To achieve fast and accurate channel estimation of reconfigurable intelligent surface (RIS)-assisted multiple-input single-output (MISO) systems, we propose an accelerated bilinear alternating least squares algorithm (ABALS) based on parallel factor decomposition. Firstly, we build a tensor model of the received signal, and expand it to obtain the unfolded forms of the model. Secondly, we derive the expression of the estimation problem of two channels based on the unfolded forms to transform the problem into a cost function problem. Furthermore, we solve the cost function problem by introducing a simpler iterative optimization constraint and linear interpolation. Finally, we provide a strategy on the receiver design based on the feasibility conditions discussed in this paper, which can guarantee the uniqueness of the channel estimation problem. Simulation results show that the proposed algorithm can obtain a faster estimation speed and less iteration steps than the alternating least squares (ALS) algorithm, and the accuracy of the two algorithms is very close.
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