Approximate distribution of log2(A + x2)

This study concerns the approximate distribution of the random variable log₂(A + χ²) and its applications in the performance analysis of communication systems where A is 0 or 1 and χ² a chi-square distributed random variable. The authors prove that log₂(A + χ²) is approximately Gaussian distributed and derive the expressions of the mean and variance of the approximate distribution. The approximate Gaussian distribution provides a new way to simplify the derivation of performance metrics and obtain analytical results. Then the authors utilise the approximate results in two applications, which are the approximation of the Gaussian Q-function and capacity analysis, respectively. For one thing, the approximate distribution can be explored to deduce a new approximate equivalent expression of the Q-function on the basis of which an accurate approximation of the Gaussian Q-function can be developed. For another, the approximate Gaussian distribution provides an intuitive approach to analyse the channel capacity of Rayleigh-fading multiple antenna systems. The approximate statistical distributions of the channel capacities of orthogonal space-time block codes, single-input multiple-output, multiple-input single-output, transmit antenna selection with maximal-ratio combining and multiple-input multiple-output systems are presented. The applicability of the approximate distribution can be demonstrated through simulation results in both applications.