Kolmogorov-Smirnov Criterion-Based Gamma Approximation for Lognormal Shadowing Models

Zhongli Wang, Shuping Dang, Haiqiang Chen, Chengzhong Li, Raed M. Shubair

Abstract: To promote the applications of gamma approximation for lognormal shadowing models in a multitude of applications, we propose to use the Kolmogorov-Smirnov (K-S) criterion to enable channel parameter mapping in this letter. The resulting K-S criterion based lognormal-to-gamma channel model substitution (CMS) technique aims to provide statistically robust parameter mapping relations by minimizing the integrated squared error (ISE) between the original lognormal shadowing model and its gamma substitute. We study the ISE minimization problem in depth for this lognormal-to-gamma CMS technique and for the first time prove its convexity with respect to both the scale and shape parameters of the gamma substitute. Therefore, we can employ numerical optimization methods to solve the ISE minimization problem with the assured convergence and optimality. Numerical results presented in this letter verify the effectiveness and efficiency of the K-S criterion based lognormal-to-gamma CMS technique in comparison with those based on the moment matching (MM) and Kullback-Leibler (K-L) criteria.