Optimal Interference Exploitation Waveform Design with Relaxed Block-Level Power Constraints

This paper investigates constructive interference (CI)-based waveform design for phase shift keying and quadrature amplitude modulation symbols under relaxed block-level power constraints in multi-user multiple-input single-output (MU-MIMO) communication systems. Existing linear CI-based precoding methods, including symbol-level precoding (SLP) and block-level precoding (BLP), suffer from performance limitations due to strict symbol-level power budgets or insufficient degrees of freedom over the block. To overcome these challenges, we propose a nonlinear waveform optimization framework that introduces additional optimization variables and maximizes the minimum CI metric across the transmission block. The optimal waveform is derived in closed form using the function and Karush Kuhn Tucker conditions, and the solution is explicitly expressed with respect to the dual variables. Moreover, the original problems are equivalently reformulated as tractable quadratic programming (QP) problems. To efficiently solve the derived QP problems, we develop an improved alternating direction method of multipliers (ADMM) algorithm by integrating a linear-time projection technique, which significantly enhances the computational efficiency. Simulation results demonstrate that the proposed algorithms substantially outperform the conventional CI-SLP and CI-BLP approaches, particularly under high-order modulations and large block lengths.