Robust fitting of multilinear models with application to blind multiuser receivers: iterative weighted median filtering approach

PARAllel FACtor (PARAFAC) analysis is an extension of low-rank matrix decomposition to higher-way arrays. It decomposes a given array in a sum of multilinear terms. PARAFAC analysis generalizes and unifies common array processing models, like joint diagonalization and ESPRIT. The prevailing fitting algorithm in all these applications is based on alternating least squares (ALS) optimization, which is matched to Gaussian noise. In many cases, however, measurement errors are far from being Gaussian. An iterative algorithm for least absolute error (robust) fitting of general multilinear models based on linear programming (LP) has been recently developed. However, the computational complexity of this method remains high. In this paper, we develop a new iterative algorithm for robust fitting of multilinear models based on iterative weighted median filtering (WMF), which is appealing from a simplicity viewpoint. Performance of the proposed method is illustrated with application to the blind multiuser separation-detection problem, and compared to the performance of trilinear alternating least squares (TALS), trilinear alternating least absolute error based on linear programming (TALAE-LP), and the pertinent Cramer-Rao bounds (CRBs) in Laplacian, Cauchy, and Gaussian noise environments.