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.

翻译：本文考虑一个单发射机单接收机通信系统。发射天线被划分为互不相交的组，除标准总功率约束外，每组还必须满足平均功率约束。针对以下情形获得了发射天线的最优功率分配（OPA）：（i）固定多输入多输出（MIMO）正交信道，（ii）独立同分布衰落MIMO正交信道，以及（iii）独立同分布瑞利衰落多输入单输出（MISO）和MIMO信道。信道正交性出现在实际大规模MIMO信道在有利传播条件下。利用Karush-Kuhn-Tucker（KKT）条件得到了固定信道OPA的闭式解，该解类似于标准注水算法，同时增加了组平均功率约束的影响。针对衰落信道，提出了一种给出OPA的算法，并通过主要化不等式和Schur-凹性证明了算法的收敛性。