Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals and Their Applications to Statistical Analysis of Wireless Systems

Abstract

We present tight yet tractable approximations and 1 bounds for the ergodic capacity of any communication system 2 in the form of a weighted sum of logarithmic functions, with 3 the focus on the Nakagami and lognormal distributions that 4 represent key building blocks for more complicated systems. 5 A minimax optimization technique is developed to derive their 6 coefficients resulting in uniform absolute or relative error. These 7 approximations and bounds constitute a powerful tool for the 8 statistical performance analysis as they enable the evaluation 9 of the ergodic capacity of various communication systems that 10 experience small-scale fading together with the lognormal shad-11 owing effect and allow for simplifying the complicated integrals 12 encountered when evaluating the ergodic capacity in different 13 communication scenarios. Simple and tight closed-form solutions 14 for the ergodic capacity of many classic and timely application 15 examples are derived using the logarithmic approximations. The 16 high accuracy of the proposed approximations is verified by 17 numerical comparisons with existing approximations and with 18 those obtained directly from numerical integration methods.19