Block-Level Interference Exploitation Precoding for MU-MISO: An ADMM Approach

We study constructive interference based block-level precoding (CI-BLP) in the downlink of multi-user multiple-input single-output (MU-MISO) systems. Specifically, our aim is to extend the analysis on CI-BLP to the case when the number of symbol slots in a given transmission block is smaller than the number of users. To this end, we mathematically prove the feasibility of using the pseudo-inverse to obtain a closed-form structure of the optimal CI-BLP precoding matrix. Similar to the case when the number of symbol slots in a given transmission block is not smaller than the number of users, we show that a quadratic programming (QP) optimization on simplex can be constructed. We also design a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework, which can achieve a flexible trade-off between communication performance and execution time by modifying the maximum number of iterations. We further analyze the convergence and complexity of the proposed algorithm. Numerical results validate our analysis and the optimality of the QP optimization, and further show that the proposed ADMM algorithm can provide satisfactory results in dozens of iterations, which motivates the use of CI-BLP in practical wireless systems.