多载波PSWFs-CPM联合调制信号设计与分析

doi:10.12305/j.issn.1001-506X.2021.10.36

摘要/Abstract

摘要：

连续相位调制(continuous phase modulation, CPM)信号具有恒包络、较高功率效率等优势, 基于椭圆球面波函数(prolate spheroidal wave functions, PSWFs)信号多载波调制解调系统具有较高频带利用率。结合CPM技术和基于PSWFs信号的多载波调制方法, 提出一种基于PSWFs信号的多载波调制与CPM联合调制信号(multi-carriers modulation based on PSWFs with CPM，MCM-PSWFs-CPM)模型, 对该信号的功率谱特性、峰均功率比、误码率性能等进行了分析。仿真结果表明, 相比现有基于PSWFs的多载波调制解调系统, 该模型所得信号功率谱带外衰减可以相对较快, 当载波数为64、互补累计分布函数(complementary cumulative distribution function, CCDF)为10^-3时, 可有效降低峰均功率比值约2.70 dB, 采用多符号周期检测方法, 可以获得较好的解调增益, 且符号数越大, 检测性能越好, 但是检测复杂度也会相应增加。

关键词: 椭圆球面波函数, 连续相位调制, 联合调制, 峰均功率比

Abstract:

Continuous phase modulation (CPM) signal has the advantages of constant envelope characteristics, higher power efficiency, etc., and the multi-carries modulation and demodulation system based on the prolate spheroidal wave functions (PSWFs) signal has high spectral efficiency. Combining CPM technology and multi-carriers modulation method based on PSWFs signal, a signal model of multi-carriers modulation based on PSWFs with CPM (MCM-PSWFs-CPM) model is proposed. The power spectral density (PSD) characteristics, peak to average power ratio (PAPR), and bit error ratio (BER) performance of the signal are analyzed. The simulation results show that compared with the existing PSWFs-based multi-carriers modulation and demodulation system, the out-of-band attenuation of the signal power spectrum obtained by this model relatively faster, when the number of carriers is 64 and the complementary cumulative distribution function (CCDF) is 10^-3, the PAPR can be effectively reduced by about 2.70 dB, using multi-symbol detection (MSD) method can obtain better demodulation gain, and as the number of symbols increases, the detection performance is better, but the detection complexity will increase accordingly.

Key words: prolate spheroidal wave functions, continuous phase modulation, joint modulation, peak to average power ratio (PAPR)

中图分类号:

TN914.3

杨大伟, 王红星, 张磊, 刘传辉, 康家方. 多载波PSWFs-CPM联合调制信号设计与分析[J]. 系统工程与电子技术, 2021, 43(10): 3000-3007.

Dawei YANG, Hongxing WANG, Lei ZHANG, Chuanhui LIU, Jiafang KANG. Design and analysis of multi-carriers PSWFs-CPM joint modulation signal[J]. Systems Engineering and Electronics, 2021, 43(10): 3000-3007.

图/表 14

图1

图2

图3

图4

图5

表1

图6

图7

表2

表3

图8

表4

图9

表5

参考文献 32

1	ZAHNG J , LI H Y , WANG L L . Ball prolate spheroidal wave functions in arbitrary dimensions[J]. Applied and Computational Harmonic Analysis, 2018, 48 (2): 539- 569.
2	BOULSANE M , JAMING P , SOUABNI A . Mean convergence of prolate spheroidal series and their extensions[J]. Journal of Functional Analysis, 2019, 227 (12): 108295.
3	MAHATA K , HYDER M . Frequency estimation from arbitrary time samples[J]. IEEE Trans.on Signal Processing, 2016, 64 (21): 5634- 5643. doi: 10.1109/TSP.2016.2600507
4	MOUMNI T . Solution of the energy concentration problem and application[J]. Afrika Matematika, 2018, 29 (5): 929- 938.
5	CHENG D , KOU K I . Novel sampling formulas associated with quaternionic prolate spheroidal wave functions[J]. Advances in Applied Clifford Algebras, 2017, 27 (4): 2961- 2983. doi: 10.1007/s00006-017-0815-x
6	ZOU C , KOU K I , MORAIS J . Prolate spheroidal wave functions associated with the quaternionic Fourier transform[J]. Mathematical Methods in the Applied Sciences, 2017, 41 (11): 4003- 4020.
7	OSIPOV A , ROKHLIN R , XIAO H . Prolate spheroidal wave functions of order zero[M]. New York: Springer Science Business Media, 2013: 7- 20.
8	张健. 基于索引调制的多载波系统关键技术研究[D]. 浙江: 浙江大学, 2017.
	ZHANG J. Research on multicarrier systems with index modulation[D]. Zhejiang: Zhejiang University, 2017.
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: ZL200810159238.3, 2011-02-02.
	WANG H X, ZHAO Z Y, LIU X G, et al. The non-sinusoidal orthogonal modulation in time domain[P]. China: ZL200810159238.3, 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, 34 (10): 2331- 2335.
	ZHAO Z Y , WANG H X , LIU X G , et al. Orthogonal prolate spheroidal wave function pulse modulation method[J]. Journal of Electronics & Information Technology, 2012, 34 (10): 2331- 2335.
11	LI N , LI M J , DENG Z L . A modified Hadamard based on SLM without side information for PAPR reduction in OFDM system[J]. China Communications, 2019, 16 (12): 124- 131. doi: 10.23919/JCC.2019.12.009
12	KHALED T , ADDA A P , HMAIED S , et al. Iterative dicho-tomy PAPR reduction method for multicarrier waveforms[J]. IEEE Communications Letters, 2019, 23 (11): 2073- 2076. doi: 10.1109/LCOMM.2019.2935439
13	SELAHATTIN G , TONI L , TANELI , et al. Frequency-selective PAPR reduction for OFDM[J]. IEEE Trans.on Vehicular Technology, 2019, 68 (6): 6167- 6171. doi: 10.1109/TVT.2019.2909643
14	王式林, 徐友云, 蔡云飞. 现代数字调制及其应用[M]. 北京: 人民邮电出版社, 2015.
	WANG S L , XU Y Y , CAI Y F . Modern digital modulation and its application[M]. Beijing: Publishing House of Electro-nics Industry, 2015.
15	CHANRYEOL R , SEHYUN P , HYUNGSUK L . Optimal rate for continuous phase modulation in standing surface acoustic waves[J]. Journal of Mechanical Science and Technology, 2019, 33 (8): 3819- 3829. doi: 10.1007/s12206-019-0725-z
16	PAN X C , LIU C , ZHU J Q . Phase retrieval with extended field of view based on continuous phase modulation[J]. Ultra-microscopy, 2019, 204 (5): 10- 17.
17	XUE R , SUN Y B , ZHAO D F . CPM signals for satellite navigation in the S and C bands[J]. Sensors, 2015, 15 (6): 13184- 13200. doi: 10.3390/s150613184
18	ZAIDI Y , VAN Z R . A GMSK VHF-uplink/UHF-downlink transceiver for the CubeSat missions[J]. CEAS Space Journal, 2018, 10 (3): 453- 467. doi: 10.1007/s12567-018-0217-5
19	WANG Y , WANG Y P . Research on the system performance of Gaussian minimum-shift keying with M-distribution in satellite-to-ground laser communication[J]. Optics Communications, 2020, 459 (3): 124994.
20	IRFAN M , LEE S H , SHIN S Y . Introduction to CPM-OFDM: an energy efficient multiple access transmission scheme[J]. Journal of Communication and Computer, 2015, 12 (1): 37- 43.
21	SAJAD R , ABBAS M , NAVVAB A , et al. Realization of constant envelope OFDM using quantization and CPM technique[J]. International Journal of Electronics and Communications, 2017, 80 (6): 172- 178.
22	孙锦华, 何恒. 现代调制解调技术[M]. 西安: 西安电子科技大学出版社, 2014: 120- 124.
	SUN J H , HE H . Modern modulation and demodulation techniques[M]. Xi'an: Xidian University Press, 2014: 120- 124.
23	YUE W , ZHI T . Multiple symbol differential detection for non-coherent communications with large-scale antenna arrays[J]. IEEE Wireless Communications Letters, 2018, 7 (2): 190- 193.
24	YOU Z , KE R L , FENG D R , et al. A symbol timing synchronization algorithm for multiple symbol detection in range tele-metry[J]. Journal of Terahertz Science and Electronic Information Technology, 2019, 17 (3): 196- 217.
25	PROAKIS J G, SALEHI M. 数字通信[M]. 第5版. 张力军, 张宗橙, 宋荣方, 等译. 北京: 电子工业出版社, 2017: 168-176.
26	PERCIVAL D B , WALDEN A T . Spectral analysis for physical applications[M]. Cambridge: Cambridge University Press, 1993: 378- 390.
32	PERCIVAL D B, WALDEN A T. Spectral analysis for physical applications[M]. Cambridge: Cambridge University Press, 1993: 378-390.

名称	数值
进制数M	2
PSWFs时间带宽积c/(Hz·s)	70、36
载波数	64、32
时间周期T/s	0.02
过采样点倍数	128
多符号检测周期D	3、5、7
PSWF产生方式	DPSS^[26]
调制方式	基带

调制方式(载波数为64)	PAPR
调制方式(载波数为64)	MCM-PSWFs-PAM	MCM-PSWFs-BPSK	MCM-PSWFs-CPM (h=0.5)
CCDF=10^-3	12.70	12.60	10.00
PAPR降低值	-	-	2.70

调制方式(载波数为64)	PAPR
调制方式(载波数为64)	MCM-PSWFs-CPM (h=0.75)	MCM-PSWFs-CPM (h=2/3)	MCM-PSWFs-CPM (h=4/7)	MCM-PSWFs-CPM (h=0.25)
CCDF=10^-3	11.60	11.40	10.70	11.60
PAPR降低值	1.10	1.30	2.00	1.10

调制方式	MCM-PSWFs-PAM (载波数为64)	MCM-PSWFs-CPM (载波数为64, h=0.5)	MCM-PSWFs-PAM (载波数为32)	MCM-PSWFs-CPM (载波数为32, h=0.5)
CCDF=10^-3	12.70	10.00	12.20	9.80
PAPR降低值	-	2.70	-	2.40

调制方式	算法复杂度
MCM-PSWFs-PAM	O_PSWFs+O(2nN+n)
MCM-PSWFs-BPSK	O_PSWFs+O(2n(N+1))
MCM-PSWFs-CPM(差分)	O_PSWFs+O(2nN+8n+3)
MCM-PSWFs-CPM(相关)	O_PSWFs+O(2nN+7n+1)
MCM-PSWFs-CPM(MSD)	O_PSWFs+O(2nN+10n+D2^D/2)