Largest eigenvalue distribution of noncircularly symmetric Wishart-type matrices with application to Hoyt-faded MIMO communications

Abstract

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.