[论文解读] Deep unfolding of the weighted MMSE beamforming algorithm

Lissy Pellaco, Mats Bengtsson+1 more|arXiv (Cornell University)|Jun 15, 2020

Direction-of-Arrival Estimation Techniques参考文献 56被引用 9

一句话总结

本文提出一种针对MISO下行链路信道的加权最小均方误差（WMMSE）波束成形算法的深度展开方法，通过投影梯度下降重新表述该算法，从而实现可训练的神经网络层，使其结构与原始算法保持一致。该方法在计算复杂度更低的情况下，实现了与传统WMMSE相当或更优的加权和速率性能，尤其在高信噪比（SNR）条件及优化步长下表现更优。

ABSTRACT

Downlink beamforming is a key technology for cellular networks. However, computing the transmit beamformer that maximizes the weighted sum rate subject to a power constraint is an NP-hard problem. As a result, iterative algorithms that converge to a local optimum are used in practice. Among them, the weighted minimum mean square error (WMMSE) algorithm has gained popularity, but its computational complexity and consequent latency has motivated the need for lower-complexity approximations at the expense of performance. Motivated by the recent success of deep unfolding in the trade-off between complexity and performance, we propose the novel application of deep unfolding to the WMMSE algorithm for a MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE algorithm into trainable neural network layers, whose architecture reflects the structure of the original algorithm. With respect to traditional end-to-end learning, deep unfolding naturally incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the formulation of the WMMSE algorithm, as described in Shi et al., is not amenable to be unfolded due to a matrix inversion, an eigendecomposition, and a bisection search performed at each iteration. Therefore, we present an alternative formulation that circumvents these operations by resorting to projected gradient descent. By means of simulations, we show that, in most of the settings, the unfolded WMMSE outperforms or performs equally to the WMMSE for a fixed number of iterations, with the advantage of a lower computational load.

研究动机与目标

• 解决传统WMMSE算法在下行链路波束成形中计算复杂度高的问题。
• 在保持高 spectral efficiency 的同时，降低基站的延迟和功耗。
• 通过将专家知识融入神经网络架构，克服端到端深度学习的局限性。
• 通过结构化、可微分的层实现对标准化深度学习硬件的高效部署。
• 在计算复杂度与加权和速率性能之间实现更优的权衡。

提出的方法

• 使用投影梯度下降（PGD）重新表述WMMSE算法，以可微分操作替代矩阵求逆、特征分解和二分搜索。
• 将投影梯度下降的每一轮迭代映射为可训练的神经网络层，同时保留原始算法的结构。
• 采用固定层数（L）来近似迭代式WMMSE过程，每层具有可学习的步长。
• 通过反向传播端到端训练网络，以优化波束成形权重和步长。
• 为每层引入步长约束，并逐步延长梯度下降的步长序列，以提升性能。
• 通过避免昂贵的矩阵运算，转而依赖适合深度学习加速器的向量运算，确保计算效率。

实验结果

研究问题

• RQ1 尽管WMMSE算法依赖于矩阵求逆和特征分解，是否仍可将其重新表述以支持深度展开？
• RQ2 在固定计算复杂度下，所提出的展开式WMMSE是否能实现与原始WMMSE相当或更优的加权和速率性能？
• RQ3 随着迭代次数（L）和信噪比（SNR）的增加，展开式WMMSE的性能如何变化？
• RQ4 可学习的步长是否能提升展开式WMMSE的收敛性与性能，超越固定步长基线？
• RQ5 展开式WMMSE架构是否适合在标准化深度学习硬件上部署？

主要发现

• 当L = 1和L = 2时，展开式WMMSE在加权和速率方面优于或等同于原始WMMSE，尤其在高SNR下表现更优。
• 当L = 3时，尽管计算复杂度更低，展开式WMMSE的加权和速率仍可达到与原始WMMSE收敛时相当的水平。
• 所提方法将复杂度从WMMSE的O(LM³)降低至O(LKM²)，且运算更适配深度学习加速器。
• 将PGD步长序列逐步扩展至八步显著提升性能，使展开式WMMSE在L ≤ 3时可超越原始WMMSE。
• 为每层设置约束步长的性能优于在所有PGD步骤中共享单一步长的方案。
• 在高SNR条件下，展开式WMMSE与原始WMMSE之间的性能差距进一步扩大，表明展开版本在低复杂度下更有效地利用了高SNR条件。