A delayed error least mean squares adaptive filtering algorithm and its performance analysis

High sampling rate realizations of the least mean squares (LMS) adaptive filtering algorithm require that the inherent recursive computational bottleneck in the impulse response updating be broken by introducing algorithmic delays into the error feedback path. The well known delayed LMS (DLMS) technique achieves this by convolving delayed error samples with delayed input samples. This paper proposes a possible realization that convolves delayed error samples with undelayed input samples, motivated by systolization and pipelining requirements that use only the delays introduced in the error feedback path. We provide a convergence analysis of this delayed error LMS (DELMS) algorithm along with experimental simulations that prove the stability of this adaptation technique under desired operating conditions and improved tracking performance in nonstationary environments, compared with the DLMS algorithm.