Downlink Signal-to-Interference Ratio and Spectral Efficiency of MIMO Cellular Networks Using Truncated Lognormal Approximation

This work focuses on analytical performance evaluation of a multiple-input multiple-output (MIMO) multicellular radio access network, while taking into account distance-dependent path loss, lognormal-distributed shadowing, and Rayleigh-distributed multipath fading. We propose a truncated moment-matching method for approximating the distribution of the sum of independent lognormal random variables in order to model the statistical behavior of the downlink signal-to-interference ratio (SIR) experienced by user equipment at a particular location in the presence of cochannel interference. The proposed method offers a good match with the simulated results in terms of the downlink SIR as well as mean and outage spectral efficiency for various MIMO schemes such as transmit and receive diversity, closed- and open-loop spatial diversity, and closed-loop multiuser MIMO. We compare the semianalytical results with that obtained from Monte Carlo simulations and quantify the relative error in terms of statistical metrics such as Kullback-Leibler divergence and Kolmogorov-Smirnov distance. In contrast to the existing works, the proposed model is useful for a wide range of shadowing standard deviation (4-12 dB) and activity of neighboring base stations (0.4-1). Moreover, the presented method is shown to achieve a comparable accuracy with the state of the art in spite of being less time consuming.