Estimation of Memoryless Nonlinearity of Multiple Amplifiers with Low Complexity and High Stability Based on Orthonormal Systems and Quadrature

Abstract

Estimation of memoryless nonlinearity is the simplest problem of nonlinearity and one of the most important problems on wireless communications. In some wireless communication fields such as pre-distortion of multiple-input and multiple-output systems, dual-input digital Doherty, and wireless physical layer identification, there is a demand to estimate the nonlinearity of multiple amplifiers simultaneously. In this paper, we presents a novel estimation method of memoryless nonlinearity of multiple amplifiers with low complexity and high stability based on weighted least squares, numerical integration, and good properties of orthonormal systems. While the conventional least-squares method is derived by focusing on the effect of noise added to the output, the proposed method focuses on the error of the polynomial approximation and is derived from the numerical integration of its probability expectation. In addition, we derive the theoretical analysis of the estimation error of the proposed method. The simulation results show that the proposed method achieves better estimation accuracy, higher stability, and lower computational cost than the conventional least squares. Also, the theoretical results and simulation results are consistent with each other.