Partial-update (PU) algorithms offer reduced computational complexity to adaptive second-order Volterra filters (SOV) in nonlinear systems while retaining acceptable performance. In this paper, a new selective partial-update technique for the normalized LMS (NLMS) SOV algorithm is proposed, which requires lesser number of comparison operations per iteration than existing methods while providing close performance to the standard M-Max NLMS-SOV algorithm. Convergence properties of the proposed algorithm are enhanced by making the algorithm step-size time varying based on the natural logarithm function. Simulation experiments compare the proposed algorithm with existing PU and variable step-size NLMS-SOV algorithms, which illustrate the advantageous properties of the new algorithm. The proposed algorithm achieves both lower steady-state misalignment and faster convergence speed when compared with the fixed step-size full-update NLMS-SOV algorithm. Simulations also show that comparison operations overhead of the proposed algorithm is reduced significantly compared to that of the standard M-Max NLMS-SOV algorithm.

中文翻译：

---

二阶自适应沃尔泰拉滤波器的可变步长部分更新归一化最小均方算法

部分更新 (PU) 算法降低了非线性系统中自适应二阶 Volterra 滤波器 (SOV) 的计算复杂度，同时保持可接受的性能。在本文中，提出了一种新的用于归一化 LMS (NLMS) SOV 算法的选择性部分更新技术，与现有方法相比，每次迭代需要更少的比较操作次数，同时提供与标准 M-Max NLMS-SOV 算法相近的性能。通过基于自然对数函数使算法步长时变，增强了所提出算法的收敛性。仿真实验将所提算法与现有的PU和变步长NLMS-SOV算法进行了比较，说明了新算法的优越性。与固定步长全更新 NLMS-SOV 算法相比，该算法实现了更低的稳态失准和更快的收敛速度。仿真还表明，与标准 M-Max NLMS-SOV 算法相比，所提出算法的比较操作开销显着降低。