SPARLS: the sparse RLS algorithm

  • Authors:
  • Behtash Babadi;Nicholas Kalouptsidis;Vahid Tarokh

  • Affiliations:
  • School of Engineering and Applied Sciences, Harvard University, Cambridge, MA;Department of Informatics and Telecommunications, Division of Communications and Signal Processing, University of Athens, Athens, Greece;School of Engineering and Applied Sciences, Harvard University, Cambridge, MA

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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Abstract

We develop a recursive L1-regularized least squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an expectation-maximization type algorithm. We prove the convergence of the SPARLS algorithm to a near-optimal estimate in a stationary environment and present analytical results for the steady state error. Simulation studies in the context of channel estimation, employing multipath wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely used recursive least squares (RLS) algorithm in terms. of mean squared error (MSE). Moreover, these simulation studies suggest that the SPARLS algorithm (With slight modifications) can operate with lower computational requirements than the RLS algorithm, when applied to tap-weight vectors with fixed Support.