Waveform-level Precoding with Simple Energy Detector Receiver for Wideband Communication

Transcription

1 Waveform-level Precoding with Simple Energy Detector Receiver for Wideband Communication Nan Guo, Zhen Hu, Amanpreet S Saini, Robert Qiu Department of Electrical and Computer Engineering, Center for Manufacturing Research Tennessee Tech University, Cookeville TN, USA {nguo, zhu1, assaini1, rqiu}@tntech.edu Abstract Wideband waveform-level precoding with simple energy detector receiver is investigated in this paper. The motivation is to provide a cheap radio network with simple receivers and sophisticated transmitters. The energy detector receiver performs relatively poorly, but waveform-level precoding can be used to compensate for the performance loss. Waveform-level precoding is a transmitter-side processing taking advantage of known channel information. Given channel impulse response (CIR), transmitted waveform can be optimized in some criterion. In this paper the optimization goal is to maximize an equivalent signal-to-noise ratio (SNR) at the receiver, assuming no inter-symbol-interference (ISI). Close-form expressions are derived based on the Park s empirical model for evaluating the receiver operating characteristic (ROC) of energy-detector. Numerical approach is adopted to handle continuous time signals. Channel data measured in office area is used to obtain numerical results. Performance comparison with time reversal precoding as benchmark shows that the optimal waveform can offer gains of several decibels. Index Terms Energy detector, waveform optimization, time reversal. I. INTRODUCTION Recent advances in miniaturization, low-power electronics and wireless communications, stimulated by increasing demands for automation in home and industrial areas, have triggered tremendous interests in the wireless sensor network (WSN) research, development and deployment. Designing WSNs is a big challenge due to tough constraints and conditions posed by specific applications and environments. Examples of these constraints and conditions include power consumption, node simplicity, node cost, low signal leakage and non-line-of-sight propagation, severe multipath, etc. Mainly due to potentially low implementation complexity, suboptimal reception strategies, such as transmitted reference (TR) [1] [8] and its variants [9] [13] as well as energy (or square law) detector [14] [17], have received increasing attention for complexity and cost constrained wideband applications. These suboptimal schemes are of low-complexity in the sense that no channel estimation is required and they are less sensitive to timing error. Of course, their performances are poor comparing to those of the optimal receivers. One philosophy to use simple receivers without sacrificing overall performance is to shift part of receiver side functions to the transmitter side, i.e., add preprocessing at the transmitter to compensate performance loss, which is meaningful for a centralized network where one powerful central station communicates with a large number of nodes. In particular, high-bandwidth waveform level precoding is feasible as giga- Hertz sampling rate becomes practical. Real-time arbitrary waveform precoding provides a new platform for ultimate performance optimization using channel information. Depending upon the channel information, each pair of transmitter and receiver in the system chooses a transmitted waveform that is optimal in some sense. An example of waveform precoding is time reversal pre-filtering at the transmitter to focus the signal in time at the receiver [18] [4], where the transmitted waveform is simply a time-reversed version of the channel impulse response (CIR). In such a system the receivers can be very simple, because they do not need special means (like a RAKE combiner) to capture dispersed energy over time, and even equalizers may not be necessary. Waveform precoding can take into account both receive signal-to-noise ratio (SNR) and inter-symbol-interference (ISI). A common shortcoming is that the mentioned simple receivers are not able to work with typical linear equalization techniques, thus they are not suitable for applications when ISI exists apparently. Unlike linear receiver, the equivalent discrete channels of some suboptimal schemes behave nonlinearly, where an equivalent discrete-time channel has data input at one end and it outputs decision statistic plus noise at the other end [17], [4] [6]. The decision statistic contains a desired signal and a nonlinear ISI component that cannot be well handled by normal linear equalization techniques. This fact suggests the use of some waveform-level channel shortening techniques. In addition, in a rich multipath environment waveform precoding combined with multiple transmitter antennas can focus signal into a spot spatially. This spatial focusing feature can enable spatial division multiple access (SDMA) or enhance physical-layer security without consuming additional radio resources [1], [7], [8]. In this paper, a radio system combining waveform precoding and simple energy detector receiver is considered. Both on-off keying (OOK) and pulse position modulation (PPM) can be adopted as modulation schemes. The receiver uses an integrator to accumulate signal energy. For better performance the signal can be weighted prior to integration and there must be a best weighting function depending on the signal waveform and the noise level [9] [33]. In fact, implementation of weighting function is not of low complexity and

2 this contradicts the philosophy of low-complexity receiver design. A relatively simpler weighting method is a gating function which is equivalent to the use of a proper integration interval [17], [4], [34], [35]. A practical implementation of a smart integrator is to control the integrator s on-duration. Denoted by R b the symbol rate and consider a received symbol waveform with most of the energy concentrated in an interval T I. If T I < T b 1/R b, then integrating over the interval T I outperforms integrating over the interval T b, since both gather almost the same amount of signal energy but the latter gathers more noise. This paper tries to answer a fundamental question: given the transmission bandwidth and CIR, what are the best transmitted waveform and the best integration window size? Unlike performance evaluation of a linear receiver, analyzing an energy detector receiver is relative difficult. Park s model is adopted as an approximate analytical tool to formulate the equivalent SNR. Waveform optimization can be conducted based on this equivalent SNR. However, for arbitrary CIR to find a continuous time closed-form optimal solution is not feasible. Instead, a numerical approach using matrix operation is adopted. This work is to be tested on a realtime wideband radio test-bed. To obtain meaningful and convincing results, measured channel data is used to process numerical results. The rest of the paper is organized as follows. The system is described in Section II. Theoretical analysis is presented in Section III. In Section IV, channel sounding are discussed. Numerical results are provided in Section V, followed by some remarks given in Section VI. II. SYSTEM DESCRIPTION We limit our discussion to a single-user scenario. Assume the channel remains static during a data burst (say 1µs [8]) and CIR is available at the transmitter. How CIR is obtained is not a task of this paper. An ideal low-pass filter with onesided bandwidth W is placed at the receiver s front-end. The transmitted signal with OOK modulation is s(t) d j p(t jt b ), (1) j where T b is the symbol duration, p(t) is the transmitted symbol waveform defined over [, T p ], and d j {, 1} is j-th transmitted bit. Without loss of generality, assume the minimal propagation delay is equal to zero. The energy of p(t) is normalized and defined as, Tp p (t) dt 1 () The received noise-polluted signal at the output of the receiver front-end filter is r(t) h(t) s(t) + n(t) d j x(t jt b ) + n(t), (3) j BPF Fig. 1. Square Law Integration zk Energy-detector receiver. where h (t), t [, T h ] is the multipath impulse response that takes into account the effect of the RF front-end including the transceiver antennas. denotes convolution operation. n(t) is a low-pass additive zero-mean Gaussian noise with one-sided bandwidth W and one-sided power spectral density N, and x(t) is the received noiseless symbol- 1 waveform defined as x(t) h(t) p(t). (4) def We further assume that T b T h + T p T x, i.e. no existence of ISI. An energy detector receiver performs squaring operation, integration over a given time window T I, and threshold decision. Corresponding to the time index k, the k-th decision variable at the output of the integrator is given by z k ktb +T I +T I kt b +T I r (t)dt (5) ktb +T I +T I kt b +T I (d k x(t kt b ) + n(t)) dt (6) where T I is the starting time of integration for each symbol and T I < T I + T I T x T b. A. Equivalent SNR III. WAVEFORM DESIGN Analyzing an energy detector receiver as shown in Figure 1 is not as easy as analyzing linear receiver. The decision statistic z k can be approximated as a chi-square or a noncentral chi-square random variable, with T W degrees of freedom [36], [37]. A number of approximating models have been proposed to evaluate the performance of receiver operating characteristic (RCO) [38]. When T W is large, the chi-square or a non-central chi-square pdfs asymptotically become Gaussian by the central limit theorem. In this case, the required receive SNR and decision threshold can be determined, given the probability of false alarm P f and the probability of detection P d [38]. With the notation used in this paper, the received SNR before the square law is expressed as, TI +T I T d I I x (t) dt (7) T I W N The ROC formulas based on Gaussian approximation can be extended to handle arbitrary value of T W by introducing an empirical loss function C(d I ) [39], [4], with its general form C(d I ) b + d I d I, (8) where a and b are constants. In the following formula, the loss function links the received SNR and an equivalent SNR VT

3 which provides the same detection performance when applied to a coherent receiver, SNR eq at IW d I C(d I ) (9) at IW d I (1) b + d I ( ) TI +T I T I x (t) dt.3t I W N + N TI +T I T I x (t) dt (11) The equivalent SNR SNR eq is used as a performance indicator in this paper. The parameters a and b take and.3, respectively, the same as Park s selection in [39]. B. Waveform Optimization In order to get the better performance, the equivalent SNR SNR eq should be maximized. Define, E I TI +T I T I x (t) dt (1) For given T I and W, SNR eq is the increasing function of E I. So the maximization of SNR eq in Equation 9 is equvalent to the maximization of E I in Equation 1. So the optimization problem is shown below, max T I +T I T I x (t) dt s.t. T p p (t) dt 1 (13) In order to solve the optimization problem 13, p(t), h(t) and x(t) will be uniformly sampled and the count-part of the optimization problem 13 in the digital domain will be solved. Assume the sampling period is T s. T p /T s N p, T h /T s N h and T x /T s N x. So N x N p + N h. p(t), h(t) and x(t) are represented by p i, i, 1,..., N p, h i, i, 1,..., N h and x i, i, 1,..., N x respectively, where, p i p (it s ) (14) h i h (it s ) (15) x i x (it s ) (16) So the count-part of Equation 4 in the digital domain is shown as, and Define, x i p i h i (17) N p p j h i j (18) j p [p p 1 p Np ] T (19) x [x x 1 x Nx ] T () Construct channel matrix H (Nx+1) (N p+1), { hi j, i j N (H) i,j h, else (1) where ( ) i,j denotes the entry in the i-th row and j-th column of the matrix. Thus the matrix expression of Equation 17 is, x Hp () and the constraint in the optimization problem 13 can be expressed as, p T s 1 (3) where denotes the norm- of the vector. Meanwhile assume T I /T s N I and T I /T s N I, so the valid entries in x for integration constitute x I as, x I [x NI x NI +1 x NI +N I ] T (4) and E I in Equation 1 can be equivalently shown as, E I x I T s (5) Similar to Equation, x I can be obtained by, x I H I p (6) where (H I ) i,j (H) NI +i,j and i 1,,..., N I + 1 as well as j 1,,..., N p + 1. So the count-part of the optimization problem 13 in the digital domain can be expressed as, max E I s.t. p T s 1 (7) This optimization problem can be solved by Lagrange Multiplier method. Define objective function as, ( ) J E I + λ 1 p T s (8) ( ) H I p T s + λ 1 p T s (9) where λ is Lagrange Multiplier. From J p, it is obtained that, H T I H I p λp (3) So the optimal solution p is the eigen-vector corresponding to the maximum eigen-value in eigen-function 3 and p satisfies Equation 3. Furthermore, EI will be obtained. IV. CHANNEL SOUNDING The time domain channel sounding is employed to get h(t). This kind of channel sounding consists of a pulse generator, a signal generator, a low noise amplifier (LNA), a transmitter antenna and a receiver antenna, and a digital sampling oscilloscope (DSO). Figure shows the setup of the time domain channel sounding. The signal generator, the pulse generator and the transmitter antenna constitute the transmitter part and DSO along with the receiver antenna and LNA constitutes the receiver part. The signal generator is used to trigger the pulse generator and the pulse generator generates the pulse that is transmitted through the channel. On the receiver side the signal is amplified by LNA and then displayed and recorded on DSO. A triggering signal from the signal generator is also used to synchronize DSO to

4 Tx Antenna Rx Antenna 15 Digital Signal Pulse Low Noise Sampling Generator Generator Amplifier Oscilloscope Trigger Signal Fig.. The setup of the time domain channel sounding Optimal SNR eq (db) 1 5 /N 3dB 5 /N 4dB /N 7dB 1 /N 1dB /N 13dB CIR..1 Fig. 4. SNR eq (T I ) /N 3dB /N 4dB /N 7dB Time (ns) Fig. 3. CIR. Time Reversal SNR eq (db) 5 5 /N 1dB /N 13dB record the data of the received signal. The tapped-delay-line model of CIR will be estimated using CLEAN, a matching pursuit algorithm based on the recorded data from DSO and the noiseless waveform template of the transmitted pulse. Raised-cosine filter is used in this paper to emulate the RF front-end filter including the transceiver antennas, so h(t) can be obtained by convolving CIR and the raised-cosine filter with bandwidth W. V. NUMERICAL RESULTS Figure 3 shows CIR under investigation in this paper and the energy of h(t) is normalized. W 1GHz. T s.5ns, T h 1ns, T p 1ns and T I + T I 1ns. If the optimal waveform p is transmitted, EI (T I) and SNR eq (T I ) will be obtained. If the transmitted waveform is time reversed h(t), EI TIR (T I ) and eq (T I ) will be obtained. Figure 4 shows SNR eq (T I ) and Figure 5 shows eq (T I ). For the relatively low /N region, the optimal T I is less than 5ns seen from Figure 4 and Figure 5. Increasing T I will introduce more noise and the performance will degrade. For the relatively high /N region, we can choose the proper T I such that the larger T I can not bring the obvious increase of SNR eq. Let s define two gains to quantify the performance of optimal waveform using time reversal as benchmark. One is an energy gain, G e (T I ) E I (T I) EI TIR (T I ) and the other is an SNR eq gain, G SNReq (T I ) SNR eq (T I ) eq (T I ) (31) (3) Fig. 5. eq (T I ). Figure 6 and Figure 7 show the energy gain and SNR eq gain respectively. When T I, the energy gain and the SNR eq gain approach 1. In this kind of situation, the optimal waveform is the time reversed h(t). So, from peak detection s point of view, time reversal is the optimal waveform-level precoding. However, when T I increases, the optimal waveform can bring obvious performance enhancement not only for the energy gain but also for the SNR eq gain. Define, TI arg max eq (T I ) (33) T I If eq (TI ) is used as the benchmark, then the other SNR eq gain is defined as, G SNR eq (T I ) SNR eq (T I ) eq (T I ) (34) Figure 8 shows G SNR eq (T I ). In the relatively high /N region, the performance of optimal waveform can be improved by a few decibels over the time reversal scheme with optimal integration window when T I for optimal waveform is larger than a certain threshold. While if /N is relatively low, the optimal T I for optimal waveform is still needed to get the better performance. VI. CONCLUSION Wideband waveform-level precoding with energy detector receiver has been studied. This work is a part of our effort

5 Energy Gain (db) Fig. 6. Energy gain. SNR eq Gain (db) 1 Fig /N 3dB /N 4dB /N 7dB E 1 b /N 1dB /N 13dB SNR eq gain using eq `T I as the benchmark. 8 REFERENCES SNR eq Gain (db) /N 3dB /N 4dB /N 7dB /N 1dB /N 13dB Fig. 7. SNR eq gain. in searching for simple-receiver solutions with enhanced performance. Thanks to the empirical loss function, elegant analytical frame has been established, enabling derivation of closed-form optimization results. Numerical results show that performance can be improved by a few decibels over the time reversal scheme with optimal integration window, meaning that time reversal is not the best waveform-level precoding for energy detector receiver. This research suggests that waveform-level precoding can significantly extend the communication range without consuming extra transmitted power. The results of this paper will be verified on the realtime wideband radio test-bed. ACKNOWLEDGMENT This work is funded by the Office of Naval Research through a grant (N ), and National Science Foundation through a grant (ECS-615). The authors wants to thank their sponsors Santanu K. Das (ONR), and Robert Ulman (ARO) for inspiration and vision. The director of Center for Manufacturing Research (CMR) at TTU (Kenneth Currie) and the chair of ECE (Stephen Parke) at TTU has provided the authors with good support for carrying out this research. P. K. Rajan is helpful in many discussions. [1] J. Pierce and A. Hopper, Nonsynclronous Time Division with Holding and with Random Sampling, Proceedings of the IRE, vol. 4, no. 9, pp , 195. [] C. Rushforth, Transmitted-Reference Techniques for random or unknown Channels, IEEE Transactions on Information Theory, vol. 1, no. 1, pp. 39 4, [3] G. Hingorani and J. Hancock, A Transmitted Reference System for Communication in Random of Unknown Channels, IEEE Transactions on Communications Technology, vol. 13, no. 3, pp , [4] N. van Stralen, A. Dentinger, K. Welles, R. Gauss, R. Hoctor, and H. Tomlinson, Delay Hopped Transmitted Reference Experimental Results, in IEEE Conference on Ultra Wideband Systems and Technologies,, pp [5] J. Choi and W. Stark, Performance of Ultra-Wideband Communications with Suboptimal Receivers in Multipath Channels, IEEE Journal on Selected Areas in Communications, vol., no. 9, pp ,. [6] D. Goeckel and Q. Zhang, Slightly Frequency-Shifted Reference Ultra-Wideband (UWB) Radio: TR-UWB without the Delay Element, in IEEE Military Communications Conference, 5, pp [7] D. Goeckel, J. Mehlman, and J. Burkhart, A Class of Ultra Wideband (UWB) Systems with Simple Receivers, in IEEE Military Communications Conference, 7, pp [8] H. Liu, A. Molisch, S. Zhao, D. Goeckel, and P. Orlik, Hybrid Coherent and Frequency-Shifted-Reference Ultrawideband Radio, in IEEE Global Telecommunications Conference, 7, pp [9] M. Ho, V. Somayazulu, J. Foerster, and S. Roy, A Differential Detector for an Ultra-wideband Communications System, IEEE 55th Vehicular Technology Conference, vol. 4, pp ,. [1] Y. Chao and R. Scholtz, Optimal and Suboptimal Receivers for Ultra-wideband Transmitted Reference Systems, in IEEE Global Telecommunications Conference, vol., 3, pp [11] S. Zhao, H. Liu, and Z. Tian, A Decision-Feedback Autocorrelation Receiver for Pulsed Ultra-wideband Systems, in IEEE Radio and Wireless Conference, 4, pp [1] N. Guo and R. Qiu, Improved Autocorrelation Demodulation Receivers based on Multiple-Symbol Detection for UWB communications, IEEE Transactions on Wireless Communications, vol. 5, pp. 6 31, 6. [13] L. V. and T. Z., Multiple Symbol Differential Detection for UWB communications, IEEE Trans. Wireless Commun., vol. 7, pp , 8. [14] Y. Souilmi and R. Knopp, On the Achievable Rates of Ultra-wideband PPM with Non-Coherent Detection in Multipath Environments, in IEEE International Conference on Communications, vol. 5, 3, pp [15] M. Weisenhorn and W. Hirt, Robust Noncoherent Receiver Exploiting UWB Channel Properties, in International Workshop on Ultra Wideband Systems, Joint with Conference on Ultrawideband Systems and Technologies, 4, pp

6 [16] S. Paquelet, L. Aubert, B. Uguen, I. Mitsubishi, and F. Rennes, An Impulse Radio Asynchronous Transceiver for High Data rates, in International Workshop on Ultra Wideband Systems, Joint with Conference on Ultrawideband Systems and Technologies, 4, pp [17] N. Guo, J. Zhang, R. Qiu, and S. Mo, UWB MISO Time Reversal With Energy Detector Receiver Over ISI Channels, in 4th IEEE Consumer Communications and Networking Conference, 7, pp [18] N. Guo, R. C. Qiu, Q. Zhang, B. M. Sadler, Z. Hu, P. Zhang, Y. Song, and C. M. Zhou, Handbook of Sensor Networks. World Scientific Publishing, 9, ch. Time Reversal for Ultra-Wideband Communications: Architecture and Test-bed, pp [19] M. Fink, Time Reversal of Ultrasonic Fields. Part-I: Basic principles, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 39, no. 5, pp , 199. [] A. Akogun, R. Qiu, and N. Guo, Demonstrating Time Reversal in Ultra-wideband Communications Using Time Domain Measurements, in 51st International Instrumentation Symposium, 5, pp [1] N. Guo, R. Qiu, and B. Sadler, An Ultra-Wideband Autocorrelation Demodulation Scheme with Low-Complexity Time Reversal Enhancement, in IEEE Military Communications Conference, 5, pp [] R. Qiu, C. Zhou, N. Guo, and J. Zhang, Time Reversal With MISO for Ultrawideband Communications: Experimental Results, IEEE Antennas and Wireless Propagation Letters, vol. 5, p. 69, 6. [3] N. Guo, J. Zhang, R. Qiu, and S. Mo, UWB MISO Time Reversal With Energy Detector Receiver Over ISI Channels, in IEEE Consumer Commun. and Networking Conf, 7, pp [4] N. Guo, B. Sadler, and R. Qiu, Reduced-Complexity UWB Timereversal Techniques and Experimental Results, IEEE Transactions on Wireless Communications, vol. 6, no. 1, pp , 7. [5] K. Witrisal, G. Leus, M. Pausini, and C. Krall, Equivalent System Model and Equalization of Differential Impulse Radio UWB Systems, IEEE Journal on Selected Areas in Communications, vol. 3, no. 9, pp , 5. [6] M. Pausini, G. Janssen, and K. Witrisal, Performance Enhancement of Differential UWB Autocorrelation Receivers Under ISI, IEEE Journal on Selected Areas in Communications, vol. 4, no. 4 Part 1, pp , 6. [7] R. Wilson, D. Tse, and R. Scholtz, Channel Identification: Secret Sharing Using Reciprocity in Ultrawideband Channels, IEEE Transactions on Information Forensics and Security, vol., no. 3 Part 1, pp , 7. [8] M. Bloch, J. Barros, M. Rodrigues, and S. McLaughlin, Wireless Information-Theoretic Security, IEEE Transactions on Information Theory, vol. 54, no. 6, pp , 8. [9] J. Romme, G. Durisi, I. GmbH, and G. Kamp-Lintfort, Transmit Reference Impulse Radio Systems using Weighted Correlation, in International Workshop on Ultra Wideband Systems, Joint with Conference on Ultrawideband Systems and Technologies, 4, pp [3] Y. Chao and R. Scholtz, Weighted Correlation Receivers for Ultra- Wideband Transmitted Reference Systems, in IEEE Global Telecommunications Conference, vol. 1, 4, pp [31] J. Romme and K. Witrisal, Transmitted-Reference UWB Systems Using Weighted Autocorrelation Receivers, IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 4, pp , 6. [3] Z. Tian and B. Sadler, Weighted Energy Detection of Ultra-Wideband Signals, in IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 5, pp [33] J. Wu, H. Xiang, and Z. Tian, Weighted Noncoherent Receivers for UWB PPM Signals, IEEE COMMUNICATIONS LETTERS, vol. 1, no. 9, p. 655, 6. [34] S. Franz and U. Mitra, Integration Interval Optimization and Performance Analysis for UWB Transmitted Reference Systems, in International Workshop on Ultra Wideband Systems, Joint with Conference on Ultrawideband Systems and Technologies., 4, pp [35] Y. Chao, Optimal Integration Time for UWB Transmitted Reference Correlation Receivers, in Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, vol. 1, 4. [36] H. Urkowitz, Energy Detection of unknown Deterministic Signals, Proceedings of the IEEE, vol. 55, no. 4, pp , [37] D. Torrieri, Principles of Secure Communication Systems. Artech House, Inc. Norwood, MA, USA, 199. [38] R. Mills and G. Prescott, A Comparison of Various Radiometer Detection Models, IEEE Transactions on Aerospace and Electronic Systems, vol. 3, no. 1, pp , [39] K. Park, Performance Evaluation of Energy Detectors, IEEE Transactions on Aerospace and Electronic Systems, vol. 14, pp , [4] D. Barton, Simple Procedures for Radar Detection Calculations, IEEE Transactions on Aerospace and Electronic Systems, vol. 5, pp , 1969.