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Adaptive Trellis Coded Modulation over Predicted Flat Fading Channels  



Sorour Falahati , Mei Hong , Arne Svensson and Mikael Sternad 

Department of Signals and Systems, Uppsala University, P.O. Box 528, SE-751 20 Uppsala, Sweden. Tel.: +46 18 471 3071, Fax: +46 18 555 096, Email: [email protected] 

Department of Information Technology, Uppsala University, P.O. Box 337, SE-751 05 Uppsala, Sweden. Tel.: +46 18 471 7840, Fax: +46 18 503 611, Email: [email protected] 

Department of Signals and Systems, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden. Tel.: +46 31 772 1751, Fax: +46 70 388 8055, Email: [email protected] 

Department of Signals and Systems, Uppsala University, P.O. Box 528, SE-751 20 Uppsala, Sweden. Tel.: +46 18 471 3078, Fax: +46 18 555 096, Email: [email protected]

Submitted to IEEE Vehicular Technology Conference, Orlando, Florida, USA, October 4-9, 2003. Designated to the Technical Subject Area Transmission Technology.

Abstract

Link adaptation techniques aim at the efficient utilization of the scarce bandwidth of mobile radio links while satisfying the users’ demands. A competitive candidate for these purposes is an adaptive scheme based on the Trellis Coded Modulation (TCM) which increases the noise robustness without bandwidth expansion, in comparison with an uncoded scheme. We consider the optimum design of an adaptive scheme based on TCM and predicted Channel State Information (CSI) for flat Rayleigh fading channels, intended for the fast link adaptation. We answer the question of how to optimally adjust the data rate to maximize the spectral efficiency, subject to a Bit Error Rate (BER) constraint when imperfect CSI is taken into account. We derive an optimum solution based on the predicted Signal-to-Noise Ratio (SNR) and the prediction Mean Square Error (MSE) variance. Finally, we illustrate the performance of the adaptive TCM scheme utilizing seven 4-D trellis codes based on the International Telecommunications Union’s ITU-T V.34 modem standard.

I. I NTRODUCTION The problems of spectrum utilization in the hostile mobile environment, stimulate a great deal of research, especially in the area of adaptive transmission. The premise of adaptive transmission is to adjust the signaling parameters as the channel varies, with the best possible usage of resources. Recently, adaptive transmission based on uncoded M-ary Quadrature Amplitude Modulation (M-QAM) has gained considerable attention [1]. To improve the obtainable spectral efficiency, more complex schemes are required. A competitive candidate for this purpose is TCM which has the potential of attaining a target BER at a lower average SNR, or provide a higher spectral efficiency for a given average SNR, as compared to the non-adaptive TCM or adaptive uncoded M-QAM [2]. The adaptive transmission techniques often rely on the CSI being available at the transmitter. Perfect CSI is usually assumed in the design of adaptive modulation schemes. However, in order for the scheme to meet up to the expectations in practice, realistic assumptions should be used in the design [3]. The CSI is estimated at the receiver and sent through a feedback channel to the transmitter. For very slowly fading channels, the outdated estimates of CSI are still useful for adaptation purposes. However, for fast fading channels, the feedback delays result in inaccurate CSI estimates at the time of transmission. Hence, it is reasonable to perform fast link adaptation based on channel predictions. The optimum adaptive scheme considered here is based on TCM and takes the statistical information of predicted Rayleigh fading channels into account. This approach distinguishes the present work from other solutions found in the literature. The objective is to increase the spectral efficiency. The channel predictions utilized in this study are obtained through an unbiased quadratic regression of the past noisy channel estimates. For this type of predictor, there exists a statistical model for the prediction error which yields the mean, variance and probability density function (pdf) of the errors. The statistical information is exploited to improve the overall system performance. II. S YSTEM

MODEL AND PROBLEM STATEMENT

The proposed adaptive TCM scheme utilizes a set of two-dimensional (  -D) trellis codes, being a positive integer, with different constellation sizes. Let



denote the number of constellations available at the transmitter, each of size  with    bits per  symbol for   . A  -D signal constellation is obtained by -fold Cartesian products of 2-D signal constellations. At every th transmission time instant, the encoder encodes  !"#$ bits into % &! coded bits which are mapped onto symbols, each  from a 2-D constellation of size ' for   . consecutive symbol These symbols are sent during intervals. Hence, the instantaneous data rate becomes ( ) +*,-#.*/102435350167 where 687 is the symbol period. Moreover, let 9 and :9 denote the instantaneous true and predicted SNR, respectively. The rate region HG , boundaries, denoted by ; are presumed. At each even time instant,  information bits are encoded to *  ) coded bits which are mapped onto two symbols, each   + - AD/C .10 , and are from a 2-D constellation of size , transmitted during next two time instants. Based on these assumptions, the BER approximations for AWGN channels based on (4) are found which are tight within 1 dB in comparison with the corresponding simulated BER. The adaptive TCM scheme is designed for flat Rayleigh fading channels. The optimum rate region boundaries subject to the BER constraint given by (2) for different values of  prediction error variance,    , and various values of the  average SNR, 9 , are evaluated and the corresponding

(bps/Hz)

C TCM  4  QAM for  eh.e , is suggested where *Z:9 3 and are the   transmitted power and the average transmitted power, PSfrag replacements 2 3 2  respectively. Here, *]:9 3) . The % parameters 0   0 5 10 5 4 15 20 25 and ;   * 3 > E are real numbers where ;  * 3 > E dB C C the latter set takes only non-negative values. Both sets Fig. 1. The average spectral efficiency of the adaptive transmission are determined by using curve fitting techniques. 

based on TCM and uncoded M-QAM schemes versus average received SNR. The upper and lower plots correspond to 687:9= [email protected]"B'D [email protected]"BC and , respectively. The solid, dashed and dashed-dotted @H @[email protected]"? @H @? @HJ? lines correspond to EG F  = , and , respectively.

R EFERENCES [1] S. T. Chung and A. J. Goldsmith, “Degrees of Freedom in Adaptive Modulation: A Unified View,” IEEE Transactions on Communications, vol. 49, no. 9, pp. 1561–1571, Sept. 2001. [2] Kjell J. Hole, Henrik Holm, and Geir E. Øien, “Adaptive Multidimensional Coded Modulation Over Flat Fading Channels,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 7, pp. 1153–1158, July 2000. [3] D. L. Goeckel, “Adaptive Coding for Time-Varying Channels Using Outdated Fading Estimates,” IEEE Transactions on Communications, vol. 47, no. 6, pp. 844–855, June 1999. [4] T. Ekman, M. Sternad, and A. Ahl´en, “Unbiased Power Prediction on Broadband Channel,” in Proc. IEEE Vehicular Technology Conference, Vancouver, Canada, Sept. 2002. [5] T. Ekman, “Prediction of Mobile Radio Channels, Modeling and Design,” PhD thesis, Signals and Systems, Uppsala University, Uppsala, Sweden. http://www.signal.uu.se/Publications/abstracts/a023.html, Oct. 2002. [6] S. Falahati, “Adaptive Modulation and Coding in Wireless Communications with Feedback,” PhD thesis, Signals and Systems, Chalmers University of Technology, G¨oteborg, Sweden, http://www.s2.chalmers.se/publications/, Oct. 2002.

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