Effects of Time Variant Channel on a Time ... - Semantic Scholar
Effects of Time Variant Channel on a Time Reversal UWB System I. H. Naqvi, P. Besnier, G. El Zein Institute of Electronics and Telecommunications of Rennes, IETR-UMR CNRS 6164 INSA, 20 Avenue des Buttes de Co¨esmes, 35043, Rennes, France. (ijaz-haider.naqvi, philippe.besnier, ghais.el-zein)@insa-rennes.fr Abstract—Time reversal (TR) is gaining more and more attention due to its potential to simplify the receiver for an ultra-wideband communication system. The temporal and spatial focusing properties of a TR communication system allow the detection of the received signal with simple receivers. However, the transmitter system becomes complicated as perfect channel estimation is required on regular basis. However, if the TR system is robust and can resist the changes in the channel, frequency of the estimation cycles will be less resulting in an increased transmission throughput. In this paper, we study the robustness of a TR system in a time varying channel environment. Different TR characteristics are compared and the ability of a TR system to resist the varying channel is shown. Index Terms—Time reversal (TR), ultra-wideband (UWB), cross correlation, robustness, changing channel, reverberating chamber.
I. I NTRODUCTION Ultra-wideband (UWB) communication has drawn considerable attention recently. Due to its large bandwidth, UWB system can resolve individual multi-path components. However, large number of resolvable paths and low power limitations necessitate a complex receiver system. Different types of receiver systems such as Rake, transmit-reference or the decision feedback autocorrelation receivers can be implied [1]-[3] to detect such a signal. Each technique has different difficulties and drawbacks. Time reversal (TR) shifts the design complexity from the receiver to the transmitter. Classically, TR has been applied in acoustics and under water communication applications [4],[5], but recently, UWB TR communication has been studied in a number of articles [6]-[16]. The received signal in a TR system is considerably focused in spatial and temporal domains. Thus, the received power is concentrated within few taps and can be detected by using a simple energy threshold detector [6]. However, TR system also has few disadvantages. It is thought that a TR system requires regular channel estimation. It makes the transmission system quite complicated. If the TR system is robust enough and can withstand the variations in the channel, the frequency of estimation cycles will be less and thus throughput of the system increases. In this paper, the robustness of the TR system with respect to a time varying channel is studied in a mode stirred reverberating chamber (RC). The RC is an electrically large, high quality factor cavity 1 Work
supported by ANR project MIRTEC and French research ministry.
that obtains statistically uniform fields by either mechanical stirring or frequency stirring [17]. It generates a large number of propagation modes and the resulting wave pattern can be interpreted as a combination of plane waves giving a very dense multipath environment. The rotation of a metallic stirrer enables to permanently modify the field distribution in the enclosure. From a time reversal (TR) perspective, this rich multipath environment favours TR but at the same time, TR is very sensitive to the changes in the environment. In this paper the metallic stirrer is used to adjust the correlation between channel impulse responses in a deterministic and controllable way. The RC is an isolated and highly controllable test environment and can be considered as a reference environment. To the best of authors’ knowledge, this is the first demonstration of the robustness of the TR system. A variety of factors can change the channel environment. If the transmitter and the receiver do not change their position, the time varying environment can cause the channel to change. The channel is also varied if either the transmitter or the receiver is displaced. We study both the cases for a TR system. A stirrer is used to change the environment in the RC. TR experiments are performed for different degrees of stirrer rotation. Effects of a displaced receiver are also studied by using a precise robotic positionner. The channel impulse responses (CIR) and the TR responses are measured at varying positions of the stirrer and the receiver. Cross correlation coefficients between the CIRs and TR responses are studied. Furthermore, different TR characteristics like root mean square (RMS) delay spread, TR peak performance, signal to side-lobe ratio (SSR), focusing gain (FG) and increased average power are studied in a time varying channel environment for a bandwidth of 2 GHz. The rest of the paper is organized as follows. A brief introduction of TR is presented in section II. Experimental setup is described in section III. Measurement results are presented and analyzed in section IV. Finally, section V concludes this paper. II. T IME R EVERSAL Time reversal (TR) transmission scheme uses a time reversed channel impulse response (CIR) as a transmitter prefilter. The signal then propagates in an invariant channel following the same paths and results in coherently adding all the received signals in the delay and spatial domains. With
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this technique, strong temporal compression and high spatial focusing can be achieved [14]. The temporal compression reduces the RMS delay spread and inter symbol interference (ISI) while multi-user interference is reduced due to spatial focusing. The received signal at the intended receiver (j) can be mathematically represented as: (t) yj (t) = s(t) hj (−t) hj (t) ≈ s(t) Rhauto j hj
(1)
hj (t)
is the estimated (measured) CIR from the transwhere mitting point to an intended receiver (j), s(t) is the transmitted (t) is the signal, denotes convolution product and Rhauto j hj approximate autocorrelation function of the CIR, hj (t). The received signal at any non intended receiver (k) is: (t) yk (t) = s(t) hj (−t) hk (t) ≈ s(t) Rhcross j hk
Fig. 1: A snapshot of the interior of the reverberating chamber with horn antenna and the stirrer
(2)
where hk (t) is the CIR from the transmitting point to an (t) is the approximate unintended receiver (k) and Rhcross j hk cross-correlation function of the CIRs hk (t) and hj (t). If the channels are not correlated, then the signal transmitted for one receiver will act as a noise for a receiver at any other location. Therefore, a secure communication is achieved with a low probability of interception. Some of the TR characteristics are defined in the following: TR received peak power is defined as the power of the received peak for a TR system for a fixed transmitted energy. Signal to side lobe ratio (SSR) is defined as ratio of the power of the first to second strongest peak in a TR received signal: yj (tpeak ) (3) SSR = 20 log10 yj (tpeak ) where tpeak is the time for strongest peak and tpeak is the time for the second strongest peak. SSR is an important parameter and is a measure of the quality of the received signal. Focusing gain (FG) of a TR system is defined as the ratio of the strongest tap power of the received signal in TR scheme to the strongest tap power of the pulsed system: max|yj (t)| (4) F G = 20 log10 max|hj (t)| It is also an important TR property as higher FG can translate into higher communication range for a communication system as compared to a pulsed UWB communication system. The average received power with the TR scheme increases as compared to the pulsed system for a fixed transmitted energy. Another important TR characteristic is the instantaneous RMS delay spread (στ ). It can be calculated by the first and the second moment of the measured TR response or the CIR: 2 N N 2 l=1 P DP (l)τl l=1 P DP (l)τl − (5) στ = N N l=1 P DP (l) l=1 P DP (l) where P DP (l) = |yj (l)|2 or |hj (l)|2 , yj is the measured TR response, hj is the measured CIR, τl is the excess time delay and N is the total number of taps in the PDP. RMS delay spread is considered as a metric for temporal compression in
8.7m Stirrer
Tx Antenna 4.5m
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Rx Antenna
Network Control AWG 7052 Tektronix
DSO 6124C Tektronix
Fig. 2: Measurement setup
TR systems. The comparison of all these TR characteristics is made in a varying channel environment where channel is changed with movement of the stirrer or the receiver. III. E XPERIMENTAL S ETUP Reverberating chamber (RC) is a metallic chamber of dimensions 8.7m×3.7m×2.9m present inside IETR laboratory. The interior of the RC with a horn antenna and the stirrer is shown in Fig. 1. All experiments are performed inside the RC which produces large number of wave reflections and allows accomplishing very high temporal and spatial focusing. Measurement setup is illustrated in Fig. 2. Two horn antennas are used as the transmitter receiver pair. The height of the transmitter and the receiver is 1m from the ground. Distance between the transmitter and receiver is 4.5 m. The pulse is generated with the Arbitrary Waveform Generator (AWG 7052) which has a maximum sampling rate of 5 GS/s. The receiver is a Digital Storage Oscilloscope (Tektronix DSO 6124C) with a maximum sampling rate of 40 GS/s. DSO captures the CIR of the channel. Once CIR is measured, the time reversed version of the CIR is created through MATLAB and is retransmitted with AWG in the same channel to measure the TR response which is captured by DSO. DSO is operated in average mode so that 32 samples are taken and averaged together to reduce the captured noise. IV. M EASUREMENT R ESULTS AND A NALYSIS TR experiments are performed in a mode stirred reverberating chamber for different positions of the stirrer (θ) and
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where s0◦ θ◦ is the covariance of hj (0◦ ) and hj (θ◦ ), s0◦ 0◦ and sθ◦ θ◦ are the variances of hj (0◦ ) and hj (θ◦ ) respectively. The dashed line in the Fig. 3 shows the cross correlation coefficients between the TR received signals for θ ◦ (yj (θ◦ )) and the TR received signal at θ = 0 ◦ (yj (0◦ )). The correlation coefficients are evaluated from (6). For the sake of clarity, the dependence of the all these variables on time (t) is omitted. The CIRs are rapidly de-correlated with the rotation of the stirrer. For θ ≥ 3 ◦ , hj (θ◦ ) and hj (0◦ ) are almost totally de-correlated. On the other hand, the TR received signal decorrelates a lot less rapidly. Even if the CIR has changed from the original CIR, TR response has a sufficient correlation with the original TR response (yj (0◦ )). For instance, yj (0◦ ) and yj (1◦ ) have a correlation coefficient in the order of 0.7 while hj (0◦ ) and hj (1◦ ) have a correlation coefficient in the order of only 0.2. Fig. 4a shows the Power Delay Profile (PDP) of the TR received signals (yj (θ◦ )) in a mode stirred RC for θ ∈ {0 ◦ , 1 ◦ , 2 ◦ , 3 ◦ }, for the same transmitted signal (θ = 0 ◦ ). The PDPs of the yj (θ◦ ) for θ ≥ 1 ◦ are separately shown in Fig. 4 b,c,d. It can be seen that for θ ≥ 1◦ (Fig. 4b,c,d), even though the strength of received signal peak has reduced, the signals are focused in time and has a high signal to sidelobe ratio (SSR).
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Fig. 4: PDP of the TR received signals a) yj (θ◦ ) b) yj (1◦ ) c) yj (2◦ ) d) yj (3◦ )
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The transmitter and the receiver are stationary and do not change their positions. The channel is changed with the precise rotation of the stirrer. In a mode stirred reverberation chamber, a small movement of the stirrer can cause large changes in the channel. The solid line in the Fig. 3 shows the cross correlation coefficients between the measured CIRs for rotation of the stirrer by θ ◦ (hj (θ ◦ ) and a measured CIR at θ = 0 ◦ (hj (0◦ )). Mathematically it can be written as: s0◦ θ◦ (6) ρ(θ◦ ) = √ s0◦ 0◦ sθθ
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Fig. 5: Partial correlation between ai and bi extracted from CIRs hj (0◦ ) and hj (3 ◦ ) respectively
To investigate why the TR received signal does not degrade in the same way as CIR does, we evaluate the partial correlation of hj (0◦ ) and hj (3◦ ) having a bandwidth of 2.0 GHz. The two CIRs are arbitrarily divided into 100 parts. Let these parts be ai for hj (0◦ ) and bi for hj (3◦ ). The correlation coefficients for each ai and its respective bi are taken. Both ai and bi correspond to 0.2 μs. Fig. 5 shows the curve for these partial correlations. Although the correlation coefficient
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(b) Fig. 6: Correlated part of the measured CIRs hj (0◦ ) and hj (3 ◦ ) TABLE I: Comparison of delay spread of the TR received signal (yj (θ◦ )) and the measured CIR (hj (θ◦ )) θ (degree) 0 1 2 3 4 5
hj (0◦ )
hj (3◦ )
στT R (μs) 0.00055 0.00060 0.00065 1.2007 1.7118 1.9946
στCIR (μs) 5.50 5.51 5.50 5.51 5.50 5.49
for and is in the order of 0.1 (see Fig. 3), the partial correlation coefficients reveal some interesting facts. Fig. 5 shows that some parts of the CIR hj (0◦ ) have very strong correlation with their respective parts of the CIR hj (3◦ ). Thus, a part of the CIR maintains its form and does not decorrelate. Fig. 6 shows the correlated parts of the two CIRs having a length of 40 ns. This correlation affects the received signal peak and in spite of a totally de-correlated channel (in total), TR achieves high signal quality, i.e. high SSR and FG and relatively lower RMS delay spread. Table I compares the RMS delay spread of the TR received signal and the CIR for different bandwidths. To reduce the noise components, signal taps having a power less than the threshold of 2% (-39 dB) of the maximum peak power are forced to zero. Once a tap crosses the threshold, all the taps are included in the selected signal until the signal taps reaches a stage after which they never cross the threshold. Fig. 7 shows the TR received signal, yj (5◦ ) along with the threshold and the selected signal for the calculation of delay spread. The comparison (Table I) shows that the delay spread of the TR received signal is in the order of 0.5-0.7 ns for the first three positions of the stirrer. As the stirrer moves by θ = 3 ◦ , a substantial increase in the RMS delay spread is
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Fig. 8: For TR received signal at varying θ a) Received peak power b) Signal to sidelobe ratio c) Focusing gain d) Increased average power
observed. However, for θ = 1 ◦ , 2 ◦ , the RMS delay spread does not increase by much and remains in the order of 0.6 ns. The robustness of the TR system is evident from these observations. Even if the channel is de-correlated from its original state (θ = 1 ◦ , 2 ◦ ), the TR received signal has a very short delay spread. For θ ≥ 3 ◦ , it is quite large (in the order of 1-3 μs) but still it is less than the RMS delay spread of the CIR which remains almost constant for all the positions of the stirrer. Fig. 8 shows the effects of the rotation of the stirrer on different TR characteristics. Even though the CIR changes rapidly with θ, received peak power does not decrease as severely with θ (see Fig. 8a) as does the correlation coefficient of the CIR (see Fig. 3). More importantly, SSR does not degrade a great deal with θ (see Fig. 8b). Thus, the signal quality remains
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almost constant. Focusing gain (Fig. 8c) and the increased average power (Fig. 8d) experience a decrease with θ but this degradation can be considered as small compared to the channel de-correlation. Thus, TR system can resist a change in the channel if a part of the channel is not totally de-correlated. TR system results in a good signal quality even if the channel is de-correlated (in total). For instance, for θ = 2 ◦ , CIR has a correlation coefficient of 0.06 but still the TR system has a FG 19.26 dB, SSR of 2.87 dB, increased average power of 3.15 dB. B. Experiments with Moving Receiver Experiments are also performed in the RC with moving receiver. The receiver is moved by using a precise robotic positionner with a spatial resolution of 2.5 cm. The lower frequency for the TR signal (bandwidth of 2 GHz) is 700 MHz which corresponds to the wavelengths (λ) of 42.86 cm. The wavelengths λ is calculated for the lower frequency (fL ) of the bandwidth as the dimension of the focusing zone is governed by fL [15]. The solid line in the Fig. 9 compares the cross correlation coefficients (evaluated from (6)) of CIR at reference position (hj (0 cm)) and CIRs (hj (d cm)), where d is the distance from the reference position. At d ≥ 10cm, the CIRs are almost totally de-correlated. The dashed line shows the cross correlation of the TR received signal yj (0 cm) and yj (d cm). For d ≥ 10 cm, which is a little less than λ4 at 700 MHz, the TR received signal (yj (d cm)) has a very low correlation with yj (0 cm). Thus, TR received signal is also totally de-correlated by a small movement of the receiver. In the case of moving receiver, as it was expected, the partial correlation also disappears quite rapidly. Fig. 10 shows the partial correlation between the CIRs hj (0 cm) and hj (10 cm). Both CIRs are divided into 100 parts (named as ai and bi ) and then the correlation coefficients between the respective parts are calculated. It is observed that no part is highly correlated with its respective part. Thus, movement of the receiver in the order of λ4 entirely de-correlates the CIR. Table II compares the RMS delay spread of the TR received
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Fig. 10: Partial correlation between ai and bi extracted from the CIRs hj (d = 0 cm) and hj (d = 10 cm) respectively TABLE II: Comparison of delay spread of the TR received signal and the CIR for different movements of the receiver Movement (cm) 0 5 10 15 20 25
στT R (μs) 0.00057 0.00064 0.6491 1.4306 1.6635 2.1177
στCIR (μs) 5.68 5.70 5.70 5.70 5.69 5.68
signal and the CIR for movement of the receiver by 0-25 cm. For a 10 cm (or more) movement of the receiver, the RMS delay spread increases rapidly. However, the RMS delay spread is always less than the spread of the CIR. The effects of the channel change by the movement of the receiver are studied on different TR characteristics and are plotted in Fig. 11. The performance is degraded quite rapidly. For instance for a 20 cm movement of the receiver, the received peak power is decreased by 15.28 dB, focusing gain is decreased by 19 dB, SSR is decreased by 2.47 dB and the average increased power is decreased by 3.66 dB. Thus in a RC, a very small movement of the receiver degrades the performance substantially. C. Result Analysis and Future Prospects In this paper, it is discussed that the TR system can resist a partial change in the CIR. As long as some part of the CIR maintains its form, the TR system gives a good performance. In a real environment, say typical indoor environment, this is a result of significant importance. In such cases, if the channel is changed due to the variation in the environment, e.g. movement of the people, it is highly likely that some part of CIR will remain intact depending on the position and number of people. In this case, TR robustness can play a vital role. There is no need to re-estimate the CIR if there are minor changes in the environment e.g. movement of the people. This property can be very attractive for WLAN and wireless streaming applications. However, when the receiver moves its position or there is significant change in the layout
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rotation of the stirrer has a correlation coefficient of 0.06 with the CIR of θ = 0 ◦ , but still the TR system achieves a RMS delay spread of only 0.65 ns, a focusing gain of 19.26 dB, signal to side lobe ratio of 2.87 dB, increased average power of 3.15 dB. On the other hand, if the receiver is displaced form its position, the channel gets totally de-correlated and does not maintain any partial correlation with the original CIR for a movement in the order of λ4 , where λ is the wavelength of lower frequency fL . Thus, in a RC, TR system can not support even a small movement of the receiver. R EFERENCES
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Fig. 11: For TR received signals at varying positions of the receiver, a) Received peak power b) Signal to sidelobe ratio c) Focusing gain d) Increased average power
of the furniture, the channel de-correlates rapidly and reestimation of the CIR is required. Thus, TR is beneficial in a non stationary channel where non stationarity is caused by the changes in the environment. The experiments in the RC have provided a good platform for the study of the robustness of a TR system. Realistic environments (such as typical indoor environment) create lesser number of multi-paths and are less sensitive to the changes in the environment than the RC. Thus, it can be intuitively stated that natural changes in the channel do not de-correlate the CIR completely and CIR will maintain a better partial correlation with the previous state than RC. Therefore, TR will be even more robust in such cases. However, if the change in the CIR is occurred due the movement of either the transmitter or the receiver, it is expected that the channel will de-correlate rapidly from the original state (less rapidly than RC) and TR will not be robust in that case. V. C ONCLUSION In this paper, the robustness of a time reversal (TR) communication system is studied in a time varying channel environment. TR experiments are performed in the reverberation chamber (RC) with the rotation of the stirrer or the movement of the receiver. The results suggest that TR system can give a robust performance even if the channel environment has changed partially. If the channel maintains some partial correlation with the previous channel, TR can give a good performance even if the total correlation of the channels is very low. For instance, channel impulse response with a 2 ◦
[1] R. Hoctor and H. Tomlinson, “Delay-Hopped Transmitted-Reference RF Communications,” Proc. IEEE 2nd Ultra Wideband Systems and Technologies (UWBST02), Baltimore, MD, pp. 265-269, May 2002. [2] R. J. Fontana, E. Richley, and J. Barney, “Commercialization of an Ultra Wideband Precision Asset Location System,” Proc. IEEE Conference UWB systems and Technologies, Reston, VA, 2003. [3] J. D. Choi and W. E. Stark, “Performance of Ultra-Wideband Communications with Suboptimal Receivers in Multipath Channels,” IEEE Journal on Selected Areas in Communications, vol. 20, pp. 1754-1766, Dec. 2002. [4] M. Fink, “Time-reversed acoustic”, Scientific Amer., pp. 67-73, Nov.1999. [5] A. Derode, A. Tourin, J. D. Rosny, M. Tanter, S. Yon, and M.Fink, “Taking advantage of multiple scattering to communicate with timereversal antennas”, Phys. Rev. Lett., vol. 90, no. 1, pp. 10143011014301-4, 2003. [6] H. T. Nguyen, I. Z. Kovcs, P. C.F. Eggers, “A Time Reversal Transmission Approach for Multiuser UWB Communications”, IEEE Transactions On Antennas and Propagation, Vol. 54, NO. 11, November 2006. [7] P. Kyritsi, G. Papanicolaou, P. Eggers, and A. Oprea, “MISO time reversal and delay-spread compression for FWA channels at 5 G Hz”, IEEE Antennas Wireless Propag. Lett., vol. 3, no. 6, pp. 96-99, 2004. [8] P. Kyritsi, G. Papanicolaou, P. Eggers, and A. Oprea, “One-bit Time Reversal for WLAN Applications”, Personal, Indoor and Mobile Radio Communications, 2005. PIMRC 2005. [9] A. E. Akogun, R. C. Qiu, and N. Guo, “Demonstrating time reversal in ultra-wideband communications using time domain measurements,” in 51st Int. Instrument. Symp., Knoxville, TN, May 8-12, 2005. [10] C. Oestges, J. Hansen, S. M. Emami, A. D. Kim, G. Papanicolaou, A. J. Paulraj, “Time Reversal Techniques for Broadband Wireless. Communication Systems.” European Microwave Conference (Workshop), Amsterdam, The Netherlands, October 2004, 2004, 49-66. [11] H. T. Nguyen, J. B. Andersen, and G. F. Pedersen, “The potential use of time reversal technique in multiple elements antenna systems”, IEEE Commun. Lett., vol. 9, no. 1, pp. 40-42, Jan. 2005. [12] T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and P. J. Arogyaswami, “Application of time-reversal with MMSE equalizer to UWB communications”, in Proc. IEEE Global Telecommunications Conf. (GlobeCom), Dec. 2004, vol. 5, pp. 3123-3127. [13] R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time Reversal with MISO for Ultra-Wideband Communications: Experimental Results”, IEEE Antenna and Wireless Propagation Letters, 2006. [14] A. Khaleghi, G. El Zein, I. H. Naqvi, “Demonstration of Time-Reversal in Indoor Ultra-Wideband Communication: Time Domain Measurement, ISWCS 2007, Trondheim, Norway. [15] A. Khaleghi, G. El Zein, “Signal Frequency And Bandwidth Effects On The Performance Of UWB Time-Reversal Technique”, Loughborough Antennas and Propagation Conference 2007, Loughborough, UK. [16] I. H. Naqvi, A. Khaleghi, G. El Zein “Performance Enhancement of a Multiuser Time Reversal UWB Communication System”, IEEE International Symposium on Wireless Communication Systems 2007, Trondheim, Norway. [17] D.A. Hill, “Electromagnetic Theory of Reverberation Chambers”, National Institute of Standards and Technology (US) Technical Note 1506, December 1998.
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I. I NTRODUCTION Ultra-wideband (UWB) communication has drawn considerable attention recently. Due to its large bandwidth, UWB system can resolve individual multi-path components. However, large number of resolvable paths and low power limitations necessitate a complex receiver system. Different types of receiver systems such as Rake, transmit-reference or the decision feedback autocorrelation receivers can be implied [1]-[3] to detect such a signal. Each technique has different difficulties and drawbacks. Time reversal (TR) shifts the design complexity from the receiver to the transmitter. Classically, TR has been applied in acoustics and under water communication applications [4],[5], but recently, UWB TR communication has been studied in a number of articles [6]-[16]. The received signal in a TR system is considerably focused in spatial and temporal domains. Thus, the received power is concentrated within few taps and can be detected by using a simple energy threshold detector [6]. However, TR system also has few disadvantages. It is thought that a TR system requires regular channel estimation. It makes the transmission system quite complicated. If the TR system is robust enough and can withstand the variations in the channel, the frequency of estimation cycles will be less and thus throughput of the system increases. In this paper, the robustness of the TR system with respect to a time varying channel is studied in a mode stirred reverberating chamber (RC). The RC is an electrically large, high quality factor cavity 1 Work
supported by ANR project MIRTEC and French research ministry.
that obtains statistically uniform fields by either mechanical stirring or frequency stirring [17]. It generates a large number of propagation modes and the resulting wave pattern can be interpreted as a combination of plane waves giving a very dense multipath environment. The rotation of a metallic stirrer enables to permanently modify the field distribution in the enclosure. From a time reversal (TR) perspective, this rich multipath environment favours TR but at the same time, TR is very sensitive to the changes in the environment. In this paper the metallic stirrer is used to adjust the correlation between channel impulse responses in a deterministic and controllable way. The RC is an isolated and highly controllable test environment and can be considered as a reference environment. To the best of authors’ knowledge, this is the first demonstration of the robustness of the TR system. A variety of factors can change the channel environment. If the transmitter and the receiver do not change their position, the time varying environment can cause the channel to change. The channel is also varied if either the transmitter or the receiver is displaced. We study both the cases for a TR system. A stirrer is used to change the environment in the RC. TR experiments are performed for different degrees of stirrer rotation. Effects of a displaced receiver are also studied by using a precise robotic positionner. The channel impulse responses (CIR) and the TR responses are measured at varying positions of the stirrer and the receiver. Cross correlation coefficients between the CIRs and TR responses are studied. Furthermore, different TR characteristics like root mean square (RMS) delay spread, TR peak performance, signal to side-lobe ratio (SSR), focusing gain (FG) and increased average power are studied in a time varying channel environment for a bandwidth of 2 GHz. The rest of the paper is organized as follows. A brief introduction of TR is presented in section II. Experimental setup is described in section III. Measurement results are presented and analyzed in section IV. Finally, section V concludes this paper. II. T IME R EVERSAL Time reversal (TR) transmission scheme uses a time reversed channel impulse response (CIR) as a transmitter prefilter. The signal then propagates in an invariant channel following the same paths and results in coherently adding all the received signals in the delay and spatial domains. With
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this technique, strong temporal compression and high spatial focusing can be achieved [14]. The temporal compression reduces the RMS delay spread and inter symbol interference (ISI) while multi-user interference is reduced due to spatial focusing. The received signal at the intended receiver (j) can be mathematically represented as: (t) yj (t) = s(t) hj (−t) hj (t) ≈ s(t) Rhauto j hj
(1)
hj (t)
is the estimated (measured) CIR from the transwhere mitting point to an intended receiver (j), s(t) is the transmitted (t) is the signal, denotes convolution product and Rhauto j hj approximate autocorrelation function of the CIR, hj (t). The received signal at any non intended receiver (k) is: (t) yk (t) = s(t) hj (−t) hk (t) ≈ s(t) Rhcross j hk
Fig. 1: A snapshot of the interior of the reverberating chamber with horn antenna and the stirrer
(2)
where hk (t) is the CIR from the transmitting point to an (t) is the approximate unintended receiver (k) and Rhcross j hk cross-correlation function of the CIRs hk (t) and hj (t). If the channels are not correlated, then the signal transmitted for one receiver will act as a noise for a receiver at any other location. Therefore, a secure communication is achieved with a low probability of interception. Some of the TR characteristics are defined in the following: TR received peak power is defined as the power of the received peak for a TR system for a fixed transmitted energy. Signal to side lobe ratio (SSR) is defined as ratio of the power of the first to second strongest peak in a TR received signal: yj (tpeak ) (3) SSR = 20 log10 yj (tpeak ) where tpeak is the time for strongest peak and tpeak is the time for the second strongest peak. SSR is an important parameter and is a measure of the quality of the received signal. Focusing gain (FG) of a TR system is defined as the ratio of the strongest tap power of the received signal in TR scheme to the strongest tap power of the pulsed system: max|yj (t)| (4) F G = 20 log10 max|hj (t)| It is also an important TR property as higher FG can translate into higher communication range for a communication system as compared to a pulsed UWB communication system. The average received power with the TR scheme increases as compared to the pulsed system for a fixed transmitted energy. Another important TR characteristic is the instantaneous RMS delay spread (στ ). It can be calculated by the first and the second moment of the measured TR response or the CIR: 2 N N 2 l=1 P DP (l)τl l=1 P DP (l)τl − (5) στ = N N l=1 P DP (l) l=1 P DP (l) where P DP (l) = |yj (l)|2 or |hj (l)|2 , yj is the measured TR response, hj is the measured CIR, τl is the excess time delay and N is the total number of taps in the PDP. RMS delay spread is considered as a metric for temporal compression in
8.7m Stirrer
Tx Antenna 4.5m
3.7m
Reverberating Chamber
Rx Antenna
Network Control AWG 7052 Tektronix
DSO 6124C Tektronix
Fig. 2: Measurement setup
TR systems. The comparison of all these TR characteristics is made in a varying channel environment where channel is changed with movement of the stirrer or the receiver. III. E XPERIMENTAL S ETUP Reverberating chamber (RC) is a metallic chamber of dimensions 8.7m×3.7m×2.9m present inside IETR laboratory. The interior of the RC with a horn antenna and the stirrer is shown in Fig. 1. All experiments are performed inside the RC which produces large number of wave reflections and allows accomplishing very high temporal and spatial focusing. Measurement setup is illustrated in Fig. 2. Two horn antennas are used as the transmitter receiver pair. The height of the transmitter and the receiver is 1m from the ground. Distance between the transmitter and receiver is 4.5 m. The pulse is generated with the Arbitrary Waveform Generator (AWG 7052) which has a maximum sampling rate of 5 GS/s. The receiver is a Digital Storage Oscilloscope (Tektronix DSO 6124C) with a maximum sampling rate of 40 GS/s. DSO captures the CIR of the channel. Once CIR is measured, the time reversed version of the CIR is created through MATLAB and is retransmitted with AWG in the same channel to measure the TR response which is captured by DSO. DSO is operated in average mode so that 32 samples are taken and averaged together to reduce the captured noise. IV. M EASUREMENT R ESULTS AND A NALYSIS TR experiments are performed in a mode stirred reverberating chamber for different positions of the stirrer (θ) and
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tp tp+1 Time (ns)
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where s0◦ θ◦ is the covariance of hj (0◦ ) and hj (θ◦ ), s0◦ 0◦ and sθ◦ θ◦ are the variances of hj (0◦ ) and hj (θ◦ ) respectively. The dashed line in the Fig. 3 shows the cross correlation coefficients between the TR received signals for θ ◦ (yj (θ◦ )) and the TR received signal at θ = 0 ◦ (yj (0◦ )). The correlation coefficients are evaluated from (6). For the sake of clarity, the dependence of the all these variables on time (t) is omitted. The CIRs are rapidly de-correlated with the rotation of the stirrer. For θ ≥ 3 ◦ , hj (θ◦ ) and hj (0◦ ) are almost totally de-correlated. On the other hand, the TR received signal decorrelates a lot less rapidly. Even if the CIR has changed from the original CIR, TR response has a sufficient correlation with the original TR response (yj (0◦ )). For instance, yj (0◦ ) and yj (1◦ ) have a correlation coefficient in the order of 0.7 while hj (0◦ ) and hj (1◦ ) have a correlation coefficient in the order of only 0.2. Fig. 4a shows the Power Delay Profile (PDP) of the TR received signals (yj (θ◦ )) in a mode stirred RC for θ ∈ {0 ◦ , 1 ◦ , 2 ◦ , 3 ◦ }, for the same transmitted signal (θ = 0 ◦ ). The PDPs of the yj (θ◦ ) for θ ≥ 1 ◦ are separately shown in Fig. 4 b,c,d. It can be seen that for θ ≥ 1◦ (Fig. 4b,c,d), even though the strength of received signal peak has reduced, the signals are focused in time and has a high signal to sidelobe ratio (SSR).
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Fig. 4: PDP of the TR received signals a) yj (θ◦ ) b) yj (1◦ ) c) yj (2◦ ) d) yj (3◦ )
0.6
ρ(ai,bi)
The transmitter and the receiver are stationary and do not change their positions. The channel is changed with the precise rotation of the stirrer. In a mode stirred reverberation chamber, a small movement of the stirrer can cause large changes in the channel. The solid line in the Fig. 3 shows the cross correlation coefficients between the measured CIRs for rotation of the stirrer by θ ◦ (hj (θ ◦ ) and a measured CIR at θ = 0 ◦ (hj (0◦ )). Mathematically it can be written as: s0◦ θ◦ (6) ρ(θ◦ ) = √ s0◦ 0◦ sθθ
0.4
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Fig. 5: Partial correlation between ai and bi extracted from CIRs hj (0◦ ) and hj (3 ◦ ) respectively
To investigate why the TR received signal does not degrade in the same way as CIR does, we evaluate the partial correlation of hj (0◦ ) and hj (3◦ ) having a bandwidth of 2.0 GHz. The two CIRs are arbitrarily divided into 100 parts. Let these parts be ai for hj (0◦ ) and bi for hj (3◦ ). The correlation coefficients for each ai and its respective bi are taken. Both ai and bi correspond to 0.2 μs. Fig. 5 shows the curve for these partial correlations. Although the correlation coefficient
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Fig. 7: TR received signal (yj (5◦ )) with a 2% threshold
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(b) Fig. 6: Correlated part of the measured CIRs hj (0◦ ) and hj (3 ◦ ) TABLE I: Comparison of delay spread of the TR received signal (yj (θ◦ )) and the measured CIR (hj (θ◦ )) θ (degree) 0 1 2 3 4 5
hj (0◦ )
hj (3◦ )
στT R (μs) 0.00055 0.00060 0.00065 1.2007 1.7118 1.9946
στCIR (μs) 5.50 5.51 5.50 5.51 5.50 5.49
for and is in the order of 0.1 (see Fig. 3), the partial correlation coefficients reveal some interesting facts. Fig. 5 shows that some parts of the CIR hj (0◦ ) have very strong correlation with their respective parts of the CIR hj (3◦ ). Thus, a part of the CIR maintains its form and does not decorrelate. Fig. 6 shows the correlated parts of the two CIRs having a length of 40 ns. This correlation affects the received signal peak and in spite of a totally de-correlated channel (in total), TR achieves high signal quality, i.e. high SSR and FG and relatively lower RMS delay spread. Table I compares the RMS delay spread of the TR received signal and the CIR for different bandwidths. To reduce the noise components, signal taps having a power less than the threshold of 2% (-39 dB) of the maximum peak power are forced to zero. Once a tap crosses the threshold, all the taps are included in the selected signal until the signal taps reaches a stage after which they never cross the threshold. Fig. 7 shows the TR received signal, yj (5◦ ) along with the threshold and the selected signal for the calculation of delay spread. The comparison (Table I) shows that the delay spread of the TR received signal is in the order of 0.5-0.7 ns for the first three positions of the stirrer. As the stirrer moves by θ = 3 ◦ , a substantial increase in the RMS delay spread is
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Fig. 8: For TR received signal at varying θ a) Received peak power b) Signal to sidelobe ratio c) Focusing gain d) Increased average power
observed. However, for θ = 1 ◦ , 2 ◦ , the RMS delay spread does not increase by much and remains in the order of 0.6 ns. The robustness of the TR system is evident from these observations. Even if the channel is de-correlated from its original state (θ = 1 ◦ , 2 ◦ ), the TR received signal has a very short delay spread. For θ ≥ 3 ◦ , it is quite large (in the order of 1-3 μs) but still it is less than the RMS delay spread of the CIR which remains almost constant for all the positions of the stirrer. Fig. 8 shows the effects of the rotation of the stirrer on different TR characteristics. Even though the CIR changes rapidly with θ, received peak power does not decrease as severely with θ (see Fig. 8a) as does the correlation coefficient of the CIR (see Fig. 3). More importantly, SSR does not degrade a great deal with θ (see Fig. 8b). Thus, the signal quality remains
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1
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Fig. 9: Cross-correlation coefficients between hj (θ◦ ) and hj (0 ◦ ) and between yj (θ◦ ) and yj (0 ◦ )
almost constant. Focusing gain (Fig. 8c) and the increased average power (Fig. 8d) experience a decrease with θ but this degradation can be considered as small compared to the channel de-correlation. Thus, TR system can resist a change in the channel if a part of the channel is not totally de-correlated. TR system results in a good signal quality even if the channel is de-correlated (in total). For instance, for θ = 2 ◦ , CIR has a correlation coefficient of 0.06 but still the TR system has a FG 19.26 dB, SSR of 2.87 dB, increased average power of 3.15 dB. B. Experiments with Moving Receiver Experiments are also performed in the RC with moving receiver. The receiver is moved by using a precise robotic positionner with a spatial resolution of 2.5 cm. The lower frequency for the TR signal (bandwidth of 2 GHz) is 700 MHz which corresponds to the wavelengths (λ) of 42.86 cm. The wavelengths λ is calculated for the lower frequency (fL ) of the bandwidth as the dimension of the focusing zone is governed by fL [15]. The solid line in the Fig. 9 compares the cross correlation coefficients (evaluated from (6)) of CIR at reference position (hj (0 cm)) and CIRs (hj (d cm)), where d is the distance from the reference position. At d ≥ 10cm, the CIRs are almost totally de-correlated. The dashed line shows the cross correlation of the TR received signal yj (0 cm) and yj (d cm). For d ≥ 10 cm, which is a little less than λ4 at 700 MHz, the TR received signal (yj (d cm)) has a very low correlation with yj (0 cm). Thus, TR received signal is also totally de-correlated by a small movement of the receiver. In the case of moving receiver, as it was expected, the partial correlation also disappears quite rapidly. Fig. 10 shows the partial correlation between the CIRs hj (0 cm) and hj (10 cm). Both CIRs are divided into 100 parts (named as ai and bi ) and then the correlation coefficients between the respective parts are calculated. It is observed that no part is highly correlated with its respective part. Thus, movement of the receiver in the order of λ4 entirely de-correlates the CIR. Table II compares the RMS delay spread of the TR received
50 i
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Fig. 10: Partial correlation between ai and bi extracted from the CIRs hj (d = 0 cm) and hj (d = 10 cm) respectively TABLE II: Comparison of delay spread of the TR received signal and the CIR for different movements of the receiver Movement (cm) 0 5 10 15 20 25
στT R (μs) 0.00057 0.00064 0.6491 1.4306 1.6635 2.1177
στCIR (μs) 5.68 5.70 5.70 5.70 5.69 5.68
signal and the CIR for movement of the receiver by 0-25 cm. For a 10 cm (or more) movement of the receiver, the RMS delay spread increases rapidly. However, the RMS delay spread is always less than the spread of the CIR. The effects of the channel change by the movement of the receiver are studied on different TR characteristics and are plotted in Fig. 11. The performance is degraded quite rapidly. For instance for a 20 cm movement of the receiver, the received peak power is decreased by 15.28 dB, focusing gain is decreased by 19 dB, SSR is decreased by 2.47 dB and the average increased power is decreased by 3.66 dB. Thus in a RC, a very small movement of the receiver degrades the performance substantially. C. Result Analysis and Future Prospects In this paper, it is discussed that the TR system can resist a partial change in the CIR. As long as some part of the CIR maintains its form, the TR system gives a good performance. In a real environment, say typical indoor environment, this is a result of significant importance. In such cases, if the channel is changed due to the variation in the environment, e.g. movement of the people, it is highly likely that some part of CIR will remain intact depending on the position and number of people. In this case, TR robustness can play a vital role. There is no need to re-estimate the CIR if there are minor changes in the environment e.g. movement of the people. This property can be very attractive for WLAN and wireless streaming applications. However, when the receiver moves its position or there is significant change in the layout
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rotation of the stirrer has a correlation coefficient of 0.06 with the CIR of θ = 0 ◦ , but still the TR system achieves a RMS delay spread of only 0.65 ns, a focusing gain of 19.26 dB, signal to side lobe ratio of 2.87 dB, increased average power of 3.15 dB. On the other hand, if the receiver is displaced form its position, the channel gets totally de-correlated and does not maintain any partial correlation with the original CIR for a movement in the order of λ4 , where λ is the wavelength of lower frequency fL . Thus, in a RC, TR system can not support even a small movement of the receiver. R EFERENCES
Increased average power (dB)
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Fig. 11: For TR received signals at varying positions of the receiver, a) Received peak power b) Signal to sidelobe ratio c) Focusing gain d) Increased average power
of the furniture, the channel de-correlates rapidly and reestimation of the CIR is required. Thus, TR is beneficial in a non stationary channel where non stationarity is caused by the changes in the environment. The experiments in the RC have provided a good platform for the study of the robustness of a TR system. Realistic environments (such as typical indoor environment) create lesser number of multi-paths and are less sensitive to the changes in the environment than the RC. Thus, it can be intuitively stated that natural changes in the channel do not de-correlate the CIR completely and CIR will maintain a better partial correlation with the previous state than RC. Therefore, TR will be even more robust in such cases. However, if the change in the CIR is occurred due the movement of either the transmitter or the receiver, it is expected that the channel will de-correlate rapidly from the original state (less rapidly than RC) and TR will not be robust in that case. V. C ONCLUSION In this paper, the robustness of a time reversal (TR) communication system is studied in a time varying channel environment. TR experiments are performed in the reverberation chamber (RC) with the rotation of the stirrer or the movement of the receiver. The results suggest that TR system can give a robust performance even if the channel environment has changed partially. If the channel maintains some partial correlation with the previous channel, TR can give a good performance even if the total correlation of the channels is very low. For instance, channel impulse response with a 2 ◦
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