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In this paper, impact of mismatch in the estimation of Signal-to-Noise Ratio (SNR) on the performance of MAP detector is studied. Among all possible receivers, individually optimum receiver (symbol-by-symbol MAP detector) gives the minimum probability of bit error. However, as compared to other detectors, MAP detector needs knowledge of SNR at the receiver. Performance of MAP detector degrades with mismatch in SNR estimation at the receiver. The authors have shown that the behavior of bit error probability of MAP detector with the estimated noise variance, for any kind of mixture of data, instantaneous or convolutive, is piece-wise monotonic in the sense that it has one global minima.
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