A MLE-based blind signal separation method for time–frequency overlapped signal using neural network

The blind signal separation (BSS) algorithm obtains each original/source signal from the observed signal collected by the receiving antenna or sensor. Objective/loss/cost function and optimization method are two key parts of BSS algorithm. Modifying the objective function and optimization from the perspective of neural network (NN) is a novel concept in BSS domain. L 2 regularization is adopted as a term of maximum likelihood estimation (MLE)-based objective function like in Liu et al. (Sensors 21(3):973, 2021); however, we modified the probability density function (PDF) term of the objective function and used the kernel density estimation method for time–frequency overlapped digital communication signal. Multiple optimizers are studied in this paper, and we figure out the right optimizer for our application scenario. A varies of comparison experiments—whose separation results will be provided in forms of correlation coefficient and performance index—are carried out, which indicate our method can converge quickly and achieve satisfactory separation results with performance index (PI) lower than 0.02 when signal-to-noise ratio (SNR) no less than 10dB. Additionally, it demonstrates performance of our method is better than that of typical separation—FastICA, especially for the lower SNR environment, and it shows that our method is not sensitive to the frequency overlap level (FOL) of the source signal, even FOL as high as 100 % ; it still can get high-precision separation results with PI < 0.02 .