A New Look at the $\eta$-$\mu$ Fading Model

In this paper, the
$\eta$
-
$\mu$
fading model is looked at with a unifying perspective, through which correlation and power imbalance between its quadrature processes are simultaneously taken into account. It is formally shown that these two phenomena, quantified by two respective parameters, do not alter the resulting envelope statistics but have a great impact on the corresponding phase. To this end, an exact, simple, closed-form formulation is found that maps these parameters into a resulting
$\eta$
parameter that keeps the envelope probability density function (PDF) unaltered. An exact formulation is also found for the phase PDF, given in easily computable infinite series. Closed-form approximation for such a PDF is also found that yields excellent results as compared with the exact one. As a particular case of the general phase formulation, the phase of the Hoyt process is extended to include power imbalance and correlation, and this is given in simple closed-form. Additionally, and as a by-product, some useful mathematical identities are obtained.