  Prior asymptotic performance analyses are based on the series expansion of
the moment-generating function (MGF) or the probability density function (PDF)
of channel coefficients. However, these techniques fail for lognormal fading
channels because the Taylor series of the PDF of a lognormal random variable is
zero at the origin and the MGF does not have an explicit form. Although
lognormal fading model has been widely applied in wireless communications and
free-space optical communications, few analytical tools are available to
provide elegant performance expressions for correlated lognormal channels. In
this work, we propose a novel framework to analyze the asymptotic outage
probabilities of selection combining (SC), equal-gain combining (EGC) and
maximum-ratio combining (MRC) over equally correlated lognormal fading
channels. Based on these closed-form results, we reveal the followings: i) the
outage probability of EGC or MRC becomes an infinitely small quantity compared
to that of SC at large signal-to-noise ratio (SNR); ii) channel correlation can
result in an infinite performance loss at large SNR. More importantly, the
analyses reveal insights into the long-standing problem of performance analyses
over correlated lognormal channels at high SNR, and circumvent the
time-consuming Monte Carlo simulation and numerical integration.
