A useful lemma for bit error rate of the noise imbalanced MRC combining over correlated and uncorrelated fading channels

In the literature, much attention has been devoted to the analysis of maximal-ratio combining (MRC) whose diversity branches are subjected to the balanced noise levels. However, this paper considers the noise imbalanced MRC (NI-MRC), i.e., the multi-branch MRC whose diversity branches are together subjected to some significant imbalance of noise levels due to the estimation error of the noise power knowledges used to maximize combining the signals from diversity branches. To the best of our knowledge, this paper proposes the first analytical approach in the literature to exactly evaluate the bit error rate (BER) of binary modulation schemes over either correlated or uncorrelated fading channels. Based on moment generating function (MGF), the proposed approach is exemplified for the well-known correlated fading conditions, and verified by computer based simulations to elucidate the effect of noise imbalance (NI) on the BER performance.