Eigenvalue Distributions of MIMO Rayleigh-Product Channels with Arbitrary-Power Co-Channel Interference and Noise

This paper studies the eigenvalue distributions of multiple-input multiple-output (MIMO) Rayleigh-product channels in the presence of both co-channel interference and thermal noise. We first present exact expressions for the marginal ordered eigenvalue distributions of the channel Gram matrix when multichannel beamforming is employed, from which we obtain exact results of the outage probability on each eigenmode. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel, allowing for transmission on any numbers of eigensubchannels, with any numbers of antennas, any numbers of scatterers in the environment, and any numbers of interferers with arbitrary powers. Also, for the particular case of keyhole channels, simplified closed-form expressions for the asymptotic distributions of the non-zero eigenvalue of the channel Gram matrix are derived, which indicate that the diversity order is only determined by the minimum of the number of transmit and receive antennas.