An accurate BER bound for linear-combining-based decoders in decode-and-forward relay channels

For a decode-and-forward (DF) relay network, it is typically assumed that the destination adopts a decoder based on maximal-ratio combining (MRC) or its variant. However, due to the presence of error propagation from the relay, an accurate error performance analysis of such decoders is still unavailable. By taking decoding errors at the relay into consideration, we derive an analytical upper bound on the bit error rate (BER) of the linear-combining-based decoders for DF relay channels. We show that this upper bound can be calculated by the cumulative distribution function (CDF) of a multivariate normal distribution for which all the elements are negative. Based on this analytical BER upper bound, the improved combining weighting factors can be calculated. Simplification of the BER upper bound has also been derived under some conditions. Numerical results demonstrate a close agreement between our analytical results and the simulations.