Double-talk Robust Multichannel Acoustic Echo Cancellation Using Least Squares MIMO Adaptive Filtering: Transversal, Array, and Lattice Forms

In this paper, we address the problem of noise-robust multiple-input multiple-output (MIMO) adaptive filtering that is optimal in least-squares sense with application to multichannel acoustic echo cancellation. We formulate the problem as minimization of a multichannel least squares cost function that incorporates near-end speech and noise statistics resulting in a novel noise-robust framework for MIMO adaptive filtering. Although the issue of numerical stability has been widely explored in the context of recursive least squares (RLS) filtering, a rigorous mathematical treatment of the MIMO case in the context of numerically stable noise-robust multichannel echo cancellation remains absent. Guided by quantization-error modeling, we resolve the issue of numerical instability in our noise-robust scheme by utilizing transversal RLS filtering of Type 2. Thereafter, an explicit derivation of its inverse QR-decomposition (IQRD) counterpart based on Givens rotations is presented. We also derive computationally efficient lattice forms for our noise-robust RLS Type-2 and IQRD algorithms. It is highlighted that propagation of angle-normalized errors occurs naturally within the numerically stable least squares lattice (LSL). Thus, our approach combines the four sought after attributes in a multichannel echo cancellation scheme, i.e., computational efficiency, numerical stability, fast convergence and tracking, and robustness against noise. We analyze our formulations using simulations in terms of convergence, re-convergence, robustness in the presence of double-talk, and numerical stability.