Cascade Adaptive Filters and Applications to Acoustic Echo Cancellation

Typical approaches to acoustic echo cancellation (AEC) in mobile telephones employ adaptive linear algorithms, such as the normalized least mean squares (NLMS) algorithm. Smaller, cheaper components on these devices introduce nonlinearities into the echo path, which adversely affect performance of linear AEC systems and necessitate means of nonlinear compensation. Memoryless nonlinear blocks that compute output via interpolation between a set of control points are especially attractive solutions since they are computationally inexpensive compared to full-scale Volterra approaches and can take the the shape of any arbitrary profile. We consider normalized cascade architectures of adaptive memoryless nonlinear components – in particular the cubic B-spline function and piecewise linear function – and linear, FIR adaptive filters for purposes of nonlinear acoustic echo cancellation. Furthermore, it is well known that the NLMS algorithm converges to the optimal Wiener linear filter, which for stationary and ergodic input signals is equivalent the least squares linear filter. We apply the least squares method to the cubic spline and piecewise linear functions to compute the optimal configuration of these nonlinear components. Although least squares estimation is in general a more difficult problem to solve for cascade architectures, we introduce an iterative method which computes the solution by performing least squares estimation on each component of the cascade separately. The result of this off-line iterative scheme serves to benchmark the performance of the on-line cascade adaptive filters.