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In this study, the authors propose an l 0-norm penalised shrinkage linear least mean squares (l 0-SH-LMS) algorithm and an l 0-norm penalised shrinkage widely linear least mean squares (l 0-SH-WL-LMS) algorithm for sparse system identification. The proposed algorithms exploit the priori and the posteriori errors to calculate the varying step-size, thus they can adapt to the time-varying channel. Meanwhile, in the cost function they introduce a penalty term that favours sparsity to enable the applicability for sparse condition. Moreover, the l 0-SH-WL-LMS algorithm also makes full use of the non-circular properties of the signals of interest to improve the tracking capability and estimation performance. Quantitative analysis of the convergence behaviour for the l 0-SH-WL-LMS algorithm verifies the capabilities of the proposed algorithms. Simulation results show that compared with the existing least mean squares-type algorithms, the proposed algorithms perform better in the sparse channels with a faster convergence rate and a lower steady-state error. When channel changes suddenly, a filter with the proposed algorithms can adapt to the variation of the channel quickly.

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