dpd_pdf.rar_预失真_DPD_通讯编程文档下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/624fc51774bc5c0105531052/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc51774bc5c0105531052/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 10, OCTOBER 2008 2237</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">Digital Predistortion for Envelope-Tracking</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls1 ws0">Power Ampliﬁers Using Decomposed</div><div class="t m0 x4 h3 y4 ff1 fs1 fc0 sc0 ls1 ws0">Piecewise Volterra Series</div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls1 ws0">Anding Zhu, Member, IEEE, Paul J. Draxler, Member, IEEE, Chin Hsia, Thomas J. Brazil, Fellow, IEEE,</div><div class="t m0 x6 h4 y6 ff1 fs2 fc0 sc0 ls1 ws0">Donald F. Kimball, Member, IEEE, and Peter M. Asbeck, Fellow, IEEE</div><div class="t m0 x7 h5 y7 ff3 fs3 fc0 sc0 ls1 ws0">Abstract—Due to dynamic changes of supply voltage, envelope-</div><div class="t m0 x1 h6 y8 ff4 fs3 fc0 sc0 ls1 ws0">tracking (ET) power ampliﬁers (PAs) exhibit very distinct charac-</div><div class="t m0 x1 h6 y9 ff4 fs3 fc0 sc0 ls1 ws0">teristics in different power regions. It is very difﬁcult to compen-</div><div class="t m0 x1 h6 ya ff4 fs3 fc0 sc0 ls1 ws0">sate the distortion induced by these ampliﬁers by employing con-</div><div class="t m0 x1 h6 yb ff4 fs3 fc0 sc0 ls1 ws0">ventional digital predistortion techniques. In this paper, by intro-</div><div class="t m0 x1 h6 yc ff4 fs3 fc0 sc0 ls1 ws0">ducing a new piecewise Volterra model based on a vector threshold</div><div class="t m0 x1 h6 yd ff4 fs3 fc0 sc0 ls1 ws0">decomposition technique, we ﬁrst set several thresholds in the input</div><div class="t m0 x1 h6 ye ff4 fs3 fc0 sc0 ls1 ws0">power level according to the PA characteristics, and decompose</div><div class="t m0 x1 h6 yf ff4 fs3 fc0 sc0 ls1 ws0">the input complex envelope signal into several sub-signals by using</div><div class="t m0 x1 h6 y10 ff4 fs3 fc0 sc0 ls1 ws0">these thresholds. We then process each sub-signal separately by</div><div class="t m0 x1 h5 y11 ff4 fs3 fc0 sc0 ls1 ws0">employing the dynamic deviation reduction-based Volterra series,</div><div class="t m0 x1 h6 y12 ff4 fs3 fc0 sc0 ls1 ws0">and ﬁnally recombine them together to produce the predistorted</div><div class="t m0 x1 h6 y13 ff4 fs3 fc0 sc0 ls1 ws0">output. Experimental results show that by using this new decom-</div><div class="t m0 x1 h6 y14 ff4 fs3 fc0 sc0 ls1 ws0">posed piecewise digital predistorter model, the distinct character-</div><div class="t m0 x1 h6 y15 ff4 fs3 fc0 sc0 ls1 ws0">istics of the ET system at different signal power levels can be accu-</div><div class="t m0 x1 h6 y16 ff4 fs3 fc0 sc0 ls1 ws0">rately modeled, and thus, the distortion, including both static non-</div><div class="t m0 x1 h6 y17 ff4 fs3 fc0 sc0 ls1 ws0">linearities and memory effects, caused by the ampliﬁer nonlinear</div><div class="t m0 x1 h6 y18 ff4 fs3 fc0 sc0 ls1 ws0">behavior can be effectively compensated.</div><div class="t m0 x7 h5 y19 ff3 fs3 fc0 sc0 ls1 ws0">Index Terms—Behavioral modeling, envelope tracking (ET), lin-</div><div class="t m0 x1 h6 y1a ff4 fs3 fc0 sc0 ls1 ws0">earization, power ampliﬁer (PA), predistorter, Volterra series.</div><div class="t m0 x8 h7 y1b ff1 fs4 fc0 sc0 ls1 ws0">I. INTRODUCTION</div><div class="t m0 x1 h8 y1c ff4 fs6 fc0 sc0 ls1 ws0">I</div><div class="t m0 x9 h7 y1d ff1 fs4 fc0 sc0 ls1 ws0">N MODERN wireless communication systems, non-</div><div class="t m0 x9 h7 y1e ff1 fs4 fc0 sc0 ls1 ws0">constant envelope modulation techniques are normally</div><div class="t m0 x1 h7 y1f ff1 fs4 fc0 sc0 ls1 ws0">employed. The traditional approach to linearly amplifying</div><div class="t m0 x1 h7 y20 ff1 fs4 fc0 sc0 ls1 ws0">these nonconstant envelope signals is to “backoff” the output</div><div class="t m0 x1 h7 y21 ff1 fs4 fc0 sc0 ls1 ws0">power of RF power ampliﬁers (PAs) until the distortion level</div><div class="t m0 x1 h7 y22 ff1 fs4 fc0 sc0 ls1 ws0">is within acceptable limits. Unfortunately, this results in low</div><div class="t m0 x1 h7 y23 ff1 fs4 fc0 sc0 ls1 ws0">power efﬁciency since these modulated signals often have a</div><div class="t m0 x1 h7 y24 ff1 fs4 fc0 sc0 ls1 ws0">high peak-to-average power ratio (PAPR) [1].</div><div class="t m0 xa h7 y25 ff1 fs4 fc0 sc0 ls1 ws0">Envelope tracking (ET) is one of the most promising tech-</div><div class="t m0 x1 h7 y26 ff1 fs4 fc0 sc0 ls1 ws0">niques for high efﬁciency operation for nonconstant envelope</div><div class="t m0 xb h9 y27 ff1 fs5 fc0 sc0 ls1 ws0">Manuscript received February 1, 2008; revised July 24, 2008. First published</div><div class="t m0 x1 h9 y28 ff1 fs5 fc0 sc0 ls1 ws0">September 23, 2008; current version published October 8, 2008. This work was</div><div class="t m0 x1 h9 y29 ff1 fs5 fc0 sc0 ls1 ws0">supported by the Science Foundation Ireland under the Principal Investigator</div><div class="t m0 x1 h9 y2a ff1 fs5 fc0 sc0 ls1 ws0">Award, University College Dublin, Dublin, Ireland, and in part by the Center</div><div class="t m0 x1 h9 y2b ff1 fs5 fc0 sc0 ls1 ws0">for Wireless Communications, University of California at San Diego.</div><div class="t m0 xb h9 y2c ff1 fs5 fc0 sc0 ls1 ws0">A. Zhu and T. J. Brazil are with the School of Electrical, Electronic and</div><div class="t m0 x1 h9 y2d ff1 fs5 fc0 sc0 ls1 ws0">Mechanical Engineering, University College Dublin, Dublin 4, Ireland (e-mail:</div><div class="t m0 x1 h9 y2e ff1 fs5 fc0 sc0 ls1 ws0">anding.zhu@ucd.ie; tom.brazil@ucd.ie).</div><div class="t m0 xb h9 y2f ff1 fs5 fc0 sc0 ls1 ws0">P. J. Draxler is with the Department of Electrical and Computer Engineering,</div><div class="t m0 x1 h9 y30 ff1 fs5 fc0 sc0 ls1 ws0">University of California at San Diego, La Jolla, CA 92093 USA, and also</div><div class="t m0 x1 h9 y31 ff1 fs5 fc0 sc0 ls1 ws0">with Qualcomm Inc., San Diego, CA 92121 USA (e-mail: pdraxler@qual-</div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls1 ws0">comm.com).</div><div class="t m0 xb h9 y33 ff1 fs5 fc0 sc0 ls1 ws0">C. Hsia, D. F. Kimball, and P. M. Asbeck are with the Department of Elec-</div><div class="t m0 x1 h9 y34 ff1 fs5 fc0 sc0 ls1 ws0">trical and Computer Engineering, University of California at San Diego, La</div><div class="t m0 x1 h9 y35 ff1 fs5 fc0 sc0 ls1 ws0">Jolla, CA 92093 USA (e-mail: chhsia@ucsd.edu; dfkimball@soe.ucsd.edu; as-</div><div class="t m0 x1 h9 y36 ff1 fs5 fc0 sc0 ls1 ws0">beck@ece.ucsd.edu).</div><div class="t m0 xb h9 y37 ff1 fs5 fc0 sc0 ls1 ws0">Color versions of one or more of the ﬁgures in this paper are available online</div><div class="t m0 x1 h9 y38 ff1 fs5 fc0 sc0 ls1 ws0">at http://ieeexplore.ieee.org.</div><div class="t m0 xb h9 y39 ff1 fs5 fc0 sc0 ls1 ws0">Digital Object Identiﬁer 10.1109/TMTT.2008.2003529</div><div class="t m0 xc h7 y3a ff1 fs4 fc0 sc0 ls1 ws0">signals [2]. By superimposing the envelope signal at the drain</div><div class="t m0 xc h7 y3b ff1 fs4 fc0 sc0 ls1 ws0">voltage, the RF transistor in the PA can be operated continu-</div><div class="t m0 xc h7 y3c ff1 fs4 fc0 sc0 ls1 ws0">ously in the compression regime over a wide range of power</div><div class="t m0 xc h7 y3d ff1 fs4 fc0 sc0 ls1 ws0">levels, which signiﬁcantly increases power efﬁciency of the PA.</div><div class="t m0 xc h7 y3e ff1 fs4 fc0 sc0 ls1 ws0">However, the ET system has inherent nonlinearities associated</div><div class="t m0 xc h7 y3f ff1 fs4 fc0 sc0 ls1 ws0">with the gain and phase variations as the drain voltage changes.</div><div class="t m0 xc h7 y40 ff1 fs4 fc0 sc0 ls1 ws0">As standard RF PAs, for wideband and high-power operation,</div><div class="t m0 xc h7 y41 ff1 fs4 fc0 sc0 ls1 ws0">memory effects will also become apparent in the ET system. In</div><div class="t m0 xc h7 y42 ff1 fs4 fc0 sc0 ls1 ws0">order to improve the system performance, it is necessary to em-</div><div class="t m0 xc h7 y43 ff1 fs4 fc0 sc0 ls1 ws0">ploy digital predistortion techniques to remove nonlinear distor-</div><div class="t m0 xc h7 y44 ff1 fs4 fc0 sc0 ls1 ws0">tion and memory effects [3].</div><div class="t m0 xd h7 y45 ff1 fs4 fc0 sc0 ls1 ws0">Previously, we proposed an open-loop digital predistorter</div><div class="t m0 xc h7 y46 ff1 fs4 fc0 sc0 ls1 ws0">(DPD) for RF PAs with a ﬁxed supply voltage in [4]. This</div><div class="t m0 xc h7 y47 ff1 fs4 fc0 sc0 ls1 ws0">DPD approach is derived from the</div><div class="t m0 xe ha y48 ff2 fs4 fc0 sc0 ls1 ws0">dynamic deviation re-</div><div class="t m0 xc h7 y49 ff2 fs4 fc0 sc0 ls1 ws0">duction-based Volterra series [5] that allows simultaneous</div><div class="t m0 xc h7 y4a ff1 fs4 fc0 sc0 ls1 ws0">compensation for nonlinear distortion and memory effects with</div><div class="t m0 xc h7 y4b ff1 fs4 fc0 sc0 ls1 ws0">a small number of parameters. Based on the</div><div class="t m0 xf h7 y4c ff1 fs4 fc0 sc0 ls1 ws0">th-order post-in-</div><div class="t m0 xc h7 y4d ff1 fs4 fc0 sc0 ls1 ws0">verse theory [6], the parameters of this DPD can be directly</div><div class="t m0 xc h7 y4e ff1 fs4 fc0 sc0 ls1 ws0">estimated from the measured input and output of the PA with</div><div class="t m0 xc h7 y4f ff1 fs4 fc0 sc0 ls1 ws0">a simple ofﬂine characterization process. This eliminates the</div><div class="t m0 xc h7 y50 ff1 fs4 fc0 sc0 ls1 ws0">real-time closed-loop adaptation requirement, and removes the</div><div class="t m0 xc h7 y51 ff1 fs4 fc0 sc0 ls1 ws0">necessity to implement the parameter-estimation algorithms</div><div class="t m0 xc h7 y52 ff1 fs4 fc0 sc0 ls1 ws0">in real digital circuits, which signiﬁcantly reduces system</div><div class="t m0 xc h7 y53 ff1 fs4 fc0 sc0 ls1 ws0">complexity and implementation cost. However, this type of</div><div class="t m0 xc h7 y54 ff1 fs4 fc0 sc0 ls1 ws0">model cannot be applied directly to the ET system. Since the</div><div class="t m0 xc h7 y55 ff1 fs4 fc0 sc0 ls1 ws0">ampliﬁer in the ET system exhibits very distinct characteristics</div><div class="t m0 xc h7 y56 ff1 fs4 fc0 sc0 ls1 ws0">at the different power levels, it is very difﬁcult to characterize</div><div class="t m0 xc h7 y57 ff1 fs4 fc0 sc0 ls1 ws0">the behavior of the ET PA by using a single dynamic Volterra</div><div class="t m0 xc h7 y58 ff1 fs4 fc0 sc0 ls1 ws0">function for the entire range of the input signal level.</div><div class="t m0 xd h7 y59 ff1 fs4 fc0 sc0 ls1 ws0">In this paper, we propose an extension to the Volterra model</div><div class="t m0 xc h7 y5a ff1 fs4 fc0 sc0 ls1 ws0">employed in [4] so that the DPD approach proposed in [4] can</div><div class="t m0 xc h7 y5b ff1 fs4 fc0 sc0 ls1 ws0">be used to linearize the ET system. This is achieved by intro-</div><div class="t m0 xc h7 y5c ff1 fs4 fc0 sc0 ls1 ws0">ducing a new decomposed piecewise Volterra model based on</div><div class="t m0 xc h7 y5d ff1 fs4 fc0 sc0 ls1 ws0">a vector threshold decomposition technique. In this approach,</div><div class="t m0 xc h7 y5e ff1 fs4 fc0 sc0 ls1 ws0">we ﬁrst set several thresholds in the input power level according</div><div class="t m0 xc h7 y5f ff1 fs4 fc0 sc0 ls1 ws0">to the characteristics of the PA. We then decompose the input</div><div class="t m0 xc h7 y60 ff1 fs4 fc0 sc0 ls1 ws0">complex envelope signal into several sub-signals by using these</div><div class="t m0 xc h7 y61 ff1 fs4 fc0 sc0 ls1 ws0">thresholds, and continue to process each sub-signal separately</div><div class="t m0 xc h7 y62 ff1 fs4 fc0 sc0 ls1 ws0">by employing a low-order dynamic deviation reduction-based</div><div class="t m0 xc h7 y63 ff1 fs4 fc0 sc0 ls1 ws0">Volterra series, and ﬁnally recombine them together to produce</div><div class="t m0 xc h7 y64 ff1 fs4 fc0 sc0 ls1 ws0">the predistorted output. By employing this new piecewise type</div><div class="t m0 xc h7 y65 ff1 fs4 fc0 sc0 ls1 ws0">of DPD model, the distinct characteristics of the ET system at</div><div class="t m0 xc h7 y66 ff1 fs4 fc0 sc0 ls1 ws0">different signal power levels can be accurately modeled, and</div><div class="t m0 xc h7 y67 ff1 fs4 fc0 sc0 ls1 ws0">thus, the distortion caused by the nonlinear behavior of the ET</div><div class="t m0 xc h7 y68 ff1 fs4 fc0 sc0 ls1 ws0">system can be effectively compensated. As in the model in [4]</div><div class="t m0 x10 h9 y69 ff1 fs5 fc0 sc0 ls1 ws0">0018-9480/$25.00 © 2008 IEEE</div><div class="t m0 x11 hb y6a ff5 fs7 fc0 sc0 ls1 ws0">Authorized licensed use limited to: University College Dublin. Downloaded on October 8, 2008 at 08:06 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.616162,0.000000,0.000000,1.616162,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc51774bc5c0105531052/bg2.jpg"><div class="t m0 x12 h2 y1 ff6 fs0 fc0 sc0 ls0 ws0">2238 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 10, OCTOBER 2008</div><div class="t m0 x12 h9 y6b ff6 fs5 fc0 sc0 ls1 ws0">Fig. 1. Block diagram of an ET system.</div><div class="t m0 x12 h7 y6c ff6 fs4 fc0 sc0 ls1 ws0">and [5], the output of this new model is also linear in relation to</div><div class="t m0 x12 h7 y6d ff6 fs4 fc0 sc0 ls1 ws0">all of its parameters so that the model can be easily character-</div><div class="t m0 x12 h7 y6e ff6 fs4 fc0 sc0 ls1 ws0">ized by using the same linear estimation algorithms as presented</div><div class="t m0 x12 h7 y6f ff6 fs4 fc0 sc0 ls1 ws0">in [4].</div><div class="t m0 x13 h7 y70 ff6 fs4 fc0 sc0 ls1 ws0">This paper is organized as follows. In Section II, we brieﬂy</div><div class="t m0 x12 h7 y71 ff6 fs4 fc0 sc0 ls1 ws0">introduce the ET system. Section III presents some conven-</div><div class="t m0 x12 h7 y72 ff6 fs4 fc0 sc0 ls1 ws0">tional approaches to linearizing the ET system. Section IV in-</div><div class="t m0 x12 h7 y73 ff6 fs4 fc0 sc0 ls1 ws0">troduces the vector threshold decomposition technique and the</div><div class="t m0 x12 h7 y74 ff6 fs4 fc0 sc0 ls1 ws0">new digital predistortion model structure. Parameter-extraction</div><div class="t m0 x12 h7 y75 ff6 fs4 fc0 sc0 ls1 ws0">procedures and system implementation are also discussed in this</div><div class="t m0 x12 h7 y76 ff6 fs4 fc0 sc0 ls1 ws0">section. The experimental results are given in Section V. A con-</div><div class="t m0 x12 h7 y77 ff6 fs4 fc0 sc0 ls1 ws0">clusion is then presented in Section VI.</div><div class="t m0 x14 h7 y78 ff6 fs4 fc0 sc0 ls1 ws0">II. ET S</div><div class="t m0 x15 h9 y79 ff6 fs5 fc0 sc0 ls1 ws0">YSTEM</div><div class="t m0 x13 h7 y7a ff6 fs4 fc0 sc0 ls1 ws0">A block diagram of an ET system is shown in Fig. 1. The</div><div class="t m0 x12 h7 y7b ff6 fs4 fc0 sc0 ls1 ws0">envelope signal is ﬁrst detected from the original input signal</div><div class="t m0 x12 h7 y7c ff6 fs4 fc0 sc0 ls1 ws0">and then ampliﬁed by an envelope ampliﬁer, providing a dy-</div><div class="t m0 x12 h7 y7d ff6 fs4 fc0 sc0 ls1 ws0">namic drain (or collector) voltage to the RF transistor in the</div><div class="t m0 x12 h7 y7e ff6 fs4 fc0 sc0 ls1 ws0">main PA. At the same time, the RF signal is ampliﬁed by the</div><div class="t m0 x12 h7 y7f ff6 fs4 fc0 sc0 ls1 ws0">main RF PA. The delay line is to compensate the misalignment</div><div class="t m0 x12 h7 y80 ff6 fs4 fc0 sc0 ls1 ws0">between the envelope and RF signal. In modern ET systems,</div><div class="t m0 x12 h7 y81 ff6 fs4 fc0 sc0 ls1 ws0">the envelop signal can be directly generated from the baseband</div><div class="t m0 x12 h7 y82 ff6 fs4 fc0 sc0 ls1 ws0">in-phase/quadrature (I/Q) waveforms [1].</div><div class="t m0 x13 h7 y83 ff6 fs4 fc0 sc0 ls1 ws0">In the ET system, the gate (or base) of the RF transistor in the</div><div class="t m0 x12 h7 y84 ff6 fs4 fc0 sc0 ls1 ws0">main PA is normally biased in the class AB or class C mode, but</div><div class="t m0 x12 h7 y85 ff6 fs4 fc0 sc0 ls1 ws0">the drain (or collector) voltage is dynamically controlled by the</div><div class="t m0 x12 h7 y86 ff6 fs4 fc0 sc0 ls1 ws0">envelope ampliﬁer and is changing in proportion to the envelope</div><div class="t m0 x12 h7 y87 ff6 fs4 fc0 sc0 ls1 ws0">of the RF input. This tracking process can be continued down</div><div class="t m0 x12 h7 y88 ff6 fs4 fc0 sc0 ls1 ws0">to a selected point on the low-voltage side, and up to a point</div><div class="t m0 x12 h7 y89 ff6 fs4 fc0 sc0 ls1 ws0">where the RF swing reaches breakdown level. Due to full rail-to-</div><div class="t m0 x12 h7 y8a ff6 fs4 fc0 sc0 ls1 ws0">rail voltage swing, in this system, the RF PA is continuously</div><div class="t m0 x12 h7 y8b ff6 fs4 fc0 sc0 ls1 ws0">operated in or near saturation for all envelope signal levels, and</div><div class="t m0 x12 h7 y8c ff6 fs4 fc0 sc0 ls1 ws0">therefore, high power efﬁciency can be obtained [1].</div><div class="t m0 x13 h7 y8d ff6 fs4 fc0 sc0 ls1 ws0">Although the output of the ET PA can be kept linear with</div><div class="t m0 x12 h7 y8e ff6 fs4 fc0 sc0 ls1 ws0">the input over a wide range, there are inherent nonlinearities in</div><div class="t m0 x12 h7 y8f ff6 fs4 fc0 sc0 ls1 ws0">the ET system [7]–[11]. Due to dynamic changes of the supply</div><div class="t m0 x12 h7 y90 ff6 fs4 fc0 sc0 ls1 ws0">voltage, the ET PA exploits very distinct characteristics in dif-</div><div class="t m0 x12 h7 y91 ff6 fs4 fc0 sc0 ls1 ws0">ferent power regions. This nonlinear behavior is very different</div><div class="t m0 x12 h7 y92 ff6 fs4 fc0 sc0 ls1 ws0">from what we normally see in the typical linear ampliﬁers with</div><div class="t m0 x12 h7 y93 ff6 fs4 fc0 sc0 ls1 ws0">a ﬁxed supply voltage. For instance, Fig. 2 shows an example</div><div class="t m0 x12 h7 y94 ff6 fs4 fc0 sc0 ls1 ws0">of gain and phase characteristics of a gallium nitride (GaN)</div><div class="t m0 x12 h7 y95 ff6 fs4 fc0 sc0 ls1 ws0">ET PA excited by a wideband code division multiple access</div><div class="t m0 x12 h7 y96 ff6 fs4 fc0 sc0 ls1 ws0">(WCDMA) signal, where we can see that large gain reduction</div><div class="t m0 x16 h9 y97 ff6 fs5 fc0 sc0 ls1 ws0">Fig. 2. Sample characteristics of an ET PA. (a) Normalized gain versus normal-</div><div class="t m0 x16 h9 y98 ff6 fs5 fc0 sc0 ls1 ws0">ized input magnitude. (b) Phase changes versus normalized input magnitude.</div><div class="t m0 x16 h7 y99 ff6 fs4 fc0 sc0 ls1 ws0">occurs as the input signal (and ) is changed to the lower</div><div class="t m0 x16 h7 y9a ff6 fs4 fc0 sc0 ls1 ws0">values, which leads to gain expansion. While the power is in-</div><div class="t m0 x16 h7 y9b ff6 fs4 fc0 sc0 ls1 ws0">creased to the higher level, the gain is compressed again. The</div><div class="t m0 x16 h7 y9c ff6 fs4 fc0 sc0 ls1 ws0">phase remains ﬂat at low and medium power, but it changes</div><div class="t m0 x16 h7 y9d ff6 fs4 fc0 sc0 ls1 ws0">rapidly in high power. This behavior is device dependent, as</div><div class="t m0 x16 h7 y9e ff6 fs4 fc0 sc0 ls1 ws0">will become evident in Section V, where very different char-</div><div class="t m0 x16 h7 y9f ff6 fs4 fc0 sc0 ls1 ws0">acteristics are found for a silicon laterally diffused metal oxide</div><div class="t m0 x16 h7 ya0 ff6 fs4 fc0 sc0 ls1 ws0">semiconductor (Si LDMOS) PA.</div><div class="t m0 x17 h7 ya1 ff6 fs4 fc0 sc0 ls1 ws0">In the ET system, to avoid the</div><div class="t m0 x18 h7 ya2 ff6 fs4 fc0 sc0 ls1 ws0">voltage dropping to zero,</div><div class="t m0 x16 h7 ya3 ff6 fs4 fc0 sc0 ls1 ws0">detroughing is normally employed [8]. As a result, the drain</div><div class="t m0 x16 h7 ya4 ff6 fs4 fc0 sc0 ls1 ws0">voltage may not replicate the signal envelope with great accu-</div><div class="t m0 x16 h7 ya5 ff6 fs4 fc0 sc0 ls1 ws0">racy, which may introduce distortion to the system, especially at</div><div class="t m0 x16 h7 ya6 ff6 fs4 fc0 sc0 ls1 ws0">low power levels. Some memory effects from the bias networks</div><div class="t m0 x16 h7 ya7 ff6 fs4 fc0 sc0 ls1 ws0">may be reduced in the ET system compared to the ﬁxed-</div><div class="t m0 x16 h7 ya8 ff6 fs4 fc0 sc0 ls1 ws0">PAs because the drain voltage dynamically changes with the</div><div class="t m0 x16 h7 ya9 ff6 fs4 fc0 sc0 ls1 ws0">amplitude of the envelope. For wideband and high-power op-</div><div class="t m0 x16 h7 yaa ff6 fs4 fc0 sc0 ls1 ws0">eration, memory effects still become apparent. For example,</div><div class="t m0 x16 h7 yab ff6 fs4 fc0 sc0 ls1 ws0">thermal transients and trapping effects can introduce signiﬁ-</div><div class="t m0 x16 h7 yac ff6 fs4 fc0 sc0 ls1 ws0">cant memory effects to the system. Furthermore, due to limited</div><div class="t m0 x16 h7 yad ff6 fs4 fc0 sc0 ls1 ws0">bandwidth of the envelope ampliﬁer, frequency cutoff of the ET</div><div class="t m0 x16 h7 yae ff6 fs4 fc0 sc0 ls1 ws0">signal also causes memory effects. As shown in Fig. 2, memory</div><div class="t m0 x16 h7 yaf ff6 fs4 fc0 sc0 ls1 ws0">effects may appear differently in different power regions. These</div><div class="t m0 x16 h7 yb0 ff6 fs4 fc0 sc0 ls1 ws0">nonlinear distortion and memory effects can signiﬁcantly reduce</div><div class="t m0 x16 h7 yb1 ff6 fs4 fc0 sc0 ls1 ws0">the overall output signal quality.</div><div class="t m0 x11 hb y6a ff5 fs7 fc0 sc0 ls1 ws0">Authorized licensed use limited to: University College Dublin. Downloaded on October 8, 2008 at 08:06 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.616162,0.000000,0.000000,1.616162,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc51774bc5c0105531052/bg3.jpg"><div class="t m0 x1 h2 y1 ff6 fs0 fc0 sc0 ls0 ws0">ZHU et al.: DIGITAL PREDISTORTION FOR ET PAs USING DECOMPOSED PIECEWISE VOLTERRA SERIES 2239</div><div class="t m0 x19 h7 yb2 ff6 fs4 fc0 sc0 ls1 ws0">III. LINEARIZING ET S</div><div class="t m0 x1a h9 yb3 ff6 fs5 fc0 sc0 ls1 ws0">YSTEM</div><div class="t m0 xa h7 yb4 ff6 fs4 fc0 sc0 ls1 ws0">To remove nonlinear distortion and improve system perfor-</div><div class="t m0 x1 h7 yb5 ff6 fs4 fc0 sc0 ls1 ws0">mance, DPDs are often employed in ET systems. In recent</div><div class="t m0 x1 h7 yb6 ff6 fs4 fc0 sc0 ls1 ws0">decades, various DPD systems have been proposed [3] with</div><div class="t m0 x1 h7 yb7 ff6 fs4 fc0 sc0 ls1 ws0">the main differences usually lying either in the implementa-</div><div class="t m0 x1 h7 yb8 ff6 fs4 fc0 sc0 ls1 ws0">tion of predistortion architectures or in parameter-extraction</div><div class="t m0 x1 h7 yb9 ff6 fs4 fc0 sc0 ls1 ws0">algorithms. There are two distinct methods to implement DPD</div><div class="t m0 x1 h7 yba ff6 fs4 fc0 sc0 ls1 ws0">algorithms, which are: 1) lookup tables (LUTs) and 2) analyt-</div><div class="t m0 x1 h7 ybb ff6 fs4 fc0 sc0 ls1 ws0">ical functions.</div><div class="t m0 xa h7 ybc ff6 fs4 fc0 sc0 ls1 ws0">The LUT-based DPD has been widely used because it is rela-</div><div class="t m0 x1 h7 ybd ff6 fs4 fc0 sc0 ls1 ws0">tively simple and easily implemented. Moreover, it can be ﬁtted</div><div class="t m0 x1 h7 ybe ff6 fs4 fc0 sc0 ls1 ws0">to any type of characteristics, including that of the ET. How-</div><div class="t m0 x1 h7 ybf ff6 fs4 fc0 sc0 ls1 ws0">ever, while wireless systems are migrating to wideband oper-</div><div class="t m0 x1 h7 yc0 ff6 fs4 fc0 sc0 ls1 ws0">ations, the bandwidth and dynamic range of the signals to be</div><div class="t m0 x1 h7 yc1 ff6 fs4 fc0 sc0 ls1 ws0">transmitted are expanded dramatically. In order to cover all of</div><div class="t m0 x1 h7 yc2 ff6 fs4 fc0 sc0 ls1 ws0">the operating regions, the LUT requires a large memory to store</div><div class="t m0 x1 h7 yc3 ff6 fs4 fc0 sc0 ls1 ws0">sufﬁcient data, which signiﬁcantly increases the system com-</div><div class="t m0 x1 h7 yc4 ff6 fs4 fc0 sc0 ls1 ws0">plexity. Furthermore, it is very difﬁcult to embed compensation</div><div class="t m0 x1 h7 yc5 ff6 fs4 fc0 sc0 ls1 ws0">for “memory effects” into the LUT.</div><div class="t m0 xa h7 yc6 ff6 fs4 fc0 sc0 ls1 ws0">The analytical function-based DPDs normally require less</div><div class="t m0 x1 h7 yc7 ff6 fs4 fc0 sc0 ls1 ws0">memory storage than the LUTs, and can operate with a small</div><div class="t m0 x1 h7 yc8 ff6 fs4 fc0 sc0 ls1 ws0">number of pre-decided parameters. Additionally, memory ef-</div><div class="t m0 x1 h7 yc9 ff6 fs4 fc0 sc0 ls1 ws0">fects can be easily built into these functions. A number of ana-</div><div class="t m0 x1 h7 yca ff6 fs4 fc0 sc0 ls1 ws0">lytical function-based memory DPDs have been developed and</div><div class="t m0 x1 h7 ycb ff6 fs4 fc0 sc0 ls1 ws0">some of them have been widely used, especially the polynomial-</div><div class="t m0 x1 h7 ycc ff6 fs4 fc0 sc0 ls1 ws0">like models, e.g., memory polynomials [12], [13], Hammerstein</div><div class="t m0 x1 h7 ycd ff6 fs4 fc0 sc0 ls1 ws0">and Wiener models [14], and various simpliﬁed Volterra-se-</div><div class="t m0 x1 h7 yce ff6 fs4 fc0 sc0 ls1 ws0">ries-based models [15]–[18].</div><div class="t m0 xa h7 ycf ff6 fs4 fc0 sc0 ls1 ws0">However, it has been found exceedingly difﬁcult to imple-</div><div class="t m0 x1 h7 yd0 ff6 fs4 fc0 sc0 ls1 ws0">ment these single function-based models in the ET system</div><div class="t m0 x1 h7 yd1 ff6 fs4 fc0 sc0 ls1 ws0">[8]–[11]. This is because, in this system, the characteristics</div><div class="t m0 x1 h7 yd2 ff6 fs4 fc0 sc0 ls1 ws0">of the PA are very different at different power regions. For</div><div class="t m0 x1 h7 yd3 ff6 fs4 fc0 sc0 ls1 ws0">instance, to linearize the PA shown in Fig. 2, the AM/AM and</div><div class="t m0 x1 h7 yd4 ff6 fs4 fc0 sc0 ls1 ws0">AM/PM characteristics of the DPD would look like the plots in</div><div class="t m0 x1 h7 yd5 ff6 fs4 fc0 sc0 ls1 ws0">Fig. 3, where both gain expansion and gain compression occur,</div><div class="t m0 x1 h7 yd6 ff6 fs4 fc0 sc0 ls1 ws0">and amplitude and phase change inconsistently in different</div><div class="t m0 x1 h7 yd7 ff6 fs4 fc0 sc0 ls1 ws0">regions. To ﬁt this distinct behavior over the entire power levels,</div><div class="t m0 x1 h7 yd8 ff6 fs4 fc0 sc0 ls1 ws0">a very high degree of nonlinearity order is required if a single</div><div class="t m0 x1 h7 yd9 ff6 fs4 fc0 sc0 ls1 ws0">polynomial-like model (e.g., a Volterra model) is employed.</div><div class="t m0 x1 h7 yda ff6 fs4 fc0 sc0 ls1 ws0">High-order nonlinear terms lead to very poor extrapolation</div><div class="t m0 x1 h7 ydb ff6 fs4 fc0 sc0 ls1 ws0">of the model, which sometimes dramatically degrades system</div><div class="t m0 x1 h7 ydc ff6 fs4 fc0 sc0 ls1 ws0">performance.</div><div class="t m0 xa h7 ydd ff6 fs4 fc0 sc0 ls1 ws0">One possible solution to model these distinct nonlinearities in</div><div class="t m0 x1 h7 yde ff6 fs4 fc0 sc0 ls1 ws0">the ET system is piecewise curve ﬁtting, whereby we can divide</div><div class="t m0 x1 h7 ydf ff6 fs4 fc0 sc0 ls1 ws0">the nonlinear curves into several segments based on the input</div><div class="t m0 x1 h7 ye0 ff6 fs4 fc0 sc0 ls1 ws0">power level, and then ﬁt each segment separately using different</div><div class="t m0 x1 h7 ye1 ff6 fs4 fc0 sc0 ls1 ws0">functions [19]. For example, the output of the DPD (</div><div class="t m0 x1b h7 ye2 ff6 fs4 fc0 sc0 ls1 ws0">) can</div><div class="t m0 x1 h7 ye3 ff6 fs4 fc0 sc0 ls1 ws0">be obtained from</div><div class="t m0 x1c h7 ye4 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1c h7 ye5 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1c h7 ye6 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1d h7 ye4 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1d h7 ye5 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1d h7 ye6 ff6 fs4 fc0 sc0 ls1 ws0">.</div><div class="t m0 x1e h7 ye7 ff6 fs4 fc0 sc0 ls1 ws0">(1)</div><div class="t m0 x1 h7 ye8 ff6 fs4 fc0 sc0 ls1 ws0">where</div><div class="t m0 x1f h7 ye9 ff6 fs4 fc0 sc0 ls1 ws0">is the complex input I/Q signal, and returns</div><div class="t m0 x1 h7 yea ff6 fs4 fc0 sc0 ls1 ws0">its magnitude value.</div><div class="t m0 x20 h7 yeb ff6 fs4 fc0 sc0 ls1 ws0">is the nonlinear transfer function for</div><div class="t m0 x1 h7 yec ff6 fs4 fc0 sc0 ls1 ws0">the signal whose magnitude falls in the interval</div><div class="t m0 x21 h7 yed ff6 fs4 fc0 sc0 ls1 ws0">. Typ-</div><div class="t m0 x1 h7 yee ff6 fs4 fc0 sc0 ls1 ws0">ically, the ﬁtting functions</div><div class="t m0 x22 h7 yef ff6 fs4 fc0 sc0 ls1 ws0">can be polynomials, splines, or</div><div class="t m0 xc h9 yf0 ff6 fs5 fc0 sc0 ls1 ws0">Fig. 3. Sample characteristics of an ET DPD. (a) Normalized output magnitude</div><div class="t m0 xc h9 yf1 ff6 fs5 fc0 sc0 ls1 ws0">versus normalized input magnitude. (b) Phase changes versus normalized input</div><div class="t m0 xc h9 yf2 ff6 fs5 fc0 sc0 ls1 ws0">magnitude.</div><div class="t m0 xc h9 yf3 ff6 fs5 fc0 sc0 ls1 ws0">Fig. 4. Example of piecewise curve ﬁtting.</div><div class="t m0 xc h7 yf4 ff6 fs4 fc0 sc0 ls1 ws0">other similar functions, and the parameters of these functions in</div><div class="t m0 xc h7 yf5 ff6 fs4 fc0 sc0 ls1 ws0">different segments can be identiﬁed separately.</div><div class="t m0 xd h7 yf6 ff6 fs4 fc0 sc0 ls1 ws0">This polynomial curve ﬁtting has been widely employed in</div><div class="t m0 xc h7 yf7 ff6 fs4 fc0 sc0 ls1 ws0">modeling many electronic circuits [19], [20]. An example of</div><div class="t m0 xc h7 yf8 ff6 fs4 fc0 sc0 ls1 ws0">the implementation of this approach is shown in Fig. 4. The</div><div class="t m0 x11 hb y6a ff5 fs7 fc0 sc0 ls1 ws0">Authorized licensed use limited to: University College Dublin. Downloaded on October 8, 2008 at 08:06 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.616162,0.000000,0.000000,1.616162,0.000000,0.000000]}'></div></div>