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

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