宽带/双频数字预失真研究
摘要
凭借其成本适中、编程灵活以及性能卓越的优势,数字预失真(Digital Predistortion,DPD)成为现代通信发射机中主流的线性化技术。在高速宽带数据业务需求以及多标准多频带通信体制发展推动下,宽带/双频DPD技术成为当前的研究热点。本文围绕宽带/双频DPD的行为建模、模型参数辨识以及预失真系统学习结构展开研究。
在宽带DPD系统中,为了降低反馈回路中模数转换器的采样速率,对反馈回路进行带限处理,利用带限建模技术进行预失真建模。本文对带限建模方法进行分析,理论上证明带限模型参数辨识归结为广义最小二乘问题。从频域角度解释带限模型参数辨识的物理意义,并提出一种基于频域数据的带限模型参数辨识算法。所提出的频域模型辨识算法能够取得与传统的时域算法相当的性能,然而计算复杂度大大降低。将传统的DPD系统学习结构推广到带限DPD情况,利用所提出的频域模型辨识算法研究了不同学习结构能够达到的线性化性能。
为了同时补偿交调失真和互调失真,双频DPD系统中每个频段的预失真器被建模为双输入单输出系统。二维记忆多项式(Two Dimensional Memory Polynomial,2D-MP)能够有效地建模并发双频功放的失真特性,但数值稳定差,且模型复杂度高。提出二维正交多项式缓解数值不稳定问题,在有限精度的数字处理系统中鲁棒性更好。提出一种包含同阶包络交叉项的简化2D-MP模型,在模型复杂度和建模精度之间取得良好的折中,同时便于利用一维查找表实现。提出基于乘法单元的双频模型,能够以较低的模型复杂度取得良好的线性化性能。
提出一种直接学习DPD模型参数的一步辨识算法。利用基带失真分量迭代注入技术得到期望的预失真信号,然后通过最小二乘估计对DPD模型参数进行一步辨识。该算法能够取得与传统直接学习DPD参数辨识算法相当的线性化性能,然而计算复杂度更低。将该算法用于直接学习带限/双频DPD系统参数辨识,得到了良好的线性化效果,进一步证明所提算法的有效性。
Owing to its advantages of moderate cost, high flexibility and superior performance, digital predistortion (DPD) has become the mainstream linearization technique in modern communication transmitters. Spurred by the demands of high-speed wideband data service and multi-standard/multi-band communication systems, wideband and dual-band DPD are the highlights in DPD research at present. This dissertation focuses on behavioral modeling, model identification and DPD learning architectures for wideband and dual-band DPD.
To reduce the sampling rate of analog to digital converters in the distortion acquisition path, the feedback loop is band-limited in a wideband DPD system, which requires a band-limited modeling technique for satisfactory performance. The author proves that the band-limited modeling technique can be formulated as a generalized least squares problem, with clear physical meaning from a frequency domain perspective. A frequency domain data based model extraction algorithm is proposed, which provides as good linearization performance as the conventional time domain data based algorithm with greatly reduced computational complexity. Conventional DPD learning architectures are extended for band-limited DPD, and their linearization performances are studied with the proposed algorithm.
To compensate for cross-band modulation distortion as well as intra-band intermodulation distortion in a concurrent dual-band power amplifier (PA), a dual-band behavioral model of either band takes the form of a dual-input-single-output system. The reported two dimensional memory polynomial (2D-MP) shows high modeling accuracy for characterizing distortion behaviors in a concurrent dual-band PA, but it exhibits numerical instability and suffers from high complexity. To alleviate the numerical instability problem,2D orthogonal polynomials are proposed, which show robust performance in finite precision processing. To reduce the model complexity of2D-MP, a simplified2D-MP model with envelop cross terms of equal order is proposed, which proves to be a good tradeoff between complexity and performance, and facilates implementation with1D lookup tables. A multiplicative cell based dual-band model is also proposed, which yields good linearization performance with low model complexity.
A one-step model identification algorithm is proposed for direct learning DPD. The expected predistortion signal is firstly derived by iterative injection of the baseband distortion components, which facilitates one-step model extraction of the DPD model by least squares estimation afterwards. The algorithm yields comparable linearization performance to the conventional algorithm, but bears much lower computational complexity. It is applied to model extraction of direct learning based wideband and dual-band DPD systems, and good linearization performance is achieved, which validates the effectiveness of the proposed algorithm.
在宽带DPD系统中,为了降低反馈回路中模数转换器的采样速率,对反馈回路进行带限处理,利用带限建模技术进行预失真建模。本文对带限建模方法进行分析,理论上证明带限模型参数辨识归结为广义最小二乘问题。从频域角度解释带限模型参数辨识的物理意义,并提出一种基于频域数据的带限模型参数辨识算法。所提出的频域模型辨识算法能够取得与传统的时域算法相当的性能,然而计算复杂度大大降低。将传统的DPD系统学习结构推广到带限DPD情况,利用所提出的频域模型辨识算法研究了不同学习结构能够达到的线性化性能。
为了同时补偿交调失真和互调失真,双频DPD系统中每个频段的预失真器被建模为双输入单输出系统。二维记忆多项式(Two Dimensional Memory Polynomial,2D-MP)能够有效地建模并发双频功放的失真特性,但数值稳定差,且模型复杂度高。提出二维正交多项式缓解数值不稳定问题,在有限精度的数字处理系统中鲁棒性更好。提出一种包含同阶包络交叉项的简化2D-MP模型,在模型复杂度和建模精度之间取得良好的折中,同时便于利用一维查找表实现。提出基于乘法单元的双频模型,能够以较低的模型复杂度取得良好的线性化性能。
提出一种直接学习DPD模型参数的一步辨识算法。利用基带失真分量迭代注入技术得到期望的预失真信号,然后通过最小二乘估计对DPD模型参数进行一步辨识。该算法能够取得与传统直接学习DPD参数辨识算法相当的线性化性能,然而计算复杂度更低。将该算法用于直接学习带限/双频DPD系统参数辨识,得到了良好的线性化效果,进一步证明所提算法的有效性。
Owing to its advantages of moderate cost, high flexibility and superior performance, digital predistortion (DPD) has become the mainstream linearization technique in modern communication transmitters. Spurred by the demands of high-speed wideband data service and multi-standard/multi-band communication systems, wideband and dual-band DPD are the highlights in DPD research at present. This dissertation focuses on behavioral modeling, model identification and DPD learning architectures for wideband and dual-band DPD.
To reduce the sampling rate of analog to digital converters in the distortion acquisition path, the feedback loop is band-limited in a wideband DPD system, which requires a band-limited modeling technique for satisfactory performance. The author proves that the band-limited modeling technique can be formulated as a generalized least squares problem, with clear physical meaning from a frequency domain perspective. A frequency domain data based model extraction algorithm is proposed, which provides as good linearization performance as the conventional time domain data based algorithm with greatly reduced computational complexity. Conventional DPD learning architectures are extended for band-limited DPD, and their linearization performances are studied with the proposed algorithm.
To compensate for cross-band modulation distortion as well as intra-band intermodulation distortion in a concurrent dual-band power amplifier (PA), a dual-band behavioral model of either band takes the form of a dual-input-single-output system. The reported two dimensional memory polynomial (2D-MP) shows high modeling accuracy for characterizing distortion behaviors in a concurrent dual-band PA, but it exhibits numerical instability and suffers from high complexity. To alleviate the numerical instability problem,2D orthogonal polynomials are proposed, which show robust performance in finite precision processing. To reduce the model complexity of2D-MP, a simplified2D-MP model with envelop cross terms of equal order is proposed, which proves to be a good tradeoff between complexity and performance, and facilates implementation with1D lookup tables. A multiplicative cell based dual-band model is also proposed, which yields good linearization performance with low model complexity.
A one-step model identification algorithm is proposed for direct learning DPD. The expected predistortion signal is firstly derived by iterative injection of the baseband distortion components, which facilitates one-step model extraction of the DPD model by least squares estimation afterwards. The algorithm yields comparable linearization performance to the conventional algorithm, but bears much lower computational complexity. It is applied to model extraction of direct learning based wideband and dual-band DPD systems, and good linearization performance is achieved, which validates the effectiveness of the proposed algorithm.
引文
[1]Bassam S. A., Chen W. H., Helaoui M., Ghannouchi F. M. Transmitter architecture for ca[J]. IEEE Microw. Mag.,2013,14 (5):78-86.
[2]Sun G., Jansen R. H. Broadband doherty power amplifier via real frequency technique[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (1):99-111.
[3]Piazzon L., Giofre R., Colantonio P., Giannini F. A wideband doherty architecture with 36% of fractional bandwidth[J]. IEEE Microw. Wireless Compon. Lett,2013,23 (11):626-628.
[4]Shao J., Zhou R. G., Ren H., Arigong B., Zhou M., Kim H. S., Zhang H. L. Design of gan doherty power amplifiers for broadband applications[J]. IEEE Microw. Wireless Compon. Lett., 2014,24 (4):248-250.
[5]Giofre R., Colantonio P., Giannini F., Piazzon L. New output combiner for doherty amplifiers[J]. IEEE Microw. Wireless Compon. Lett,2013,23 (1):31-33.
[6]Xia J., Zhu X. W., Zhang L., Zhai J. F., Sun Y. J. High-efficiency gan doherty power amplifier for 100-mhz Ite-advanced application based on modified load modulation network[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (8):2911-2921.
[7]Ma C. H., Pan W. S., Shao S. H., Qing C. J., Tang Y. X. A wideband doherty power amplifier with 100 mhz instantaneous bandwidth for lte-advanced applications[J]. IEEE Microw. Wireless Compon. Lett.,2013,23 (11):614-616.
[8]Nghiem X. A., Negra R. Design of a concurrent quad-band gan-hemt doherty power amplifier for wireless applications[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[9]Saad P., Colantonio P., Piazzon L., Giannini F., Andersson K., Fager C. Design of a concurrent dual-band 1,8-2.4-ghz gan-hemt doherty power amplifier[J]. IEEE Trans. Microw. Theory Tech., 2012,60(6):1840-1849.
[10]Nghiem X. A., Guan J. Q., Hone T., Negra R. Design of concurrent multiband doherty power amplifiers for wireless applications[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (12): 4559-4568.
[11]Cripps S. C. Rfpower amplifiers for wireless communications[M]. Artech House,2006.
[12]Wright P., Lees J., Benedikt J., Tasker P. J., Cripps S. C. A methodology for realizing high efficiency class-j in a linear and broadband pa[J]. IEEE Trans. Microw. Theory Tech.,2009,57 (12):3196-3204.
[13]Moon J., Kim J., Kim B. Investigation of a class-j power amplifier with a nonlinear c-out for optimized operation[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (11):2800-2811.
[14]Mimis K., Morris K. A., Bensmida S., McGeehan J. P. Multichannel and wideband power amplifier design methodology for 4g communication systems based on hybrid class-j operation[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (8):2562-2570.
[15]Cripps S. C., Tasker P. J., Clarke A. L., Lees J., Benedikt J. On the continuity of high efficiency modes in linear rf power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (10): 665-667.
[16]Carrubba V., Akmal M., Quay R., Lees J., Benedikt J., Cripps S. C., Tasker P. J. The continuous inverse class-f mode with resistive second-harmonic impedance[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (6):1928-1936.
[17]Carrubba V., Clarke A. L., Akmal M., Lees J., Benedikt J., Tasker P. J., Cripps S. C. The continuous class-f mode power amplifier[C]. in 2010 European Microwave Conference (EuMC), 2010:1674-1677.
[18]Carrubba V., Lees J., Benedikt J., Tasker P. J., Cripps S. C. A novel highly efficient broadband continuous class-f rfpa delivering 74% average efficiency for an octave bandwidth[C]. in 2011 IEEE MTT-S International Microwave Symposium Digest (IMS),2011:1-4.
[19]Junghwan M., Seunghoon J., Jungjoon K., Junghwan S., Seungchan K., Juyeon L., Seokhyeon K., Kim B. Investigation of a class-if power amplifier with a nonlinear output capacitor[C]. in 2011 European Microwave Integrated Circuits Conference (EuMIC),2011:124-127.
[20]Tuffy N., Guan L., Zhu A., Brazil T. J. A simplified broadband design methodology for linearized high-efficiency continuous class-f power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (6):1952-1963.
[21]Chen K. L., Peroulis D. Design of broadband highly efficient harmonic-tuned power amplifier using in-band continuous class-if/f mode transferring[J]. IEEE Trans. Microw. Theory Tech., 2012,60 (12):4107-4116.
[22]Ghannouchi F. M., Hammi O. Behavioral modeling and predistortion[J]. IEEE Microw. Mag., 2009,10 (7):52-64.
[23]Saleh A. A. M. Frequency-independent and frequency-dependent nonlinear models of twt amplifiers[J]. IEEE Trans. Commun.,1981,29(11):1715-1720.
[24]Rapp C. Effects of hpa-nonlinearity on a 4-dpsk/ofdm-signal for a digital sound broadcasting signal[C]. in 2nd European Conference on Satellite Communications (ECSC-2),1991:179-184.
[25]Cavers J. K. Amplifier linearization using a digital predistorter with fast adaptation and low memory requirements[J]. IEEE Trans. Veh. Technol,1990,39 (4):374-382.
[26]D'Andrea A. N., Lottici V., Reggiannini R. Rf power amplifier linearization through amplitude and phase predistortion[J]. IEEE Trans. Commun.,1996,44 (11):1477-1484.
[27]Kim J., Konstantinou K. Digital predistortion of wideband signals based on power amplifier model with memory[J]. Electron. Lett.,2001,37 (23):1417-1418.
[28]Ding L., Zhou G. T. Effects of even-order nonlinear terms on power amplifier modeling and predistortion linearization[J]. IEEE Trans. Veh. Technol.,2004,53 (1):156-162.
[29]Eun C., Powers E. J. A new volterra predistorter based on the indirect learning architecture[J]. IEEE Trans. Signal Process.,1997,45 (1):223-227.
[30]Ding L., Zhou G. T., Morgan D. R., Ma Z. X., Kenney J. S., Kim J., Giardina C. R. A robust digital baseband predistorter constructed using memory polynomials[J]. IEEE Trans. Commun., 2004,52 (1):159-165.
[31]Hammi O., Ghannouchi F. M., Vassilakis B. A compact envelope-memory polynomial for rf transmitters modeling with application to baseband and rf-digital predistortion[J]. IEEE Microw. Wireless Compon. Lett.,2008,18 (5):359-361.
[32]Morgan D. R., Ma Z. X., Kim J., Zierdt M. G., Pastalan J. A generalized memory polynomial model for digital predistortion of rf power amplifiers[J]. IEEE Trans. Signal Process.,2006,54 (10):3852-3860.
[33]Zhu A. D., Draxler P. J., Hsia C., Brazil T. J., Kimball D. F., Asbeck P. M. Digital predistortion for envelope-tracking power amplifiers using decomposed piecewise volterra series[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (10):2237-2247.
[34]Zhu A. D., Pedro J. C, Cunha T. R. Pruning the volterra series for behavioral modeling of power amplifiers using physical knowledge[J]. IEEE Trans. Microw. Theory Tech.,2007,55 (5): 813-821.
[35]Zhu A. D., Draxler P. J., Yan J. M. J., Brazil T. J., Kimball D. F., Asbeck P. M. Open-loop digital predistorter for rf power amplifiers using dynamic deviation reduction-based volterra series[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (7):1524-1534.
[36]Zhu A. D., Pedro J. C., Brazil T. J. Dynamic deviation reduction-based volterra behavioral modeling of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2006,54 (12): 4323-4332.
[37]Guan L., Zhu A. D. Simplified dynamic deviation reduction-based volterra model for doherty power amplifiers[C]. in 2011 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2011:1-4.
[38]Guan L., Zhu A. D. Low-cost fpga implementation of volterra series-based digital predistorter for rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (4):866-872.
[39]Zhai J. F., Zhang L., Zhou J. Y, Zhu X. W., Hong W. A nonlinear filter-based volterra model with low complexity for wideband power amplifiers[J]. IEEE Microw. Wireless Compon. Lett., 2014,24 (3):203-205.
[40]Gilabert P. L., Montoro G., Bertran E. Fpga implementation of a real-time narma-based digital adaptive predistorter[J]. IEEE Trans. Circuits Syst. II, Exp. Briefs,2011,58 (7):402-406.
[41]Gilabert P. L., Cesari A., Montoro G., Bertran E., Dilhac J. M. Multi-lookup table fpga implementation of an adaptive digital predistorter for linearizing rf power amplifiers with memory effects[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (2):372-384.
[42]Liu T. J., Boumaiza S., Ghannouchi F. M. Dynamic behavioral modeling of 3g power amplifiers using real-valued time-delay neural networks[J]. IEEE Trans. Microw. Theory Tech.,2004,52 (3):1025-1033.
[43]Rawat M., Rawat K., Ghannouchi P. M. Adaptive digital predistortion of wireless power amplifiers/transmitters using dynamic real-valued focused time-delay line neural networks[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (1):95-104.
[44]Liu T. J., Boumaiza S., Ghannouchi F. M. Augmented hammerstein predistorter for linearization of broad-band wireless transmitters[J]. IEEE Trans. Microw. Theory Tech.,2006,54 (4): 1340-1349.
[45]Liu T. J., Boumaiza S., Ghannouchi F. M. Deembedding static nonlinearities and accurately identifying and modeling memory effects in wide-band rf transmitters[J]. IEEE Trans. Microw. Theory Tech.,2005,53 (11):3578-3587.
[46]Junghwan M., Bumman K. Enhanced hammerstein behavioral model for broadband wireless transmitters[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (4):924-933.
[47]Hammi O., Ghannouchi F. M. Twin nonlinear two-box models for power amplifiers and transmitters exhibiting memory effects with application to digital predistortion[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (8):530-532.
[48]Younes M., Hammi O., Kwan A., Ghannouchi F. M. An accurate complexity-reduced "plume" model for behavioral modeling and digital predistortion of rf power amplifiers[J]. IEEE Trans. Ind. Electron.,2011,58 (4):1397-1405.
[49]Yu C., Guan L., Zhu A. Band-limited volterra series-based behavioral modeling of rf power amplifiers[C]. in 2012 IEEE MTT-S International Microwave Symposium Digest (IMS),2012: 1-3.
[50]Yu C., Guan L., Zhu E., Zhu A. Band-limited volterra series-based digital predistortion for wideband rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (12):4198-4208.
[51]Guan L., Yu C., Zhu A. Bandwidth-constrained least squares-based model extraction for band-limited digital predistortion of rf power amplifiers[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[52]Zhang S. L., Chen W. H., Feng Z. H. Low sampling rate digital predistortion of power amplifier assisted by bandpass rf filter[C]. in 2012 Asia Pacific Microwave Conference Proceedings (APMC),2012:962-964.
[53]Liu Y., Pan W. S., Shao S. H., Tang Y. X. A new digital predistortion for wideband power amplifiers with constrained feedback bandwidth[J]. IEEE Microw. Wireless Compon. Lett.,2013, 23 (12):683-685.
[54]Ding L., Mujica F., Yang Z. Digital predistortion using direct learning with reduced bandwidth feedback[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013: 1-3.
[55]Yu X. Digital predistortion using feedback signal with incomplete spectral information[C]. in 2012 Asia-Pacific Microwave Conference Proceedings (APMC),2012:950-952.
[56]Ma Y., Yamao Y., Akaiwa Y., Ishibashi K. Wideband digital predistortion using spectral extrapolation of band-limited feedback signal[J]. IEEE Trans. Circuits Syst. I, Reg. Papers, 2014, PP (99):1-10.
[57]Guan L., Zhu A. D. Dual-loop model extraction for digital predistortion of wideband rf power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2011,21 (9):501-503.
[58]Kwan A., Ghannouchi F. M., Hammi O., Helaoui M., Smith M. R. Look-up table-based digital predistorter implementation for field programmable gate arrays using long-term evolution signals with 60 mhz bandwidth[J]. IET Science, Measurement & Technology,2012,6 (3): 181-188.
[59]Wu H. J., Xia J., Zhai J. F., Tian L., Yang M. S., Zhang L., Zhu X. W. A wideband digital pre-distortion platform with 100 mhz instantaneous bandwidth for lte-advanced applications[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[60]Bassam S. A., Helaoui M., Ghannouchi F. M.2-d digital predistortion (2-d-dpd) architecture for concurrent dual-band transmitters[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (10): 2547-2553.
[61]Chen W. H., Bassam S. A., Li X., Liu Y. C., Rawat K., Helaoui M., Ghannouchi F. M., Feng Z. H. Design and linearization of concurrent dual-band doherty power amplifier with frequency-dependent power ranges[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (10): 2537-2546.
[62]Bassam S. A., Chen W. H., Helaoui M., Ghannouchi F. M., Feng Z. H. Linearization of concurrent dual-band power amplifier based on 2d-dpd technique[J]. IEEE Microw. Wireless Compon. Lett.,2011,21 (12):685-687.
[63]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Ghannouchi F. M. Behavioral modeling for concurrent dual-band power amplifiers using 2d hammerstein/wiener models[J]. Int. J. RF Microwave CAE,2013,23 (6):646-654.
[64]Liu Y. J., Chen W. H., Zhou B. H., Zhou J., Ghannouchi F. M.2d augmented hammerstein model for concurrent dual-band power amplifiers[J]. Electron. Lett.,2012,48 (19):1214-1216.
[65]Moon J., Saad P., Son J., Fager C., Kim B.2-d enhanced hammerstein behavior model for concurrent dual-band power amplifiers[C]. in 2012 42nd European Microwave Conference (EuMC),2012:1249-1252.
[66]Xiang H. X., Yu C. P., Gao J. C, Li S. L., Wu Y. L., Su M., Liu Y. A. Dynamic deviation reduction-based concurrent dual-band digital predistortion[J]. Int. J. RF Microwave CAE,2014, 24 (3):401-411.
[67]Fehri B., Boumaiza S. Baseband equivalent volterra series for digital predistortion of dual-band power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2014,62 (3):700-714.
[68]Naraharisetti N., Quindroit C, Roblin P., Gheitanchi S., Mauer V., Fitton M.2d cubic spline implementation for concurrent dual-band system[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[69]Zhang S. L., Chen W. H., Liu Y. J., Ghannouchi F. M. A time misalignment tolerant 2d-memory polynomials predistorter for concurrent dual-band power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2013,23 (9):501-503.
[70]Rawat M., Rawat K., Younes M., Ghannouchi F. Joint mitigation of nonlinearity and modulator imperfections in dual-band concurrent transmitter using neural networks[J]. Electron. Lett., 2013,49 (4):253-255.
[71]Liu Y. J., Zhou J., Chen W. H., Zhou B. H., Ghannouchi F. M. Low-complexity 2d behavioural model for concurrent dual-band power amplifiers[J]. Electron. Lett.,2012,48 (11):620-621.
[72]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Ghannouchi F. M. Digital predistortion for concurrent dual-band transmitters using 2-d modified memory polynomials[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (1):281-290.
[73]Kwan A. K., Bassam S. A., Helaoui M., Ghannouchi F. M. Concurrent dual band digital predistortion using look up tables with variable depths[C]. in 2013 IEEE Topical Conference on Power Amplifiers for Wireless and Radio Applications (PAWR),2013:25-27.
[74]Ding L., Yang Z., Gandhi H. Concurrent dual-band digital predistortion[C]. in 2012 IEEE MTT-S International Microwave Symposium Digest (IMS),2012:1-3.
[75]Zhang S. L., Chen W. H., Ghannouchi F. M., Chen Y. Q. An iterative pruning of 2-d digital predistortion model based on normalized polynomial terms[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[76]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Liu Y. N. Joint predistortion of iq impairments and pa nonlinearity in concurrent dual-band transmitters[C]. in 2012 42nd European Microwave Conference (EuMC),2012:132-135.
[77]Younes M., Ghannouchi F. M. On the modeling and linearization of a concurrent dual-band transmitter exhibiting nonlinear distortion and hardware impairments[J]. IEEE Trans. Circuits Syst. I, Reg. Papers,2013,60 (11):3055-3068.
[78]Quindroit C., Naraharisetti N., Roblin P., Gheitanchi S., Mauer V., Fitton M. Concurrent dual-band digital predistortion for power amplifier based on orthogonal polynomials[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[79]Yang G., Liu F. L., Li L., Wang H. Y., Zhao C. H., Wang Z. Y.2d orthogonal polynomials for concurrent dual-band digital predistortion[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-3.
[80]Younes M., Kwan A., Rawat M., Ghannouchi F. M. Linearization of concurrent tri-band transmitters using 3-d phase-aligned pruned volterra model[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (12):4569-4578.
[81]Younes M., Kwan A., Rawat M, Ghannouchi F. M. Three-dimensional digital predistorter for concurrent tri-band power amplifier linearization[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[82]Rugh W. J. Nonlinear system theory:The volterra/wiener approach[M]:Johns Hopkins University Press,1981.
[83]Ogunfunmi T. Adaptive nonlinear system identification:The volterra and wiener model approaches[M]:Springer,2007.
[84]Raich R., Qian H., Zhou G. T. Orthogonal polynomials for power amplifier modeling and predistorter design[J]. IEEE Trans. Veh. Technol.,2004,53 (5):1468-1479.
[85]Vuolevi J. H. K., Rahkonen T., Manninen J. P. A. Measurement technique for characterizing memory effects in rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2001,49 (8): 1383-1389.
[86]Pan W. S., Liu Y., Tang Y. X. A predistortion algorithm based on accurately solving the reverse function of memory polynomial model[J]. IEEE Wireless Communications Letters,2012,1 (4): 384-387.
[87]Braithwaite R. N., Carichner S. An improved doherty amplifier using cascaded digital predistortion and digital gate voltage enhancement[J]. IEEE Trans. Microw. Theory Tech.,2009, 57(12):3118-3126.
[88]Hammi O., Younes M., Vassilakis B., Ghannouchi F. M. Digital predistorters sensitivity to delay alignment resolution[C]. in 2009 IEEE Radio and Wireless Symposium (RWS),2009:606-609.
[89]Hammi O., Ghannouchi F. M., Vassilakis B. On the sensitivity of rf transmitters'memory polynomial model identification to delay alignment resolution[J]. IEEE Microw. Wireless Compon. Lett.,2008,18 (4):263-265.
[90]Farabegoli A., Sogl B., Mueller J., Weigel R. A novel, fast, and precise method to perform time alignment estimation and compensation[C]. in 2013 IEEE Topical Conference on Power Amplifiers for Wireless and Radio Applications (PAWR),2013:28-30.
[91]Huang H., Qian H., Xu H., Wang X. Fractional delay compensation in digital predistortion system[C]. in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),2012:3569-3572.
[92]Hoflehner M., Springer A. On the impact of timing mismatch and memory length on digital predistortion systems[C]. in 2012 42nd European Microwave Conference (EuMC),2012: 1257-1260.
[93]Boumaiza S., Helaoui M., Hammi O., Liu T, Ghannouchi F. M. Systematic and adaptive characterization approach for behavior modeling and correction of dynamic nonlinear transmitters[J]. IEEE Trans. Instrum. Meas.,2007,56 (6):2203-2211.
[94]Golub G. H., Van Loan C. F. Matrix computation[M]. Baltimore, MD:The Johns Hopkins Uni. Press,1996.
[95]Moon T. K., Stirling W. C. Mathematical methods and algorithms for signal processing[M]. Upper Saddle River, NJ:Prentice Hall,2000.
[96]Ims2014 student design competition, http://dpdcompetition.com/
[97]尤览,丁瑶,杨光,刘发林.采用寄生补偿的高效率逆f类gan hemt功率放大器[J].微波学报,2011,27(5)：50-54.
[98]Guan L., Zhu A. D. Optimized low-complexity implementation of least squares based model extraction for digital predistortion of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech., 2012,60 (3):594-603.
[99]Kaufman L. A variable projection method for solving separable nonlinear least squares problems[J]. BIT,1975,15 (1):49-57.
[100]Zhou D. Y., DeBrunner V. E. Novel adaptive nonlinear predistorters based on the direct learning algorithm[J]. IEEE Trans. Signal Process.,2007,55 (1):120-133.
[101]Dani A., Roberg M., Popovic Z. Pa efficiency and linearity enhancement using external harmonic injection[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (12):4097-4106.
[102]Aitchison C. S., Mbabele M., Moazzam M. R., Budimir D., Ali F. Improvement of third-order intermodulation product of rf and microwave amplifiers by injection[J]. IEEE Trans. Microw. Theory Tech.,2001,49 (6):1148-1154.
[103]Li S. M., Jing D., Chan W. S. Verification of practicality of using the second harmonic for reducing imd[J]. Electron. Lett.,1998,34 (11):1097-1098.
[104]Kwon Y. P., Jeong Y. C., Kim Y., Kim C. D. A design of predistortion linearizer using 2nd order low frequency intermodulation signal injection[C]. in 2003 33rd European Microwave Conference (EuMC),2003:249-252.
[105]Modeste M., Budimir D., Moazzam M. R., Aitchison C. S. Analysis and practical performance of a difference frequency technique for improving the multicarrier imd performance of rf amplifiers [C]. in 1999 IEEE MTT-S Symposium on Technologies for Wireless Applications, 1999:53-56.
[106]Yang Y. G., Woo Y. Y., Kim B. New predistortion linearizer using low-frequency even-order intermodulation components[J]. IEEE Trans. Microw. Theory Tech.,2002,50 (2):446-452.
[107]Cho K. J., Jang D. H., Kim S. H., Kim J. H., Lee B., Kim N. Y., Lee J. C., Stapleton S. P. Multi-order predistortion of power amplifiers using a second harmonic based technique[J]. IEEE Microw. Wireless Compon. Lett.,2003,13 (10):452-454.
[108]Cho K. J., Jang D. H., Kim S. H., Kim J. Y., Kim J. H., Stapleton S. P. An analog compensation method for asymmetric imd characteristics of power amplifier[J]. IEEE Microw. Wireless Compon. Lett.,2004,14 (4):153-155.
[109]Bulja S., Mirshekar-Syahkal D. Combined low frequency and third harmonic injection in power amplifier linearization[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (9):584-586.
[110]Xiao M., Gardner P. Characterisation, analysis and injection of two-tone third-order intermodulation products in an amplifier[J]. IET Microw. Antennas & Propag.,2009,3 (3): 443-455.
[111]Mizusawa N., Kusunoki S. Third-and fifth-order baseband component injection for linearization of the power amplifier in a cellular phone[J]. IEEE Trans. Microw. Theory Tech., 2005,53 (11):3327-3334.
[112]Xiao M., Gardner P. Digital baseband injection techniques to reduce spectral regrowth in power amplifier[C]. in 2008 IEEE MTT-S International Microwave Symposium Digest (IMS),2008: 1520-1523.
[113]Bondar D., Budimir D. A digital predistorter for wireless transmitters[J]. Int. J. RF Microwave CAE,2009,19 (4):453-459.
[114]Bondar D., Budimir D., Shelkovnikov B. Distortion components iterative injection technique for linearization of power amplifiers[C]. in 2009 19th International Crimean Conference Microwave & Telecommunication Technology (CriMiCo 2009),2009:115-118.
[115]Cabarkapa M., Neskovic N., Neskovic A., Budimir D. Adaptive nonlinearity compensation technique for 4g wireless transmitters[J]. Electron. Lett.,2012,48 (20):1308-1309.
[116]Bondar D., Budimir D. A new digital predistortion for linearity improvement and suppression of memory effects[C]. in 2009 37th European Microwave Conference (EuMC),2009:1437-1440.
[117]Mishali M., Eldar Y. C., Elron A. J. Xampling:Signal acquisition and processing in union of subspaces[J]. IEEE Trans. Signal Process.,2011,59 (10):4719-4734.
[118]Mishali M., Eldar Y. C. Xampling:Analog data compression[C]. in 2010 Data Compression Conference (DCC 2010),2010:366-375.
[119]Nader C., Van Moer W., Barbe K., Bjorsell N., Handel P. Harmonic sampling and reconstruction of wideband undersampled waveforms:Breaking the code[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (11):2961-2969.
[120]Nader C., Van Moer W., Bjorsell N., Barbe K., Handel P. Reducing the analog and digital bandwidth requirements of rf receivers for measuring periodic sparse waveforms[J]. IEEE Trans. Instrum. Meas.,2012,61 (11):2960-2971.
[121]Braithwaite R. N. Implementing crest factor reduction (cfr) by offsetting digital predistortion (dpd) coefficients[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[122]Braithwaite R. N. A combined approach to digital predistortion and crest factor reduction for the linearization of an rf power amplifier[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (1): 291-302.
[123]Nader C., Landin P. N., Van Moer W., Bjorsell N., Handel P., Ronnow D. Peak-power controlling technique for enhancing digital pre-distortion of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (11):3571-3581.
[124]Landin P. N., Van Moer W., Isaksson M., Handel P. Peak-power controlled digital predistorters for rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (11):3582-3590.
[2]Sun G., Jansen R. H. Broadband doherty power amplifier via real frequency technique[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (1):99-111.
[3]Piazzon L., Giofre R., Colantonio P., Giannini F. A wideband doherty architecture with 36% of fractional bandwidth[J]. IEEE Microw. Wireless Compon. Lett,2013,23 (11):626-628.
[4]Shao J., Zhou R. G., Ren H., Arigong B., Zhou M., Kim H. S., Zhang H. L. Design of gan doherty power amplifiers for broadband applications[J]. IEEE Microw. Wireless Compon. Lett., 2014,24 (4):248-250.
[5]Giofre R., Colantonio P., Giannini F., Piazzon L. New output combiner for doherty amplifiers[J]. IEEE Microw. Wireless Compon. Lett,2013,23 (1):31-33.
[6]Xia J., Zhu X. W., Zhang L., Zhai J. F., Sun Y. J. High-efficiency gan doherty power amplifier for 100-mhz Ite-advanced application based on modified load modulation network[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (8):2911-2921.
[7]Ma C. H., Pan W. S., Shao S. H., Qing C. J., Tang Y. X. A wideband doherty power amplifier with 100 mhz instantaneous bandwidth for lte-advanced applications[J]. IEEE Microw. Wireless Compon. Lett.,2013,23 (11):614-616.
[8]Nghiem X. A., Negra R. Design of a concurrent quad-band gan-hemt doherty power amplifier for wireless applications[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[9]Saad P., Colantonio P., Piazzon L., Giannini F., Andersson K., Fager C. Design of a concurrent dual-band 1,8-2.4-ghz gan-hemt doherty power amplifier[J]. IEEE Trans. Microw. Theory Tech., 2012,60(6):1840-1849.
[10]Nghiem X. A., Guan J. Q., Hone T., Negra R. Design of concurrent multiband doherty power amplifiers for wireless applications[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (12): 4559-4568.
[11]Cripps S. C. Rfpower amplifiers for wireless communications[M]. Artech House,2006.
[12]Wright P., Lees J., Benedikt J., Tasker P. J., Cripps S. C. A methodology for realizing high efficiency class-j in a linear and broadband pa[J]. IEEE Trans. Microw. Theory Tech.,2009,57 (12):3196-3204.
[13]Moon J., Kim J., Kim B. Investigation of a class-j power amplifier with a nonlinear c-out for optimized operation[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (11):2800-2811.
[14]Mimis K., Morris K. A., Bensmida S., McGeehan J. P. Multichannel and wideband power amplifier design methodology for 4g communication systems based on hybrid class-j operation[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (8):2562-2570.
[15]Cripps S. C., Tasker P. J., Clarke A. L., Lees J., Benedikt J. On the continuity of high efficiency modes in linear rf power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (10): 665-667.
[16]Carrubba V., Akmal M., Quay R., Lees J., Benedikt J., Cripps S. C., Tasker P. J. The continuous inverse class-f mode with resistive second-harmonic impedance[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (6):1928-1936.
[17]Carrubba V., Clarke A. L., Akmal M., Lees J., Benedikt J., Tasker P. J., Cripps S. C. The continuous class-f mode power amplifier[C]. in 2010 European Microwave Conference (EuMC), 2010:1674-1677.
[18]Carrubba V., Lees J., Benedikt J., Tasker P. J., Cripps S. C. A novel highly efficient broadband continuous class-f rfpa delivering 74% average efficiency for an octave bandwidth[C]. in 2011 IEEE MTT-S International Microwave Symposium Digest (IMS),2011:1-4.
[19]Junghwan M., Seunghoon J., Jungjoon K., Junghwan S., Seungchan K., Juyeon L., Seokhyeon K., Kim B. Investigation of a class-if power amplifier with a nonlinear output capacitor[C]. in 2011 European Microwave Integrated Circuits Conference (EuMIC),2011:124-127.
[20]Tuffy N., Guan L., Zhu A., Brazil T. J. A simplified broadband design methodology for linearized high-efficiency continuous class-f power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (6):1952-1963.
[21]Chen K. L., Peroulis D. Design of broadband highly efficient harmonic-tuned power amplifier using in-band continuous class-if/f mode transferring[J]. IEEE Trans. Microw. Theory Tech., 2012,60 (12):4107-4116.
[22]Ghannouchi F. M., Hammi O. Behavioral modeling and predistortion[J]. IEEE Microw. Mag., 2009,10 (7):52-64.
[23]Saleh A. A. M. Frequency-independent and frequency-dependent nonlinear models of twt amplifiers[J]. IEEE Trans. Commun.,1981,29(11):1715-1720.
[24]Rapp C. Effects of hpa-nonlinearity on a 4-dpsk/ofdm-signal for a digital sound broadcasting signal[C]. in 2nd European Conference on Satellite Communications (ECSC-2),1991:179-184.
[25]Cavers J. K. Amplifier linearization using a digital predistorter with fast adaptation and low memory requirements[J]. IEEE Trans. Veh. Technol,1990,39 (4):374-382.
[26]D'Andrea A. N., Lottici V., Reggiannini R. Rf power amplifier linearization through amplitude and phase predistortion[J]. IEEE Trans. Commun.,1996,44 (11):1477-1484.
[27]Kim J., Konstantinou K. Digital predistortion of wideband signals based on power amplifier model with memory[J]. Electron. Lett.,2001,37 (23):1417-1418.
[28]Ding L., Zhou G. T. Effects of even-order nonlinear terms on power amplifier modeling and predistortion linearization[J]. IEEE Trans. Veh. Technol.,2004,53 (1):156-162.
[29]Eun C., Powers E. J. A new volterra predistorter based on the indirect learning architecture[J]. IEEE Trans. Signal Process.,1997,45 (1):223-227.
[30]Ding L., Zhou G. T., Morgan D. R., Ma Z. X., Kenney J. S., Kim J., Giardina C. R. A robust digital baseband predistorter constructed using memory polynomials[J]. IEEE Trans. Commun., 2004,52 (1):159-165.
[31]Hammi O., Ghannouchi F. M., Vassilakis B. A compact envelope-memory polynomial for rf transmitters modeling with application to baseband and rf-digital predistortion[J]. IEEE Microw. Wireless Compon. Lett.,2008,18 (5):359-361.
[32]Morgan D. R., Ma Z. X., Kim J., Zierdt M. G., Pastalan J. A generalized memory polynomial model for digital predistortion of rf power amplifiers[J]. IEEE Trans. Signal Process.,2006,54 (10):3852-3860.
[33]Zhu A. D., Draxler P. J., Hsia C., Brazil T. J., Kimball D. F., Asbeck P. M. Digital predistortion for envelope-tracking power amplifiers using decomposed piecewise volterra series[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (10):2237-2247.
[34]Zhu A. D., Pedro J. C, Cunha T. R. Pruning the volterra series for behavioral modeling of power amplifiers using physical knowledge[J]. IEEE Trans. Microw. Theory Tech.,2007,55 (5): 813-821.
[35]Zhu A. D., Draxler P. J., Yan J. M. J., Brazil T. J., Kimball D. F., Asbeck P. M. Open-loop digital predistorter for rf power amplifiers using dynamic deviation reduction-based volterra series[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (7):1524-1534.
[36]Zhu A. D., Pedro J. C., Brazil T. J. Dynamic deviation reduction-based volterra behavioral modeling of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2006,54 (12): 4323-4332.
[37]Guan L., Zhu A. D. Simplified dynamic deviation reduction-based volterra model for doherty power amplifiers[C]. in 2011 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2011:1-4.
[38]Guan L., Zhu A. D. Low-cost fpga implementation of volterra series-based digital predistorter for rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (4):866-872.
[39]Zhai J. F., Zhang L., Zhou J. Y, Zhu X. W., Hong W. A nonlinear filter-based volterra model with low complexity for wideband power amplifiers[J]. IEEE Microw. Wireless Compon. Lett., 2014,24 (3):203-205.
[40]Gilabert P. L., Montoro G., Bertran E. Fpga implementation of a real-time narma-based digital adaptive predistorter[J]. IEEE Trans. Circuits Syst. II, Exp. Briefs,2011,58 (7):402-406.
[41]Gilabert P. L., Cesari A., Montoro G., Bertran E., Dilhac J. M. Multi-lookup table fpga implementation of an adaptive digital predistorter for linearizing rf power amplifiers with memory effects[J]. IEEE Trans. Microw. Theory Tech.,2008,56 (2):372-384.
[42]Liu T. J., Boumaiza S., Ghannouchi F. M. Dynamic behavioral modeling of 3g power amplifiers using real-valued time-delay neural networks[J]. IEEE Trans. Microw. Theory Tech.,2004,52 (3):1025-1033.
[43]Rawat M., Rawat K., Ghannouchi P. M. Adaptive digital predistortion of wireless power amplifiers/transmitters using dynamic real-valued focused time-delay line neural networks[J]. IEEE Trans. Microw. Theory Tech.,2010,58 (1):95-104.
[44]Liu T. J., Boumaiza S., Ghannouchi F. M. Augmented hammerstein predistorter for linearization of broad-band wireless transmitters[J]. IEEE Trans. Microw. Theory Tech.,2006,54 (4): 1340-1349.
[45]Liu T. J., Boumaiza S., Ghannouchi F. M. Deembedding static nonlinearities and accurately identifying and modeling memory effects in wide-band rf transmitters[J]. IEEE Trans. Microw. Theory Tech.,2005,53 (11):3578-3587.
[46]Junghwan M., Bumman K. Enhanced hammerstein behavioral model for broadband wireless transmitters[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (4):924-933.
[47]Hammi O., Ghannouchi F. M. Twin nonlinear two-box models for power amplifiers and transmitters exhibiting memory effects with application to digital predistortion[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (8):530-532.
[48]Younes M., Hammi O., Kwan A., Ghannouchi F. M. An accurate complexity-reduced "plume" model for behavioral modeling and digital predistortion of rf power amplifiers[J]. IEEE Trans. Ind. Electron.,2011,58 (4):1397-1405.
[49]Yu C., Guan L., Zhu A. Band-limited volterra series-based behavioral modeling of rf power amplifiers[C]. in 2012 IEEE MTT-S International Microwave Symposium Digest (IMS),2012: 1-3.
[50]Yu C., Guan L., Zhu E., Zhu A. Band-limited volterra series-based digital predistortion for wideband rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (12):4198-4208.
[51]Guan L., Yu C., Zhu A. Bandwidth-constrained least squares-based model extraction for band-limited digital predistortion of rf power amplifiers[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[52]Zhang S. L., Chen W. H., Feng Z. H. Low sampling rate digital predistortion of power amplifier assisted by bandpass rf filter[C]. in 2012 Asia Pacific Microwave Conference Proceedings (APMC),2012:962-964.
[53]Liu Y., Pan W. S., Shao S. H., Tang Y. X. A new digital predistortion for wideband power amplifiers with constrained feedback bandwidth[J]. IEEE Microw. Wireless Compon. Lett.,2013, 23 (12):683-685.
[54]Ding L., Mujica F., Yang Z. Digital predistortion using direct learning with reduced bandwidth feedback[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013: 1-3.
[55]Yu X. Digital predistortion using feedback signal with incomplete spectral information[C]. in 2012 Asia-Pacific Microwave Conference Proceedings (APMC),2012:950-952.
[56]Ma Y., Yamao Y., Akaiwa Y., Ishibashi K. Wideband digital predistortion using spectral extrapolation of band-limited feedback signal[J]. IEEE Trans. Circuits Syst. I, Reg. Papers, 2014, PP (99):1-10.
[57]Guan L., Zhu A. D. Dual-loop model extraction for digital predistortion of wideband rf power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2011,21 (9):501-503.
[58]Kwan A., Ghannouchi F. M., Hammi O., Helaoui M., Smith M. R. Look-up table-based digital predistorter implementation for field programmable gate arrays using long-term evolution signals with 60 mhz bandwidth[J]. IET Science, Measurement & Technology,2012,6 (3): 181-188.
[59]Wu H. J., Xia J., Zhai J. F., Tian L., Yang M. S., Zhang L., Zhu X. W. A wideband digital pre-distortion platform with 100 mhz instantaneous bandwidth for lte-advanced applications[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[60]Bassam S. A., Helaoui M., Ghannouchi F. M.2-d digital predistortion (2-d-dpd) architecture for concurrent dual-band transmitters[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (10): 2547-2553.
[61]Chen W. H., Bassam S. A., Li X., Liu Y. C., Rawat K., Helaoui M., Ghannouchi F. M., Feng Z. H. Design and linearization of concurrent dual-band doherty power amplifier with frequency-dependent power ranges[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (10): 2537-2546.
[62]Bassam S. A., Chen W. H., Helaoui M., Ghannouchi F. M., Feng Z. H. Linearization of concurrent dual-band power amplifier based on 2d-dpd technique[J]. IEEE Microw. Wireless Compon. Lett.,2011,21 (12):685-687.
[63]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Ghannouchi F. M. Behavioral modeling for concurrent dual-band power amplifiers using 2d hammerstein/wiener models[J]. Int. J. RF Microwave CAE,2013,23 (6):646-654.
[64]Liu Y. J., Chen W. H., Zhou B. H., Zhou J., Ghannouchi F. M.2d augmented hammerstein model for concurrent dual-band power amplifiers[J]. Electron. Lett.,2012,48 (19):1214-1216.
[65]Moon J., Saad P., Son J., Fager C., Kim B.2-d enhanced hammerstein behavior model for concurrent dual-band power amplifiers[C]. in 2012 42nd European Microwave Conference (EuMC),2012:1249-1252.
[66]Xiang H. X., Yu C. P., Gao J. C, Li S. L., Wu Y. L., Su M., Liu Y. A. Dynamic deviation reduction-based concurrent dual-band digital predistortion[J]. Int. J. RF Microwave CAE,2014, 24 (3):401-411.
[67]Fehri B., Boumaiza S. Baseband equivalent volterra series for digital predistortion of dual-band power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2014,62 (3):700-714.
[68]Naraharisetti N., Quindroit C, Roblin P., Gheitanchi S., Mauer V., Fitton M.2d cubic spline implementation for concurrent dual-band system[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[69]Zhang S. L., Chen W. H., Liu Y. J., Ghannouchi F. M. A time misalignment tolerant 2d-memory polynomials predistorter for concurrent dual-band power amplifiers[J]. IEEE Microw. Wireless Compon. Lett.,2013,23 (9):501-503.
[70]Rawat M., Rawat K., Younes M., Ghannouchi F. Joint mitigation of nonlinearity and modulator imperfections in dual-band concurrent transmitter using neural networks[J]. Electron. Lett., 2013,49 (4):253-255.
[71]Liu Y. J., Zhou J., Chen W. H., Zhou B. H., Ghannouchi F. M. Low-complexity 2d behavioural model for concurrent dual-band power amplifiers[J]. Electron. Lett.,2012,48 (11):620-621.
[72]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Ghannouchi F. M. Digital predistortion for concurrent dual-band transmitters using 2-d modified memory polynomials[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (1):281-290.
[73]Kwan A. K., Bassam S. A., Helaoui M., Ghannouchi F. M. Concurrent dual band digital predistortion using look up tables with variable depths[C]. in 2013 IEEE Topical Conference on Power Amplifiers for Wireless and Radio Applications (PAWR),2013:25-27.
[74]Ding L., Yang Z., Gandhi H. Concurrent dual-band digital predistortion[C]. in 2012 IEEE MTT-S International Microwave Symposium Digest (IMS),2012:1-3.
[75]Zhang S. L., Chen W. H., Ghannouchi F. M., Chen Y. Q. An iterative pruning of 2-d digital predistortion model based on normalized polynomial terms[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[76]Liu Y. J., Chen W. H., Zhou J., Zhou B. H., Liu Y. N. Joint predistortion of iq impairments and pa nonlinearity in concurrent dual-band transmitters[C]. in 2012 42nd European Microwave Conference (EuMC),2012:132-135.
[77]Younes M., Ghannouchi F. M. On the modeling and linearization of a concurrent dual-band transmitter exhibiting nonlinear distortion and hardware impairments[J]. IEEE Trans. Circuits Syst. I, Reg. Papers,2013,60 (11):3055-3068.
[78]Quindroit C., Naraharisetti N., Roblin P., Gheitanchi S., Mauer V., Fitton M. Concurrent dual-band digital predistortion for power amplifier based on orthogonal polynomials[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[79]Yang G., Liu F. L., Li L., Wang H. Y., Zhao C. H., Wang Z. Y.2d orthogonal polynomials for concurrent dual-band digital predistortion[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-3.
[80]Younes M., Kwan A., Rawat M., Ghannouchi F. M. Linearization of concurrent tri-band transmitters using 3-d phase-aligned pruned volterra model[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (12):4569-4578.
[81]Younes M., Kwan A., Rawat M, Ghannouchi F. M. Three-dimensional digital predistorter for concurrent tri-band power amplifier linearization[C]. in 2013 IEEE MTT-S International Microwave Symposium Digest (IMS),2013:1-4.
[82]Rugh W. J. Nonlinear system theory:The volterra/wiener approach[M]:Johns Hopkins University Press,1981.
[83]Ogunfunmi T. Adaptive nonlinear system identification:The volterra and wiener model approaches[M]:Springer,2007.
[84]Raich R., Qian H., Zhou G. T. Orthogonal polynomials for power amplifier modeling and predistorter design[J]. IEEE Trans. Veh. Technol.,2004,53 (5):1468-1479.
[85]Vuolevi J. H. K., Rahkonen T., Manninen J. P. A. Measurement technique for characterizing memory effects in rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2001,49 (8): 1383-1389.
[86]Pan W. S., Liu Y., Tang Y. X. A predistortion algorithm based on accurately solving the reverse function of memory polynomial model[J]. IEEE Wireless Communications Letters,2012,1 (4): 384-387.
[87]Braithwaite R. N., Carichner S. An improved doherty amplifier using cascaded digital predistortion and digital gate voltage enhancement[J]. IEEE Trans. Microw. Theory Tech.,2009, 57(12):3118-3126.
[88]Hammi O., Younes M., Vassilakis B., Ghannouchi F. M. Digital predistorters sensitivity to delay alignment resolution[C]. in 2009 IEEE Radio and Wireless Symposium (RWS),2009:606-609.
[89]Hammi O., Ghannouchi F. M., Vassilakis B. On the sensitivity of rf transmitters'memory polynomial model identification to delay alignment resolution[J]. IEEE Microw. Wireless Compon. Lett.,2008,18 (4):263-265.
[90]Farabegoli A., Sogl B., Mueller J., Weigel R. A novel, fast, and precise method to perform time alignment estimation and compensation[C]. in 2013 IEEE Topical Conference on Power Amplifiers for Wireless and Radio Applications (PAWR),2013:28-30.
[91]Huang H., Qian H., Xu H., Wang X. Fractional delay compensation in digital predistortion system[C]. in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),2012:3569-3572.
[92]Hoflehner M., Springer A. On the impact of timing mismatch and memory length on digital predistortion systems[C]. in 2012 42nd European Microwave Conference (EuMC),2012: 1257-1260.
[93]Boumaiza S., Helaoui M., Hammi O., Liu T, Ghannouchi F. M. Systematic and adaptive characterization approach for behavior modeling and correction of dynamic nonlinear transmitters[J]. IEEE Trans. Instrum. Meas.,2007,56 (6):2203-2211.
[94]Golub G. H., Van Loan C. F. Matrix computation[M]. Baltimore, MD:The Johns Hopkins Uni. Press,1996.
[95]Moon T. K., Stirling W. C. Mathematical methods and algorithms for signal processing[M]. Upper Saddle River, NJ:Prentice Hall,2000.
[96]Ims2014 student design competition, http://dpdcompetition.com/
[97]尤览,丁瑶,杨光,刘发林.采用寄生补偿的高效率逆f类gan hemt功率放大器[J].微波学报,2011,27(5)：50-54.
[98]Guan L., Zhu A. D. Optimized low-complexity implementation of least squares based model extraction for digital predistortion of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech., 2012,60 (3):594-603.
[99]Kaufman L. A variable projection method for solving separable nonlinear least squares problems[J]. BIT,1975,15 (1):49-57.
[100]Zhou D. Y., DeBrunner V. E. Novel adaptive nonlinear predistorters based on the direct learning algorithm[J]. IEEE Trans. Signal Process.,2007,55 (1):120-133.
[101]Dani A., Roberg M., Popovic Z. Pa efficiency and linearity enhancement using external harmonic injection[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (12):4097-4106.
[102]Aitchison C. S., Mbabele M., Moazzam M. R., Budimir D., Ali F. Improvement of third-order intermodulation product of rf and microwave amplifiers by injection[J]. IEEE Trans. Microw. Theory Tech.,2001,49 (6):1148-1154.
[103]Li S. M., Jing D., Chan W. S. Verification of practicality of using the second harmonic for reducing imd[J]. Electron. Lett.,1998,34 (11):1097-1098.
[104]Kwon Y. P., Jeong Y. C., Kim Y., Kim C. D. A design of predistortion linearizer using 2nd order low frequency intermodulation signal injection[C]. in 2003 33rd European Microwave Conference (EuMC),2003:249-252.
[105]Modeste M., Budimir D., Moazzam M. R., Aitchison C. S. Analysis and practical performance of a difference frequency technique for improving the multicarrier imd performance of rf amplifiers [C]. in 1999 IEEE MTT-S Symposium on Technologies for Wireless Applications, 1999:53-56.
[106]Yang Y. G., Woo Y. Y., Kim B. New predistortion linearizer using low-frequency even-order intermodulation components[J]. IEEE Trans. Microw. Theory Tech.,2002,50 (2):446-452.
[107]Cho K. J., Jang D. H., Kim S. H., Kim J. H., Lee B., Kim N. Y., Lee J. C., Stapleton S. P. Multi-order predistortion of power amplifiers using a second harmonic based technique[J]. IEEE Microw. Wireless Compon. Lett.,2003,13 (10):452-454.
[108]Cho K. J., Jang D. H., Kim S. H., Kim J. Y., Kim J. H., Stapleton S. P. An analog compensation method for asymmetric imd characteristics of power amplifier[J]. IEEE Microw. Wireless Compon. Lett.,2004,14 (4):153-155.
[109]Bulja S., Mirshekar-Syahkal D. Combined low frequency and third harmonic injection in power amplifier linearization[J]. IEEE Microw. Wireless Compon. Lett.,2009,19 (9):584-586.
[110]Xiao M., Gardner P. Characterisation, analysis and injection of two-tone third-order intermodulation products in an amplifier[J]. IET Microw. Antennas & Propag.,2009,3 (3): 443-455.
[111]Mizusawa N., Kusunoki S. Third-and fifth-order baseband component injection for linearization of the power amplifier in a cellular phone[J]. IEEE Trans. Microw. Theory Tech., 2005,53 (11):3327-3334.
[112]Xiao M., Gardner P. Digital baseband injection techniques to reduce spectral regrowth in power amplifier[C]. in 2008 IEEE MTT-S International Microwave Symposium Digest (IMS),2008: 1520-1523.
[113]Bondar D., Budimir D. A digital predistorter for wireless transmitters[J]. Int. J. RF Microwave CAE,2009,19 (4):453-459.
[114]Bondar D., Budimir D., Shelkovnikov B. Distortion components iterative injection technique for linearization of power amplifiers[C]. in 2009 19th International Crimean Conference Microwave & Telecommunication Technology (CriMiCo 2009),2009:115-118.
[115]Cabarkapa M., Neskovic N., Neskovic A., Budimir D. Adaptive nonlinearity compensation technique for 4g wireless transmitters[J]. Electron. Lett.,2012,48 (20):1308-1309.
[116]Bondar D., Budimir D. A new digital predistortion for linearity improvement and suppression of memory effects[C]. in 2009 37th European Microwave Conference (EuMC),2009:1437-1440.
[117]Mishali M., Eldar Y. C., Elron A. J. Xampling:Signal acquisition and processing in union of subspaces[J]. IEEE Trans. Signal Process.,2011,59 (10):4719-4734.
[118]Mishali M., Eldar Y. C. Xampling:Analog data compression[C]. in 2010 Data Compression Conference (DCC 2010),2010:366-375.
[119]Nader C., Van Moer W., Barbe K., Bjorsell N., Handel P. Harmonic sampling and reconstruction of wideband undersampled waveforms:Breaking the code[J]. IEEE Trans. Microw. Theory Tech.,2011,59 (11):2961-2969.
[120]Nader C., Van Moer W., Bjorsell N., Barbe K., Handel P. Reducing the analog and digital bandwidth requirements of rf receivers for measuring periodic sparse waveforms[J]. IEEE Trans. Instrum. Meas.,2012,61 (11):2960-2971.
[121]Braithwaite R. N. Implementing crest factor reduction (cfr) by offsetting digital predistortion (dpd) coefficients[C]. in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC),2012:1-3.
[122]Braithwaite R. N. A combined approach to digital predistortion and crest factor reduction for the linearization of an rf power amplifier[J]. IEEE Trans. Microw. Theory Tech.,2013,61 (1): 291-302.
[123]Nader C., Landin P. N., Van Moer W., Bjorsell N., Handel P., Ronnow D. Peak-power controlling technique for enhancing digital pre-distortion of rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (11):3571-3581.
[124]Landin P. N., Van Moer W., Isaksson M., Handel P. Peak-power controlled digital predistorters for rf power amplifiers[J]. IEEE Trans. Microw. Theory Tech.,2012,60 (11):3582-3590.