Algorithm and VLSI Architecture Design of Proportionate-Type LMS Adaptive Filters for Sparse System Identification
Proportionate-type normalized LMS (Pt-NLMS) family of adaptive filtering algorithms for sparse system identification pose significant implementation challenges due to their high computational complexity especially for real-time applications like network echo cancelation. In this paper, we make the first attempt to implement Pt-NLMS algorithms in hardware. Several reformulations are proposed to simplify the original Pt-NLMS algorithms, thereby making them amenable to real time VLSI implementations and the reformulated algorithms referred as delayed µ-law proportionate LMS (DMPLMS) algorithm for white input and delayed wavelet MPLMS (DWMPLMS) for colored input are then implemented in hardware. Simulation studies demonstrate that the performance loss is very small for the proposed reformulations. We implemented the proposed designs considering 16-bit fixed point representation in hardware, and synthesis results show that the DMPLMS architecture with ˜30% increase in hardware over the state-of-the-art conventional delayed LMS architecture achieves 3× improvement in convergence rate for white input and the DWMPLMS architecture with ˜70% increase in hardware achieves 10× improvement in convergence rate for correlated input conditions.