Polynomial fitting based on least squares approximates for first-order Tracy-Widom distribution

Abstract

Tracy-Widom distribution can primely describe the limit distribution of the largest eigenvalue of noise matrix, so it is widely used in the field of signal processing and wireless communication. The exact expression of this distribution is very complex and difficult to be applied in practice. Therefore, an approximate method of Tracy-Widom distribution based on least squares is proposed, in which the optimal fitting order and optimal fitting coefficient are determined by minimizing the average fitting uncertainty. The simulation results show that the fitting results can accurately predict the largest eigenvalue distribution of the noise matrix, which proves the effectiveness of the polynomial fitting method to approximate the first-order Tracy-Widom distribution.