A Novel Method for Realization of NonSinusoidal Orthogonal Modulation System in Time Domain Based on Fourier Transform

Abstract

Abstract:

Abstract： In the application of the non-sinusoidal orthogonal modulation system based on PSWF (prolate spheroidal wave function) in time domain it is difficult to generate PSWF in real-time and complex to realize the non-sinusoidal orthogonal modulation system. Therefore, starting from the Fourier series expansion of PSWF, the relationships between the expansion coefficients and the energy and orthogonality of PSWFs were analyzed. Then, a modulation method based on the inverse discrete Fourier transform (IDFT) and a demodulation method based on the discrete Fourier transform (DFT) were deduced. After that, structures of the modulator and demodulator based on the (inverse) fast Fourier transform (FFT & IFFT) were given. As the idea of Fourier transform was introduced to the realization of non-sinusoidal communication system, the connection between nonsinusoidal communication system and (inverse) discrete Fourier transform was established. This method may provide reference for the study of nonsinusoidal technology.

Key words: nonsinusoidal orthogonal modulation in time domain, prolate spheroidal wave function (PSWF), inverse discrete Fourier transformation (IDFT), inverse fast Fourier transformation (IFFT)

CLC Number:

TN 911.3

KANG Jiafanga,WANG Hongxinga,b,ZHONG Peilina,CHEN Zhaonana,HU Haoa. A Novel Method for Realization of NonSinusoidal Orthogonal Modulation System in Time Domain Based on Fourier Transform[J]. Journal of Shanghai Jiaotong University, 2014, 48(10): 1415-1420.

References

［1］Slepian D, Pollak H O. Prolate spheroidal wave functions, Fourier analysis and uncertainty. I［J］. Bell System Technical Journal, 1961, 40(1): 4364.

［2］Moore I C, Cada M. Prolate spheroidal wave functions, an introduction to the Slepian series and its properties［J］. Appl Comput Harmon Anal, 2004(16): 208230.

［3］Kazuto U, Zhang H, Masao N. Mary pulse shape modulation for PSWFbased UWB systems in multipath fading environment［C］∥IEEE Communications Society Globecom. Dallas, USA: IEEE, 2004:34983504.

［4］Sacchi C, Rossi T, Ruggieri M, et al. Efficient waveform design for highbitrate wband satellite transmissions［J］. Aerospace and Electronic Systems, IEEE Transactions on, 2011, 47(2): 974995.

［5］Dullaert W, Rogier H, Boeykens F. Advantages of PSWFbased models for UWB systems［C］∥IEEEAPWC. Cape Town, South Africa: IEEE, 2012:10241027.

［6］Feng Y, Debes C, Zoubir A M. Parametric waveform design using discrete prolate spheroidal sequences for enhanced detection of extended targets［J］. Signal Processing, IEEE Transactions on, 2012, 60(9): 45254536.

［7］Liying W, Kennedy R A, Lamahewa T A. An optimal basis of bandlimited functions for signal analysis and design［J］. IEEE Transactions on Signal Processing, 2010, 58(11): 57445755.

［8］Lindquist M A, CunHui Z, Glover G, et al. A generalization of the twodimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods［J］. IEEE Transactions on Image Processing, 2006, 15(9): 27922804.

［9］王红星，赵志勇，刘锡国，等. 非正弦时域正交调制方法［P］.中国专利：ZL 2008 10159238.3, 20110202.

［10］赵志勇，王红星，刘锡国，等. 正交椭圆球面波函数脉冲调制方法［J］. 电子与信息学报, 2012(10): 23312335.

ZHAO Zhiyong, WANG Hongxing, LIU Xiguo, et al. Orthogonal prolate spheroidal wave functions pulse modulation method［J］. Journal of Electronics & Information Technology, 2012(10): 23312335.

［11］Abderrazek K, Tahar M. New efficient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues［J］. Applied and Computational Harmonic Analysis, 2008, 24(3): 269289.

［12］Parr B, Cho B, Wallace K. A novel ultrawideband pulse design algorithm［J］. IEEE Communication Letters, 2003, 7(5): 219221.

［13］赵志勇，王红星，陈昭男，等. 非正弦时域正交调制信号的解调性能分析［J］. 系统工程与电子技术, 2011,33(1): 179182.

ZHAO Zhiyong, WANG Hongxing, CHEN Zhaonan, et al. Demoduation performance for nonsinusoidal orthogonal modulation signals in time domain［J］. Systems Engineering and Electronics, 2011,33(1): 179182.

[1]	ZHAO Ziren1, DU Shichang1, HUANG Delin1, REN Fei2, LIANG Xinguang2. Modelling and Bottleneck Analysis of Product Quality in Transient Phase#br# of MultiStage Manufacturing Systems Based on Markovian Chains [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1166-1173.
[2]	ZHOU Penghui, MA Hongzhan, CHEN Dongping, CHEN Mengyue, CHU Xuening. Identification of Product Redesign Modules Based on#br# Fuzzy Random Failure Mode and Effects Analysis [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1189-1195.
[3]	LI Changxi1, 2, ZHOU Yan1, LIN Han3, LI Lingzhi1, GUO Ge1. TemporalSpatial Sequential Fusion Recognition Method of#br# Ballistic Missile Target Based on MIMOFNN Model [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1138-.
[4]	FENG Mingyue, HE Minghao, HAN Jun, YU Chunlai. High Resolution Direction of Arrival Estimation Based on#br# Covariance Fitting Estimation of Signal Parameters by#br# Rotational Invariance Technique Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1145-.
[5]	?YANG Ping1,SHENG Jie1,WANG Yucheng2,LI Zhuyong1,JIN Zhijian1,HONG Zhiyong1. Quench Propagation Characteristics Influenced by NonUniform Properties of YBa2Cu3O7δ High Temperature Superconducting Tape [J]. Journal of Shanghai Jiaotong University, 2017, 51(9): 1090-1096.
[6]	WANG Xing, ZHOU Yipeng, TIAN Yuanrong, CHEN You, ZHOU Dongqing, HE Jiyuan. Sparse Decomposition for Frequency Modulation Radar Signal Based on#br# Advanced Genetic Algorithm and SinChirplet Atom [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1124-1130.
[7]	ZHANG Liangjun1, 2, LI Xiaoci1, WU Jingyi1, CAI Aifeng1. ThermalStructure Coupling Analysis of #br# Microgravity Environment Simulation Suspension Structure for #br# Large Space Deployable Mechanisms [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 954-961.
[8]	XIA Hailiang1, 2, LIU Yakun1, 2, LIU Quanzhen3, LIU Baoquan3, FU Zhengcai1, 2. Metal Ablation Affected by Electrode Shapes Under#br# Long Continuing Lightning Current [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 903-908.
[9]	LIN Da, ZHU Yijia, WEI Xiaodong, WANG Zhiyu, ZHANG Wugao. Combustion and Particle Emission Characteristics Affected by#br# Fuel Supply Parameters for a Diesel Engine Fuelled with#br# Polyoxymethylene Dimethyl Ethers/Diesel [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 787-795.
[10]	GU Jiayang, XIE Yulin, TAO Yanwu, HUANG Xianghong, WU Jie. Numerical Simulation and Experimental Study on VortexInduced#br# Motion of a New Type of Floating Drilling Production Storage Offloading [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 878-885.
[11]	MENG Qingyang1, YAN Weiwu1, HU Yong1, CHENG Jianlin1, CHEN Shihe2, ZHANG Xi2. Model Identification Based on Subspace Model Identification of#br# Superheated Steam System in UltraSupercritical CoalFired Power Unit [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 672-678.
[12]	JIANG Huajuna, CAI Yana, b, LI Chaohaoa, LI Fanga, b, HUA Xueminga, b. Recognition Method for Gas Pores on XRay Image of Lap Joints#br# Based on the Improved Sobel Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 665-671.
[13]	DONG Guanhua,YIN Qin,YIN Guofu,XIANG Zhaowei. Identification and Modeling of Coupling Dynamic Stiffness in Joints of Machine Tool [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1263-1434.
[14]	XIE Qijiang,YU Haidong. Coupling Relationship Between Loads on Cutterhead of Tunnel Boring Machine and Contact Stiffness of Gripper Shoes and Rocks [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1269-1275.
[15]	ZHONG Jianlin1,MA Dawei1,REN Jie1,LI Shijun2,WANG Xu3. Static Compression Analysis of Rubber Hollow Cylinder Based on Plane Strain Assumption [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1276-1280.