Theoretical Investigation of Digital Predistortion System

Abstract

Some doubt has been cast upon the predistortion system applying indirect learning structure (IDLS). In this paper, using the polynomial model for the predistorter (PD), theoretical investigation and simulation on the predistortion system performance basing on IDLS is put out. The result shows that the performance of IDLS predistortion system is affected by PD modeling error and the measurement noise, and the upper bound of the system normalized nean square error (NMSE) caused by the measurement noise is just the noise to signal ration, and if the measurement noise is low enough, there is a NMSE floor caused by modeling error. This is a novel result which can help to make predict approximate estimation of the factual IDLS predistortion system performance. Introduction Power amplifier (PA) is indispensable for modern wireless communication systems, but the inherent nonlinearity of PA leads to signal distortion. Predistortion methods are widely investigated in recent years for compensating PA nonlinearity, and the baseband predistortion method is been focused on for its effectiveness and lower cost [1-3]. In exiting researches, there are two kinds of predistorter (PD) structure, direct learning structure (DLS) and indirect learning structure (IDLS). IDLS is put forward by Gao in 1991 to improve the linearity of speaker [4]. And in 2003 Marsalek applied IDLS in a polynomial modeled baseband predistortion system [5]. The key idea of IDLS is using postdistorter, which can distort the amplified signal back to its original form, as PD. Although it is proved by experiments that IDLS exhibits good in improving linearity of PA system [3, 6], there are still voices of doubt to it. For example, Morgan believed that noise inevitable found in measurement system bring bias error to the IDLS PD parameter estimation [7], which will degrade the PD performance significantly. As a result, later studies mainly concentrated on DLS Predistortion system [8], which has much complex algorithm and system structure. In this paper, the effect of measurement noise and modeling error on IDLS PD algorithm is provided by theoretical analysis, and proved by simulation. This will be a direct evidence for the effectiveness of IDLS Predistortion system. System model Predistortion system using IDLS is shown in Fig. 1. The baseband equivalent model of PA is defined as ( ) G • , u is the input signal and v is the feedback signal of PA, defined as ( ) v G u = . The expected output of the postdistorter ( ) post F • is u , i.e. ( ) post u F v = . Obviously, ( ) post F • is the inverse function of ( ) G • , and 1 ( ) ( ) post F G − • = • . If PD is copied from postdistorter, it must satisfy 1 ( ( )) ( ( )) pre G F s G G s s − = = . Here, PD is modeled as L+1 order polynomial: ( ) 0 L l l l u PD v c v v = = =∑ International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 1150 Where ( 0.. ) l c l L = is coefficient of the polynomial. The actual feedback signal is y v a = + , where a is the measurement noise. In Morgan’s view, because [ ] [ ] l l E y E v ≠ , the estimation of l c derived from y is biased. But the amount of this bias is not given and the effect on system performance is not discussed. In the following section, with measurement noise a , theoretical analysis and simulation on predistortion system using IDLS is shown, here Least-square (LS) algorithm is applied to estimate PD parameters l c . PD algorithm v s u ( ) pre F • ( ) G •