Gaussian Class Multivariate alpha - mu Distribution: Theory and Applications over Correlated Fading Channels

Novel expressions for the multivariate probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of arbitrarily correlated and unbalanced α - μ fading channels are derived. The derived expressions are expressed in terms of well known functions which are available in common mathematical software. The new results are then used to derive the MGF of the signal-to-noise ratio (SNR) at the equal gain combiner (EGC) output. For such a scenario, the derived MGF of the SNR at the EGC output is used directly to evaluate the average bit error probability for differential quadrature phase shift keying (DQPSK) signals, with postdetection diversity reception and combining over additive white Gaussian noise and slow nonselective arbitrarily correlated and unbalanced α - μ fading channels.