Second order statistics for maximal-ratio combining in unbalanced Nakagami channels

Previous studies on the second statistics, that is, level crossing rates (LCR) and average fade durations (AFD), of maximum ratio combining for uncorrelated Nakagami channels assume identical diversity branches. This assumption rarely holds in the real systems. In this paper, we derive closed-form expressions of the LCR and AFD for a general case of independent diversity branches with unequal average signal powers. Our analysis reveals that unbalance in the diversity branches acts as if there were correlations among them. Simulation results demonstrate that larger LCR and AFD are resulted when the unbalance exists among the diversity branches. Furthermore, the effects of the decay rate, the fading severity, and the total number of unbalanced diversity branches on the LCR and AFD are discussed.