Energy-Efficient Precoding for Massive MIMO Systems with Low-Resolution Quantizers

In this paper, we propose a precoding method to maximize energy efficiency (EE) in a downlink multiuser massive multiple-input multiple-output system with low-resolution quantizers. To this end, we formulate an EE maximization problem with respect to precoders by incorporating the quantization errors caused by the low-resolution quantizers. The main challenges exist: i) the quantization errors are entangled with the precoders, ii) a objective function is non-convex, and iii) unlike a spectral efficiency (SE) maximization problem, a precoding power needs to be jointly optimized. To address these challenges, we first adopt a Dinkenbach method and reformulate the EE problem to a more tractable form. We further decompose the problem into an optimal precoding direction and transmit power problems. To find the optimal direction, we derive a first-order Karush-Kuhn-Tucker (KKT) condition and interpret the condition as a generalized eigenvalue problem. Accordingly, adopting a generalized power iteration-based precoding method, we find the principal eigenvector which is the best sub-optimal precoder. Regarding the transmit power optimization, the objective function becomes concave for given other variables. Hence, the transmit power level is optimized by using a gradient descent method. Via simulations, we demonstrate that the proposed algorithm provides the highest EE performance compared to baseline methods.