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Effect of noisy channel estimates on the performance of convolutionally coded systems with transmit diversity

  • Author(s): Jootar, Jittra
  • et al.
Abstract

This dissertation focuses on the effect of noisy channel estimates on the performance of finite-depth convolutionally coded system with different types of transmit diversity algorithms. Three transmit diversity algorithms analyzed are no transmit diversity, the Alamouti space-time code and the closed-loop transmit diversity.

The dissertation begins with the derivation of the theoretical pairwise error probability of a finite-depth convolutionally coded system without transmit diversity assuming that channel estimates are calculated by an FIR filter from noisy channel estimates. With the assumptions that an FIR filter is used as the channel estimator and the interleaving depth is finite, 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 can be investigated. In addition, this section also verifies that, in the limit when the channel estimates are perfect, the result presented in this dissertation is the same as the well-known result derived from a different mathematical approach. To verify the analysis, 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.

The dissertation continues with the analysis of the Alamouti space-time code with and without convolutional codes in time-varying fading channels also assuming that channel estimates are noisy. Two types of receivers are investigated for the conventional Alamouti space-time code without convolutional codes, 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. A comparison between the analytical results and the simulation results shows that the analysis can predict the simulation results accurately.

Finally, the closed-loop transmit diversity analyses are presented. The closed-form expressions for the uncoded bit error probability of closed-loop transmit diversity algorithms with two transmit antennas and noisy channel estimates in time- varying Rayleigh fading channels are derived. Two closed- loop transmit diversity algorithms considered are the phase-amplitude closed-loop transmit diversity (PA-CLTD), where the transmit antennas may transmit with different signal energy, and the phase-only closed-loop transmit diversity (PO-CLTD), where the transmit antennas must transmit with the same signal energy. The results have shown that PA-CLTD performs slightly better than PO-CLTD although PA-CLTD requires significantly more feedback information. 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. In addition to the uncoded bit error probability, this dissertation also derives the pairwise error probability when finite-depth interleaved convolutional codes are used with the closed-loop transmit diversity algorithms with two transmit antennas and noisy channel estimates in time- varying Rayleigh fading channels are derived. Two closed- loop transmit diversity algorithms considered are the phase-amplitude closed-loop transmit diversity (PA-CLTD), where the transmit antennas may transmit with different signal energy, and the phase-only closed-loop transmit diversity (PO-CLTD), where the transmit antennas must transmit with the same signal energy. The results have shown that PA-CLTD performs slightly better than PO-CLTD although PA-CLTD requires significantly more feedback information. 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. In addition to the uncoded bit error probability, this dissertation also derives the pairwise error probability when finite-depth interleaved convolutional codes are used with the closed-loop transmit diversity algorithms. The analytical results show that, when the Doppler spread is large, the performance of the closed-loop transmit diversity may degrade significantly. 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.

This work was done at UCSD's California Institute for Telecommunications and Information Technology (CalIT2), under the Core Grant No. 02-10109 sponsored by Ericsson and the U.S. Army Research Office under the Multi University Initiative (MURI) grant No. W911NF-04-1-0224

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