Modified gram-schmidt orthogonalization and QR decompositon extraction for digital predistorter

Digital baseband predistorter modeled by a memory polynomial and implemented by an indirect learning architecture is among the most cost effective method for linearizing power amplifier. Due to high correlation between each element of polynomial, general parameter extraction algorithms, e.g. Cholesky decomposition combined with linear least square method, have worse numerical stability when higher order terms are included. Orthogonal polynomials are good substitutes, but finding closed-form expressions for orthogonal polynomials for an arbitrary distribution is generally a difficult problem, and the derivations are not easily generalized. Based on modified Gram-Schmidt (MGS) orthogonalization method, the article put forward an easy, novel method to find orthogonal basis for random input signal with distribution function of uniformly distributed between 0 and 1. At same time, we use QR decomposition not linear least squares to obtain coefficients of predistorter. The method guarantees good numerical stability from above two aspects, and can be easily realized in real engineering. Simulation exhibits the effective of the methods.