Tight approximation of bit error probability for L-diversity non-coherent M-ary FSK frequency hopping system with binary convolutional code and soft Viterbi decoder: diversity, bit interleaver size and Reed-Solomon outer code effects analysis on receiver performance for M=8

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A tight approximation of a bit error probability analysis is derived for a L-diversity non-coherent 8-ary FSK frequency hopping system with binary convolutional code and soft Viterbi decoder. For this, we compare a traditional coded 8FSK receiver using a binary Viterbi decoder with the optimal decoder based on the maximum likelihood (ML) criterion. For this ML decoder (MLD) receiver, bit error probability is written as an expression depending on the pairwise 8FSK symbol error probability, and new codeword spectrum c'(d). We analyze the behavior of these receivers: a conventional receiver with Viterbi decoder and a MLD decoder receiver, versus L-diversity and concatenated code, when a bit interleaver is present or not. We show that bit error probability is very similar for these two receivers when the interleaver is present. We then deduce an analytical expression giving the exact behavior of traditional and AGC 8FSK receiver with concatenated code and soft Viterbi decoder under Gaussian noise and partial-band noise jamming.