Deep-Learning-Aided Alternating Least Squares for Tensor CP Decomposition and Its Application to Massive MIMO Channel Estimation

CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive 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 (CPD) algorithms are desired. The CP alternating least squares (CPALS) is the workhorse algorithm for calculating the CPD. 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 CPD. 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 CPD. 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-OFDM channel estimation. Experimental results demonstrate the significant improvements of the proposed method in terms of both speed and accuracy for CPD and channel estimation.