Application of the Dirichlet transformation to the performance evaluation of generalized selection combining over Nakagami-m fading channels

Abstract

The Dirichlet transformation may be used to simplify certain multiple integrals which occur in the distribution theory of ordered gamma random variables. The evaluation of the average error rate performance of generalized selection combining receivers for digital signals transmitted over Nakagami-m channels involves just such a multiple integral and thus is a perfect application for the transformation. A well-structured procedure for obtaining the average error rate in a simple form suitable for numerical evaluation is presented for the generic problem of selection combining L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> (≤ L) out of L received paths and specific results are presented for a number of examples both numerically and as simple closed form expressions. As a byproduct of the general results, some interesting closed form expressions are presented for certain single and multiple definite integrals which heretofore appear not to have been tabulated.