基于椭圆球面波信号的连续相位调制及其频谱性能分析

doi:10.11959/j.issn.1000-0801.2020277

摘要/Abstract

摘要：

椭圆球面波信号（PSWF）是时频域最佳能量聚集性信号，探索性地将PSWF信号应用于连续相位调制（CPM）技术，对基于椭圆球面波信号的CPM调制信号产生过程进行了描述；给出了采用自相关函数法对基于PSWF的CPM调制信号功率谱密度计算方法；结合数值计算、分析对比了最小频移键控、正弦频移键控、高斯最小频移键控以及基于高斯函数的CPM调制信号功率谱密度及其信号占用带宽等特性。数值计算结果表明椭圆球面波信号相比矩形脉冲、升余弦脉冲、高斯脉冲及（类）高斯脉冲作为CPM的基带调频信号，可以获得频谱性能、能量聚集性较好的CPM信号。

关键词: 椭圆球面波, 连续相位调制, 频谱性能

Abstract:

Prolate spheroidal wave function (PSWF) signals are the best energy-gathering signals in the time-frequency domain,here is an exploratory application of PSWF signals to continuous phase modulation technology.Firstly,the process of generating CPM modulated signals based on PSWF signals was described.Secondly,a calculation method for the power spectral density of CPM modulated signals based on PSWF using the autocorrelation function method was given.Finally,combined with numerical calculation and analysis,the power spectral density and signal occupied bandwidth characteristics of minimum frequency shift keying,sinusoidal frequency shift keying,Gaussian filtered minimum shift keying and CPM modulation signal based on Gaussian function were compared.Numerical calculation results show that the PSWF signal can obtain CPM modulation signal with better spectral performance and energy concentration,compared with rectangular pulse,raised cosine pulse,Gaussian pulse and Gauss-like pulse as the baseband frequency modulation signal of CPM.

Key words: prolate spheroidal wave functions, continuous phase modulation, spectrum performance

中图分类号:

TN914.3

杨大伟,刘传辉,康家方. 基于椭圆球面波信号的连续相位调制及其频谱性能分析[J]. 电信科学, 2020, 36(11): 68-78.

Dawei YANG,Chuanhui LIU,Jiafang KANG. PSWF signal based continuous phase modulation and its spectrum performance analysis[J]. Telecommunications Science, 2020, 36(11): 68-78.

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名称	数值
码元周期T	0.02 s
符号个数n	10⁴
符号进制M	2
PSWF时间带宽积c	2 Hz·s、4 Hz·s、8 Hz·s
时域采样点个数N	256
PSWF产生方式	DPSS^[27]

调制方式	功率占比（带宽2BT）
调制方式	90%	99%	99.9%
MSK	0.78	1.20	2.78
SFSK	0.93	2.21	2.91
CPM-PSWF(c=2 Hz·s)	0.84	1.32	2.43
CPM-PSWF(c=4 Hz·s)	0.92	2.16	2.87
CPM-PSWF(c=8 Hz·s)	1.01	2.63	4.28

调制方式	功率占比（带宽2BT）
调制方式	90%	99%	99.9%
GMSK(BT=0.25)	0.57	0.88	1.12
GMSK(BT=0.3)(GSM)	0.61	0.93	1.16
GMSK(BT=0.5)	0.69	1.05	1.38
CPM-GAUSS(BT=0.25)	0.61	0.92	1.17
CPM-GAUSS(BT=0.3)	0.66	1.01	1.28
CPM-GAUSS(BT=0.5)	0.81	1.29	2.51
CPM-PSWF(c=2 Hz·s)	0.51	0.78	1.10
CPM-PSWF(c=4 Hz·s)	0.58	0.88	1.13
CPM-PSWF(c=8 Hz·s)	0.68	1.02	1.32

调制方式	功率占比（带宽2BT）
调制方式	90%	99%	99.9%
CPM-PSWF(c=2 Hz·s)	0.84	1.32	2.43
CPM-PSWF(c=3 Hz·s)	0.88	1.78	2.68
CPM-PSWF(c=4 Hz·s)	0.92	2.16	2.87
CPM-PSWF(c=5 Hz·s)	0.96	2.33	3.14
CPM-PSWF(c=6 Hz·s)	0.98	2.46	3.45
CPM-PSWF(c=7 Hz·s)	1.00	2.56	4.04
CPM-PSWF(c=8 Hz·s)	1.01	2.63	4.28
CPM-PSWF(c=9 Hz·s)	1.03	2.69	4.42
CPM-PSWF(c=10 Hz·s)	1.05	2.76	4.54