Optimal power allocation for a wireless multi-antenna energy harvesting node with arbitrary input distribution

The lifetime of autonomous wireless nodes can be extended by using energy harvesters in the node. This additional source of energy implies a loss of optimality of the traditional transmission strategies such as waterfilling. In this paper, the precoding strategy along N independent channel uses that maximizes the mutual information in linear vector Gaussian channels for arbitrarily distributed inputs is studied, under non-causal knowledge of the harvested energy over time. Precisely, the optimal right singular vectors and singular values of each precoder are derived. The derivation of the left singular vectors is a computationally hard problem, similarly as in the case of non-harvesting nodes, and is left as an open problem. At each channel use, the observed channel is diagonalized and power is allocated following the proposed MIMO Mercury Water-Flowing solution.