In this paper, performance of the Alamouti space- time code (STC) [1] and performance of the concatenation between the convolutional code and the Alamouti STC are derived. In order to describe realistic performance issues, we assume that the channel estimates are calculated from linear filters using noisy pilot symbols. We also assume non-quasi- static channels, spatially correlated transmit antennas and finite- depth interleaving. Two types of receivers are investigated for the Alamouti STC, namely, the linear-combining space-time decoder (LC-STD) and the maximum-likelihood space-time decoder (ML- STD). Two types of receivers are investigated for the concatenated system, namely, the LC-STD with the ML convolutional decoder and the joint Alamouti and convolutional ML decoder. The results have shown that the LC-STD is more sensitive to the Doppler spread than the ML-STD. However, since the ML- STD is very sensitive to the channel estimation error, the gains provided by the decoder in fast fading channels will be offset unless an optimized channel estimator is employed. Performance comparisons between the Alamouti systems and the SISO systems indicate that, when the system environment is not ideal, the SISO systems may outperform the Alamouti systems. Lastly, analytical results are compared with simulation results to illustrate the accuracy of the analysis.

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.

In this paper, closed-form expressions of the bit error probability of closed-loop transmit diversity (CLTD) schemes with two transmit antennas and noisy channel estimates in time-varying Rayleigh fading channels are derived. Two CLTD schemes considered are the phase-only CLTD (PO-CLTD), where the transmit antennas transmit with the same power, and the phase-amplitude CLTD (PA-CLTD), where the transmit antennas can transmit with different powers. The results have indicated that, with the same channel estimation accuracy, PA-CLTD generally performs slightly better than PO-CLTD. We have also compared the performance of PA-CLTD with the performance of a system without transmit diversity and the performance of a system with the Alamouti space-time code employing the linear-combining decoder. The results have illustrated that, PA-CLTD is outperformed by the other two systems when the pilot SNR is very small and the Doppler spread is large.

In this paper, we derive the Chernoff bound of the pairwise error probability (PEP) and the exact PEP of convolutional codes in a time-varying Rician fading channel. With the assumptions that the channel estimator is a finite impulse response filter and the interleaving depth is finite, we are able to investigate the estimation-diversity tradeoff resulting from the effects of the Doppler spread on the system performance, via the channel estimation accuracy and the channel diversity. In addition, we verify that, in the special case when the pilot signal-to-noise ratio is infinitely large and the channel estimator is well-designed, our analysis leads to the same result as the existing perfect channel-state information analysis. 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.

In this paper, we derive the Chernoff bound of the pairwise error probability (PEP) and the exact PEP of convolutional codes in a time-varying Rician fading channel. With the assumptions that the channel estimator is a finite impulse response filter and the interleaving depth is finite, we are able to investigate the estimation-diversity tradeoff resulting from the effects of the Doppler spread on the system performance via the channel-estimation accuracy and the channel diversity. In addition, we verify that, in the special case when the pilot signal-to-noise ratio is infinitely large and the channel estimator is well-designed, our analysis leads to the same result as the existing perfect channel-state information analysis. 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

In this paper, we derive the theoretical performance of the Alamouti space-time code in time-varying Rayleigh fading channels with noisy channel estimates. The receiver algorithms presented in this paper are the maximum-likelihood (ML) symbol detector with the linear combining scheme, which was suggested by Alamouti (1998), and the ML space-time decoder. The bit error probability for the linear combining scheme and the sequence error probability for the ML space-time decoder are presented as functions of the pilot filter coefficients, the multipath power profile, the normalized Doppler frequency, the pilot SNR and the data SNR. We also compare the bit error performance of the linear combining scheme with the bit error performance of the system without transmit diversity. The results indicate that the Alamouti space-time code with the linear combining scheme is outperformed by the no transmit diversity system at high Doppler frequency or low pilot SNR.

The reduction in the average required transmit power in order to achieve the desired system performance is determined when using a receive antenna array employing polarization diversity as opposed to spatial diversity only. Cross-polar-discrimination (XPD) and envelope correlation are used to model the correlation between the horizontal and vertical polarizations. The characteristic function for an M-branch diversity receiver, using maximal-ratio-combining, is used to obtain the analytical expressions for the average required transmit power, assuming Rayleigh fading channels, perfect channel information at the transmitter and the receiver, and perfect fast or average power control. Based on the measurement data of XPD and envelope correlation in an urban environment, two spatially separated dual-polarized antennas are shown to outperform two spatially separated vertical antennas between 2.25-2.4 dB and 4-4.3 dB for the perfect fast power control and the perfect average power control, respectively.