A novel sparse adaptive algorithm using wavelets

This paper proposes a novel use of wavelets in adaptive sparse system identification. The motivation is to exploit the time localization property of wavelets to improve convergence speed and reduce computation for the identification problem. A previous study employed the Haar transform to identify non-zero impulse response coefficients for adaptation. This paper extends this by using any orthogonal or bi-orthogonal wavelets instead of the Haar transform. The advantage of using longer wavelets is that they provide better decorrelation for colored input, allowing an increase in convergence speed, at the cost of slightly increased number of adapting coefficients. The computational complexity of the proposed algorithm is below LMS for practical sparse systems. The performance of the proposed algorithm is applied to echo-cancellation application through simulations for different wavelets.