A Revisit to Chiani’s Framework and Identity With Applications to Hoyt Faded MIMO and Beyond

This correspondence studies the marginal eigenvalue distribution for a random ensemble generated by non-circularly-symmetric complex Gaussian matrices and termed the crossover between Laguerre orthogonal and unitary ensembles. We propose a new derivation approach that utilizes a framework for the marginalization, an identity for the integration, both developed by Chiani
et al.
, and a reformulation proposed by Ordóñez
et al.
We obtain a unified expression on the marginal probability density function of any subset of the ordered eigenvalues. That expression not only extends Moreno-Pozas’s result on the largest eigenvalue, but also enlarges the scope of possible applications. As illustrative examples, we then apply the one-point marginal to evaluating the error rate of a Hoyt faded communication system that employs multiple-input multiple-output (MIMO) eigen-mode transmission, and also apply the multi-point marginal to deriving a new PDF for the energy-level spacings of a heavy nucleus in nuclear physics.