Transform domain LMF algorithm for sparse system identification under low SNR

In this work, a transform domain Least Mean Fourth (LMF) adaptive filter for a sparse system identification, in the case of low Signal-to-Noise Ratio (SNR), is proposed. Unlike the Least Mean Square (LMS) algorithm, the LMF algorithm, because of its error nonlinearity, performs very well in these environments. Moreover, its transform domain version has an outstanding performance when the input signal is correlated. However, it lacks sparse information capability. To overcome this limitation, a zero attractor mechanism, based on the l₁ norm is implemented to yield the Zero-Attractor Transform-Domain LMF (ZA-TD-LMF) algorithm. The ZA-TD-LMF algorithm ensures fast convergence and attracts all the filter coefficients to zero. Simulation results conducted to substantiate our claim are found to be very effective.