The Least lncosh (Llncosh) algorithm is a promising adaptive algorithm due to its robustness in impulsive interference and has a faster convergence rate than the classical sign algorithm (SA). However, when the input signal is correlated, it may still suffer from a slow convergence rate. To address this problem, this paper incorporates the method of data-reusing into the lncosh cost function to develop a family of affine projection-type Llncosh (AP-Llncosh) algorithms. To promote its performance for sparse system identification, a low-order norm constraint is also considered. Moreover, to address the problem of tradeoff between fast convergence rate and small steady-state misalignment, we optimize its step-size by minimizing the mean-square deviation (MSD). Simulation results are provided to verify the superior performance of the proposed algorithms.

最小lncosh（Llncosh）算法由于其对脉冲干扰的鲁棒性和比经典符号算法（SA）更快的收敛速度而成为一种很有前途的自适应算法。然而，当输入信号相关时，它可能仍然会遇到收敛速度缓慢的问题。针对这一问题，本文将数据重用的方法结合到lncosh代价函数中，开发了一系列仿射投影型Llncosh（AP-Llncosh）算法。为了提高其稀疏系统识别的性能，还考虑了低阶范数约束。此外，为了解决快速收敛速度和小的稳态失准之间的权衡问题，我们通过最小化均方偏差 (MSD) 来优化其步长。