Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems

• Published in: IEEE journal on selected areas in communications Vol. 21; no. 3; pp. 418 - 426
• Main Authors: Ming Kang, Alouini, M.-S.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Array signal processing; Channels; Closed-form solution; Computer simulation; Diversity reception; Eigenvalues; Eigenvalues and eigenfunctions; Mathematical analysis; Mathematical models; Matrices; MIMO; Monte Carlo methods; Performance analysis; Probability; Rayleigh channels; Receiving antennas; Studies; Transmitting antennas
• ISSN: 0733-8716; 1558-0008
• DOI: 10.1109/JSAC.2003.809720

This paper extends Khatri (1964, 1969) distribution of the largest eigenvalue of central complex Wishart matrices to the noncentral case. It then applies the resulting new statistical results to obtain closed-form expressions for the outage probability of multiple-input-multiple-output (MIMO) systems employing maximal ratio combining (known also as "beamforming" systems) and operating over Rician-fading channels. When applicable these expressions are compared with special cases previously reported in the literature dealing with the performance of (1) MIMO systems over Rayleigh-fading channels and (2) single-input-multiple-output (SIMO) systems over Rician-fading channels. As a double check these analytical results are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interest are plotted and discussed. These results show that, given a fixed number of total antenna elements and under the same scattering condition (1) SIMO systems are equivalent to multiple-input-single-output systems and (2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for a minimum outage probability performance.