Performance analysis of hybrid ARQ with code combining over interleaved Rayleigh fading channel

In this paper, an approximate method is proposed to derive the probability density function of the sum's power of multiple independent fading random variables. It is revealed that the product of two independent Rayleigh distributed random variables could be approximated by a sum of two Gamma variables. Moreover, by employing the proposed analysis, the same approximation could be derived as that of the Nakagami approximation when the involved variables' statistical moments are the same. Then the approximate analysis is utilized to obtain the performance estimate of hybrid automatic repeat request with code combining over the ideally interleaved Rayleigh fading channel. Both the lower and upper estimates of pairwise error probability are derived to enable suitable performance evaluation, and are validated by both the numerical and simulation results. In addition, it is shown that the previous known reliability estimate of the forward error correction scheme could be regarded as a special case of the performance estimates derived in this paper.