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The Capacity of MIMO Channels with Per-Antenna Power Constraint

We establish the optimal input signaling and the capacity of MIMO channels under per-antenna power constraint. While admitting a linear eigenbeam structure, the optimal input is no longer diagonalizable by the channel right singular vectors as with sum power constraint. We formulate the capacity optimization as an SDP problem and solve in closed-form the optimal input covariance as a function of the dual variable. We then design an efficient algorithm to find this optimal input signaling for all channel sizes. The proposed algorithm allows for straightforward implementation in practical systems in real time. Simulation results show that with equal constraint per antenna, capacity with per-antenna power can be close to capacity with sum power, but as the constraint becomes more skew, the two capacities diverge. Forcing input eigenbeams to match the channel right singular vectors achieves no improvement over independent signaling and can even be detrimental to capacity.