A Fully Complex-Valued Gradient Neural Network for Rapidly Computing Complex-Valued Linear Matrix Equations

This paper concerns online solution of complex-valued linear matrix equations in the complex domain. Differing from the real-valued neural network, which is only designed for solving real-valued linear matrix equations in the real domain, a fully complex-valued Gradient neural network (GNN) is developed for computing complex-valued linear matrix equations. The fully complex-valued GNN model has the merit of reducing the unnecessary complexities in theoretical analysis and realtime computation, as compared to the real-valued neural network. Besides, the convergence analysis of the proposed complex-valued GNN model is presented, and simulation experiments are performed to substantiate the effectiveness and superiority of the proposed complex-valued GNN model for online computing the complex-valued linear matrix equations in the complex domain.