L1 Norm Penalized Bias Compensated Linear Constrained Affine Projection Algorithm

Rajni Yadav,Chandra Shekhar Rai,

doi:10.35940/ijeat.c4815.029320

Abstract

This paper presents an l1-norm penalized bias compensated linear constrained affine projection (l1-BC-CAP) algorithm for sparse system identification having linear phase aspectin the presence of noisy colored input. The motivation behind the development of the proposed algorithm is formulated on the concept of reusing the previous projections of input signal in affine projection algorithm (APA) that makes it suitable for colored input. At First, l1-CAP algorithm is derived by adding zero attraction based on l1-norm into constrained affine projection (CAP) algorithm. Then, the proposed l1-BC-CAP algorithm is derived by addinga bias compensator into the filter coefficient update equation of l1-norm constrained affine projection (l1-CAP) algorithm to alleviate the adverse consequence of input noise on the estimation performance. Hence, the resulting l1-BC-CAP algorithm excels the estimation performance when applied to linear phase sparse system in the existence of noisy colored input. Further, this work also examines the stability concept of the proposed algorithm

Highlights

Use of linear constrained adaptive filtering in many digital signal processing applications has been on a steady rise owing to their utility in considering the prior knowledge about the framework to be estimated
Based on the above concept of bias compensation, this paper presents l1-norm penalized bias compensated constrained affine projection (l1-BC-CAP) algorithm that takes into account the input noise
This paper presents an l1-norm penalized bias compensated linear constrained affine projection (l1-BC-CAP) algorithm

Summary

INTRODUCTION

Use of linear constrained adaptive filtering in many digital signal processing applications has been on a steady rise owing to their utility in considering the prior knowledge about the framework to be estimated. This paper first develops l1-norm constrained affine projection (l1-CAP) algorithm that appends the zero attraction based on l1-norm to consider the sparsity of the system. Based on the above concept of bias compensation, this paper presents l1-norm penalized bias compensated constrained affine projection (l1-BC-CAP) algorithm that takes into account the input noise. The proposed work adds a bias compensator into update equation of l1-CAP algorithm to mitigate the unfavorable impact of input noise on the estimation performance in constrained applications against colored input. The coefficient recursive equation of l1-norm penalized linear constrained affine projection (l1-CAP) algorithm becomes:. The coefficient recursion equation of the proposed l1-norm penalized bias compensator constrained affine projection algorithm becomes:.

CONVERGENCE ANALYSIS

AND DISCUSSION

CONCLUSION