Adaptive filtering of nonlinear systems with memory by quantized mean field annealing [digital subscriber loop example]

A technique for adaptive filtering of nonlinear systems with memory that combines quantized mean field annealing (QMFA) and conventional recursive-least-squares/fast-transversal-filter (RLS/FTF) adaptive filtering is developed. This technique can efficiently handle large-order nonlinearities with or without memory. The nonlinear channel is divided into a memory nonlinearity followed by a dispersive linear system. QMFA is applied to obtain the coefficients and the order of the memory of the nonlinearity, and RLS/FTF is applied to determine the weights of the dispersive linear system. Statistical thermodynamic analysis that provides theoretical measures for making annealing algorithms computationally efficient. The method is applied to a full duplex digital subscriber loop. Simulations show a performance improvement of over 40 dB compared to ordinary RLS/FTF and steepest descent algorithms, and the solution is robust