Conditioning Analysis of Orthogonal Polynomial Models for Receiver Nonlinear Behavioral Model

Receiver nonlinear distortion severely impacts modern wireless systems. Traditional power series polynomial models suffer from numerical instability in parameter estimation, especially at high orders or with memory. This paper investigates orthogonal memory polynomial models from the perspectives of memory depth, nonlinear order, input signal distribution, and temporal correlation of the input signal, focusing on effective methods for improving the condition number. Comprehensive analysis reveals that the condition number of the Gram matrix grows rapidly with polynomial order and memory depth for the conventional polynomial, while orthogonal polynomials remain well-conditioned due to their inherent orthogonality and normalization. Notably, orthogonal polynomials maintain robust performance even when the input distribution does not perfectly match the basis weight function. Experiments using OFDM and 3-carrier WCDMA signals confirm that orthogonal polynomials achieve condition numbers orders of magnitude lower than those of power series, along with superior fitting accuracy.