Algorithmic analysis and implementation of a novel natural gradient adaptive filter for sparse systems

We present analytical results, and details of implementation for a novel adaptive filter incorporating an approximate natural gradient tap-update algorithm, termed the simplified signed sparse LMS algorithm (SSSLMS). Each tap-update equation includes a term proportional to the tap-value, so that larger taps adapt more quickly than for a corresponding Least Mean Square (LMS) update. Results indicate that the algorithm is suited for use in sparse channels. The bounds on its maximum allowable stepsize differ from LMS, and simulations are provided that indicate potentially more robust convergence for larger step-sizes than LMS. A theoretical expression for the excess mean square error (MSE) is also derived, and confirmed by numerical simulation. Fixed point simulations of the algorithm using a proposed hardware architecture are also presented. The computational complexity is of the same order as the standard LMS. Finally, profiling of the power consumption of the SSSLMS implementation indicate that the architecture consumes approximately twice as much power as a standard LMS implementation.