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A fully adaptive normalized nonlinear gradient descent algorithm for complex-valued nonlinear adaptive filters

A fully adaptive normalized nonlinear complex-valued gradient descent (FANNCGD) learning algorithm for training nonlinear (neural) adaptive finite impulse response (FIR) filters is derived. First, a normalized nonlinear complex-valued gradient descent (NNCGD) algorithm is introduced. For rigour, the remainder of the Taylor series expansion of the instantaneous output error in the derivation of NNCGD is made adaptive at every discrete time instant using a gradient-based approach. This results in the fully adaptive normalized nonlinear complex-valued gradient descent learning algorithm that is suitable for nonlinear complex adaptive filtering with a general holomorphic activation function and is robust to the initial conditions. Convergence analysis of the proposed algorithm is provided both analytically and experimentally. Experimental results on the prediction of colored and nonlinear inputs show the FANNCGD outperforming other algorithms of this kind.