Computing the capacity of a MIMO fading channel under PSK signaling

We study the constrained capacity of a multiple-input multiple-output (MIMO) fading channel with a phase-shift keying (PSK) input alphabet and show a uniform prior distribution is capacity achieving. An expression for the capacity is derived which requires a single expectation and can be evaluated easily through simulation. The simulations are facilitated by analytical expressions for the eigenvalues and eigenvectors of a required covariance matrix. The derived expression is used to provide good approximations to the capacity at low signal-to-noise ratios (SNRs) as well as to compare the input-constrained MIMO capacity to the unconstrained MIMO capacity.