Dual diversity over correlated log-normal fading channels

A great deal of attention has been devoted in the literature to studying the bit error rate (BER) performance of diversity combining systems in the presence of Rayleigh, Rice, and Nagakami-m fading. By comparison, the literature is relatively sparse in comparable analyses over log-normal channels which typically characterize shadowing from indoor obstacles and moving human bodies. One reason for this disparity stems from the difficulty in evaluating the exact average BER when log-normal variates are involved, using, for example, the moment-generating function (MGF) approach, due to the inability of expressing the MGF itself in a simple closed form. Since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function (CDF) associated with a log-normal distribution in closed form, we rather focus here on other performance measures, namely, average combined output signal-to-noise ratio, amount of fading, and outage probability. The first two performance measures depend only on the moments, whereas the outage probability depends solely on the cdf. Closed-form expressions (in terms of known functions), single-integral representations, or upper and lower bounds are obtained for these measures corresponding to maximal-ratio combining, selection combining, and switch-and-stay combining schemes, allowing for the possibility of correlation between the two branches. Numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented.