We study closed-form constructive interference based block-level precoding (CI-BLP) for scene expansion in the downlink of multi-user multiple-input single-output (MU-MISO) systems. We extend the analysis on CI-BLP to the case where the number of symbol slots in a block is smaller than the number of user. To this end, we mathematically prove the feasibility of using the pseudo-inverse to express the closed-form expression of the CI-BLP optimal precoding matrix. Building upon this, a quadratic programming (QP) optimization on simplex is obtained without being limited by the relationship between the number of symbol slots in a block and the number of users. We study the low complexity algorithm of large scale QP problem. We first mathematically obtain the rank of the quadratic coefficient matrix in the QP problem. Although the iterative closed-form algorithm for QP problems in CI-based symbol-level precoding (CI-SLP) can be used in certain scenarios, the complexity of the iterative closed algorithm for large-scale QP problems is impractical. In addition, we design a low complexity algorithm based on alternating direction method of multipliers (ADMM), 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（MU-MISO）系统下行链路中用于场景扩展的闭式构造性干扰分块级预编码（CI-BLP）。我们将对CI-BLP的分析扩展到分块内符号时隙数小于用户数的情况。为此，我们从数学上证明了利用伪逆表达CI-BLP最优预编码矩阵闭式表达式的可行性。在此基础上，得到了单纯形上的二次规划（QP）优化问题，且不受分块内符号时隙数与用户数之间关系的限制。我们研究了大规模QP问题的低复杂度算法。首先，我们从数学上获得了QP问题中二次系数矩阵的秩。虽然CI符号级预编码（CI-SLP）中QP问题的迭代闭式算法可在某些场景下使用，但大规模QP问题的迭代闭式算法复杂度不切实际。此外，我们设计了一种基于交替方向乘子法（ADMM）的低复杂度算法，该算法能有效求解大规模QP问题。我们进一步分析了所提出算法的收敛性和复杂度。数值结果验证了我们的分析以及所提出算法的最优性，并进一步表明通过限制最大迭代次数，该算法提供了灵活的性能-复杂度权衡，这促进了CI-BLP在实际无线系统中的应用。