  Gaussian MIMO channel under total transmit and interference power constraints
(TPC and IPC) is considered. A closed-form solution for the optimal transmit
covariance matrix in the general case is obtained using the KKT-based approach
(up to dual variables). While closed-from solutions for optimal dual variables
are possible in special cases, an iterative bisection algorithm (IBA) is
proposed to find the optimal dual variables in the general case and its
convergence is proved for some special cases. Numerical experiments illustrate
its efficient performance. Bounds for the optimal dual variables are given,
which facilitate numerical solutions. An interplay between the TPC and IPC is
studied, including the transition from power-limited to interference-limited
regimes as the total transmit power increases. Sufficient and necessary
conditions for each constraint to be redundant are given. A number of explicit
closed-form solutions are obtained, including full-rank and rank-1
(beamforming) cases as well as the case of identical eigenvectors (typical for
massive MIMO settings). A bound on the rank of optimal covariance is
established. A number of unusual properties of optimal covariance matrix are
pointed out.
