Analysis of the Level Crossing Rates for Ordered Random Processes

Given n independent but not necessarily identical random processes, this paper investigates the general problem of determining how frequently, on average, any given process becomes at least the p-th (p = 1, 2, . . . , n - 1) largest among all processes. This problem requires determining the level crossing rate (LCR) of a carefully defined ordered process, which we solve by developing a general mathematical framework based on the theory of permanents. Our results are very general and may be applicable for a wide range of engineering applications which involve ordered random processes. To demonstrate the applicability to wireless communications, we present closed-form formulas for the LCR for the case where the processes correspond to time-varying Rayleigh fading channels, and use these to characterize the required switching rate for a particular branch of a generalized selection combining diversity receiver.