Performance of transform-domain LMS adaptive digital filters

In this paper we analyze the performance, particularly the convergence behavior, of the transform-domain least mean-square (LMS) adaptive digital filter (ADF) using the discrete Fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms. We first obtain the optimum Wiener solution and the minimum mean-squared error (MSE) in the transform domain. It is shown that the two minimum MSE's in the time and transform domains are identical independently of the transforms used. We then study the convergence conditions and the steady-state excess MSE's of the transform-domain LMS (TRLMS) algorithms both for the cases of having a constant and a time-varying convergence factors. When a constant convergence factor is used, the convergence behaviors of the LMS and TRLMS ADF's appear to be almost identical, provided that each has an appropriate value of the convergence factor depending on the transform used. Also, based on the concept of a self-orthogonalizing algorithm in the transform domain, it is shown that the convergence speed of the TRLMS ADF can be improved significantly for the same excess MSE as that of the LMS ADF. In addition, we compare the computational complexities of the LMS and TRLMS ADF'S. Finally, we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the TRLMS ADF.