Combination of Approximate L_0-Norm Regularized Multiple Adaptive Lattice Filters in Sparse Cognitive Radio Channel Identification

Abstract

A priori recursive least squares (RLS) lattice algorithm has been regularized by adding an approximation of $\ell _{0}$-norm constraint penalty term to the cost function ${s}\text{o}$ as to introduce sparsity awareness to the previously proposed lattice filter combination schemes, i.e., Regular Combination of Multiple Lattice Filters (R-CMLF) and Decoupled Combination of Multiple Lattice Filter (D-CMLF) schemes, in cognitive radio (CR) channel identification framework. Fast convergence and low steady state mean square deviation (MSD) performance under sparse channel conditions has been brought together with the use of different exponential weighting factors in sparsity aware component filters. The performances of lattice component filters with sparsity aware algorithms under white and colored Gaussian input signal conditions are demonstrated by means of MSD simulations, and the performances of combination filters of the proposed schemes have been compared against those of the $\ell _{1}$-norm Regularized R-CMLF ($\ell _{1}-\mathrm {R}-\mathrm {R}$-CMLF) and D-CMLF $(\ell _{1}$-R-D-CMLF) schemes, and approximately $\ell _{0}$-norm as Well as $\ell _{1}$-norm Regularized Combinations of Least Mean Square Filters ($\ell _{0-}$ and $\ell _{1}-\mathrm {R}$-CLMSF) schemes.