© Urban & Fischer Verlag http://www.urbanfischer.de/journals/aeue Sequence Estimation with Transmit Diversity for Wireless Communications * Erdal Panayırcı, Ümit Aygölü, and Ali Emre Pusane Abstract: In this paper, an optimum sequence estimation algo- rithm for wireless systems with Alamouti’s two transmitter di- versity in the presence of multipath fading is proposed. The al- gorithm is based on a jointly iterative channel and sequence es- timation according to the maximum likelihood (ML) criterion, using the Expectation-Maximization (EM) algorithm employing an M-level phase-shift keying (M-PSK) modulation scheme with addi- tive Gaussian noise. The discrete multipath channel is represented in terms of the channel gains from each transmit antenna to the receive antenna. EM algorithm estimates jointly the complex chan- nel parameters of each channel and the data sequence transmitted, iteratively, which converges to the true ML solution. The chan- nel estimation is achieved in a simple way through the iterative equations by decoupling of the signals transmitted from different antennas. The algorithm is applied to the trellis coded modula- tion systems and the efficiency of the algorithm proposed has been shown with computer simulations. The simulation results show that the EM algorithm converges quickly for fast fading channels. The performance of the EM-based decoder approaches that of the ML receiver which has perfect knowledge of the channel. Keywords: Sequence estimation, Transmit diversity, EM algo- rithm, Multipath fading channels 1. Introduction Transmitter diversity is an effective technique for com- bating fading in multipath wireless channels. It has been observed recently that transmitter (spatial) diversity may be the only option when the frequency and time diver- sity techniques are not always available. For instance, frequency diversity cannot be achieved in a frequency non-selective channel, and in a slow fading channel, ei- ther time diversity is not effective, or significant delays must be introduced to achieve it because of the required large interleaver size. Transmit diversity has been studied only recently to reduce the detrimental effects in wireless Received September 2, 2002. Revised March 13, 2003. E. Panayırcı, Department of Electronics Engineering, I¸ sık Univer- sity, Maslak, 80670, Istanbul, Turkey. E-mail: eepanay@isikun.edu.tr Ü. Aygölü, Faculty of Electrical and Electronics Engineering, Istan- bul Technical University, Maslak, 80626, Istanbul, Turkey. A. E. Pusane, Department of Electrical Engineering, University of Notre Dame, Notre Dame, 46556, IN, U.S.A. Correspondence to: E. Panayırcı. * This work was supported by the Scientific and Technical Research Council of Turkey under grant no 100E006. fading channels because of its relative simplicity of imple- mentation and feasibility of having multiple antennas at the base stations. Several transmit diversity techniques were studied ex- tensively in the past. Wittneben [1] proposed the first bandwidth efficient transmit scheme and subsequently, a delay diversity scheme was introduced by Seshadri and Winters, [2]. More recently, space-time trellis coding has been proposed by Tarokh, Seshadri and Calderbank [3] which combines signal processing at the receiver with coding techniques appropriate to multiple transmit anten- nas. These so-called space-time codes perform well in slowly-fading channels, assuming perfect channel infor- mation(CSI) at the receiver. With the presence of channel mismatch, however, system performance suffers a signifi- cant degradation. Recently, Alamouti proposed a remarkable transmit diversity scheme for transmission using two transmit antennas, [4]. This scheme has been generalized later in [5, 6] to an arbitrary number of transmit antennas and is thus able to achieve the full diversity promised by the transmit and receive antennas. Assuming that the channel state information is somehow available, the orth- ogonal structure of these space-time block codes enables the ML decoding to be implemented in a simple way through decoupling of the signal transmitted from dif- ferent antennas rather than by joint detection. However, channel state information is usually difficult to obtain. In the absence of perfect channel state information, evalua- tion of the ML function requires the expectation over the joint statistics of the channel fading coefficients, which is usually mathematically intractable. To cope with this technical difficulty, in this paper, we apply the method of Georghiades and Han [7] to the sequence estimation in the presence of multipath fading channels for wire- less systems with two-transmitter diversity. The algorithm is based on a jointly iterative channel and sequence es- timation according to the ML criterion, using the EM algorithm, [8–10]. The last part of the paper provides simulation results on the convergence of the EM algo- rithm. The performance is presented in terms of the bit error rate for a system employing trellis coded 8-PSK signaling. The extensive computer simulations show that a formulation of the sequence estimation based on the EM algorithm is a promising technique for highly efficient data transmission over mobile wireless channels, and it performs close to the performance of a maximum likeli- hood decoder that assumes perfect CSI. The paper is organized in four sections following this introduction. In Section 2, the system model is introduced, Int. J. Electron. Commun. (AE ¨ U) 57 (2003) No. 5, 309-316 1434-8411/03/57/05-309 $15.00/0