Parallelizable First-Order Fast Algorithm for Symbol-Level Precoding in Lage-Scale Systems

We investigate constructive interference (CI)-based symbol-level precoding (SLP) in large-scale systems with massive connectivity of users to minimize the transmit power subject to the instantaneous signal-to-interference-plus-noise-ratio (SINR) and CI constraints. By converting the considered problem into a novel separable formulation, we reveal the existence of separability in SLP, which is therefore well-suited for decomposition. The proximal Jacobian alternating direction method of multipliers (PJ-ADMM) framework is adopted to decompose the reformulated problem into multiple subproblems, which can be solved in parallel with closed-form solutions. We further linearize the second-order terms by approximation, which leads to a parallelizable first-order fast solution to SLP. Our derivations are validated by simulation results, which also show that our algorithm can provide optimal performance with substantially lower computational complexity than state-of-the-art algorithms.