Information theoretic bounds for compound MIMO Gaussian channels
IEEE Transactions on Information Theory
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This paper presents the optimal guaranteed performance for a multiple-antenna wireless compound channel with M antennas at the transmitter and N antennas at the receiver on a Ricean fading channel with a static specular component. The channel is modeled as a compound channel with a Rayleigh component and an unknown rank-one deterministic specular component. The Rayleigh component remains constant over a block of T symbol periods, with independent realizations over each block. The rank-one deterministic component is modeled as an outer product of two unknown deterministic vectors of unit magnitude. Under this scenario, to guarantee service, it is required to maximize the worst case capacity (min-capacity). It is shown that for computing min-capacity, instead of optimizing over the joint density of T · M complex transmitted signals, it is sufficient to maximize over a joint density of min{T, M} real transmitted signal magnitudes. The optimal signal matrix is shown to be equal to the product of three independent matrices - a T × T unitary matrix, a T × M real nonnegative diagonal matrix, and an M × M unitary matrix. A tractable lower bound on capacity is derived for this model, which is useful for computing achievable rate regions. Finally, it is shown that the average capacity (avg-capacity) computed under the assumption that the specular component is constant but random with isotropic distribution is equal to min-capacity. This means that avg-capacity, which, in general, has no practical meaning for nonergodic scenarios, has a coding theorem associated with it in this particular case.