The widely linear model has attracted much attention due to its good features for non-circular adaptive signal processing in recent years. In this paper, a sparsity-induced augmented complex-valued NLMS algorithm is proposed to promote the performance of the adaptive filter for estimating sparse systems, which is established by incorporating the \(l_0\)-norm regularization into the squared error normalized by the input vector. To address the problem of trade-off between fast convergence rate and low steady-state misalignment, we minimize the variance of the a posteriori error to derive an optimal step-size and then some practical problems are considered. Simulation results are provided to verify the superior performance of the proposed algorithm.

近年来，广泛的线性模型因其非圆形自适应信号处理的良好功能而备受关注。为了提高稀疏系统的自适应滤波器性能，提出了一种稀疏诱导的增强复值NLMS算法，该算法是通过将\（l_0 \）-范数正则化合并到由输入向量。为了解决快速收敛速度和低稳态失准之间的权衡问题，我们将后验误差的方差最小化以得出最佳步长，然后考虑一些实际问题。仿真结果证明了所提算法的优越性能。