General PDF for the signal envelope in multipath fading channels using Laguerre polynomials

Multipath fading usually degrades the performance of communication systems, severely. To describe this random phenomenon, it is necessary to derive expressions for the PDF of the received signal envelope in multipath fading channels. In this paper, two expansions for the envelope PDF's are derived under general channel characteristics: an infinite power series and an infinite Laguerre series. Uniform upper bounds are derived for the truncation errors of these two infinite series. Moreover, these uniform upper bounds are minimized using a free parameter β, defined consciously. It has also been shown that the Laguerre series is superior to the power series, in the sense that for a fixed number of terms, it yields less truncation error. Based on an extensive literature survey, reported partly in the paper, it seems that such closed form expressions for the envelope PDF has not been derived previously, under the general conditions considered here.