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UBC Theses and Dissertations

Optimal weighted partial decision combining for fading channel diversity Kot, Alan Douglas


A diversity combining scheme is examined that utilizes a demodulator's hard decisions in conjunction with knowledge of each decision's reliability. A maximum-likelihood bit decision is made, based on these partial decisions from the demodulator and on measurements of the state of the fading channel. The technique is sub-optimal since hard decisions are processed, but it may find application in low cost receiver design. The technique is optimal in the sense that a minimum probability of bit error is achieved, given a set of partial decisions and knowledge of their reliability. Performance analysis for the case of non-coherent frequency shift keying on a slow Rayleigh fading channel with additive white Gaussian noise includes the derivation of a tight upper bound on the probability of bit error, and estimates of the asymptotic performance relative to standard diversity schemes such as majority-voting, selection diversity, square-law, and maximal ratio combining. These results are supported by simulation results for bit and packet error rates in an example system. With five independent bit repeats and a BER of 10⁻³, the receiver is about 3 dB more efficient than majority-voting, and about 1 dB more efficient than selection diversity. The gain in efficiency, relative to the standard partial decision combination schemes, increases with the number of repeats. The degradation in performance in a practical receiver implementation is addressed, and it is demonstrated that near ideal performance may be obtained with only a few reliability weights quantized to a small number of levels. Furthermore, this performance is maintained over a wide range of average signal to noise ratio without having to adapt the reliability weights. When the reliability estimate is corrupted by additive white Gaussian noise, it is demonstrated that simple low- pass filtering of the signal strength estimate is sufficient to obtain near ideal performance. The performance is degraded in the presence of cochannel interference, but for a moderate level of interference the performance is demonstrated to be superior to majority-voting or selection diversity. Other results include a method to estimate the optimal quantization thresholds, and a method to obtain the probability of error of selection diversity receivers employing signal to noise ratio measurement quantization. The selection diversity analysis is applicable to the more general case of Rician fading.

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