Null Space Projection Enhanced LMS Filters

Abstract

The least mean squares (LMS) filter is one of the most important adaptive filters used in digital signal processing applications. We present a performance improvement method for LMS filters based on null space projection. The approach uses buffering and a subsequent null space projection denoising. Interestingly, while the performance of this approach scales with the buffer length, the complexity in terms of multiplications per sample does not. We show the performance gains obtained by this method and present an architecture implementing an LMS filter as well as the proposed null space projection enhancement. We give complexity comparisons as well as synthesis results for a field-programmable gate array (FPGA) showing the low complexity overhead of the proposed method. We furthermore present hardware validated bit-true simulation results demonstrating the performance capabilities of the approach.