Transform-domain delayed LMS algorithm and architecture

The least mean square (LMS) algorithm is one of the most widely applied adaptive methods in communication systems due to its simplicity. In applications that require high-speed sampling rate and very long tap FIR filter, the delayed LMS (DLMS) is usually employed. However, the value of the delay stage (D) will lead to degradation of the convergence speed, which is not acceptable in fast time-varying communication channels. In this paper, we propose a new DLMS algorithm called "Transform-domain DLMS (TD-DLMS)" to overcome the aforementioned speed degradation. It is derived based on the multirate FIR filtering structure, and the operations are performed in the transform domain. By doing so, the delay stage (D) in the DLMS can be reduced to DIM -1+2 log(2) (2M), where M is the decimation factor. As a result, we can reduce the value of D that causes slow convergence rate in the DLMS. Besides, since the adaptive filtering is performed in the transform domain, we can apply the technique of "power normalization" to further improve the convergence rate.