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

Abstract

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.