Differential Spatial Modulation Mapping Algorithms

doi:10.12142/ZTECOM.202403014

摘要/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

. [J]. ZTE Communications, 2024, 22(3): 116-122.

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

图/表 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

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