The convergence behavior of least-mean-square (LMS) algorithm is highly dependent on the correlation of the input data and, consequently, on the eigenvalue spread of its correlation matrix. To overcome this issue, LMS algorithm is studied in different transform domains in order to decrease this eigenvalue spread. In this paper, we propose a new transform domain LMS algorithm with function controlled variable step-size for sparse system identification.
The proposed algorithm imposes a transform domain to the input signal and an approximate l0 norm penalty term in the cost function of the function controlled variable step-size LMS (FC-VSSLMS) algorithm. The algorithm has been tested in the presence of highly correlated signals, i.e., Electrocardiography (ECG) and Electromyography (EMG) signals, and has shown very remarkable performance compared to those of the sparse FC-VSSLMS (SFCVSSLMS) and transform domain reweighted zero-attracting LMS (TD-RZALMS) algorithms.