PERFORMANCE OF CONVOLUTIONAL CODING AND VITERBI DECODING ON THE SLOW NON-SELECTIVE RAYLEIGH FADING CHANNEL WITH DIVERSITY RECEPTION

Abstract

We consider a convolutionally coded sequence of equiprobable digital data transmitted using PSK modulation over L independent additive white Gaussian noise (AWGN) channels with slow non-selective Rayleigh fading. Assuming block interleaving/de-interleaving at the two ends of the channel and diversity reception, the sequence estimation (SE) problem is to determine the transmitted sequence with minimum sequence error probability. In this thesis, we present a solution to the SE problem by proposing a two-stage receiver in which the random complex channel fading process is estimated with the aid of a symbol-by-symbol (SBS) receiver in the first-stage prior to data sequence estimation in the second-stage. The receiver can be shown to be partially coherent, with perfect coherence being achieved asymptotically in the limit of perfect estimation of the fading process. This receiver is shown to perform adequately, and leads to an efficient receiver-decoders for Viterbi decoding of convolutionally /trellis-coded sequences. The bit error probability of the receiver-decoders is analyzed for the case of BPSK and QPSK modulations, respectively. For illustration purposes, numerical performance results are presented for the case of a rate-1/2 constraint length-3 convolutional code and a Markov model for the channel fading process. Simulation studies are carried out to evaluate the impact of the interleaver size on error performance and to determine the actual performance of the receiver-decoders in the presence of decision errors in the first-stage SBS receiver which affects the estimation of the complex channel fading process.