On the Performance of Closed-Loop Transmit Diversity with Noisy Channel Estimates and Finite-Depth Interleaved Convolutional Codes

In this paper, closed-form expressions for the uncoded bit error probability of closed-loop transmit diversity (CLTD) algorithms with two transmit and one receive antennas and noisy channel state information (CSI) in time-varying Rayleigh fading channels are derived. Two CLTD algorithms considered are the phase-amplitude CLTD (PA-CLTD), where the transmit antennas may transmit with different signal energy, and the phase-only CLTD (PO-CLTD), where the transmit antennas must transmit with the same signal energy. In addition to the uncoded bit error probability, this paper also derives the pairwise error probability when finite-depth interleaved convolutional codes are used with CLTD algorithms. However, due to the complexity of the coded system, the pairwise error probabilities are not in the closed-form expressions. The results have shown that PA-CLTD performs slightly better than PO-CLTD although PA-CLTD requires significantly more feedback information and that, when the Doppler spread is large, the performance of CLTD algorithms may degrade significantly. Moreover, a comparison between PA-CLTD, the Alamouti space-time code and the SISO system indicates that PA-CLTD outperforms the other two systems when the Doppler spread is small and the pilot SNR is large. Finally, the analytical results are compared with results from Monte Carlo simulation and the comparison shows that the analytical results match well with the simulation results.