Non-iterative solution for PARAFAC with a Toeplitz matrix factor

Recently, tensor signal processing has received an increased attention, particularly in the context of wireless communication applications. The so-called PARAllel FACtor (PARAFAC) decomposition is certainly the most used tensor tool. In general, the parameter estimation of a PARAFAC decomposition is carried out by means of the iterative ALS algorithm, which exhibits the following main drawbacks: convergence towards local minima, a high number of iterations for convergence, and difficulty to take, optimally, special matrix structures into account. In this paper, we propose a non-iterative parameter estimation method for a PARAFAC decomposition when one matrix factor has a Toeplitz structure, a situation that is commonly encountered in signal processing applications. We illustrate the proposed method by means of simulation results.