Complex Field-Trainable ISTA for Linear and Nonlinear Inverse Problems

Complex-field linear/nonlinear inverse problems are central issues in wireless communication systems. In this paper, we propose a novel trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA), which is an extension of recently proposed trainable iterative soft thresholding algorithm (TISTA) for real-valued compressed sensing. The proposed C-TISTA consists of a gradient step with Wirtinger derivatives, projection step with a shrinkage function, and error-variance estimator whose trainable parameters are learned by standard deep learning techniques. We examine the performance of C-TISTA in three distinct problems: complex-valued compressed sensing, discrete signal detection for an underdetermined system, and discrete signal recovery for nonlinear clipped OFDM systems. Numerical results indicate that C-TISTA provides remarkable signal recovery performance in these problems, which suggests a promising potential of C-TISTA to a wide range of inverse problems.