Outage Common Randomness Capacity Characterization of Multiple-Antenna Slow Fading Channels

We investigate the problem of common randomness (CR) generation from discrete correlated sources aided by one-way communication over single-user multiple-input multiple-output (MIMO) slow fading channels with additive white Gaussian noise (AWGN) and arbitrary state distribution. MIMO slow fading channels are indispensable in many scenarios in modern wireless communication. We completely solve the MIMO slow fading case by providing first an outage formulation of its channel capacity that holds for arbitrary state distribution. For this purpose, we provide an achievable rate for a specific MIMO compound Gaussian channel. Second, we establish the outage CR capacity over the MIMO slow fading channel using our result on its outage transmission capacity.