  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.
