Subband adaptive convex combination of two NLMS based filters for sparse impulse response systems

Abstract

It is well known, combination scheme is suitable for improving the performance of adaptive algorithms. In this paper, we propose a subband combination scheme for sparse impulse response systems. The combination is carried out in subband domain. In this convex combination, SIPNLMS and SNLMS are derived for fast convergence and small steady state error respectively. And mixing parameters are described by minimum mean square error and stochastic gradient algorithm. In adaptive system identification scenario, the advantages of this proposed method are illustrated. Keywords-convex; subband; adaptive filter; NLMS; sparse system I.INTRODUCTION In acoustic signal processing, echoes are generated acoustically by coupling between the loudspeaker and microphone via the impulse response of a room. Removal of these echoes requires the precise knowledge of the impulse response of echo path which has time varying and sparse characteristic. In various adaptive signal processing applications, the normalized least mean square (NLMS) is known as a popular adaptive algorithm because of its simplicity and robust performance. In acoustic echo cancellation application, the input signal is highly correlated, and the impulse response of acoustic path is very long and sparse. These characteristics lead to degraded performance of adaptive filter employing NLMS [1]. Improved proportionate NLMS (IPNLMS) and subband adaptive filtering (SAF) may solve the above problems [2][3][4][5]. Sparse impulse response system like as an acoustic channel has a small percentage of its components with significant magnitude, while the rest has nearly zero or small magnitude. In highly sparse impulse response systems, however, IPNLMS shows large steady state error than NLMS. The SAF which combines filter bank and adaptive algorithm is an alternative technique to improve the performances of LMS based algorithms.In SAF, the eigenvalue spread of input signal correlation matrix is significantly reduced in each subband, therefore, convergence rate can be improved. Also, SAF algorithms which employ polyphase decomposition and noble identity show improved performance without additional computation compare to full band algorithm.Furthermore, in the real applications which require long length filter, the use of polyphase decomposition, noble identity and decimation lead to fast convergence rate because adaptive sub-filters in each subband have reduced filter length than full band case [4,5]. Recently, a combination schemes receive attention in adaptive filter applications [6][7][8]. The aim of combination scheme is to get overall improved quality through the mixed output of several filters. The advantages of combination scheme are that it can obtain fast convergence rate and small steady state error simultaneously. In this paper, we propose a new subband adaptive combination scheme which employs polyphase decomposition and noble identity for sparse