Evaluation of Blind Signal Separation Objective Function Constructed using Nonlinear Functions

The goal of the blind signal separation (BSS) algorithm is to extract each original signal from observed mixing signals gathered by receiving antennas or sensors. Objective functions and optimization techniques are vital elements of the BSS algorithm. Independent Component Analysis (ICA) stands as one of the most prevalent methods utilized for BSS. Typically, ICA algorithms establish objective functions by considering criteria like maximizing negentropy, minimizing mutual information, or maximizing likelihood. However, these objective functions often require prior knowledge of the probability density of the source signals, which are typically unknown in most blind separation scenarios. Therefore, scholars have proposed using nonlinear functions as objective functions for ICA, such as the FastlCA algorithm. This article introduces a nonlinear function-Softplus function-for the first time to construct ICA objective function. This innovation not only broadens the scope of objective function representation but also serves as a bridge for implementing objective function optimization using machine learning models. This advancement is anticipated to significantly enhance the universality and computational efficiency of signal separation algorithms. Furthermore, this paper validates the accuracy of the method for separating multidimensional overlapping signals in complex electronic surveillance fields and provides performance analysis. When the Signal-to-Noise Ratio (SNR) is not less than 15dB, the performance index (PI) is below 0.005, and the cor-relation coefficient between the original signal and its estimated signal is more 0.95. Additionally, in low SNR environments, the separation performance of the Softplus function even slightly outperforms that of traditional nonlinear functions.