A method for regularizing a linear equalizer and its stability

An extended description of a new regularization method based on optimization aimed at inverting the sample covariance matrix without requiring complex calculations is presented. The method is designed for linear receivers in multi-user communication systems with a large number of antennas and operates under conditions of a limited number of samples. The study shows that the considered probability distributions of noise do not affect the optimal value of the regularization factor. Simulation results confirm that the method outperforms traditional approaches and provides better conditioning of the sample covariance matrix, reducing the computational complexity of calculating the weight matrix of the linear equalizer in the uplink channel of the communication system.