Energy harvesting transmitter with finite-alphabet inputs and statistical CSI: Online precoding by dynamic programming

This paper considers the online multi-antenna pre-coder design for energy harvesting transmitter with emphasis on finite-alphabet inputs and statistical channel state information (CSI). It formulates the problem by maximizing the sum of average mutual information of multiple time slots with causal energy constraint. This formulation leads to a 2 N²_t-dimensional stochastic dynamic programming (SDP) problem with a non-concave objective function, where N_t is the number of transmit antennas. The 2N_t²-dimensional SDP problem is prohibitively difficult to solve and prevents the development of efficient online solver. We provide an equivalence between the multidimensional SDP problem and a one-dimensional power choice problem. Solving the one-dimensional equivalence decreases the computational burden extraordinarily without loss of optimality. We also demonstrate the performance gains offered by the proposed method when compared with other algorithms.