Modified Clipped LMS Algorithm
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Modified Clipped LMS Algorithm Mojtaba Lotfizad Department of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran Email: [email protected]
Hadi Sadoghi Yazdi Department of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran Email: sadoghi [email protected] Received 30 May 2004; Revised 22 January 2005; Recommended for Publication by Mark Kahrs A new algorithm is proposed for updating the weights of an adaptive filter. The proposed algorithm is a modification of an existing method, namely, the clipped LMS, and uses a three-level quantization (+1, 0, −1) scheme that involves the threshold clipping of the input signals in the filter weight update formula. Mathematical analysis shows the convergence of the filter weights to the optimum Wiener filter weights. Also, it can be proved that the proposed modified clipped LMS (MCLMS) algorithm has better tracking than the LMS algorithm. In addition, this algorithm has reduced computational complexity relative to the unmodified one. By using a suitable threshold, it is possible to increase the tracking capability of the MCLMS algorithm compared to the LMS algorithm, but this causes slower convergence. Computer simulations confirm the mathematical analysis presented. Keywords and phrases: adaptive filter, LMS algorithm, clipped LMS algorithm, modified clipped LMS algorithm.
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INTRODUCTION
Adaptive signal processing has been one of the fastest growing fields of research in recent years. It has attained its popularity due to a broad range of useful applications in such diverse areas as communications, radar, sonar, seismology, navigation and control systems, and biomedical electronics. The LMS adaptive filter is very popular due to its simplicity, but even simpler approaches are required for many realtime applications, several different versions of the LMS algorithm have been proposed in the literature [1, 2, 3, 4, 5, 6]. Reduction of the complexity of the LMS algorithm has received attention in the area of adaptive filters [5, 7, 8, 9]. The sign algorithm and clipped data algorithm are in this category [2, 5, 8, 9, 10]. The tracking behavior of adaptive filtering algorithms is a fundamental issue in defining their performance in nonstationary operating environments. It has been established that adaptive algorithms that exhibit good convergence properties in stationary environments do not necessarily provide good tracking performance in a nonstationary environment because the convergence behavior of an adaptive filter is a transient phenomenon, whereas the tracking behavior is a steady-state property [11, 12]. Thus, much research is done for the measurement of tracking performance of variants of the LMS algorithm from different views [10, 13, 14, 15]. For applications in which slow adaptation is acceptable, the clipped LMS (CLMS) algorithm has an edge over the
others in terms of speed of processing [16]. Also fast CLMS is proposed for increasing the speed of convergence [2]. Much effort from the viewpoint of redu
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