On the distribution of the weighted sum of L independent Rician and Nakagami envelopes in the presence of AWGN

An alternative, unified, semi-analytical approach for the evaluation of the cumulative distribution function (cdf) of the weighted sum of L independent Rician (or Rayleigh as a special case) and m-Nakagami envelopes with or without the presence of Additive White Gaussian Noise (AWGN) is presented. The cdf is evaluated directly in a nested mode via the Hermite numerical integration technique. The proposed formulation avoids the calculation of complex functions and can be efficiently applied to practical wireless applications when L ≤ 3, using arbitrary statistical characteristics for the modeling parameters. Moreover, it can be also used to control the accuracy of other techniques when L > 3. Comments, comparison with other existing techniques and useful curves for several practical wireless applications such as the calculation of the error bounds for coding on fading channels in mobile satellite applications and the Equal Gain Combining (EGC), are also presented. Finally, the relation between the distribution of the sum of m-Nakagami and Rice envelopes is investigated and discussed.