This paper is concerned with the largest eigenvalue of the Wishart-type random matrix W=XX† (or W=X†X ), where 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 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.
Moreno-Pozas, L., Morales-Jimenez, D., McKay, M. R., & Martos-Naya, E. (2018). Largest Eigenvalue Distribution of Noncircularly-symmetric Wishart-type Matrices with Application to Hoyt-faded MIMO Communications. IEEE Transactions on Vehicular Technology, 67(3), 2756-2760. https://doi.org/10.1109/TVT.2017.2737718