An LMS Adaptive Filter Using Distributed Arithmetic - Algorithms and Architectures

Abstract

In recent years, adaptive filters are used in many applications, for example an echo canceller, a noise canceller, an adaptive equalizer and so on, and the necessity of their implementations is growing up in many fields. Adaptive filters require various performances of a high speed, lower power dissipation, good convergence properties, small output latency, and so on. The echo-canceller used in the videoconferencing requires a fast convergence property and a capability to track the time varying impulse response (Makino & Koizumi, 1988). Therefore, implementations of very high order adaptive filters are required. In order to satisfy these requirements, highly-efficient algorithms and architectures are desired. The adaptive filter is generally constructed by using the multipliers, adders and memories, and so on, whereas, the structure without multipliers has been proposed. The LMS adaptive filter using distributed arithmetic can be realized by using adders and memories without multipliers, that is, it can be achieved with a small hardware. A Distributed Arithmetic (DA) is an efficient calculation method of an inner product of constant vectors, and it has been used in the DCT realization. Furthermore, it is suitable for time varying coefficient vector in the adaptive filter. Cowan and others proposed a Least Mean Square (LMS) adaptive filter using the DA on an offset binary coding (Cowan & Mavor, 1981; Cowan et al, 1983). However, it is found that the convergence speed of this method is extremely degraded (Tsunekawa et al, 1999). This degradation results from an offset bias added to an input signal coded on the offset binary coding. To overcome this problem, an update algorithm generalized with 2’s complement representation has been proposed (Tsunekawa et al, 1999), and the convergence condition has been analyzed (Takahashi et al, 2002). The effective architectures for the LMS adaptive filter using the DA have been proposed (Tsunekawa et al, 1999; Takahashi et al, 2001). The LMS adaptive filter using distributed arithmetic is expressed by DA-ADF. The DA is applied to the output calculation, i.e., inner product of the input signal vector and coefficient vector. The output signal is obtained by the shift and addition of the partial-products specified with the bit patterns of the N-th order input signal vector. This process is performed from LSB to MSB direction at the every sampling instance, where the B indicates the word length. The B partial-products