Goh Su Lee, Mandic Danilo P
IEEE Trans Neural Netw. 2007 Sep;18(5):1511-6. doi: 10.1109/tnn.2007.895828.
A class of variable step-size learning algorithms for complex-valued nonlinear adaptive finite impulse response (FIR) filters is proposed. To achieve this, first a general complex-valued nonlinear gradient-descent (CNGD) algorithm with a fully complex nonlinear activation function is derived. To improve the convergence and robustness of CNGD, we further introduce a gradient-adaptive step size to give a class of variable step-size CNGD (VSCNGD) algorithms. The analysis and simulations show the proposed class of algorithms exhibiting fast convergence and being able to track nonlinear and nonstationary complex-valued signals. To support the derivation, an analysis of stability and computational complexity of the proposed algorithms is provided. Simulations on colored, nonlinear, and real-world complex-valued signals support the analysis.
提出了一类用于复值非线性自适应有限脉冲响应（FIR）滤波器的变步长学习算法。为此，首先推导了一种具有全复值非线性激活函数的通用复值非线性梯度下降（CNGD）算法。为了提高CNGD的收敛性和鲁棒性，我们进一步引入了梯度自适应步长，得到了一类变步长CNGD（VSCNGD）算法。分析和仿真表明，所提出的这类算法具有快速收敛性，并且能够跟踪非线性和非平稳复值信号。为支持推导过程，对所提算法的稳定性和计算复杂度进行了分析。对有色、非线性和实际复值信号的仿真结果支持了该分析。
