  We propose a version of least-mean-square (LMS) algorithm for sparse system
identification. Our algorithm called online linearized Bregman iteration (OLBI)
is derived from minimizing the cumulative prediction error squared along with
an l1-l2 norm regularizer. By systematically treating the non-differentiable
regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI
is bias free and compare its operation with existing sparse LMS algorithms by
rederiving them in the online convex optimization framework. We perform
convergence analysis of OLBI for white input signals and derive theoretical
expressions for both the steady state and instantaneous mean square deviations
(MSD). We demonstrate numerically that OLBI improves the performance of LMS
type algorithms for signals generated from sparse tap weights.
