Data Transmission Using Time Reversal Technique

7/29/2019 Data Transmission Using Time Reversal Technique

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Data transmission using time reversal technique -

Results of reverberating chamber measurements

Youmni ZiadeBeirut Arab UniversityTripoli, Lebanon

Email: [email protected]

Joe WiartOrange LabsParis, France

Email: [email protected]

AbstractWe propose to study the time reversal (TR) tech-nique for wireless communications. In a TR application, thetime-reversed signal of the channel impulse response (CIR) ofthe medium is retransmitted back from the base station. Thusa compensation of the multipath effects leads to a space-timefocused signal on the receiver position. Spatial focusing allows aconcentration of the signal power on the receiver position whilereducing it at positions far from the receiver. Temporal focusingreduces echoes of the received signal and simplify its processing.In this paper, we explain the method used for data transmissionand we present experimental results.

I. INTRODUCTION

Propagation of electromagnetic waves in heterogeneousmedia is the subject of different phenomena like refraction,reflection, etc, due to scatterers present in the medium. Thiscreates multi-path mechanism which causes echoes that arriveat the receiver with different time delays. Therefore, in atransmission application between two antennas, the receivedsignal will present low levels at certain positions due to adestructive addition of echoes. This leads to a need of complexanalysis of the signal at the receiver to extract the information.TR is a technique which was developed and applied initiallyin the acoustics domain [1]-[4]; then was applied in electro-magnetic domain [5]-[7]. It allows space-time focusing of thesignal in a rich scattering medium. The main idea consistsof taking advantage from the multi-paths by transmitting anadapted signal so that all echoes arrive coherently on thereceiver antenna at the same instant. Thus, TR is more efficientin richly scattering media. The measured signal will presenta high level at the receiver position due to coherent additionof echoes and low levels far from the receiver position due toincoherent addition of echoes. Though, we can talk about twotypes of focusing:

The temporal focusing ensures an elimination ofechoes and the channel equalizer is significantly sim-plified at the receiver.

The spatial focusing ensures a reduction of interfer-ence in a multi-cell system. This allows creation ofmulti-independent transmission channels and incre-ment of transmission rates.

Many studies on application of TR for wireless communica-tions have been carried out and the results have shown theefficiency of this technique, specially when ultra wide bandsignals are used [8]-[11].

In this paper, we present the method we have used toapply TR technique for data transmission and we show andanalyze results of measurements we have carried out in anIndoor environment.

II. TIME REVERSAL FORMULATION

Consider a transmission between two antennas A and B.

The received signal at B can be expressed as follows:

sB() = h(, A B) eA() (1)where denotes the convolution product, eA() is the pulsetransmitted by A and h(, A B) is the CIR. It includes allmulti-paths present in the medium. Thus, The signal sB() is atemporal spreading of the initial input pulse. The TR operationconsists of transmitting the time-reversed complex conjugatesignal of sB() from the antenna B. Because of the usualsymmetry properties of the propagation, the CIR measuredfrom A to B is the same as that measured from B to A:

h(, B A) = h(, A B) (2)The reversed signal will propagate in the medium identicallyas in the first step, i.e., via the same trajectories and takingidentical delays, so all echoes due to different paths will arriveat the antenna A at the same moment. The received signal atA after TR operation is:

sA() = h(, A B) h(, A B) eA() (3)The received signal on A is so focused in both time andspace. The time focusing is due to the fact that the delaysof the different paths are compensated in the second step. Allmulti-paths echoes arrive on A at the same moment and areadded coherently. The space focusing means that echoes fromdifferent paths arrive arbitrary on points far from the focusedarea. So there is no coherent sum of these echoes, and the

signal power decreases in comparison with the signal powerin the focused area. Results of measurements in a reverberatingchamber and in an Indoor environment and analysis based oncharacteristic parameters of temporal and spatial focusing aregiven in [12].In this paper, the transmitted signals are Gaussian pulses thathas the following form:

p() = A exp

(( 0)

2

2

)sin(2fc( 0)) (4)

where A is the amplitude of the pulse, 0 is an arbitrary timedelay that ensures the signal causality, = 3/8f (f is


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the frequency bandwidth of the pulse) and fc is the carrierfrequency. p() is formed by two signals, the baseband signaland the carrier signal:

p1() = A exp

(( 0)

2

2

)(5)

p2() = sin(2fc( 0)) (6)

III. DIGITAL COMMUNICATION USING TRA. General formulation

We can conclude from the formulation given in the previ-ous section that TR is composed of two main steps:

a first step corresponds to a learning phase wherethe transmitter gets the information about the CIR ofthe medium: the receiver transmits a pulse and thetransmitter measures the CIR of the medium;

the second step corresponds to the spatial-time focus-ing of the signal on the receiver by transmitting thetime-reversed signal of the CIR of the medium.

In a common digital communication, the transmitted signalis formed by a pulse modulated using a binary modulation.A post-processing and a demodulation of the received signalallows the reception of the binary transmitted data. This phaseof post-processing seems to be complex, specially when thereceived signal contains echoes due to multi-paths.In digital communication using TR technique, the transmittedsignal is the time-reversed of the CIR of the medium. We pro-pose to modulate this signal using a binary phase-shift keyingmodulation (BPSK). Thus, the expression of the transmittedsignal when one bit is transmitted is:

Skt (t) = kh(t0 t) p(t0 t) (7)

where k = +1 (respectively k =

1) when the transmitted bit

is 1 (respectively 0) and t0 is a constant parameter that ensuresthe signal causality. We define the signal u(t) as follows:

u(t) = p(t0 t) (8)Suppose now that we have to send N bits (a1,...aN, ai =1) with a data rate of Fb (the bit time is Tb = 1/Fb). Theexpression of the transmitted signal is :

StN(t) =

Ni=1

aih(t0 t) u(t iTb) (9)

This signal is composed by the sum of N time-reversedchannel impulse responses (convoluted with the time reversedgaussian pulse), where each response is delayed by one bit time

from the previous one. The received signal after propagationin the medium has the following expression:

SrN(t) =Ni=1

aih(t) h(t0 t) u(t iTb) (10)

This signal is composed by the sum of N elementary focusedsignals, where each elementary focused signal corresponds toa bit and is delayed by one bit time from the previous one.Note that StN(t) is a sum of delay spread signals and that thebit time Tb has the same order value as the duration (T0) ofthe gaussian pulse p(t). Tb is greatly lower than the time of

the signal Skt (t) (equation 7) which corresponds to a sent bit.The value of the signal StN(t) at a given time t = is equalto the sum of different echoes of the CIR delayed by one bittime from each other.

B. Interference between received pulses

Consider two antennas placed in a medium where thenumber of paths between the transmitter and the receiverantennas is equal to M. Each path is characterized by its timedelay j (1 < 2... < M) and the attenuation of the wavej . The expression of the CIR of this medium is:

h(t) =Mj=1

j(t j) (11)

where (t) is the dirac function. The received signal in thelearning phase is:

Sr(t) = h(t) p(t) =Mj=1

j(t j) p(t) (12)

Using the characteristic (x) = (x), the time-reversedsignal of Sr(t) is written as:

Sinv(t) =

Mj=1

j(t j + t0)) u(t)

=Mj=1

j(t + j t0)) u(t) (13)

Thus, equation 9 can be written as follows, when N bits aresent:

StN(t) =Ni=1

ai

Mj=1

j(t (t0 j))

u(t iTb) (14)The received signal after propagation of StN(t) in the mediumcan be expressed as follows:

SrN(t) = h(t) StN(t)

=

Mj1=1

j1(t j1)

Ni=1

ai

Mj2=1

j2(t (t0 j2)) u(t iTb) (15)

The expression of the received signal can be divided into two

main parts:

SrN(t) =Ni=1

ai

Mj=1

j2u(t t0 iTb) +

Ni=1

ai

Mj1=1

j2=j1

j1j2

u(t (t0 + j1 j2) iTb) (16)

The first term of the second member corresponds to the mainlobe of the focused signal, and it is formed of N successivepulses corresponding to the N sent bits. The time thatseparates two successive pulses is equal to Tb. The second


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0 0.2 0.4 0.6 0.8 1 1.2

x 106

2

1.5

1

0.5

0

0.5

1

1.5

2

Time (sec)

(a) Gaussian transmitted pulse

0 0.2 0.4 0.6 0.8 1 1.2

x 106

1.5

1

0.5

0

0.5

1

1.5

Time (sec)

Gaussian Pulse

CIR

(b) CIR of the RC

Fig. 1. Measuring the CIR of a RC - fc = 900 MHz - f = 200 MHz

0 0.2 0.4 0.6 0.8 1 1.2

x 106

3

2

1

0

1

2

3

Time (sec)

(a) Transmitted signal

0 0.5 1 1.5 2 2.5 3 3.5

x 107

4

3

2

1

0

1

2

3

4

Time (sec)

(b) Focused signal

Fig. 2. TR focusing in a RC

term of the second member corresponds to the secondarylobes of the focused signal.

C. First measurement results

We consider a base station (BS) antenna and a receiverantenna placed in a RC. The dimensions of the RC are 80 100 140 cm3. The BS is formed by one ultra wide bandomnidirectional antenna placed horizontally at 40 cm from the

top of the chamber. The receiver antenna is placed vertically-so the direct wave between the antennas is reduced- at 10 cmfrom the center of the bottom of the chamber. The Gaussianpulse p(t) has a central frequency of900 MHz and a frequencybandwidth of200 MHz. In the first step, the user sends a pulseto the BS. This pulse and the measured signal on the BS areshown in Fig. 1. We can notice the delay spread of the receivedsignal: the duration of the received signal is about 600 ns andthat of the gaussian pulse is about 6 ns. We show in Fig.2(a)the signal transmitted in the second step (which correspondsto StN(t) (equation 9), N = 10, Tb = 33.3 ns). In Fig.2(b) weshow the received focused signal. We can notice ten focusedpulses delayed by Tb. Each focused pulse corresponds to thegaussian transmitted pulse (Fig.1(a)) multiplied by +1 (for a

sent bit equal to 1) or 1 (for a sent bit equal to 0). Thus, theTR operation has allowed a separation between pulses on thereceiver, and the extraction of data from these signals will besimple, the complexity of the system is brought back to thetransmitter.

D. Demodulation of the received signal

In an ideal configuration, where the temporal focusingof the signal allows the exact reconstruction of the gaussianpulse and where the focused pulse has no secondary lobes, the

Fig. 3. Block diagram of BPSK demodulator

0 0.5 1 1.5 2 2.5 3 3.5

x 107

50

0

50

Time (sec)

Fig. 4. Baseband received signal

received signal expressed in (10) can be written as follows:

SrN(t) = Ni=1

aiu(t iTb td) (17)

where is a constant representing the multi-paths loss and tdis the time delay due to propagation in the medium. In the case

of a gaussian transmitted pulse (4), SrN(t) has the followingexpression:

SrN(t) = ANi=1

ai exp

((t teq iTb)

2

2

)

sin(2fc(t teq iTb)) (18)where teq is the equivalent delay due to all delays describedabove.The demodulator used to extract the binary data from thereceived signal is described in Fig.3. In the first step, thebaseband signal is extracted from the received signal and thensampled with a sample frequency equal to Fb. We plot in

Fig.4 the output signal before sampling, corresponding to theexample given in Fig.2. Note that in this example, we havenot an ideal configuration and interference is not negligible.We can identify the ten pulses, each of them has one positiveor negative peak corresponding to a sent bit. The instant ofdecision can be identified by detecting the maximum (or theminimum) of one received pulse.

In order to determine the appropriate instant of decision,we propose to plot the eye diagram of the signal after demod-ulation (Fig.5). Each pulse on this figure corresponds to a sent


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0 0.5 1 1.5 2 2.5 3

x 108

50

0

50

Time (sec)

Fig. 5. Eye diagram for 10 sent bits in the RC

bit and has the following expression:

pri(t) =A

2ai exp

((t teq)

2

2

)+ IESi(t) (19)

where IESi corresponds to the interference between the ith

pulse and other pulses. In an ideal configuration, the instant

of decision is equal to teq and is the same for all the pulsespri . But in the example given here, we can see in Fig.5 thatall peaks do not coincide at the same instant. The appropriateinstant of decision is deduced from the eye diagram. We firstcompute the mean pulse of pulses pri :

pr(t) =1

N

Ni=1

pri(t) (20)

The instant of decision tdec is equal to the instant where pr(t)is maximum.

IV. EVALUATION OF BIT ERROR RATE

To study the efficiency of data transmission using TRtechnique, we propose to compute the BER as a function of thesignal to noise (SNR) measured on the receiver. The sent datais composed of N bits generated by a linear feedback shiftregister (LFSR). The use of a LFSR ensures that all possibleconfigurations of interference are considered in the transmittedpulse (StN(t)). We define the SNR on the receiver as follows:

SN R =|pr(tdec)|2

2N0(21)

where N0 is the variance of the gaussian white noise added onthe receiver. We propose to compute the BER using a semi-analytical method, where the BER is given by the followingexpression:

BE R =1

2N

Ni=1

erfc

( |pri(tdec)|2N0

)(22)

where erfc is the complementary error function.

V. ANALYSIS OF MEASUREMENT RESULTS BYCOMPUTING BE R

We discuss in this section the results of measurementsmade in a RC. We study the effect of the carrier frequencyand the bandwidth of the transmitted gaussian pulse. We

10 5 0 5 10 15 20

104

103

102

101

100

SNR (dB)

BER

Fb

= 105 Mbps

Fb

= 70 Mbps

Fb = 35 Mbps

Fb

= 21 Mbps

Gaussian channel

(a) f = 100 MHz

10 5 0 5 10 15 20

104

103

102

101

100

SNR (dB)

BER

Fb

= 105 Mbps

F

b

= 70 Mbps

Fb

= 35 Mbps

Fb

= 21 Mbps

Gaussian channel

(b) f = 300 MHz

Fig. 6. BER of RC measurements - fc = 630 MHz

consider two different carrier frequencies fc1 = 630 MHzand fc2 = 900 MHz and two bandwidths f = 100, and300 MHz. We consider also different data transmission rates.

We plot in Fig.6 the BER obtained for fc = 630 MHz. Theconsidered data rates are 21, 35, 70 and 105 Mbps. On eachfigure, we can verify that BER decreases with the decrementof the data rate, and it approaches to the BER of a gaussianchannel. If we compare the effect of the frequency bandwidth,we can notice the decrement of the BER with the incrementof the bandwidth.We plot in Fig.7 the BER obtained for fc = 900 MHz. In this

case, the data transmission rates are 20, 37.5, 50, 100 and 150Mbps. We can notice the same tendency as the previous case.We show on tables I and II the values of SNR required to havea BER of 102 for fc = 630 and 900 MHz respectively andfor the values of f and Fb given below. These tables confirmthe amelioration of the BER when the bandwidth increses and

when the data rate decreases (a lower SNR is required in thiscase). We can notice a increment of BER for values of Fbgreater than 100 Mbps. At theses rates, the bit time ( 10 ns)becomes close to the duration of the Gaussian pulse, thus theinterference between symbols increases.

VI. CONCLUSION

In this paper we have used the TR technique for binarydata transmission. We have explained how this technique isused to proceed with data transmission. This method takes intoaccount the duration of the Gaussian pulse and not the duration


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5 0 5 10 15 20

104

103

102

101

100

SNR (dB)

BER

Fb

= 150 Mbps

Fb

= 100 Mbps

Fb = 50 Mbps

Fb

= 37.5 Mbps

Fb

= 30 Mbps

(a) f = 100 MHz

10 5 0 5 10 15 20

104

103

102

101

100

SNR (dB)

BER

Fb

= 150 Mbps

Fb

= 100 Mbps

Fb

= 50 Mbps

Fb

= 37.5 Mbps

Fb

= 30 Mbps

(b) f = 300 MHz

Fig. 7. BER of RC measurements - fc = 900 MHz

TABLE I. S NR FOR A BER = 102 (RC) - fc = 630 MH Z

f = 100 MHz f = 300 MHz

Fb = 21 Mbps 5.08 dB 4.7 dB

Fb = 35 Mbps 6.65 dB 5.72 dB

Fb = 70 Mbps 9.44 dB 8.5 dBFb = 105 Mbps 18.21 dB 15.45 dB

TABLE II. S NR FOR A BER = 102 (RC) - fc = 900 MH Z

f = 100 MHz f = 300 MHz

Fb = 30 Mbps 6.76 dB 5.8 dB

Fb = 37.5 Mbps 9.58 dB 6 dB

Fb = 50 Mbps 12.6 dB 7.39 dB

Fb = 100 Mbps 17.2 dB 9.8 dB

Fb = 150 Mbps > 20 dB 16.43 dB

of the CIR, which leads to high data rates when ultra wide bandsignals are used. The TR technique allows a temporal focusing

of the signal on the receiver position so that each receivedfocused signal corresponds to one transmitted bit. A simpledemodulation of the received signal allows the estimation ofthe received data. No additional processing on the receiver isneeded.Our results are based on measurements carried out in RC. RCconsists of an ideal environment to test the technique for manyreasons. First in a RC the transmitted wave is subjected tomultiple scattering before reaching the receiver. The multi-patheffect is so ensured. Secondly, the RC consists a non-variantmedium which is a main condition for an optimal applicationof TR. Dealing with measurements in a realistic environment

(like Indoor medium) consists of an important step for testingTR: in such a medium the multi-paths effect is reduced andthe medium can change (movement of persons).Further work and research could be investigated. First, acomparison with existing techniques is important to deducethe advantage brought by TR technique in such application.Second, the measurements are made in a non-variant medium.Introducing some variation to the medium allows the study of

the robustness of the technique. Als, no space in this paperhas been devoted to the analysis of the spatial focusing andthe dimension of the focused area. This study is necessarywhen we deal with a multi-user transmission. TR allowsfocusing power around the receiver. It was shown that thespatial resolution is about half the wavelength of the signal.This resolution may decrease when specific antennas are used(micro-structured antenna [13]). This allows the creation ofindependent propagation channels, each channel correspondsto a specific user, under the condition that the distance betweenusers is greater than the spatial resolution.

REFERENCES

[1] M. Fink, Time reversal of ultrasonic fields. I. Basic principles, IEEE

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[2] F. Wu, J.-L. Thomas, M. Fink, Time reversal of ultrasonic fields. Il.Experimental results, IEEE Trans. on Ultrasonics, Ferroelectrics andFrequency Control, vol. 39, no. 5, pp. 567-578, sept. 1992.

[3] D. Cassereau, M. Fink, Time-reversal of ultrasonic fields. III. Theoryof the closed time-reversal cavity, IEEE Trans. on Ultrasonics, Ferro-electrics and Frequency Control, vol. 39, no. 5, pp. 579-592, sept. 1992.

[4] T. C. Yang, Temporal resolutions of time-reversal and passive-phaseconjugation for underwater acoustic communications, IEEE Journal ofOceanic engineering, vol. 28, no. 2, april 2003.

[5] D. Liu, G. Kang, L. Li, Y. Chen, S. Vasudevan, W. Joines,Q. H. Liu, J.Krolik and L. Carin, Electromagnetic Time-Reversal Imaging of a Targetin a Cluttered Environment, IEEE Trans. on Antennas and Propagation,vol. 53, no. 9, sept. 2005.

[6] K. Sarabandi, I. Koh and M. D. Casciato, Demonstration of time reversalmethods in a multi-path environment, IEEE Antennas and PropagationSociety International Symposium, pp. 4436- 4439, 2004.

[7] L. Borcea, G. Papanicolaou, C. Tsogka and J. Berryman, Imaging andtime reversal in random media, Inverse Prob., vol. 18, pp. 1247-1279,2002.

[8] S. Q. Xiao, J. Chen, B.-Z. Wang, and X. F. Liu, A numerical studyon time-reversal electromagnetic wave for indoor ultra-wideband signaltransmission, Progress In Electromagnetics Research, PIER 77, 329342,2007.

[9] N. Guo, B. M. Sadler and R. C. Qiu, Reduced-complexity UWB time-reversal techniques and experimental results, IEEE trans. On WirelessCommunications, vol. 6, no. 12, pp. 4221-4226, december 2007.

[10] H. T. Nguyen, I. Z. Kovcs and P. C. F. Eggers, A time reversal trans-mission approach for multiuser UWB communications, IEEE Trans. onAntennas and Propagation, vol. 54, no. 11, nov. 2006.

[11] H. T. Nguyen, J. B. Andersen, G. F. Pedersen, P. Kyritsi and P. C.F. Eggers, Time reversal in wireless communications: a measurement-based investigation, IEEE trans. On Wireless Communications, vol. 5,no. 5, pp. 2242-2252, august 2006.

[12] Y. Ziade, M.-F. Wong and J. Wiart, Reverberation chamber andIndoor measurements for time reversal application, IEEE Antennas andPropagation Society International Symposium, July 2008.

[13] Y. Ziade, M.-F. Wong and J. Wiart, On the conversion of evanescentwaves to propagating waves for super-resolution in time reversal appli-cation, IEEE APS-URSI Symposium, July 2008.

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