A fast compressive sensing method with application to network echo cancellation

Compressive sensing methods have been effectively used for sparse system identification. Many methods have been proposed to exploit this sparsity to reduce the amount of data required for identification. Most though, have high computational complexity. Recently, an iterative method based on the proportionate affine projection algorithm with row action projections (iPAPA-RAP) has been shown to have good convergence properties with relatively low complexity. Here, we present extensions of that algorithm that significantly speed convergence and as a result lower overall computational complexity. The main improvement is the addition of a zero attractor step with a variable scale factor. Significantly, this scale factor is made to be a function of the sparsity of the estimated system parameters. This greatly improves the convergence behavior of the resulting algorithm. It is compared with iteratively reweighted least-squares (IRLS) and l
₀
- zero attracting projections (l
₀
-ZAP). Results show that the proposed algorithm converges faster with lower overall complexity.