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 where the considered number of symbol slots is smaller than that of the users. To this end, we mathematically prove the feasibility of using the pseudo-inverse to obtain the optimal CI-BLP precoding matrix in a closed form. Similar to the case when the number of users is small, 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 efficiently solve large-scale QP problems. We further analyze the convergence and complexity of the proposed algorithm. Numerical results validate our analysis and the optimality of the proposed algorithm, and further show that the proposed algorithm offers a flexible performance-complexity tradeoff by limiting the maximum number of iterations, which motivates the use of CI-BLP in practical wireless systems.

翻译：我们研究了多用户多输入单输出系统下行链路中基于构造性干扰的块级预编码问题。具体而言，旨在将CI-BLP的分析扩展至符号时隙数小于用户数的场景。为此，我们严格证明了利用伪逆获取最优CI-BLP预编码矩阵闭式解的可行性。与用户数较少的情形类似，我们验证了可通过单纯形上的二次规划优化实现等价构造。同时设计了一种基于交替方向乘子法框架的低复杂度算法，可高效求解大规模QP问题。进一步分析了所提算法的收敛性与复杂度。数值结果验证了理论分析及算法最优性，并表明通过限制最大迭代次数可灵活权衡性能与复杂度，这为CI-BLP在实际无线系统中的部署提供了依据。