Max-Min Fairness Precoding with Low Resolution DACs

We propose a max-min fairness (MMF) precoding algorithm for a multi-user multiple-input multiple-output (MU-MIMO) downlink system with different user weights, considering the quantization effects of low-resolution digital-to-analog converters (DACs). To find a precoder, we first formulate a problem, which jointly considers MMF and quantization. This joint problem presents some challenges that make finding a direct solution infeasible: non-smoothness and non-convexity. To address the non-smoothness, we use LogSumExp method to approximate the problem into a smooth problem. Subsequently, we derive the first-order optimality condition and cast it as a nonlinear eigenvalue problem. Lastly, we employ a generalized power iteration method to determine the superior stationary point. Simulation result demonstrates the superiority of our MMF precoding algorithm.