Largest Eigenvalue Distribution of Noncircularly Symmetric Wishart-Type Matrices With Application to Hoyt-Faded MIMO Communications - Moreno-Pozas, Laureano; Morales-Jimenez, David; McKay, Matthew R.; Martos-Naya, Eduardo (IEEE transactions on vehicular technology, 2018)
This paper is concerned with the largest eigenvalue of the Wishart-type random matrix \mathbf {W}=\mathbf {X}\mathbf {X}^\dagger (or \mathbf {W}=\mathbf {X}^\dagger \mathbf {X} ), where \mathbf {X} is a complex Gaussian matrix with unequal variances in the real and imaginary parts of its entries, i.e., X belongs to the noncircularly symmetric Gaussian subclass. By establishing a novel connection with the well-known complex Wishart ensemble, we here derive exact and asymptotic expressions for the largest eigenvalue distribution of \mathbf {W} , which provide new insights on the effect of the real-imaginary variance imbalance of the entries of X . These new results are then leveraged to analyze the outage performance of multiantenna systems with maximal ratio combining subject to Nakagami- q (Hoyt) fading.