantization levels.

We perform a series of numerical calculations to evaluate theperformance of PC versus TR as a function of quantizationlevels. Fig. 4 shows the average temporal compression andPAPR of the 15 channel impulses as a function of quantizationlevels. As explained, due to the antisymmetric property ofthe spectral phase, PC requires half-feedback load comparedwith TR for the same number of quantization levels. PC pro-vides superior gain compared with TR from both temporalcompression and PAPR gain perspectives. For instance, thePAPR gain for PC is approximately ∼6 dB higher than thecorresponding value for TR with the same number of quanti-zation levels. Both TR and PC reach a plateau approximatelyafter 26 quantization levels in which a larger quantizationlevel does not improve the performance. At this point, thelimited-rate system achieves performance of a full-feedbackTR/PC prefilter.

The BER performance for full-feedback TR and PC isstudied in [11]. Here, we focus on the BER performance oftwo-level TR and four-level PC. The simulated BER curvesare presented in Fig. 5. For a low-SNR regime (< 0 dB), thedominant noise level determines the system performances, andboth PC and TR have high BERs. BER curves for the TRprefilter reach a plateau for data rates of 500 Mb/s and above,where increasing the SNR cannot improve the performanceany further. In this high-SNR regime, the system performanceis saturated by the intersymbol interference originating fromTR sidelobes. For the PC prefilter, we have the performancesaturation only for the data rate transmissions higher than2 Gb/s. The 2-Gb/s curve for PC levels off at 10−2.1 BER,which is by far better compared with the 10−0.77 level of the

Fig. 5. Average BER for NLOS PC and TR. The performance of PC is clearlysuperior 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 showthat in limited-rate-feedback systems, PC BER performance isconsiderably superior to the TR technique.

B. Spatial Focusing

To evaluate spatial focusing of TR and PC under both fulland limited feedback, experiments were carried out in an NLOSenvironment (average propagation distance of 15 m). First, wemeasure the spatial focusing in the absence of any transmitbeamforming. We excite the channel with the chirp signaldescribed in Section III and measure the received responsesas the receive antenna moves with the step size of 2 cm overa 2 m × 2 m grid under control of an automatic antennapositioner. Then, we extract the channel impulse responses bythe deconvolution technique described in [28] and calculate thetotal signal power. Fig. 6 shows the result normalized to themaximum calculated power. As we expected, there is no sys-tematic spatial focusing that can be employed in the systemdesign.

2004 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 4, APRIL 2016

Fig. 6. Spatial focusing in the absence of any transmit beamforming. The resultis 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 beam-former calculated based on the measured impulse responsefrom the Tx to the target receiver, which is located at the centerof the described automatic antenna positioner. Then, we movethe receive antenna with the step size of 2 cm on the squaregrid and measure the received peak power as we move awayfrom the center location. The experimental results are presentedin Figs. 7 and 8. Each figure consists of 10 201 measurementpoints. 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 thefour cases along the range and cross-range directions passingthrough the center of the antenna positioner. In contrast toFig. 6, the peak power is now focused at the target receiverand 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 peaksstrongly depends on the environment geometry. To characterizethe spatial focusing, we use (15) in which R0 is the centerposition of the antenna positioner. Table II summarizes thevalues Gr and Gc 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 below3 dB with respect to the main central peak after ∼22-cm offsetin the range direction, whereas this number is only ∼5 cmfor PC. As shown in Table II, the maximum peak power isat least 10 dB lower than the central peak power after 19 cmin the range direction for both full- and limited-feedback PC;however, this never happens within the 100-cm distance of thecenter for TR. Although the four-level PC provides the bestspatial focusing (even better than full-feedback PC), the two-level TR has the worst focusing performance. This superiorperformance of PC can be exploited for the future covert high-speed UWB communication channels as an effective way toprovide spatiotemporal focusing and reduce intersymbol andinteruser interference.

V. CONCLUSION

The performance of PC and TR prefilters has been inves-tigated in NLOS environments when the digitized version of

Fig. 7. Spatial focusing of TR and PC under both full- and limited-feedbacksystems in an indoor NLOS environment. In panels (e)–(h), we zoom in at thecenter location to better show details. In contrast to Fig. 6, the peak poweris now focused at the target receiver and decays rapidly as we move away. Forboth 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. Weconducted an experimental study to assess their performancefrom both spatial and temporal focusing perspectives over thefrequency band of 2–12 GHz. To characterize the temporalfocusing, “RMS delay spread” and “PAPR” parameters arecalculated. The BERs of the measured channels are presentedfor different data rates (from 125 Mb/s to 4 Gb/s) as a functionof the received SNR. To characterize spatial focusing, weinvestigated the decay of the received response peak power aswe move away from the intended receiver. Our study suggeststhat for the same feedback rate, PC has superior spatiotemporalfocusing performance compared with TR. For instance, whilefour-level PC provides an average 12.6-dB PAPR gain, two-level TR provides only 6.4-dB gain while requiring the samequantity of information feedback as four-level PC. From thespatial focusing perspective, the peak power for two-level TR

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 IIMINIMUM 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 isonly ∼4 cm for four-level PC.

ACKNOWLEDGMENT

The authors would like to thank Dr. D. E. Leaird for hishelpful technical assistance.

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Amir Dezfooliyan (M’14) received the B.Sc. de-gree in electrical engineering from Sharif Univer-sity of Technology, Tehran, Iran, in 2009 and thePh.D. degree in electrical and computer engineeringfrom Purdue University, West Lafayette, IN, USA,in 2013.

Upon graduation, he joined Tektronix Commu-nications Co., where he is currently the Managerof RF Engineering. He is the author of morethan 20 scientific papers on multiple-antenna sys-tems, transmit beamforming, and arbitrary micro/

millimeter-waveform generation. His research interests include optical wirelesscommunications, signal propagation modeling, and ultrafast optics.

Andrew M. Weiner (F’95) received the Sc.D. de-gree in electrical engineering from the MassachusettsInstitute of Technology, Cambridge, MA, USA,in 1984.

He is the Scifres Family Distinguished Profes-sor of Electrical and Computer Engineering, PurdueUniversity, West Lafayette, IN, USA. After his Sc.D.studies, he joined Bellcore, which was then a premiertelecommunications industry research organization,first as a Member of Technical Staff and later asa Manager of Ultrafast Optics and Optical Signal

Processing Research. In 1992, he joined Purdue University, where and hassince graduated over 30 Ph.D. students. He also spent sabbaticals with theMax Born Institute for Nonlinear Optics and Ultrashort Pulse Spectroscopy,Berlin, Germany; and with JILA, University of Colorado and National Instituteof Standards and Technology, Boulder, CO, USA. He is an author of a textbookentitled Ultrafast Optics; has published eight book chapters, over 300 journalarticles, 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 extremelyhigh speed lightwave signals and ultrabroadband radio-frequency signals. He isparticularly well known for his pioneering work on programmable generation ofarbitrary ultrashort pulse waveforms, which has found application both in fiber-optic networks and in ultrafast optical science laboratories around the world.

Dr. Weiner has received numerous awards, including the Hertz FoundationDoctoral Thesis Prize (1984), the Optical Society of America’s Adolph LombMedal (1990), R. W. Wood Prize (2008), the International Commission on Op-tics Prize (1997), and the IEEE Photonics Society’s William Streifer ScientificAchievement Award (1999) and Quantum Electronics Prize (2011). At PurdueUniversity, he has been recognized with the inaugural Research ExcellenceAward from the Schools of Engineering (2003), the Provost’s OutstandingGraduate Student Mentor Award (2008), the Herbert Newby McCoy Awardfor outstanding contributions to the natural sciences (2013), and the College ofEngineering Mentoring Award (2014). In 2008, he was elected to membershipin the National Academy of Engineering. In 2009, he was named a Departmentof Defense National Security Science and Engineering Faculty Fellow. Herecently 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 ofOptics Express, an all-electronic open-access journal publishing more than3000 papers a year, emphasizing innovations in all aspects of optics andphotonics.