Differential Spatial Modulation Mapping Algorithms

doi:10.12142/ZTECOM.202403014

Abstract

Abstract:

Differential spatial modulation (DSM) is a multiple-input multiple-output (MIMO) transmission scheme. It has attracted extensive research interest due to its ability to transmit additional data without increasing any radio frequency chain. In this paper, DSM is investigated using two mapping algorithms: Look-Up Table Order (LUTO) and Permutation Method (PM). Then, the bit error rate (BER) performance and complexity of the two mapping algorithms in various antennas and modulation methods are verified by simulation experiments. The results show that PM has a lower BER than the LUTO mapping algorithm, and the latter has lower complexity than the former.

Key words: spatial modulation (SM), multiple-input multiple-output (MIMO), Look-Up Table Order (LUTO), Permutation Method (PM), mapping algorithm

WANG Chanfei, CHAI Jianxin, XU Yamei. Differential Spatial Modulation Mapping Algorithms[J]. ZTE Communications, 2024, 22(3): 116-122.

Figures/Tables 10

Table 1 Differential transmission in differential spatial modulation (DSM) with binary phase shift keying (BPSK) modulation and NT = 3

Index t	0	1	2	3
Time interval	0, 1, 2	3, 4, 5	6, 7, 8	9, 10, 11
Input bit	No information sent	01010	10100	11110
Map to $X t$	No information sent	$- 1 - 1 + 1$	$+ 1 + 1 + 1$	$- 1 + 1 + 1$
Actual transmitted signal matrix $S t$	$+ 1 + 1 + 1$	$- 1 - 1 + 1$	$- 1 - 1 + 1$	$- 1 - 1 - 1$

Table 1 Differential transmission in differential spatial modulation (DSM) with binary phase shift keying (BPSK) modulation and NT = 3

Index t	0	1	2	3
Time interval	0, 1, 2	3, 4, 5	6, 7, 8	9, 10, 11
Input bit	No information sent	01010	10100	11110
Map to $X t$	No information sent	$- 1 - 1 + 1$	$+ 1 + 1 + 1$	$- 1 + 1 + 1$
Actual transmitted signal matrix $S t$	$+ 1 + 1 + 1$	$- 1 - 1 + 1$	$- 1 - 1 + 1$	$- 1 - 1 - 1$

Table 2 Mapping table of LUTO algorithm when NT = 3

Input Bitstream	Antenna Activation Sequence	Block of Information to Send
00	(1, 2, 3)	$s 1 s 2 s 3$
01	(1, 3, 2)	$s 1 s 2 s 3$
10	(2, 1, 3)	$s 1 s 2 s 3$
11	(2, 3, 1)	$s 1 s 2 s 3$

Table 2 Mapping table of LUTO algorithm when NT = 3

Input Bitstream	Antenna Activation Sequence	Block of Information to Send
00	(1, 2, 3)	$s 1 s 2 s 3$
01	(1, 3, 2)	$s 1 s 2 s 3$
10	(2, 1, 3)	$s 1 s 2 s 3$
11	(2, 3, 1)	$s 1 s 2 s 3$

Table 3 Matrix of all signals sent with binary phase shift keying (BPSK) modulation and NT = 3 when input bit D is 00

Input Bits	Time Interval 1		Time Interval 2		Time Interval 3		Transmitted Signal Matrix
Input Bits	Antenna Index	Symbol	Antenna Index	Symbol	Antenna Index	Symbol	Transmitted Signal Matrix
00000	1	$-$ 1	2	$-$ 1	3	$-$ 1	$- 1 - 1 - 1$
00001	1	$-$ 1	2	$-$ 1	3	+1	$- 1 - 1 + 1$
00010	1	$-$ 1	2	+1	3	$-$ 1	$- 1 + 1 - 1$
00011	1	$-$ 1	2	+1	3	+1	$- 1 + 1 + 1$
00100	1	+1	2	+1	3	+1	$+ 1 + 1 + 1$
00101	1	+1	2	+1	3	$-$ 1	$+ 1 + 1 - 1$
00110	1	+1	2	$-$ 1	3	+1	$+ 1 - 1 + 1$
00111	1	+1	2	$-$ 1	3	$-$ 1	$+ 1 - 1 - 1$

Table 3 Matrix of all signals sent with binary phase shift keying (BPSK) modulation and NT = 3 when input bit D is 00

Input Bits	Time Interval 1		Time Interval 2		Time Interval 3		Transmitted Signal Matrix
Input Bits	Antenna Index	Symbol	Antenna Index	Symbol	Antenna Index	Symbol	Transmitted Signal Matrix
00000	1	$-$ 1	2	$-$ 1	3	$-$ 1	$- 1 - 1 - 1$
00001	1	$-$ 1	2	$-$ 1	3	+1	$- 1 - 1 + 1$
00010	1	$-$ 1	2	+1	3	$-$ 1	$- 1 + 1 - 1$
00011	1	$-$ 1	2	+1	3	+1	$- 1 + 1 + 1$
00100	1	+1	2	+1	3	+1	$+ 1 + 1 + 1$
00101	1	+1	2	+1	3	$-$ 1	$+ 1 + 1 - 1$
00110	1	+1	2	$-$ 1	3	+1	$+ 1 - 1 + 1$
00111	1	+1	2	$-$ 1	3	$-$ 1	$+ 1 - 1 - 1$

Table 4 All the signal schemes of Look-Up Table Order (LUTO) with binary phase shift keying (BPSK) modulation and NT = 4

		U
		U₀	U₁	U₂	U₃		U₆	U₇		U₁₃	U₁₄	U₁₅
D	D₀	00000000	00000001	00000010	00000011	…	00000110	00000111	…	00001101	00001110	00001111
	D₁	00010000	00010001	00010010	00010011	…	00010110	00010111	…	00011101	00011110	00011111
	D₂	00100000	00100001	00100010	00100011	…	00100110	00100111	…	00101101	00101110	00101111
	…	…	…	…	…	…	…	…	…	…	…	…
	D₆	01100000	01100001	01100010	01100011	…	01100110	01100111	…	01101101	01101110	01101111
	D₇	01110000	01110001	01110010	01110011	…	01110110	01110111	…	01111101	01111110	01111111
	…	…	…	…	…	…	…	…	…	…	…	…
	D₁₃	11000000	11000001	11000010	11000011	…	11000110	11000111	…	11001101	11001110	11001111
	D₁₄	11010000	11010001	11010010	11010011	…	11010110	11010111	…	11011101	11011110	11011111
	D₁₅	11110000	11110001	11110010	11110011	…	11110110	11110111	…	11111101	11111110	11111111

Table 5 All the signal schemes of Look-Up Table Order (LUTO) with binary phase shift keying (BPSK) modulation and NT = 5

		U
		U₀	U₁	U₂		U₁₄	U₁₅		U₂₉	U₃₀	U₃₁
D	D₀	00000000000	00000000001	00000000010	…	00000001110	00000001111	…	00000011101	00000011110	00000011111
	D₁	00000100000	00000100001	00000100010	…	00000101110	00000101111	…	00000111101	00000111110	00000111111
	D₂	00001000000	00001000001	00001000010	…	00001001110	00001001111	…	00001011101	00001011110	00001111111
	…	…	…	…	…	…	…	…	…	…	…
	D₁₄	00111000000	00111000001	00111000010	…	00111001110	00111001111	…	00111011101	00111011110	00111011111
	D₁₅	00111100000	00111100001	00111100010	…	00111101110	00111101111	…	00111111101	00111111110	00111111111
	…	…	…	…	…	…	…	…	…	…	…
	D₃₀	01111000000	01111000001	01111000010	…	01111001110	01111001111	…	01111011101	01111011110	01111011111
	D₃₁	01111100000	01111100001	01111100010	…	01111101110	01111101111	…	01111111101	01111111110	01111111111
	…	…	…	…	…	…	…	…	…	…	…
	D₆₁	11110100000	11110100001	11110100010	…	11110101110	11110101111	…	11110111101	11110111110	11110111111
	D₆₂	11111000000	11111000001	11111000010	…	11111001110	11111001111	…	11111011101	11111011110	11111011111
	D₆₃	11111100000	11111100001	11111100010	…	11111101110	11111101111	…	11111111101	11111111110	11111111111

Table 6 Configuration of the test host

CPU Type	Core Count	Thread Count	Core Types	Performance-Core Frequency	RAM
Core i9-13900	24	32	Alder Lake (12-th generation)	2.00 GHz	32 GB

Table 7 Performance test results

Test Items	Program Running Time/s	Test Items	Program Running Time/s
PM BPSK $N T = 3 N R = 1$	6.76	LUTO BPSK $N T = 3 N R = 1$	4.47
PM BPSK $N T = 3 N R = 2$	112.95	LUTO BPSK $N T = 3 N R = 2$	30.45
PM BPSK $N T = 3 N R = 3$	213.68	LUTO BPSK $N T = 3 N R = 3$	67.37
PM QPSK $N T = 3 N R = 1$	15.01	LUTO QPSK $N T = 3 N R = 1$	5.47
PM QPSK $N T = 3 N R = 2$	363.52	LUTO QPSK $N T = 3 N R = 2$	46.82
PM QPSK $N T = 3 N R = 3$	816.58	LUTO QPSK $N T = 3 N R = 3$	89.67
PM 8PSK $N T = 3 N R = 1$	44.54	LUTO 8PSK $N T = 3 N R = 1$	11.59
PM 8PSK $N T = 3 N R = 2$	370.16	LUTO 8PSK $N T = 3 N R = 2$	41.83
PM 8PSK $N T = 3 N R = 3$	1 969.85	LUTO 8PSK $N T = 3 N R = 3$	375.57
PM BPSK $N T = 4 N R = 1$	24.26	LUTO BPSK $N T = 3 N R = 1$	20.51
PM BPSK $N T = 4 N R = 2$	472.79	LUTO BPSK $N T = 4 N R = 2$	249.37
PM BPSK $N T = 4 N R = 3$	962.76	LUTO BPSK $N T = 4 N R = 3$	334.52
PM BPSK $N T = 4 N R = 4$	1 145.05	LUTO BPSK $N T = 4 N R = 4$	481.76
PM QPSK $N T = 4 N R = 1$	249.45	LUTO QPSK $N T = 4 N R = 1$	173.50
PM 8PSK $N T = 4 N R = 1$	1 323.63	LUTO 8PSK $N T = 4 N R = 1$	625.83
PM BPSK $N T = 5 N R = 1$	127.07	LUTO BPSK $N T = 5 N R = 1$	96.36
PM QPSK $N T = 5 N R = 1$	1 981.00	LUTO QPSK $N T = 5 N R = 1$	896.64
PM 8PSK $N T = 5 N R = 1$	56 551.78	LUTO 8PSK $N T = 5 N R = 1$	15 637.95

Table 7 Performance test results

Test Items	Program Running Time/s	Test Items	Program Running Time/s
PM BPSK $N T = 3 N R = 1$	6.76	LUTO BPSK $N T = 3 N R = 1$	4.47
PM BPSK $N T = 3 N R = 2$	112.95	LUTO BPSK $N T = 3 N R = 2$	30.45
PM BPSK $N T = 3 N R = 3$	213.68	LUTO BPSK $N T = 3 N R = 3$	67.37
PM QPSK $N T = 3 N R = 1$	15.01	LUTO QPSK $N T = 3 N R = 1$	5.47
PM QPSK $N T = 3 N R = 2$	363.52	LUTO QPSK $N T = 3 N R = 2$	46.82
PM QPSK $N T = 3 N R = 3$	816.58	LUTO QPSK $N T = 3 N R = 3$	89.67
PM 8PSK $N T = 3 N R = 1$	44.54	LUTO 8PSK $N T = 3 N R = 1$	11.59
PM 8PSK $N T = 3 N R = 2$	370.16	LUTO 8PSK $N T = 3 N R = 2$	41.83
PM 8PSK $N T = 3 N R = 3$	1 969.85	LUTO 8PSK $N T = 3 N R = 3$	375.57
PM BPSK $N T = 4 N R = 1$	24.26	LUTO BPSK $N T = 3 N R = 1$	20.51
PM BPSK $N T = 4 N R = 2$	472.79	LUTO BPSK $N T = 4 N R = 2$	249.37
PM BPSK $N T = 4 N R = 3$	962.76	LUTO BPSK $N T = 4 N R = 3$	334.52
PM BPSK $N T = 4 N R = 4$	1 145.05	LUTO BPSK $N T = 4 N R = 4$	481.76
PM QPSK $N T = 4 N R = 1$	249.45	LUTO QPSK $N T = 4 N R = 1$	173.50
PM 8PSK $N T = 4 N R = 1$	1 323.63	LUTO 8PSK $N T = 4 N R = 1$	625.83
PM BPSK $N T = 5 N R = 1$	127.07	LUTO BPSK $N T = 5 N R = 1$	96.36
PM QPSK $N T = 5 N R = 1$	1 981.00	LUTO QPSK $N T = 5 N R = 1$	896.64
PM 8PSK $N T = 5 N R = 1$	56 551.78	LUTO 8PSK $N T = 5 N R = 1$	15 637.95

References 23

1	DI RENZO M, HAAS H, GRANT P M. Spatial modulation for multiple-antenna wireless systems: A survey [J]. IEEE communications magazine, 2011, 49(12): 182–191. DOI: 10.1109/MCOM.2011.6094024
2	MESLEH R Y, HAAS H, SINANOVIC S, et al. Spatial modulation [J]. IEEE transactions on vehicular technology, 2008, 57(4): 2228–2241. DOI: 10.1109/TVT.2007.912136
3	WEN M W, ZHENG B X, KIM K J, et al. A survey on spatial modulation in emerging wireless systems: Research progresses and applications [J]. IEEE journal on selected areas in communications, 2019, 37(9): 1949–1972. DOI: 10.1109/JSAC.2019.2929453
4	LI J, DANG S P, WEN M W, et al. Index modulation multiple access for 6G communications: Principles, applications, and challenges [J]. IEEE network, 2023, 37(1): 52–60. DOI: 10.1109/MNET.002.2200433
5	LI J, DANG S P, YAN Y E, et al. Generalized quadrature spatial modulation and its application to vehicular networks with NOMA [J]. IEEE transactions on intelligent transportation systems, 2021, 22(7): 4030–4039. DOI: 10.1109/TITS.2020.3006482
6	LI J, DANG S P, HUANG Y, et al. Composite multiple-mode orthogonal frequency division multiplexing with index modulation [J]. IEEE transactions on wireless communications, 2023, 22(6): 3748–3761. DOI: 10.1109/TWC.2022.3220752
7	WEN M W, LI J, DANG S P, et al. Joint-mapping orthogonal frequency division multiplexing with subcarrier number modulation [J]. IEEE transactions on communications, 2021, 69(7): 4306–4318. DOI: 10.1109/TCOMM.2021.3066584
8	WEN M W, LIN S E, KIM K J, et al. Cyclic delay diversity with index modulation for green Internet of Things [J]. IEEE transactions on green communications and networking, 2021, 5(2): 600–610. DOI: 10.1109/TGCN.2021.3067705
9	WEN M W, CHEN X, LI Q, et al. Index modulation aided subcarrier mapping for dual-hop OFDM relaying [J]. IEEE transactions on communications, 2019, 67(9): 6012–6024. DOI: 10.1109/TCOMM.2019.2920642
10	JEGANATHAN J, GHRAYEB A, SZCZECINSKI L. Spatial modulation: optimal detection and performance analysis [J]. IEEE communications letters, 2008, 12(8): 545–547. DOI: 10.1109/LCOMM.2008.080739
11	BIAN Y Y, WEN M W, CHENG X, et al. A differential scheme for Spatial Modulation [C]//Proc. IEEE Global Communications Conference (GLOBECOM). IEEE, 2013: 3925–3930. DOI: 10.1109/GLOCOM.2013.6831686
12	ISHIKAWA N, SUGIURA S. Unified differential spatial modulation [J]. IEEE wireless communications letters, 2014, 3(4): 337–340. DOI: 10.1109/LWC.2014.2315635
13	BIAN Y Y, CHENG X, WEN M W, et al. Differential spatial modulation [J]. IEEE transactions on vehicular technology, 2015, 64(7): 3262–3268. DOI: 10.1109/TVT.2014.2348791
14	LI J, WEN M W, CHENG X, et al. Differential spatial modulation with gray coded antenna activation order [J]. IEEE communications letters, 2016, 20(6): 1100–1103. DOI: 10.1109/LCOMM.2016.2557801
15	ZHANG M, WEN M W, CHENG X, et al. A dual-hop virtual MIMO architecture based on hybrid differential spatial modulation [J]. IEEE transactions on wireless communications, 2016, 15(9): 6356–6370. DOI: 10.1109/TWC.2016.2583423
16	RAJASHEKAR R, XU C, ISHIKAWA N, et al. Algebraic differential spatial modulation is capable of approaching the performance of its coherent counterpart [J]. IEEE transactions on communications, 2017, 65(10): 4260–4273. DOI: 10.1109/TCOMM.2017.2720170
17	XU C, WANG L, NG S X, et al. Soft-decision multiple-symbol differential sphere detection and decision-feedback differential detection for differential QAM dispensing with channel estimation in the face of rapidly fading channels [J]. IEEE transactions on wireless communications, 2016, 15(6): 4408–4425. DOI: 10.1109/TWC.2016.2541665
18	WEI R Y, TSAI Y W, CHEN S L. Improved schemes of differential spatial modulation [J]. IEEE access, 2021, 9: 97120–97128. DOI: 10.1109/ACCESS.2021.3095531
19	WEN M W, CHENG X, BIAN Y Y, et al. A low-complexity near-ML differential spatial modulation detector [J]. IEEE signal processing letters, 2015, 22(11): 1834–1838. DOI: 10.1109/LSP.2015.2425042
20	WEI R Y, CHEN S L, LIN Y H, et al. Bandwidth-efficient generalized differential spatial modulation [J]. IEEE transactions on vehicular technology, 2023, 72(1): 601–610. DOI: 10.1109/TVT.2022.3202912
21	XIU H T, YU D Z, GAO P Y, et al. An enhanced system model for differential spatial modulation system under fast fading channels and a corresponding DFDD based low- complexity detector [J]. IEEE transactions on vehicular technology, 2024, 73(2): 2227–2235. DOI: 10.1109/TVT.2023.3316275
22	YANG L, XIU H T, YU D Z, et al. Reordered amplitude phase shift keying aided differential spatial modulation: DFDD-based low-complexity detector and performance analysis over fading channels [J]. IEEE transactions on wireless communications, 2022, 21(10): 7913–7925. DOI: 10.1109/TWC.2022.3162834
23	WEI R Y. Differential encoding by a look-up table for quadrature-amplitude modulation [J]. IEEE transactions on communications, 2011, 59(1): 84–94. DOI: 10.1109/TCOMM.2010.102910.100061

[1]	Sohail Taheri, Mir Ghoraishi, XIAO Pei, CAO Aijun, GAO Yonghong. Evaluation of Preamble Based Channel Estimation for MIMO-FBMC Systems [J]. ZTE Communications, 2016, 14(4): 3-10.
[2]	WEI Zhiqiang, YUAN Jinhong, Derrick Wing Kwan Ng, Maged Elkashlan, DING Zhiguo. A Survey of Downlink Non-Orthogonal Multiple Access for 5G Wireless Communication Networks [J]. ZTE Communications, 2016, 14(4): 17-25.