Finite Blocklength MIMO Precoding With Mixed Power and QoS Constraints

Multiple-input multiple-output (MIMO) technology is fundamental in communication systems, where precoding plays a crucial role in improving spectral efficiency. Most existing precoding methods either assume infinite blocklength (IBL) or handle only a single sum power constraint (SPC). However, realistic systems often operate with finite blocklength (FBL), especially in ultra-reliable low-latency communication (URLLC), and face diverse power limits, such as per-antenna and per-group power constraints. This renders the IBL rate formulation insufficient and necessitates precoding methods tackling various power constraints in the FBL regime. In this paper, we aim to enhance overall FBL rate performance of MIMO systems under quality-of-service (QoS) requirements and mixed power constraints (MPCs) that can encompass various power limitations. Unlike previous methods that directly solve the original nonconvex precoding design problem, we first convert it to an equivalent SINR-allocation problem and then propose two efficient algorithms, i.e., a bi-direction gradient method (BDGM) and an iterative water-filling (IWF) algorithm with guaranteed convergence properties. The proposed algorithms are applicable to single-cell, multi-cell, and cell-free systems, and can achieve satisfactory performance at lower complexity.