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The computation of the block-error rate on a Rayleigh-fading channel in the presence of additive white Gaussian noise Maranda, Brian Howard

Abstract

The problem of computing the probability P[sub f](M,N) of more than M bit errors in a block of N bits for a Rayleigh-fading channel in the presence of additive white Gaussian noise is considered. In the case of very slow Rayleigh fading, analytical formulas for P[sub f](M,N) have been derived in the literature, but these formulas are not well suited for numerical computation. Several simple approximations for the special case P[sub f](O,N) have also appeared in the literature, but apparently no work has been done for the case M > 0. In this thesis an accurate approximation for P[sub f](M,N) is derived, and a bound on the error in this approximation is given. Also included are approximations for P[sub f](M,N) when selection diversity is employed. If very slow fading is not assumed, there exist no known analytical methods for the computation of the block-error probability. Simulations are performed on a digital computer for this case. Furthermore, an empirical formula is derived that can be used to estimate easily and accurately the output of the simulator. The consequence is a great saving of time and effort in the computation of a value of P[sub f](M,N) that is more realistic than that provided under the assumption of very slow fading.

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