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We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS)algorithm for the estimation of a sparse tap-weight vector in the adaptivefiltering setting. The SPARLS algorithm exploits noisy observations of thetap-weight vector output stream and produces its estimate using anExpectation-Maximization type algorithm. Simulation studies in the context ofchannel estimation, employing multi-path wireless channels, show that theSPARLS algorithm has significant improvement over the conventional widely-usedRecursive Least Squares (RLS) algorithm, in terms of both mean squared error(MSE) and computational complexity.

SPARLS: A Low Complexity Recursive $\mathcal{L}_1$-Regularized Least Squares Algorithm