Developments of Adaptive Filter Algorithms for Sparse Channel Estimation

Developments of Adaptive Filter Algorithms for Sparse Channel Estimation Yingsong Li Broadband signal transmission becomes a commonly used highdata-rate technique for next-generation wireless communication systems, and the coherent detection for such broadband communication systems strongly depends on the quality of the channel estimation which can be well estimated by using adaptive filters. Furthermore, channel measurements have shown that the broadband wireless multipath channels can often be described as sparse channels. Thus, developing sparse adaptive filter algorithms for broadband multipath estimation is becoming an increasing important research topic. In this dissertation, we aim to develop efficient sparse adaptive filter algorithms for sparse channel estimation applications in terms of the convergence speed and steady-state performance. Firstly, we studies the two classes of important adaptive filter algorithms: classical adaptive filter algorithms including least-meansquare (LMS) and affine projection algorithm (APA), and sparsityaware adaptive filter algorithms which include the zero attracting (ZA) algorithms and the proportionate-type adaptive filter algorithms. We found that the classical adaptive filters have good performance for non-sparse signal estimation while these algorithms perform poorly for the sparse channel estimation. Furthermore, ZA and proportionate-type algorithms have been proposed for sparse system identifications and echo cancellation applications. However, most of the ZA algorithms were proposed based on the l1-norm penalty and LMS algorithms while most of the improved proportionate-type algorithms were concentrated on variable step size technique and gain matrix modification. Secondly, we proposed an adaptive reweighted zero-attracting sigmoid functioned variable step size LMS (ARZA-SVSS-LMS) algorithm based on variable step size technique and adaptive parameter adjustment method. In order to implement the ARZA-SVSS-LMS algorithm, it was described step-by-step. To begin with, a sigmoid functioned variable step size LMS (SVSS-LMS) algorithm was proposed, which was an improved variable step size (VSS) LMS algorithm. Next, the ZA techniques used in zero-attracting LMS (ZA-LMS) and reweighted ZA-LMS (RZA-LMS) algorithms were incorporated into the proposed SVSS-LMS algorithm in order to form the zeroattracting SVSS-LMS (ZA-SVSS-LMS) and reweighted ZA-SVSSLMS (RZA-SVSS-LMS) algorithms, respectively. At last, an adaptive parameter adjustment method was adopted to form the ARZA-SVSSLMS algorithm by adjusting the zero-attracting strength in the RZASVSS-LMS algorithm dynamically. The simulation results demonstrated that the proposed ARZA-SVSS-LMS algorithm can achieve faster convergence speed and smaller steady-state error in comparison with these of the standard LMS and previously proposed sparsityaware LMS algorithms. Thirdly, we proposed a smooth approximation l0-norm-constrained affine projection algorithm (SL0-APA) to obtain the benefits of both the APA and ZA algorithms. The proposed SL0-APA algorithm was realized via incorporating a smooth approximation l0-norm (SL0) into the cost function of the standard APA in order to construct a zero attractor, by which the convergence speed and the steady-state performance of the standard APA were significantly improved. Moreover, the theoretical analysis of the convergence speed and mean square error (MSE) were given to further understand the proposed SL0-APA. The simulation results showed that the proposed SL0-APA can achieve faster convergence speed and better steady-state performance than the standard APA, zero-attracting affine projection algorithm (ZAAPA) and reweighted ZA-APA (RZA-APA). In addition, we also proposed a discrete weighted zero-attracting affine projection algorithm (DWZA-APA) in order to reduce the computation complexity of the RZA-APA by the introduction of a piece-wise linear function instead of the sum-logarithm function in the RZA-APA. The simulation results demonstrated that the DWZA-APA reduced the multiplication complexity of the RZA-APA and had no channel estimation performance reduction in comparison with the RZA-APA in terms of the convergence speed and steady-state performance. Finally, we proposed an lp-norm-constrained PNLMS (LP-PNLMS) algorithm on the basis of the proportionate normalized least-meansquare (PNLMS) algorithm to avail both the benefits of the PNLMS algorithm and ZA techniques. The proposed LP-PNLMS algorithm was realized by incorporating a gain-matrix-weighted lp-norm penalty into the cost function of the PNLMS algorithm in order to design a zero attractor. The simulation results showed that the proposed LP-PNLMS algorithm can achieve the same convergence speed as that of the PNLMS algorithm at the early iterations, and converged faster than that of the PNLMS algorithm after the convergence of the active taps. Furthermore, the LP-PNLMS algorithm has smaller steady-state error than the PNLMS and its related commonly used algorithms, namely improved PNLMS (IPNLMS) and μ-law PNLMS (MPNLMS) algorithms.