Tensor-based blind channel identification

Abstract

We propose a blind FIR channel identification method based on the Parallel Factor (Parafac) analysis of a 3rd-order tensor composed of the 4-th order output cumulants. Our algorithm is based on a single-step least squares (LS) minimization procedure instead of using classical three-step Alternating Least Squares (ALS) methods. Using a Parafacbased decomposition, we avoid any kind of pre-processing such as the prewhitening operation, which is mandatory in most methods using higher-order statistics. Our method retrieves the channel vector without any permutation or scaling ambiguities. In addition, we establish a link between the cumulant tensor decomposition and the joint-diagonalization approach. Computer simulations illustrate the performance gains that our method provides with respect to other classical solutions. Initialization and convergence issues are also addressed.