Adaptive filter design for sparse signal estimation.

Abstract

Recently, sparse signal estimation has become an increasingly important research area in signal processing due to its wide range of applications. Efficient adaptive algorithms have been developed for estimation of various sparse signals, and the approaches developed are usually application-specific. In this dissertation, we investigate the algorithm and system design for sparse signal estimation of several applications of practical interest, specifically echo cancellation, compressive sensing, and power amplifier pre-distortion. For echo cancellation, different approaches are considered to find the optimal solution. A series of algorithms are proposed to improve the performance and reduce the cost. Specifically, we describe novel adaptive tap algorithms with selective update criteria, a μ-law proportionate technique incorporated with efficient memorized proportionate Affine Projection Algorithms, and a new class of proportionate algorithms with gradient-controlled individual step sizes which can be implemented either in the time domain or the frequency domain. For compressive sensing algorithms with the l0 norm constraint, a sparse LMS algorithm with segment zero attractors is introduced. It can achieve significant convergence and error performance improvements while providing reduced computational cost, especially for large sparse systems with colored inputs. Such filters can also be combined with cascade or multistage realizations, thereby yielding even more efficient implementations. We also describe new results for the non-linear signal estimation problem in power amplifier (PA) pre-distortion with dynamic nonlinearities, where the signal can be represented using a Volterra series with sparse coefficients. An efficient solution using a power-indexed look-up table (LUT) based digital pre-distortion (DPD) is proposed to address the current challenge of poor dynamic performance of a PA operating with wideband signals. Experimental results obtained using a 2 GHz power amplifier driven by a 2-carrier WCDMA signal demonstrate very robust and stable performance for the PA in dynamic environments.