CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a multi-domain massive multiple-input multiple-output (MIMO) system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency channel estimation, good and fast CP decomposition algorithms are desired. The CP alternating least squares (CPALS) is the workhorse algorithm for calculating the CP decomposition. However, its performance depends on the initializations, and good starting values can lead to more efficient solutions. Existing initialization strategies are decoupled from the CPALS and are not necessarily favorable for solving the CP decomposition. To enhance the algorithm's speed and accuracy, this paper proposes a deep-learning-aided CPALS (DL-CPALS) method that uses a deep neural network (DNN) to generate favorable initializations. The proposed DL-CPALS integrates the DNN and CPALS to a model-based deep learning paradigm, where it trains the DNN to generate an initialization that facilitates fast and accurate CP decomposition. Moreover, benefiting from the CP low-rankness, the proposed method is trained using noisy data and does not require paired clean data. The proposed DL-CPALS is applied to millimeter wave MIMO orthogonal frequency division multiplexing (mmWave MIMO-OFDM) channel estimation. Experimental results demonstrate the significant improvements of the proposed method in terms of both speed and accuracy for CP decomposition and channel estimation.

翻译：CANDECOMP/PARAFAC (CP) 分解是多域大规模多输入多输出（Massive MIMO）系统中对接收张量信号进行建模最常用的模型，因为接收机通常对来自不同路径或用户的分量进行求和。为实现准确且低延迟的信道估计，需要快速且高效的 CP 分解算法。CP 交替最小二乘法（CPALS）是计算 CP 分解的核心算法，但其性能依赖于初始值，好的初始值能够带来更高效的解。现有的初始化策略与 CPALS 相互独立，未必有利于 CP 分解的求解。为提升算法的速度和准确性，本文提出了一种深度学习辅助的 CPALS（DL-CPALS）方法，该方法利用深度神经网络（DNN）生成有利的初始值。所提出的 DL-CPALS 将 DNN 和 CPALS 整合到基于模型的深度学习范式下，训练 DNN 生成有利于快速且准确进行 CP 分解的初始值。此外，得益于 CP 的低秩特性，所提出的方法可使用含噪声数据进行训练，无需配对的干净数据。该 DL-CPALS 方法被应用于毫米波 MIMO 正交频分复用（mmWave MIMO-OFDM）信道估计。实验结果表明，所提方法在 CP 分解和信道估计的速度与准确性方面均有显著提升。