Contents 1. Introduction
The increasing utilization of non-constant amplitude modulations in digital communications motivates the main idea of this work1 which is the identification of the transfer characteristic of a nonlinear system (i.e. an HPA) and its subsequent application in a pre-distortion algorithm whose formulation, by means of a cost function, can achieve convergence according to some specific restrictions. The modeling and estimation of the inverse transfer characteristics of a non-linear device is an active research area looking for the maximum reduction of the harmful effects introduced by the amplitude (AM/AM) and phase (AM/PM) distortion in digital communications [1]. A comparison of some research results for the practical application of pre-distortion techniques suggest that different proposed ways for the estimation feature also different benefits in contrast to the overall system cost, where some related key points to evaluate such benefits are the power efficiency improvement, accuracy of the estimated curves and computational complexity of the implemented process. In previous work we have studied only the compensation of AM/AM distortion using coarse estimation of the statistics taken out from sampled signals at the input and output of the HPA. This current work also consider such discrete versions of the input and output of the HPA as the only available information to design and apply pre-distortion over the complex base-band input signal in a non-constant amplitude modulation scheme, such as M-QAM in OFDM. Here we spread the scope of the experiment for the compensation of the AM/PM distortion too. We note that the treatment and modeling of the AM/PM effect would strictly require to consider the signal delay introduced by analog stages in the transmission chain. However, since our main purpose is to evaluate how an specific polynomial approach fits the inverse transfer curves, this “memory” effect is constrained to be ideal defining no time delays between input and output samples at the HPA. According to that, a well known memoryless AM/AM and AM/PM non-linear model is applied to distort data in the simulations [2]. However, the algorithm herein described must be of general applicability since in a real scheme there is not a priori knowledge about the time-varying non linear response of the HPA due, for instance, to temperature changes and age of the equipment. The latter means that the adaptive capability, desirable to make the system able to follow variations in the performance of the HPA, will be determined by the convergence rate of the algorithm, which in turns depends on the input signal statistic distribution and how the non-linearity is modeled. Use of adaptive algorithms, such as LMS or RLS, have already been proposed to compensate non-linear distortions by estimating coefficients in polynomial non-linear models [3] [4]. Nevertheless, many problems have arisen when such optimization algorithms have been directly applied. Therefore its original updating structure requires modifications, and some restrictions must be stated especially when dealing with rational-based cost functions, as in this case, since they are plagued by the appearance of local minima that result in a threatened convergence capacity.
