Sparse LMS via Online Linearized Bregman Iteration
This addresses sparse signal processing for applications like communications, but it is incremental as it builds on existing sparse LMS methods.
The paper tackled sparse system identification by proposing an online linearized Bregman iteration (OLBI) algorithm, which improves performance for signals from sparse tap weights with demonstrated numerical gains.
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.