Weighted Least Squares With Orthonormal Polynomials and Numerical Integration for Estimation of Memoryless Nonlinearity

The nonlinearity of amplifiers is one of the major impairments in wireless communications. In this letter, we propose a novel estimation method for the memoryless nonlinearity of amplifiers using weighted least squares and provide its theoretical error analysis on complex Gaussian signals. In the proposed method, the input signal and weight value are obtained via numerical integration formulas. Simulation results show that the proposed method can achieve a sufficiently low reconstruction error with 10 measurement samples on the estimation of the 13th-order nonlinearity. In addition, the simulation and theoretical results are consistent with each other.