Error Probability and Capacity Performance Analysis over Composite Cascade Channels of Relay Networks

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The application of the relay networks enlarges the communication area and improves the transmission. However, the price is the increasing system complexity, which makes the performance analysis of the corresponding channel a more challenging task. To this end, we develop the probability density function (PDF) of the composite cascade channel, and later analyze the outage probability (OP), the bit error rate (BER), and the ergodic capacity over this channel. Firstly, the exact PDF of the small-scale cascade channel, which is combined by several independent and identically distributed (i.i.d.) Rayleigh/Nakagami-m channels, is derived. Then, considering the large-scale and the lognormal distributed shadow, the PDF of the composite cascade channel, following the OP, the BER, and the ergodic capacity performance under the optimal selection combining (OSC) and the maximal ratio combining (MRC) schemes are also deduced. Furthermore, in order to obtain the asymptotic lines of the BER and the ergodic capacity performance, the mixture gamma distribution is exploited. The closed-form expressions for these two kinds of asymptotic lines, both under the OSC and the MRC schemes, are proposed. The numerical simulations confirm that the proposed expressions fit well with the Monte-Carlo results.