This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1 Output Impedance Mismatch Effects on the Linearity Performance of Digitally Predistorted Power Amplifiers Efrain Zenteno, Student Member, IEEE, Magnus Isaksson, Senior Member, IEEE,and Peter Händel,SeniorMember,IEEE Abstract—This paper analyzes the effects of load impedance plifiers are one of the main contributors to nonlinear distortions mismatch in power amplifiers which linearity has been enhanced in the system. These nonlinear distortions decrease the overall using various digital predistortion (DPD) algorithms. Two dif- throughput and capacity of the network. Therefore, the enhance- ferent power amplifier architectures are considered: a class AB and a Doherty amplifier and three model structures for the DPD ment of amplifier performance has been a subject of intense re- model are compared: memoryless polynomial (MLP), general search for the last several decades. memory polynomial (GMP) and Kautz-Volterra functions (KV). One of the most attractive and extended techniques to im- This paper provides a sensitivity analysis of the linearized ampli- prove amplifier performance is digital predistortion (DPD). fiers under load mismatch conditions and reports the performance DPD is implemented entirely in digital platforms and is flexible, when dynamic parameter identification for the DPD is used to compensate for the changes in the load impedance. In general, inexpensive, and easy to implement. DPD enhances amplifier power amplifiers linearity is sensitive to load impedance mis- linearity and enables its operation at higher power levels, which match. Linearity may degrade as much as 10 dB (in normalized improves its energy efficiency [1]. Several forms of DPD have mean square error) according to the magnitude and the phase been proposed in the literature (see [2] and [3] and references of the reflection coefficient provided by the load impedance. therein). Predistorters compensate nonlinear effects presented However, depending on the amplifier design, the sensitivity to load impedance mismatch varies. While the Doherty amplifier in the transmitter, such that, the tandem connection of the studied show significant linearity degradations in the in-band and predistorter and amplifier is a linear function. Predistorters out-of-band distortions, the out-of-band distortions of the studied are constructed in various ways e.g., as Volterra models [4] class AB were less sensitive to the load impedance mismatch. In and pruned forms of Volterra series, as generalized memory adaptive DPD schemes, the performance obtained in the MLP polynomials (GMP) [5], and dynamic deviation reduction model does not benefit from the updating scheme and the perfor- mance achieved is similar to a static case, where no updates are models [1], [6]. In addition, artificial neural networks [7], [8] made. This stresses the memory requirements in the predistorter. and separable basis functions [9] are examples of different When employing the GMP and the KV models in an adaptive DPD forms of predistorter models. scheme, they tackle to a larger extent the linearity degradations Despite large research efforts aimed at studying DPD tech- due to load impedance mismatch. niques, the vast majority of these techniques have been tested under match impedance conditions. In match conditions, the Index Terms—Digital predistortion, impedance mismatch, load impedance of the load (antenna) that is connected to the am- impedance, power amplifiers. plifier is the conjugate of the output impedance of the amplifier. Hence, the maximum power transfer is achieved [10]. In this case, the antenna absorbs all the incoming power, and zero re- I. INTRODUCTION flections are returned to the amplifier. An impedance mismatch is defined as a deviation from the ideal impedance value. A load OWER amplifiers are one of the main building blocks in impedance mismatch creates reflections, which travel back to wireless networks, because they spend a significant por- P the amplifier and affect its behavior. A load impedance mis- tion of the total energy in the network. In addition, power am- match may appear because of faulty cables and transmission lines or because of objects located near the antenna creating coupling effects and altering antennaproperties.Thelatteris Manuscript received September 02, 2014; revised December 03, 2014; ac- cepted December 22, 2014. a well-known problem in the cellphone manufacturing industry E. Zenteno is with the Department of Electronics, Mathematics, and Natural [11]. Sciences, University of Gävle, SE 80176 Gävle, Sweden, and also with the De- Load impedance mismatch can be avoided by using an iso- partment of Signal Processing, Royal Institute of Technology KTH, SE-100 44 Stockholm, Sweden (e-mail: [email protected]). lator at the amplifier output; as the reflected waves will be ab- M. Isaksson is with the Department of Electronics, Mathematics, and Natural sorbed by the termination load in the isolator [10]. However, Sciences, University of Gävle, SE 80176 Gävle, Sweden (e-mail: [email protected]). isolators are not desired at the output of amplifiers because they P. Händel is with the Department of Signal Processing, Royal Institute of Technology KTH, Stockholm, Sweden (e-mail: [email protected]). are expensive and because they can be associated with nonlinear Color versions of one or more of the figures in this paper are available online distortions [12]. Furthermore, the forthcoming multiband com- at http://ieeexplore.ieee.org. munication scenarios may require the isolator to operate in sev- Digital Object Identifier 10.1109/TMTT.2014.2387060 0018-9480 © 2015 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/ redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES eral frequency bands, causing design challenges and increased pare the behavior of the different DPD models and its robust- cost [13]. For these reasons, this paper studies an isolator-free ness to load impedance mismatch. Secondly, the paper studies scenario. the performance convergence of an adaptive DPD scheme for In general, the load impedance mismatch at the ampli- an amplifier subjected to variations of the load impedance. In fier degrades the performance of a wireless network. First, this second scenario, the DPD parameters are updated for each by shrinking the coverage as total radiated power reduces. load impedance. Thus, from a linearity perspective, the steady Secondly, by decreasing the throughput because the ampli- state performance indicates how well the DPD models cope with fier changes its operating point and may produce significant a load impedance mismatch in the amplifier. Furthermore, we amount of nonlinear distortions [14]. Moreover, an amplifier compare two different hardware amplifiers architectures that are in load impedance mismatch may reduce its efficiency [15]. widely used. In summary, the effects of the load impedance mismatch may This paper outlines as follow: Section II reviews the relevant oppose the benefits obtained by using a DPD technique. Thus, background, and discusses the effects of load impedance mis- when a load impedance mismatch occurs, a DPD-enhanced match at the amplifier, particularly, for the class AB and Do- amplifier may present severe degradations such that the DPD herty. Further, Section II lists amplifier evaluation metrics and has a negative effect over the linearity of the transmitter [14]. covers the different DPD techniques studied. Section III de- A study of the effects of load impedance mismatch in dif- scribes the measurement test setup and the methodology used ferent amplifier architectures was presented in [16], but the in the experiments. The results and analysis are presented in study did not include linearization techniques as DPD for the Section IV. Finally, discussions and conclusions are provided amplifiers. A sensitivity study of a DPD-linearized amplifier in Section V and VI. under mismatch conditions [14] showed large variations for different load impedances. However, the DPD model studied was a memoryless polynomial (MLP), which is not currently II. THEORY a state-of-the-art linearization model. Several DPD models This papers studies two types of power amplifiers architec- are more powerful for amplifier linearization (see [17] and tures: A class AB and a Doherty. Despite the design differences references therein). The authors in [18] analyzed the effect from 1 transistor design of the class AB to a 2 transistors par- of load mismatch in a DPD-enhanced Doherty amplifier. The allel design of the Doherty, the main difference is that Doherty results were obtained using a black-box simulation of the have higher efficiency than class AB. amplifier under load mismatch conditions. The drawback of this approach is that a black-box model of the amplifier may not A. Power Amplifier Design be valid for different load impedances used in the simulation, as shown in [19]. Although the control or “knowledge” of the In general, power amplifier design involves the tradeoff be- load impedance may yield improved linearization techniques tween different metrics, i.e.,