Adaptive Filtering Using Subband Processing: Application to Background Noise Cancellation

Adaptive filters are often involved in many applications, such as system identification, channel estimation, echo and noise cancellation in telecommunication systems. In this context, the Least Mean Square (LMS) algorithm is used to adapt a Finite Impulse Response (FIR) filter with a relatively low computation complexity and good performance. However, this solution suffers from significantly degraded performance with colored interfering signals, due to the large eigenvalue spread of the autocorrelation matrix of the input signal (Vaseghi, 2008). Furthermore, as the length of the filter is increased, the convergence rate of the algorithm decreases, and the computational requirements increase. This can be a problem in acoustic applications such as noise cancellation, which demand long adaptive filters to model the noise path. These issues are particularly important in hands free communications, where processing power must be kept as low as possible (Johnson et al., 2004). Several solutions have been proposed in literature to overcome or at least reduce these problems. A possible solution to reduce the complexity problem has been to use adaptive Infinite Impulse Response (IIR) filters, such that an effectively long impulse response can be achieved with relatively few filter coefficients (Martinez & Nakano 2008). The complexity advantages of adaptive IIR filters are well known. However, adaptive IIR filters have the well known problems of instability, local minima and phase distortion and they are not widely welcomed. An alternative approach to reduce the computational complexity of long adaptive FIR filters is to incorporate block updating strategies and frequency domain adaptive filtering (Narasimha 2007; Wasfy & Ranganathan, 2008). These techniques reduce the computational complexity, because the filter output and the adaptive weights are computed only after a large block of data has been accumulated. However, the application of such approaches introduces degradation in the performance, including a substantial signal path delay corresponding to one block length, as well as a reduction in the stable range of the algorithm step size. Therefore for nonstationary signals, the tracking performance of the block algorithms generally becomes worse (Lin et al., 2008). As far as speed of convergence is concerned, it has been suggested to use the Recursive Least Square (RLS) algorithm to speed up the adaptive process (Hoge et al., 2008).The convergence rate of the RLS algorithm is independent of the eigenvalue spread. Unfortunately, the drawbacks that are associated with RLS algorithm including its O(N2) computational requirements, which are still too high for many applications, where high