Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation

doi:10.23919/JSEE.2024.000044

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (2): 311-322.doi: 10.23919/JSEE.2024.000044

• ELECTRONICS TECHNOLOGY •

Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation

Zhichao XU¹^,²(), Faping LU²^,*(), Lifan ZHANG³(), Dongkai YANG¹(), Chuanhui LIU²(), Jiafang KANG²(), Qi AN²(), Zhilin ZHANG²()

¹ School of Electronical and Information Engineering, Beihang University, Beijing 100191, China
² Naval Aviation University, Yantai 264001, China
³ Unit 92664 of the PLA, Qingdao 266100, China

Received:2024-01-24 Online:2025-04-18 Published:2025-05-20
Contact: Faping LU E-mail:xzc8166@163.com;lufaping@163.com;2758767464@qq.com;edkyang@buaa.edu.cn;lchgfy@163.com;13791201919@163.com;18153567186@163.com;zzl19970811@163.com
About author:
XU Zhichao was born in 1981. He received his M.S. degree from PLA University of Science and Technology in 2006. He is a lecturer in Naval Aviation University. His research interests are digital signal processing and waveform design for beyound 5G/6G. E-mail: xzc8166@163.com

LU Faping was born in 1991. He received his Ph.D. degree from Naval Aviation University in 2021. He is a lecturer in Naval Aviation University. His research interests are digital signal processing, modern communication system and waveform design for beyound 5G/6G. E-mail: lufaping@163.com

ZHANG Lifan was born in 1996. She received her M.S. degree from Naval Aviation University in 2021. She is an assistant engineer in Unit 92664 of the PLA. Her research interests are modern communication system and waveform design for beyound 5G/6G. E-mail: 2758767464@qq.com

YANG Dongkai was born in 1972. He received his B.S. degree in electronic engineering from North University of China, Taiyuan, China, in 1994, and M.S. and Ph.D degrees in communication and information systems from Beihang University, Beijing, China, in 1997 and 2000, respectively. He is a professor in Beihang University. His research interests are global navigation satellite system and its applications. E-mail: edkyang@buaa.edu.cn

LIU Chuanhui was born in 1987. He received his Ph.D. degree from Naval Aeronautical and Astronautical Engineering University. He is a lecturer in Naval Aviation University. His research interests are digital signal processing, statistical signal processing for wireless applications, waveform design for 5G and ultra wide band communication. E-mail: lchgfy@163.com

KANG Jiafang was born in 1987. He received his Ph.D. degree from Naval Aeronautical and Astronautical Engineering University in 2014. He is an associate professor in Naval Aviation University in 2014. His research interests are modern multicarrier communications over fading channels, statistical signal processing for wireless applications, and signal design for the global navigation satellite system. E-mail: 13791201919@163.com

AN Qi was born in 1994. She received her M.S. degree from Naval Aviation University in 2018. She is a teaching assistant in Naval Aviation University. Her research interests are modern communication system and waveform design for beyound 5G/6G. E-mail: 18153567186@163.com

ZHANG Zhilin was born in 1997. He received his M.S. degree from Naval Aviation University in 2021. He is currently pursuing his Ph.D. degree with the Department of Aeronautical Communication, Naval Aviation University. His research interests are modern communication systems and network resource allocation. E-mail: zzl19970811@163.com
Supported by:
This work was supported by the China National Postdoctoral Program for Innovative Talents (BX20200039) and the Special Fund Project of “Mount Taishan Scholars” Construction Project in Shandong Province (ts20081130).

Abstract

Abstract:

A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method, based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with $n $=10 subcarriers and a bit error rate of 1×10^?5, spectral efficiency can be raised by roughly 12.4%.

Key words: prolate spherical wave function (PSWF), generalized multiple-mode, index modulation, spectral efficiency

Zhichao XU, Faping LU, Lifan ZHANG, Dongkai YANG, Chuanhui LIU, Jiafang KANG, Qi AN, Zhilin ZHANG. Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation[J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 311-322.

Figures/Tables 9

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References 27

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Bit information	Signal index	Subcarrier mapping
[0,0,0]	{3,1,2}	{$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $}
[0,0,1]	{3,2,1}	{$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $}
[0,1,0]	{1,3,2}	{$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $}
[0,1,1]	{2,3,1}	{$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $}
[1,0,0]	{1,2,3}	{$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $}
[1,0,1]	{2,1,3}	{$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $}
[1,1,0]	{1,1,3}	{$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{A}}} (2) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $}
[1,1,1]	{2,2,3}	{$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (1) $,$ s_{{\mathrm{I}}} ^{{\mathrm{B}}} (2) $,$ s_{{\mathrm{I}}} ^{{\mathrm{C}}} (1) $}

Modulation method	g	n	k	m	SE/(bit/s/Hz)	(E_b/N₀)/dB	Improvement/%
BIM-MCM-PSWFs [21]	11	8	7	4	3.63	13.14	12.4
DM-MCM-PSWFs [20]	10	9	5	/	3.09	12.23	32.0
MCM-PSWFs-SGO-2PAM [19]	9	10	7	/	2.41	11.05	69.3
MCM-PSWFs-SGO-4PAM [19]	10	9	5	/	2.89	14.69	41.2
GMM-PSWFs-IM (the proposed method)	9	10	/	/	4.08	13.92	/

Modulation method	Computational complexity	n	k	m	Operation amount
DM-MCM-PSWFs-ML [20]	$O(ng{2^{\left\lfloor {{{\log }_{\text{2}}}C_n^k} \right\rfloor }})$	4	2	/	368
DM-MCM-PSWFs-ML [20]		9	4	/	5760
BIM-MCM-PSWFs-ML [21]	$ O(ng({2}^{\lfloor {\mathrm{log}}_{\text{2}}{C}_{n}^{k}\rfloor }\text{+}{2}^{\lfloor {\mathrm{log}}_{\text{2}}{C}_{k}^{m}\rfloor })) $	4	3	2	552
BIM-MCM-PSWFs-ML [21]		9	8	4	6480
BIM-MCM-PSWFs-ML [21]	$ O(ng({2}^{\lfloor {\mathrm{log}}_{\text{2}}{C}_{n}^{k}\rfloor }\text{+}{2}^{\lfloor {\mathrm{log}}_{\text{2}}{C}_{k}^{m}\rfloor })) $	8	7	4	3784
GMM-PSWFs-IM-ML (the proposed method)	$ O(ng({2}^{\lfloor {\mathrm{log}}_{2}\left({C}_{n}^{k}{M}^{k}\right)\rfloor +\lfloor \left(n-k\right){\mathrm{log}}_{2}\left(1+M\right)\rfloor })) $	10	/	/	46800

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[2]	Mussa Ally DIDA, Hao HUAN, Ran TAO, Teng WANG, Didar URYNBASSAROVA. Constant envelope FrFT OFDM: spectral and energy efficiency analysis [J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 467-473.

Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation

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