《Apenalty-enhancedsparseLMSalgorithm》由会员分享，可在线阅读，更多相关《Apenalty-enhancedsparseLMSalgorithm（3页珍藏版）》请在金锄头文库上搜索。
1、A penalty-enhanced sparse LMS algorithm Liu Zun-xiong , Zhou Tian-qing, Wang Shu-cheng School of Information in order to guarantee the convergence (i.e. ( )( )lim1 2optkEk=ww), the step size has to satisfy max01/ml1. Similar to log-sum penalty item of cost function( )2Jk, the log-arctan-sum penalty
2、item ()()()1log 1arctan1Niiiwwtt=+?is introduced as it behaves more similarly to the 0lnorm than( )1w k. Then, the coefficient vector is updated by ()( )( ) ( )( ) ( )( )( )()21sgnsgn111kke kkkkkkmmgt gg+=+ 骣?-+?+?+?桫wwxwwww(10) According to shrinkage of RZA-LMS, namely RZA-LMS selectively shrinks t
3、aps with large magnitudes and the ones with small magnitudes, the DZA-LMS should shrinks at the same step as its graph of penalty item is very similar to the former and they have also the same parameters. The dual zero attractor takes effect only on those taps whose magnitudes are comparable to t; a
4、nd there is little shrinkage exerted on the taps whose ( )iwkt?. In this way, the bias of the DZA-LMS can be reduced.4.Experimental results In this section we demonstrate our proposed DZA-LMS algorithm described in Section 3.2 by numerical simulation. We simulated the model( )( )( )Ty kkke=+w x, whe
5、re ( )kxand ( )keis input signal and noise respectively, and wis a sparse 16 element vector containing only 1 non-zero coefficient. Initially, we set the 5th tap ofwwith value 1 and others to zero for two experiments, making the system have a sparsity of 1/16. The input signal and the observed noise
6、 in the first experiment are white Guassian random sequences with variance of 1 and 10-3, respectively. The four filters (LMS, ZA-LMS, RZA-LMS and DZA-LMS) all run 200 times, using algorithm parameters2510m-=, 3510g-=, 10t =. The average estimate of mean square error deviation (MSD) is shown in Fig.
7、2. Fig. 2. Tracking and steady-state behaviors of 16-order adaptive filter, driven by white input signal.As shown in Fig.2, the sparse LMS algorithms (i.e. ZA-LMS, RZA-LMS, DZA-LMS) outperforms standard LMS both in convergence rate and steady-state, and our proposed DZA-LMS algorithm achieves best p
8、erformance in these two aspects. In the second experiment, we use correlated input signals which is generated by ( )()( )0.81x kx kke=-+to evaluate the filtering performance, where the sequence( )x kis normalized to unit variance and ( )keis a white Gaussian noise. The variance of the observed noise
9、 in this example is also set to 10-3, and the filter parameters are set as 2510m-=,5410g-=,10t =. Fig.3. shows that these filters have same convergence order with the first experiment, but their convergence rate is much less than the latter. Fig. 3.Tracking and steady-state behaviors of 16-order ada
10、ptive filter, driven by correlated input signal. 5.Conclusion In this paper we proposes a novel adaptive filter for sparse system identification, DZA-LMS. It can improve the performance of LMS with sparse systems, similar to RZA-LMS, where a zero attractor is devised to perform selective coefficient
11、 shrinkage. Under the condition of the same parameters, experiments show that the performance of DZA-LMS is better than standard LMS, ZA-LMS and RZA-LMS both in convergence rate and steady-state behavior when the system is sparse. 6. Acknowledgements This work is supported by National Natural Scienc
12、e Foundation of China (61065003). 7. References1 L. G. Liu, M. Fukumoto, S. Saiki. An improved mu-law proportionate NLMS algorithm. ICASSP, IEEE International Conference on, pp. 3797-3800, 2008. 2 R. Baraniuk. Compressive sensing. IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118-121, 2007. 3
13、 P. Wojtaszczyk. Stability of l1 minimization in compressed sensing. In Procedings of SPARS, 2009. 4 Y. Chen, Y. Gu, and A. O. Hero. Sparse LMS for system identification. in Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on. IEEE, 2009, pp. 3125 3128. 5 S. Haykin. Adaptive Filiter Theory,4th edition. Upper Saddle River,NJ,Prentice Hall,2002.
