Trigonometric Coordinate Transformation Blind Equalization Algorithm Based on Bi-Direction Long and Short-Term Memory Neural Networks

Aiming at the problem that the feedforward neural network blind equalization algorithm has a slow convergence rate and a large steady-state error when equalizing the high-order non-constant modulus signals, a trigonometric coordinate transformation blind equalization algorithm based on Bi-direction long and short-term memory (BLSTM) neural networks (BLSTM-TCT-CMA) is proposed. First, the BLSTM neural network has a strong processing ability for one-dimensional long-sequence signals, which is suitable for high-order signal sequence information. Secondly, a triangular coordinate transformation method was introduced in the BLSTM neural network loss function to transform the statistical modulus of the non-constant modulus signal into a constant modulus value, which speeds up convergence and further reduces the steady-state error. It was observed through the simulation that compared with the constant modulus blind equalization algorithm (CMA), the square contour blind equalization algorithm based on BP neural networks (SCA-BP-CMA) and the tunable activation functions blind equalization algorithm based on complex BP neural network (TAF-CBP-CMA). When the BLSTM-TCT-CMA equalized the 32QAM signal, the steady-state error was -13dB, and the loss function converged at 800 steps. When the 64QAM signal was equalized, the steady-state error was -10.5dB, and the loss function converged at 1200 steps. It is concluded that both indicators were optimal, and the CT-GRUNN-CMA output signal constellation was the clearest.