Spectral-NFP：用于加速WMMSE的认证低秩曲率主化方法
Spectral-NFP: Certified Low-Rank Curvature Majorization for Accelerating WMMSE
中文总结 AI 辅助
针对多小区MIMO加权和速率最大化，提出Spectral-NFP方法，通过保留主导曲率特征对并加速WMMSE，以低秩实现近最优性能并大幅降低计算时间。
中文摘要 AI 辅助
在多小区多输入多输出（MIMO）网络中，加权和速率最大化问题通常通过加权最小均方误差（WMMSE）算法或分数规划（FP）来解决，这两种方法在固定其辅助变量后，都需要求解一个受功率约束的二次发射问题，该问题对于大型阵列需要昂贵的稠密运算。将底层曲率矩阵替换为缩放的单位矩阵可以避免矩阵求逆运算，从而降低复杂度，但这样会丢弃曲率的特征值结构，并产生一个宽松的下界。我们提出了Spectral-NFP，它保留选定的主导曲率特征对，并使用缩放的单位矩阵在剩余子空间上从上方界定曲率。因此，保留的秩形成了一条从NFP到精确WMMSE发射更新的连续路径。在代理曲率固定的情况下，Spectral-NFP可以解释为在线性坐标变换后的欧几里得投影梯度上升，允许采用Nesterov型加速。我们推导了Spectral-NFP相对于WMMSE的单步发射目标增益的下界，该下界用曲率特征值表示。在理想化的Wishart模型下，我们在有限维和大系统极限下分析该界，得到了渐近秩选择规则。实验结果表明，保留不超过发射维度的20%，且通常少于10%，即可实现WMMSE加权和速率（WSR）的99%以上。在大型阵列设置中，实测更新时间低于WMMSE所需时间的20%。
英文摘要
Weighted sum-rate maximization in multicell multiple-input multiple-output (MIMO) networks is commonly addressed by the weighted minimum mean-square error (WMMSE) algorithm or fractional programming (FP), both of which, after fixing their auxiliary variables, solve a power-constrained quadratic transmit problem that requires costly dense operations for large arrays. Replacing the underlying curvature matrix with a scaled identity can avoid the matrix inverse operation and thereby reduce complexity, but it discards the curvature eigenvalue structure and yields a loose lower bound. We propose Spectral-NFP, which retains selected dominant curvature eigenpairs and uses a scaled identity matrix to bound the curvature on the remaining subspace from above. The retained rank thus traces a continuous path from NFP to the exact WMMSE transmit update. With the surrogate curvature fixed, Spectral-NFP can be interpreted as Euclidean projected-gradient ascent after a linear coordinate transformation, admitting Nesterov-type acceleration. We derive a lower bound on the one-step transmit-objective gain of Spectral-NFP relative to WMMSE, expressed in terms of the curvature eigenvalues. Under an idealized Wishart model, we analyze this bound in both finite dimensions and the large-system limit, obtaining an asymptotic rank-selection rule. Experimental results show that retaining at most 20% of the transmit dimension, and often less than 10%, achieves more than 99% of the WMMSE WSR. In large-array settings, the measured update time is below 20% of that required by WMMSE.
