In this paper we consider a communication system with one transmitter and one receiver. The transmit antennas are partitioned into disjoint groups, and each group must satisfy an average power constraint in addition to the standard overall one. The optimal power allocation (OPA) for the transmit antennas is obtained for the following cases: (i) fixed multiple-input multiple-output (MIMO) orthogonal channel, (ii) i.i.d. fading MIMO orthogonal channel, and (iii) i.i.d. Rayleigh fading multiple-input single-output (MISO) and MIMO channels. The channel orthogonality is encountered in the practical case of the massive MIMO channel under favorable propagation conditions. The closed-form solution to the OPA for a fixed channel is found using the Karush-Kuhn-Tucker (KKT) conditions and it is similar to the standard water-filling procedure while the effect of the per-group average power constraint is added. For a fading channel, an algorithm is proposed to give the OPA, and the algorithm's convergence is proved via a majorization inequality and a Schur-concavity property.

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