Online Precoding for Energy Harvesting Transmitter With Finite-Alphabet Inputs and Statistical CSI

Abstract

This paper considers an online multiantenna precoder design for energy harvesting transmitter based on finite-alphabet inputs and statistical channel state information (CSI). It formulates the problem by maximizing the sum of average mutual information (AMI) of multiple time slots in one channel frame with causal energy constraint. The formulated problem is a $\mbox{2}N_{t}^{2}$ - dimensional stochastic dynamic programming (SDP) problem with a nonconcave objective function, where $N_{t}$ is the number of transmit antennas. The $\mbox{2}N_{t}^{2}$ - dimensional SDP problem is prohibitively complex and prevents the development of online algorithm for multiantenna systems. We provide 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 separate the one-dimensional problem into two cases: 1) the discrete-battery-state–discrete-power-choice (DBDP) problem and 2) the continuous-battery-state–continuous-power-choice (CBCP) problem. We also develop numerical algorithms to solve them, respectively. We further analyze the computational complexity of the developed algorithms and demonstrate the significant performance gains offered by the proposed method when compared with other methods.