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2 NSC E NSC E ( ) ( ) - 2 -

3 A Per-survivor Kalman-based prediction filter for space-time coded systems NSC E dtseng@mail.ntust.edu.tw : - 3 -

4 maximum-likelihood sequence estimation (MLSE) to combat the fast fading environments. Simulation results will be demonstrated to compare this Kalman filtering approach with the conventional least mean-squares (LMS) method in terms of bit error probability based on different products of maximum fading frequency and symbol interval. : Space-time Coding, Kalman Filter, Multiple Transmit Antenna, Rayleigh Fading Channels,,, Per-Survivor Processing, Maximum-Likelihood Sequence Estimator (MLSE) Space-time coding and modulation have received a lot of attention recently as they could provide diversity and coding gains for wireless communication links. It is shown by Foschini that by employing multiple transmit/receive antennas in a Rayleigh fading environment the capacity can be increased significantly provided that the radio channel coefficients between all pairs of transmit and receive antennas are statistically independent and known in advance to the receivers. For most of the previous developed algorithms, the capacity gains could be realized by assuming perfect channel state information (CSI) is available at the receiver. More recently, noncoherent or differential space-time modulation schemes which assume no knowledge about channel state information (CSI) have been developed by Hughes and Hochwald independently. In this proposal, a Kalman filtering based prediction method is developed to track the fast Rayleigh flat fading channels which usually occur when the mobile moves significantly or the surrounding environment changes with time. Furthermore, per-survivor processing (PSP) has been operated and combined with Space-time coding and modulation have received a lot of attention recently as they could provide diversity and coding gains for wireless communication links. It is shown in {Foschini} that by employing multiple transmit/receive antennas in a Rayleigh fading environment the capacity can be increased significantly provided that the radio channel coefficients between all pairs of transmit and receive antennas are statistically independent and known in advance. Since then there have been a number of promising space-time coding algorithms proposed: trellis codes {Tarokh} and block codes {Alamouti}, {Guey}. For most of these algorithms, the capacity gains could be realized by assuming perfect channel state information (CSI) is available at the receiver. More recently, noncoherent or differential space-time modulation schemes which assume no knowledge about channel state information have been developed in {Hughes}. In modern mobile radio wireless communication systems, time varying multipath fading propagation is one of the major obstacles to cause severe performance degradation. Based on the capacity gains from space-time coding schemes, systems incorporating such scenarios could be modeled as multi-input multi-output time-variant (MIMO) channels. The receiver needs to track the channel coefficients and detect the transmitted symbols to maintain IV -

5 the overall system performance. In this paper, a Kalman filter to track the MIMO channel parameters is proposed. The channel coefficients are typically modeled as mutually uncorrelated circular complex Gaussian random processes with zero means, indicating Rayleigh fading environment. Also, the channels exhibit the time-varying property with the autocorrelation functions characterized by Clarke's 2-D isotropic scattering model {Stuber}. A simple autoregressive (AR) model for multiple time-varying channels is assumed \cite{iltis}. Such an approximated model could lead to analyze the corresponding receiver structure and performance. Per-Survivor Processing (PSP)-based adaptive receivers which approximate the maximum-likelihood sequence estimation (MLSE) over randomly time-varying channels have been proposed in the literature {Tzou},{Kubo}. In these schemes, the channel parameters for each pair of transmit and receive antennas are updated for the survivor of each state in the Viterbi algorithm. Due to the exploitation of all possible channel estimates from current epoch to next time update, these approaches generally outperform conventional methods which do not incorporate PSP characteristics on fast time-varying channels. Here an AR model is further incorporated to apply the Kalman prediction filtering. In addition, a space-time training sequence is constructed to achieve good initial channel estimate. A comparison of recursive least squares (RLS) and the proposed scheme for tracking multiple fast fading channels is carried out by computer simulation, which demonstrates that the proposed scheme performs better in terms of bit error probability. The space-time coding technique is also an efficient way of improving throughput and reliability that wireless communications systems such as W-CDMA, CDMA-2000 and Lucent's BLAST project have been designed to apply. This paper is organized as follows. In Section 2, the channel model is introduced. Section 3 presents the Kalman-based tracking approach for the space-time coded systems. A space-time training sequence design is investigated in Section 4. In Section 5 the simulation results are provided. This project was proposed by Prof. Der-Feng Tseng and the results including the detailed derivations of the proposed algorithm to resolve the obstacle were already published in Reference[1] Proceedings of 2002 IEEE International Conference on Communications Systems, Nov. 2002, in Singapore. The page number of that proceeding is from 169 to 173. The PDF format of published paper is included in the Appendix. Separate PDF file of the paper is also attached with this final report. Readers are strongly encouraged to download the original paper from IEEE Xplore web site. This project is a very good introductory signal processing algorithm applied to wireless communications systems for graduate students to practice. It combines the systems theoretical background including Kalman filter, prediction filter concept, and maximum likelihood sequence estimate for current cellular systems. Students need to understand trellis code modulation technique in the wireless communications systems to be able to simulate the programs. The final simulations results align with the predictions; exploiting Gaussian property to adapt the channel variations outperforms other conventionally used methods in a few db gain under different products of symbol duration and maximum Doppler frequency rate at the expense of moderate computational complexity. Though the completed project is a well-developed approach to space-time trellis coding systems, it still has good room to lower the bit error rate by a couple of orders of magnitude if the soft-output decoding scheme could be employed instead of hard-decision decoding method realized in the MLSE. It is well known that Expectation-Maximization (EM) algorithm is an effective iterative method to attain better performance at the expense of computational complexity. Adaptive Baum-Welch algorithm V -

6 thus is a good solution to track the channel variations while including the turbo-decoding concept utilizing soft outputs generated from channel decoding stage. This further improved strategy would be more extended and ready for next NSC s annual proposal. Der-Feng Tseng, Shu-Ming Tseng, A Per-survivor Kalman-based prediction filter forspace-time coded systems, Proceedings of IEEE International Conference on Communications Systems, pp , Nov G. Foschini, M. J. Gans, "On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas,'' Wireless Personal Commun, vol.44, no.2, pp , March Alamouti S. M. Alamouti, ''A Simple Transmitter Diversity Scheme for Wireless Communications,'' IEEE J. Select. Areas Commun. vol. 16, pp , Oct Guey J.-C., M. P. Fitz, M. R. Bell, W.-Y. Kuo, ''Signal Design for Transmitter Diversity Wireless Communication Systems overrayleigh Fading Channels, ' IEEE Trans. Commun, vol. 47, pp , Apr V. Tarokh, N. Seshadri, A. R. Calderbank, ``Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,'' IEEE Trans. Inform. Theory, vol. 44, no. 2,pp , Mar V. Tarokh, H. Jafarkhani, A. R. Calderbank, ``Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,' IEEE Trans. Inform. Theory, vol. 44, pp , Mar B. L. Hughes, ``Differential Space-Time Modulation,'' IEEE Trans. Inform. Theory, vol. 46, pp , Nov B. M. Hochwald, W. Sweldens, ``Differential Unitary Space-Time Modulation,'' IEEE Trans. Commun., vol. 48, pp , Dec R. Raheli, A. Polydoros, C-K. Tzou ``Per-Survivor Processing: A General Approach to MLSE in Uncertain Environments,'' IEEE Trans. Commun., vol. 43, pp , Feb R. A. Iltis, ``Joint Estimation of PN Code Delay and Multipath Using the Extended Kalman Filter," IEEE Trans. Commun., vol. 38, pp , Oct Q. Dai, Ed Shwedyk, ``Detection of Bandlimited Signals Over Frequency Selective Rayleigh Fading Channels," IEEE Trans. Commun., vol. 42, no. 2/3/4, pp , Feb./March/April H. Kubo, K. Murakami, T. Fujino, ``An Adaptive Maximum-Likelihood Sequence Estimator for Fast Time-Varying Intersymbol Interference Channels," IEEE Trans. Commun., vol. 42, no. 2/3/4, pp , Feb./March/April Gordon L. Stuber, Principles of Mobile Communication, Kluwer Academic Publishers, 2nd Ed VI -

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12 I I A1 8th IEEE International Conference on Communication Systems (ICCS 2002) A Per-survivor Kalman-based prediction filter for space-time coded systems 12 -

13 8th IEEE International Conference on Communication Systems (ICCS 2002)) 0 0 Carlton IEEE Communications Society : (1) (Space-time coding for high-speed wireless communications systems) (2) (Bluetooth Technology) (3) (Design of High-Capacity Wireless LANS with QOS Guarantees) (4) ISDN Lawrence W.C. Wong Mehul Motani, Hari K. Garg IEEE ICCS 13 -

14 IEEE Trans. Information Theory (packet) training sequence pilot symbol sequence Pilot symbol sequence (Doppler frequency rate) overhead pilot symbols Space-Time Coding and 14 - MIMO Systems (Session Chair) training sequence

15 Kuang-Yi Chang Nakagami CD-ROM IEEE,, 15 -

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