On the Use of High-Order Moment Matching to Approximate the Generalized-k Distribution by a Gamma Distribution

Composite fading takes place in several communication channels due to the random variations of the local average power of the received multipath-faded signal. The generalized-K (gamma-gamma) probability density function (PDF) has been proposed recently to model composite fading in wireless channels. However, further derivations using the generalized-K PDF have shown to be quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-K PDF by a gamma PDF using the moment matching method is explored. As expected, matching positive and negative moments leads to a better approximation in the upper and lower tail regions, respectively. However, due to arising limitations for small values of the multipath fading and shadowing parameters, and the higher level of accuracy sought, the use of an adjustable form for the expressions of the approximating gamma PDF parameters, obtained by matching the first two positive moments, is devised. The optimal values of the adjustment factor for different integer and non-integer values of the fading and shadowing parameters are given. The introduced approximation may simplify performance analysis in distributed antenna systems (DASs), network MIMO, multihop relay networks, radar, and sonar systems.