An Accurate Simple Approximation to the Double-Nakagami (Generalized-K) Fading Channels

The double-scattering channel model is known to constitute an accurate representation of rank-deficiency (i.e. keyhole) in multiple-input multiple-output (MIMO) channels. The double-Nakagami channel is a general case of the double-scattering model. In this paper, a simple and accurate approximate probability density function (PDF) is proposed for double-Nakagami fading based on Hankel's expression, which is found to be accurate for a wide range of the Nakagami parameters through the Kolmogorov-Smirnov test. Moreover, a new approximate PDF is deduced for the generalized-K distribution, as a sum of weighted generalized Gamma functions. The proposed approximation allows a tractable performance analysis for MIMO systems. Closed-form symbol error rate approximation expressions are also derived for multi-branch maximal ratio combining reception.