【数字预失真技术的国内外研究进展文献综述2500字】

数字预失真技术的国内外研究进展文献综述功率放大器线性化技术研究进展传统的功放线性化方法通常可分为三类：第一类直接回退功放输出功率使功放工作在线性区，又被称为功率回退技术ADDINEN.CITEADDINEN.CITE.DATA[4,5]；第二类通过设计相关电路以及线性化系统架构降低功放非线性，包括前向反馈技术ADDINEN.CITEADDINEN.CITE.DATA[6]、负反馈技术ADDINEN.CITEADDINEN.CITE.DATA[7,8]；第三类通过对功放输入进行预失真来对非线性进行补偿，从而提高功放线性度，主要包括模拟预失真技术、数字预失真技术ADDINEN.CITEADDINEN.CITE.DATA[9,10]。相比效率低下的功率回退技术、结构复杂且成本代价高的前馈技术，结构简单灵活且高效率的预失真技术得到了广泛应用。几种常见线性化技术的性能对比如REF_Ref66302347\h表11所示：预失真技术根据要处理的信号频率范围可简单分为模拟预失真和数字预失真。相比于结构复杂且性能指标等难以满足现代通信系统需求的模拟预失真，数字预失真硬件电路简单且便于数字信号处理，是目前广泛使用的预失真技术之一。通过预失真技术实现信号线性输出的原理，是在功率放大器前级联一个与其失真特性相反的结构——预失真器，通过预先产生特性相逆的失真来抵消信号后续通过功放会产生的失真。预失真技术的第一步是分析功放的特性，并依此来建立功放的行为模型，为构建逆特性的预失真器做准备。功放行为模型目前主要有三大类：查找表模型ADDINEN.CITE<EndNote><Cite><Author>Feng</Author><Year>2014</Year><RecNum>378</RecNum><DisplayText>[11]</DisplayText><record><rec-number>378</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1604839465">378</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>X.Feng</author><author>B.Feuvrie</author><author>A.Descamps</author><author>Y.Wang</author></authors></contributors><titles><title>Digitalpredistortiontechniquebasedonnon-uniformMPmodelandinterpolatedLUTforlinearisingPAswithmemoryeffects</title><secondary-title>ElectronicsLetters</secondary-title></titles><periodical><full-title>ElectronicsLetters</full-title></periodical><pages>1882-1884</pages><volume>50</volume><number>24</number><keywords><keyword>interpolation</keyword><keyword>linearisationtechniques</keyword><keyword>polynomials</keyword><keyword>poweramplifiers</keyword><keyword>spectrumregrowthsuppression</keyword><keyword>realPAZFL-2500</keyword><keyword>quadraticinterpolatedLUT</keyword><keyword>linearinterpolatedLUT</keyword><keyword>nonuniformmemorypolynomialmodel</keyword><keyword>nonlinearmemoryeffects</keyword><keyword>DPDtechnique</keyword><keyword>PAlinearization</keyword><keyword>nonuniformMPmodel</keyword><keyword>digitalpredistortiontechnique</keyword></keywords><dates><year>2014</year></dates><isbn>0013-5194</isbn><urls></urls><electronic-resource-num>10.1049/el.2014.2130</electronic-resource-num></record></Cite></EndNote>[11]、多项式模型ADDINEN.CITEADDINEN.CITE.DATA[12]和神经网络模型ADDINEN.CITE<EndNote><Cite><Author>Feng</Author><Year>2015</Year><RecNum>379</RecNum><DisplayText>[13]</DisplayText><record><rec-number>379</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1604839574">379</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>X.Feng</author><author>B.Feuvrie</author><author>A.S.Descamps</author><author>Y.Wang</author></authors></contributors><titles><title>Digitalpredistortionmethodcombiningmemorypolynomialandfeed-forwardneuralnetwork</title><secondary-title>ElectronicsLetters</secondary-title></titles><periodical><full-title>ElectronicsLetters</full-title></periodical><pages>943-945</pages><volume>51</volume><number>12</number><keywords><keyword>feedforwardneuralnets</keyword><keyword>digitalpredistortionmethod</keyword><keyword>memorypolynomial</keyword><keyword>feed-forwardneuralnetwork</keyword><keyword>basebanddigitalpredistortion</keyword><keyword>MPDPDtechnique</keyword><keyword>directlearningarchitecture</keyword><keyword>FFNNDPD</keyword><keyword>poweramplifier</keyword></keywords><dates><year>2015</year></dates><isbn>0013-5194</isbn><urls></urls><electronic-resource-num>10.1049/el.2015.0276</electronic-resource-num></record></Cite></EndNote>[13]。表STYLEREF1\s1SEQ表\*ARABIC\s11常见线性化技术的性能对比线性化技术名称复杂度线性化效果线性化带宽工程代价反馈法高一般小大前馈法高好中大模拟预失真中良好高中数字预失真低好高小查找表（LookUpTable，LUT）模型既可以看作是一种功放行为模型，也可以看作是一种预失真实现方式。这种方法依照具体算法建立一张或几张查找表，然后通过查表的方式来获取表值，最终实现对信号的预调整，本质上是一种通过权衡空间和时间，来实现高线性化和高精度的方法。多项式模型主要是利用多项式方程来拟合理想复增益曲线，用计算的方法来得到原输入信号经过预失真器的对应输出。一般根据信号和放大器带宽的大小分为无记忆和有记忆两种非线性模型。目前针对宽带信号的功率放大器具有较强的记忆效应，无记忆效应的非线性模型如Saleh模型等不再适用，而Volterra级数是当前模拟有记忆非线性模型的最精确方法之一，然而随着技术的记忆深度和系统阶数呈指数增长，系统计算量大大增加，难以达到实时处理的效果。为了解决该问题，国内外学者围绕简化Volterra级数模型做出了诸多努力。Ding等人在2001年通过去掉Volterra级数中不同延时的交叉项得到了MP（MemoryPolynomi-al）模型ADDINEN.CITE<EndNote><Cite><Author>Kim</Author><Year>2001</Year><RecNum>315</RecNum><DisplayText>[14]</DisplayText><record><rec-number>315</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1597062144">315</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>J.Kim</author><author>K.Konstantinou</author></authors></contributors><titles><title>Digitalpredistortionofwidebandsignalsbasedonpoweramplifiermodelwithmemory</title><secondary-title>ElectronicsLetters</secondary-title></titles><periodical><full-title>ElectronicsLetters</full-title></periodical><pages>1417-1418</pages><volume>37</volume><number>23</number><keywords><keyword>poweramplifiers</keyword><keyword>radiofrequencyamplifiers</keyword><keyword>linearisationtechniques</keyword><keyword>electricdistortion</keyword><keyword>mobileradio</keyword><keyword>signalprocessing</keyword><keyword>widebandsignals</keyword><keyword>poweramplifiermodel</keyword><keyword>memoryeffects</keyword><keyword>digitalpredistortion</keyword><keyword>singlecarrierUMTSsignals</keyword><keyword>multicarrierUMTSsignals</keyword><keyword>linearisationtechnique</keyword><keyword>nonlinearbehaviour</keyword><keyword>universalmobiletelecommunicationsystems</keyword></keywords><dates><year>2001</year></dates><isbn>0013-5194</isbn><urls></urls><electronic-resource-num>10.1049/el:20010940</electronic-resource-num></record></Cite></EndNote>[14]，虽然降低了模型复杂度，当非对角核比对角核模型输出贡献更大时，模型精度明显下降ADDINEN.CITE<EndNote><Cite><Author>Zhu</Author><Year>2004</Year><RecNum>380</RecNum><DisplayText>[15]</DisplayText><record><rec-number>380</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1604910382">380</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>A.Zhu</author><author>T.J.Brazil</author></authors></contributors><titles><title>BehavioralmodelingofRFpoweramplifiersbasedonprunedvolterraseries</title><secondary-title>IEEEMicrowaveandWirelessComponentsLetters</secondary-title></titles><periodical><full-title>IEEEMICROWAVEANDWIRELESSCOMPONENTSLETTERS</full-title></periodical><pages>563-565</pages><volume>14</volume><number>12</number><keywords><keyword>radiofrequencyamplifiers</keyword><keyword>poweramplifiers</keyword><keyword>Volterraseries</keyword><keyword>computationalcomplexity</keyword><keyword>prunedVolterraseries</keyword><keyword>system-levelperformance</keyword><keyword>circuitsimulation</keyword><keyword>physics-levelanalysis</keyword><keyword>nonlinearsystems</keyword><keyword>RFpoweramplifierbehavioralmodeling</keyword><keyword>near-diagonalitypruningalgorithm</keyword><keyword>FIRdigitalfilters</keyword><keyword>Radiofrequency</keyword><keyword>Powersystemmodeling</keyword><keyword>Performanceanalysis</keyword><keyword>Predictivemodels</keyword><keyword>Highpoweramplifiers</keyword><keyword>Behavioralmodel</keyword><keyword>poweramplifier</keyword></keywords><dates><year>2004</year></dates><isbn>1558-1764</isbn><urls></urls><electronic-resource-num>10.1109/LMWC.2004.837380</electronic-resource-num></record></Cite></EndNote>[15]。为了在降低系统复杂度的前提下保证对记忆效应的非线性描述，ADDINEN.CITEADDINEN.CITE.DATA[16]提出了GMP（GeneralizedMemoryPolynomial）模型，在Volterra级数模型和MP模型之间折中采用保留对角核函数及其相邻核函数的方式，通过设定保留核函数的阀值来控制系统精度和复杂度。数字预失真模型降维技术研究现状随着现代调制信号带宽的增加，即便是简化过的预失真模型估计中的计算量与复杂度依旧难以达到令人满意的程度，因此如何在保持模型性能的前提下简化模型，在5G通信系统中是一个值得研究的问题。接下来简要介绍这方面的研究现状。在降低模型复杂度方面，除了上节提到的直接对Volterra级数系列的模型进行修剪以精度的损耗换取更低的预失真系数数量之外，另一种方法是根据数学策略来挑选模型矩阵中比较重要的核函数成分，去除不重要的成分。Chen等人在ADDINEN.CITE<EndNote><Cite><Author>Chen</Author><Year>2014</Year><RecNum>445</RecNum><DisplayText>[17]</DisplayText><record><rec-number>445</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1619441572">445</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>W.Chen</author><author>S.Zhang</author><author>Y.Liu</author><author>F.M.Ghannouchi</author><author>Z.Feng</author><author>Y.Liu</author></authors></contributors><titles><title>EfficientPruningTechniqueofMemoryPolynomialModelsSuitableforPABehavioralModelingandDigitalPredistortion</title><secondary-title>IEEETransactionsonMicrowaveTheoryandTechniques</secondary-title></titles><periodical><full-title>IEEETransactionsonMicrowaveTheoryandTechniques</full-title></periodical><pages>2290-2299</pages><volume>62</volume><number>10</number><dates><year>2014</year></dates><isbn>1557-9670</isbn><urls></urls><electronic-resource-num>10.1109/TMTT.2014.2351779</electronic-resource-num></record></Cite></EndNote>[17]提到在MP模型中，不同非线性阶数对应的记忆效应有所差别，其中线性项相较于非线性项的记忆效应更重要，因此模型中各核函数项对于描述非线性失真的贡献是不同的。Reina等人在ADDINEN.CITEADDINEN.CITE.DATA[18]中提出虽然Volterra系列的模型具有数量庞大的系数，然而其中活跃的系数只有一小部分。这一部分活跃的系数对于建模的贡献是最重要的。Zhang等人ADDINEN.CITE<EndNote><Cite><Author>Zhang</Author><Year>2013</Year><RecNum>444</RecNum><DisplayText>[19]</DisplayText><record><rec-number>444</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1619441421">444</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>S.Zhang</author><author>W.Chen</author><author>F.M.Ghannouchi</author><author>Y.Chen</author></authors></contributors><titles><title>Aniterativepruningof2-Ddigitalpredistortionmodelbasedonnormalizedpolynomialterms</title><secondary-title>2013IEEEMTT-SInternationalMicrowaveSymposiumDigest(MTT)</secondary-title><alt-title>2013IEEEMTT-SInternationalMicrowaveSymposiumDigest(MTT)</alt-title></titles><pages>1-4</pages><dates><year>2013</year><pub-dates><date>2-7June2013</date></pub-dates></dates><isbn>0149-645X</isbn><urls></urls><electronic-resource-num>10.1109/MWSYM.2013.6697513</electronic-resource-num></record></Cite></EndNote>[19]提出对于2D-MP模型来说，模值较小的系数对应的模型项是相对不重要的，可以被剔除。Abdelhafiz等人在ADDINEN.CITEADDINEN.CITE.DATA[20]中认为若系数向量中大多数系数模值为零或者是接近于零的，就可以认为系数向量稀疏。对于降维的方法，Gilabert等人在ADDINEN.CITEADDINEN.CITE.DATA[21,22]中利用主成分分析法（PrincipalComponentAnalysis，PCA）对由输入信号构成的多项式模型矩阵进行修剪。Reina等人在ADDINEN.CITEADDINEN.CITE.DATA[18,23]中将压缩感知理论（Compres-sedSensing，CS）引入到数字预失真中，利用系数的稀疏性对多项式模型进行降维。贪婪类算法是压缩感知领域常用的一种技术，其中的一些算法例如正交匹配追踪（OrthogonalMatchingPursuit，OMP）在ADDINEN.CITEADDINEN.CITE.DATA[18]中被应用于DPD中，利用原子的正交性对模型降维；ADDINEN.CITEADDINEN.CITE.DATA[24]中对OMP算法改进，给出了降低复杂度的版本。为了克服Volterra系列中出现的高相关性，J.A.Becerra等人设计了DOMP（DoublyOrthogonalMatchingPursuit）算法ADDINEN.CITE<EndNote><Cite><Author>Becerra</Author><Year>2018</Year><RecNum>302</RecNum><DisplayText>[25]</DisplayText><record><rec-number>302</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1595913735">302</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>J.A.Becerra</author><author>M.J.Madero-Ayora</author><author>J.Reina-Tosina</author><author>C.Crespo-Cadenas</author><author>J.García-Frías</author><author>G.Arce</author></authors></contributors><titles><title>ADoublyOrthogonalMatchingPursuitAlgorithmforSparsePredistortionofPowerAmplifiers</title><secondary-title>IEEEMicrowaveandWirelessComponentsLetters</secondary-title></titles><periodical><full-title>IEEEMICROWAVEANDWIRELESSCOMPONENTSLETTERS</full-title></periodical><pages>726-728</pages><volume>28</volume><number>8</number><keywords><keyword>iterativemethods</keyword><keyword>poweramplifiers</keyword><keyword>DPDapplication</keyword><keyword>doublyorthogonalmatchingpursuitalgorithm</keyword><keyword>sparsepredistortion</keyword><keyword>digitalpredistortion</keyword><keyword>Gram-Schmidtorthogonalization</keyword><keyword>selectedmodelregressors</keyword><keyword>orthogonalfrequencydivisionmultiplexingsignal</keyword><keyword>Matchingpursuitalgorithms</keyword><keyword>Mathematicalmodel</keyword><keyword>Predistortion</keyword><keyword>Wirelesscommunication</keyword><keyword>Computationalmodeling</keyword><keyword>Estimation</keyword><keyword>Kernel</keyword><keyword>Behavioralmodeling</keyword><keyword>compressivesensing</keyword><keyword>digitalpredistortion(DPD)</keyword><keyword>orthogonalmatchingpursuit(OMP)</keyword><keyword>poweramplifier(PA)</keyword></keywords><dates><year>2018</year></dates><isbn>1558-1764</isbn><urls></urls><electronic-resource-num>10.1109/LMWC.2018.2845947</electronic-resource-num></record></Cite></EndNote>[25]及其低复杂度变体ADDINEN.CITE<EndNote><Cite><Author>Becerra</Author><Year>2019</Year><RecNum>296</RecNum><DisplayText>[26]</DisplayText><record><rec-number>296</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1595404363">296</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>J.A.Becerra</author><author>M.J.Madero-Ayora</author><author>J.Reina-Tosina</author><author>C.Crespo-Cadenas</author><author>J.García-Frías</author><author>G.Arce</author></authors></contributors><titles><title>AReduced-ComplexityDoublyOrthogonalMatchingPursuitAlgorithmforPowerAmplifierSparseBehavioralModeling</title><secondary-title>2019IEEETopicalConferenceonRF/MicrowavePowerAmplifiersforRadioandWirelessApplications(PAWR)</secondary-title><alt-title>2019IEEETopicalConferenceonRF/MicrowavePowerAmplifiersforRadioandWirelessApplications(PAWR)</alt-title></titles><pages>1-3</pages><keywords><keyword>computationalcomplexity</keyword><keyword>iterativemethods</keyword><keyword>matrixinversion</keyword><keyword>poweramplifiers</keyword><keyword>time-frequencyanalysis</keyword><keyword>Volterraseries</keyword><keyword>reduced-complexitydoublyorthogonalmatchingpursuitalgorithm</keyword><keyword>poweramplifiersparsebehavioralmodeling</keyword><keyword>poweramplifierVolterrabehavioralmodel</keyword><keyword>computationcomplexity</keyword><keyword>Matchingpursuitalgorithms</keyword><keyword>Mathematicalmodel</keyword><keyword>Predistortion</keyword><keyword>Correlation</keyword><keyword>Runtime</keyword><keyword>Computationalmodeling</keyword><keyword>Wirelesscommunication</keyword></keywords><dates><year>2019</year><pub-dates><date>20-23Jan.2019</date></pub-dates></dates><isbn>2473-4640</isbn><urls></urls><electronic-resource-num>10.1109/PAWR.2019.8708723</electronic-resource-num></record></Cite></EndNote>[26]，在OMP算法的基础上对已选原子和剩余原子进行施密特正交，实现二次正交过程，尽量消除每次迭代中已选原子在残余量上的投影。OMP算法通常需要已知信号稀疏度来停止迭代，在稀疏度未知的情况下，Li在ADDINEN.CITEADDINEN.CITE.DATA[27]中提出使用NMSE性能的优劣程度来作为功放建模过程中的中止条件，Reina等人ADDINEN.CITEADDINEN.CITE.DATA[18]提出使用贝叶斯信息准则（Bayesianinformationcriterion，BIC）来衡量每次迭代中的模型的后验信息。数字预失真欠采样技术研究现状另一方面，为了补偿功放的非线性失真，需要对功放输出信号进行采集拟合功放特性以求逆，反馈回路上对于信号的采样通常需要采集到五倍带宽，对于宽带信号，常规ADC已经无法满足如此高速的采样率。此外，高速的采样率会带来大量的采样数据，给传输和存储过程也带来了巨大的负担。所以本文的另一研究重点将聚焦于如何有效地降低反馈回路上的信号采样率，在降低反馈回路信号采样率方面，ADDINEN.CITE<EndNote><Cite><Author>Li</Author><Year>2020</Year><RecNum>419</RecNum><DisplayText>[28]</DisplayText><record><rec-number>419</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1614847198">419</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Y.Li</author><author>X.Wang</author><author>A.Zhu</author></authors></contributors><titles><title>SamplingRateReductionforDigitalPredistortionofBroadbandRFPowerAmplifiers</title><secondary-title>IEEETransactionsonMicrowaveTheoryandTechniques</secondary-title></titles><periodical><full-title>IEEETransactionsonMicrowaveTheoryandTechniques</full-title></periodical><pages>1054-1064</pages><volume>68</volume><number>3</number><keywords><keyword>5Gmobilecommunication</keyword><keyword>linearisationtechniques</keyword><keyword>radiofrequencyamplifiers</keyword><keyword>widebandamplifiers</keyword><keyword>powerconsumption</keyword><keyword>DPD</keyword><keyword>broadbandRFpoweramplifiers</keyword><keyword>digitalpredistortion</keyword><keyword>multistagecancellationscheme</keyword><keyword>Bandwidth</keyword><keyword>Nonlineardistortion</keyword><keyword>Powerdemand</keyword><keyword>Predistortion</keyword><keyword>Broadbandcommunication</keyword><keyword>Clocks</keyword><keyword>Aliasingeffect</keyword><keyword>behavioralmodel</keyword><keyword>digitalpredistortion(DPD)</keyword><keyword>linearization</keyword><keyword>poweramplifiers(PAs)</keyword><keyword>wirelesstransmitter</keyword></keywords><dates><year>2020</year></dates><isbn>1557-9670</isbn><urls></urls><electronic-resource-num>10.1109/TMTT.2019.2944813</electronic-resource-num></record></Cite></EndNote>[28]中通过一种分割多区间对消法降低预失真系统的采样率，来降低DPD模块的成本和功耗。Yu等人ADDINEN.CITE<EndNote><Cite><Author>Chao</Author><Year>2012</Year><RecNum>386</RecNum><DisplayText>[29]</DisplayText><record><rec-number>386</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1614583108">386</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>Chao,Yu</author><author>Lei,Guan</author><author>A.Zhu</author></authors></contributors><titles><title>Band-limitedVolterraseries-basedbehavioralmodelingofRFpoweramplifiers</title><secondary-title>2012IEEE/MTT-SInternationalMicrowaveSymposiumDigest</secondary-title><alt-title>2012IEEE/MTT-SInternationalMicrowaveSymposiumDigest</alt-title></titles><pages>1-3</pages><keywords><keyword>Bandwidth</keyword><keyword>Radiofrequency</keyword><keyword>Poweramplifiers</keyword><keyword>Timedomainanalysis</keyword><keyword>Nonlineardistortion</keyword><keyword>Frequencymeasurement</keyword><keyword>Accuracy</keyword><keyword>Behavioralmodel</keyword><keyword>Volterraseries</keyword></keywords><dates><year>2012</year><pub-dates><date>17-22June2012</date></pub-dates></dates><isbn>0149-645X</isbn><urls></urls><electronic-resource-num>10.1109/MWSYM.2012.6258396</electronic-resource-num></record></Cite></EndNote>[29]提出用带限的Volterra模型进行建模，通过限制反馈回路需要采集的信号带宽来降低采样率；Yang等人ADDINEN.CITE<EndNote><Cite><Author>Yang</Author><Year>2014</Year><RecNum>441</RecNum><DisplayText>[30]</DisplayText><record><rec-number>441</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1618404101">441</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Yang,G.</author><author>Liu,F.</author><author>Zhao,C.</author><author>Wang,Z.</author><author>Li,L.</author><author>Wang,H.</author></authors></contributors><titles><title>Frequencydomaindatabasedmodelextractionforband‐limiteddigitalpredistortionofwidebandRFpoweramplifiers</title><secondary-title>InternationalJournalofRFandMicrowaveComputer-AidedEngineering</secondary-title></titles><periodical><full-title>InternationalJournalofRFandMicrowaveComputer-AidedEngineering</full-title></periodical><pages>412-420</pages><volume>24</volume><number>3</number><dates><year>2014</year></dates><urls></urls></record></Cite></EndNote>[30]将带限Volterra模型应用至频域，相较于时域带限方法降低了复杂度。Ma等人ADDINEN.CITEADDINEN.CITE.DATA[31]将带限滤波器引入预失真系统的反馈回路，低速采集带限滤波器的输出信号后再通过频谱外推的方法恢复信号。文献ADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2017</Year><RecNum>420</RecNum><DisplayText>[32]</DisplayText><record><rec-number>420</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1614847536">420</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,Haoyu</author><author>Li,Gang</author><author>Zhou,Chongbin</author><author>Tao,Wei</author><author>Liu,Falin</author><author>Zhu,Anding</author></authors></contributors><titles><title>1-bitObservationforDirect-Learning-BasedDigitalPredistortionofRFPowerAmplifiers</title><secondary-title>IEEETransactionsonMicrowaveTheory&Techniques</secondary-title></titles><periodical><full-title>IEEETransactionsonMicrowaveTheory&Techniques</full-title></periodical><pages>2465-2475</pages><dates><year>2017</year></dates><urls></urls></record></Cite></EndNote>[32]提出一种基于闭环结构的1-bit数字预失真结构，这种方法用单比特比较器取代了传统DPD反馈链路中的高精度ADC元器件，通过量化发射信号和反馈信号的单比特误差来实现DPD系数的提取。Tropp等人ADDINEN.CITE<EndNote><Cite><Author>Tropp</Author><Year>2010</Year><RecNum>335</RecNum><DisplayText>[33]</DisplayText><record><rec-number>335</rec-number><foreign-keys><keyapp="EN"db-id="aztwz0xp65pt52efxa6xrfvedetfezzwasax"timestamp="1597210047">335</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>J.A.Tropp</author><author>J.N.Laska</author><author>M.F.Duarte</author><author>J.K.Romberg</author><author>R.G.Baraniuk</author></authors></contributors><titles><title>BeyondNyquist:EfficientSamplingofSparseBandlimitedSignals</title><secondary-title>IEEETransactionsonInformationTheory</secondary-title></titles><periodical><full-title>IEEETransactionsonInformationTheory</full-title></periodical><pages>520-544</pages><volume>56</volume><number>1</number><keywords><keyword>analogue-digitalconversion</keyword><keyword>convexprogramming</keyword><keyword>dataacquisition</keyword><keyword>demodulators</keyword><keyword>signalreconstruction</keyword><keyword>signalsampling</keyword><keyword>beyondNyquist</keyword><keyword>sparsebandlimitedsignals</keyword><keyword>widebandanalogsignals</keyword><keyword>analog-to-digitalconversion</keyword><keyword>dataacquisitionsystem</keyword><keyword>randomdemodulator</keyword><keyword>Nyquistsampling</keyword><keyword>Samplingmethods</keyword><keyword>Frequency</keyword><keyword>Demodulation</keyword><keyword>Signalprocessing</keyword><keyword>Hardware</keyword><keyword>Robustness</keyword><keyword>Performanceanalysis</keyword><keyword>compressivesampling</keyword><keyword>samplingtheory</keyword><keyword>signalrecovery</keyword><keyword>sparseapproximation</keyword></keywords><dates><year>2010</year></dates><isbn>1557-9654</isbn><urls></urls><electronic-resource-num>10.1109/TIT.2009.2034811</electronic-resource-num></record></Cite></EndNote>[33]提出采用随机解调的方式令输出信号与伪随机序列混频后低速采样，再根据采样特征进行恢复，该方法需要增加一个随机解调器。Pasquale等人ADDINEN.CITE<EndNote><Cite><Author>Daponte</Author><Year>2016</Year><RecNum>448</RecNum><DisplayText>[34,35]</DisplayText><record><rec-number>448</rec-number><fore