tailieunhanh - Báo cáo hóa học: " Research Article Convergence Analysis of a Mixed Controlled l2 − l p Adaptive Algorithm"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: IResearch Article Convergence Analysis of a Mixed Controlled l2 − l p Adaptive Algorithm | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID 893809 10 pages doi 2010 893809 Research Article Convergence Analysis of a Mixed Controlled l2 - Ip Adaptive Algorithm Abdelmalek Zidouri Electrical Engineering Department King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Correspondence should be addressed to Abdelmalek Zidouri malek@ Received 17 June 2010 Accepted 26 October 2010 Academic Editor Azzedine Zerguine Copyright 2010 Abdelmalek Zidouri. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. A newly developed adaptive scheme for system identification is proposed. The proposed algorithm is a mixture of two norms namely the l2-norm and the Ip-norm p 1 where a controlling parameter in the range 0 1 is used to control the mixture of the two norms. Existing algorithms based on mixed norm can be considered as a special case of the proposed algorithm. Therefore our algorithm can be seen as a generalization to these algorithms. The derivation of the algorithm and its convexity property are reported and detailed. Also the first moment behaviour as well as the second moment behaviour of the weights is studied. Bounds for the step size on the convergence of the proposed algorithm are derived and the steady-state analysis is carried out. Finally simulation results are performed and are found to corroborate with the theory developed. 1. Introduction The least mean square LMS algorithm 1 is one of the most widely used adaptive schemes. Several works have been presented using the LMS or its variants 2-14 such as signed LMS 8 the least mean fourth LMF algorithm and its variants 15 or the mixed LMS-LMF 16-18 all of which are intuitively motivated. The LMS algorithm is optimum only if the noise statistics are Gaussian. .