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We consider the optimal precoder design with the assumption that the transmitter only has channel covariance information, for the multi-input multi-output (MIMO) information and energy transmission system. The objective of the system design is to maximize the average system information rate, meanwhile meeting the minimum energy requirement of the energy receiver. Following this objective, we formulate the problem as a semidefinite programming (SDP) and further transform it into a dual problem. Two methods are proposed to solve this problem: the first method decomposes the transmission covariance as a product of precoders so that the constrained optimization becomes an unconstrained one, whereas the second method derives the structure of the optimal transmission covariance analytically. Both methods are proved to be convergent and their overheads and complexity are also analyzed. The achievable rate-energy (R-E) regions for the proposed methods are presented in the simulation. Under various system settings, the superiority of the proposed methods is shown by comparing with a few existing transmission schemes.

The Precoder Design with Covariance Feedback for Simultaneous Information and Energy Transmission Systems