Outage Capacity of Rayleigh Product Channels: a Free Probability Approach

The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the channel outage probability assuming slowly varying channel with delay-constrained decoding. Using techniques of free probability theory, the asymptotic variance of channel capacity is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the channel capacity is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels can be characterized by closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the relative outage performance between Rayleigh product channels and conventional Rayleigh MIMO channels.