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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (10): 2213-2220    DOI: 10.3785/j.issn.1008-973X.2025.10.022
    
CSK design scheme of visible light communication based on spatial modulation
Zongyan LI1,2(),Zheng SUN1,Han GAO1,Hongmei WANG1,Shuai MA3,Jinling SONG1,*(),Shiyin LI1
1. School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China
2. Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory, Guilin University of Electronic Technology, Guilin 541004, China
3. Department of Strategic and Advanced Interdisciplinary Research, Pengcheng Laboratory, Shenzhen 518055, China
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Abstract  

To improve the transmission quality of visible light communication systems using color-shift keying (CSK) modulation, two spatial modulation (SM)-based CSK design schemes were proposed. Based on the three-dimensional light intensity space, the value of the CSK symbol coordinate was extended to a bipolar signal. By introducing SM, the extended CSK symbol was converted into a unipolar signal, making it suitable for transmission in terms of light intensity. Criteria for symbol subset partitioning were designed based on the triangle partitioning of the CSK symbol set, and a constant intensity plane-based SM-CSK design scheme (CIP-SM-CSK) was proposed to maximize the minimum Euclidean distance (MED) of CSK symbols under the constraints of constant light intensity and white light. A multi-sphere partitioning-based SM-CSK design-scheme (MSP-SM-CSK) was proposed to further increase the MED, and the sequential quadratic programming algorithm was used to solve the optimization problem. The MEDs of CSK schemes were calculated, and the simulation results show that the proposed schemes enormously improve the bit error rate of the visible light communication system compared with the existing CSK schemes.

Key words： visible light communication      color-shift keying (CSK) modulation      spatial modulation      minimum Euclidean distance      bit error rate     
Received: 22 August 2024      Published: 27 October 2025
CLC:  TN 91  
Fund:  国家自然科学基金资助项目（62293483）；广西无线宽带通信与信号处理重点实验室基金项目资助（桂科AD25069102）.
Corresponding Authors: Jinling SONG     E-mail: lizongyan@cumt.edu.cn;jinlingsong@cumt.edu.cn
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Zongyan LI
Zheng SUN
Han GAO
Hongmei WANG
Shuai MA
Jinling SONG
Shiyin LI
Cite this article:

Zongyan LI,Zheng SUN,Han GAO,Hongmei WANG,Shuai MA,Jinling SONG,Shiyin LI. CSK design scheme of visible light communication based on spatial modulation. Journal of ZheJiang University (Engineering Science), 2025, 59(10): 2213-2220.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.10.022     OR     https://www.zjujournals.com/eng/Y2025/V59/I10/2213


基于空间调制的可见光通信CSK设计方案

为了提升色移键控（CSK）调制可见光通信系统的传输质量，提出2种基于空间调制（SM）的CSK设计方案. 基于三维光强度空间将CSK符号坐标的取值扩展为双极性信号；引入SM，将扩展CSK符号转换为单极性信号以适于在光强度上传输. 基于三角划分CSK符号集设计符号子集划分准则，在恒定光强度和白光约束下，以最大化CSK符号的最小欧式距离（MED）为目标函数，提出恒定强度面的SM-CSK设计方案（CIP-SM-CSK）. 为了进一步增大MED，提出多球面（MSP）的SM-CSK设计方案（MSP-SM-CSK），使用顺序二次规划算法进行优化问题的求解. 进行CSK方案的MED计算分析，仿真结果表明：相比现有CSK方案，所提方案极大改善了可见光通信系统的误比特率.


关键词： 可见光通信,  色移键控（CSK）调制,  空间调制,  最小欧式距离,  误比特率 
Fig.1 Visible light communication system model mapped by spatial modulation-CSK
扩展CSK信号LED索引SM-CSK信号
${s_{{\mathrm{r}},i}} \gt 0$1${s_{{\mathrm{r1}},i}} = {s_{{\mathrm{r}},i}}$
${s_{{\mathrm{g}},i}} \gt 0$2${s_{{\mathrm{g1}},i}} = {s_{{\mathrm{g}},i}}$
${s_{{\mathrm{b}},i}} \gt 0$3${s_{{\mathrm{b1}},i}} = {s_{{\mathrm{b}},i}}$
${s_{{\mathrm{r}},i}} \lt 0$4${s_{{\mathrm{r2}},i}} = \left| {{s_{{\mathrm{r}},i}}} \right|$
${s_{{\mathrm{g}},i}} \lt 0$5${s_{{\mathrm{g2}},i}} = \left| {{s_{{\mathrm{g}},i}}} \right|$
${s_{{\mathrm{b}},i}} \lt 0$6${s_{{\mathrm{b2}},i}} = \left| {{s_{{\mathrm{b}},i}}} \right|$
Tab.1 Relationship between LED selection and spatial modulation-CSK signal
比特子序列LED索引${{\boldsymbol{s}}_i}$
001${\left[ {{s_{{\mathrm{r1}},i}},0,0,0,0,0} \right]^{\text{T}}}$
012${\left[ {0,{s_{{\mathrm{g1}},i}},0,0,0,0} \right]^{\text{T}}}$
103${\left[ {0,0,{s_{{\mathrm{b1}},i}},0,0,0} \right]^{\text{T}}}$
114, 5, 6${\left[ {0,0,0,{s_{{\mathrm{r2}},i}},{s_{{\mathrm{g2}},i}},{s_{{\mathrm{b2}},i}}} \right]^{\text{T}}}$
Tab.2 Mapping rules for quaternary spatial modulation-CSK
Fig.2 Constellation diagram of constant intensity plane-based spatial modulation-CSK
M星座点
4$ {{\boldsymbol{s}}_1}{\text{ = }}{[1,0,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_2}{\text{ = }}{[0,1,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_3}{\text{ = }}{[0,0,1,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_4}{\text{ = }}{[0,0,0,0,0,0]^{\text{T}}} $
8$ {{\boldsymbol{s}}_1}{\text{ = }}{[1,0,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_2}{\text{ = }}{[0,1,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_3}{\text{ = }}{[0,0,1,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_4}{\text{ = }}{[0.333\;3,0.333\;3,0.333\;3,0,0,0]^{\text{T}}} $，
$ {{\boldsymbol{s}}_5}{\text{ = }}{[0,0,0,1,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_6}{\text{ = }}{[0,0,0,0,1,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_7}{\text{ = }}{[0,0,0,0,0,1]^{\text{T}}} $，$ {{\boldsymbol{s}}_8}{\text{ = }}{[0,0,0,0.333\;3,0.333\;3,0.333\;3]^{\text{T}}} $
16$ {{\boldsymbol{s}}_1}{\text{ = }}{[1,0,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_2}{\text{ = }}{[0,1,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_3}{\text{ = }}{[0,0,1,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_4}{\text{ = }}{[0,0.333\;3,0.666\;6,0,0,0]^{\text{T}}} $，
$ {{\boldsymbol{s}}_5}{\text{ = }}{[0,0.666\;6,0.333\;3,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_6}{\text{ = }}{[0.333\;3,0,0.666\;6,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_7}{\text{ = }}{[0.666\;6,{\text{0}},{\text{0}}{\text{.333 3}},0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_8}{\text{ = }}{[{\text{0}}{\text{.333 3}},0.666\;6,{\text{0}},0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_9}{\text{ = }}{[{\text{0}}{\text{.666 6}},{\text{ 0}}{\text{.333 3}},{\text{ }}0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{10}}{\text{ = }}{[0.333\;3,0.333\;3,0.333\;3,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{11}}{\text{ = }}{[0,0,0,1,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{12}}{\text{ = }}{[0,0,0,0,1,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{13}}{\text{ = }}{[0,0,0,0,0,1]^{\text{T}}} $，$ {{\boldsymbol{s}}_{14}}{\text{ = }}{[0,0,0,0,0.5,0.5]^{\text{T}}} $，$ {{\boldsymbol{s}}_{15}}{\text{ = }}{[0,0,0,0.5,0,0.5]^{\text{T}}} $，$ {{\boldsymbol{s}}_{16}}{\text{ = }}{[0,0,0,0.5,0.5,0]^{\text{T}}} $
Tab.3 Symbol coordinates of constant intensity plane based spatial modulation-CSK
Fig.3 Constellation diagram of octal multi-sphere partitioning-based spatial modulation-CSK
Fig.4 Constellation diagram of hexadecimal multi-sphere partitioning-based spatial modulation-CSK
M星座点
8$ {{\boldsymbol{s}}_1}{\text{ = }}{[1,0,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_2}{\text{ = }}{[0,1,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_3}{\text{ = }}{[0,0,1,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_4}{\text{ = }}{[0.666\;6,0.666\;6,0.666\;6,0,0,0]^{\text{T}}} $，
$ {{\boldsymbol{s}}_5}{\text{ = }}{[0,0,0,1,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_6}{\text{ = }}{[0,0,0,0,1,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_7}{\text{ = }}{[0,0,0,0,0,1]^{\text{T}}} $，$ {{\boldsymbol{s}}_8}{\text{ = }}{[0,0,0,0,0,0]^{\text{T}}} $
16$ {{\boldsymbol{s}}_1}{\text{ = }}{[1.339\;9,0,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_2}{\text{ = }}{[0,1.339\;9,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_3}{\text{ = }}{[0,0,1.339\;9,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_4}{\text{ = }}{[0.656\;6,0,0,0,0,0]^{\text{T}}} $，
$ {{\boldsymbol{s}}_5}{\text{ = }}{[0,0.656\;6,0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_6}{\text{ = }}{[0,0,0.656\;6,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_7}{\text{ = }}{[0,{\text{0}}{\text{.669 9}},{\text{0}}{\text{.669 9}},0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_8}{\text{ = }}{[{\text{0}}{\text{.669 9}},0,{\text{0}}{\text{.669 9}},0,0,0]^{\text{T}}} $，
$ {{\boldsymbol{s}}_9}{\text{ = }}{[{\text{0}}{\text{.669 9}},{\text{0}}{\text{.669 9}},0,0,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{10}}{\text{ = }}{[0,0,0,1.339\;9,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{11}}{\text{ = }}{[0,0,0,0,1.339\;9,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{12}}{\text{ = }}{[0,0,0,0,0,1.339\;9]^{\text{T}}} $，
$ {{\boldsymbol{s}}_{13}}{\text{ = }}{[0,0,0,0.656\;6,0,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{14}}{\text{ = }}{[0,0,0,0,0.656\;6,0]^{\text{T}}} $，$ {{\boldsymbol{s}}_{15}}{\text{ = }}{[0,0,0,0,0,0.656\;6]^{\text{T}}} $，$ {{\boldsymbol{s}}_{16}}{\text{ = }}{[0,0,0,0,0,0]^{\text{T}}} $
Tab.4 Symbol coordinates of multi-sphere partitioning-based spatial modulation-CSK
方案$ R $$ {N_{{\text{ave}}}} $$ d_{\min }^2 $方案$ R $$ {N_{{\text{ave}}}} $$ d_{\min }^2 $方案$ R $$ {N_{{\text{ave}}}} $$ d_{\min }^2 $
4-CSK21.50.678-CSK32.250.2216-CSK42.250.07
4-SCSK21.50.938-SCSK32.000.2716-SCSK42.000.11
4-MIP-CSK23.00.898-MIP-CSK32.250.3416-MIP-CSK43.380.18
4-CIP-SM-CSK23.01.788-CIP-SM-CSK31.750.6716-CIP-SM-CSK42.250.22
————8-MSP-SM-CSK32.251.0016-MSP-SM-CSK40.750.43
Tab.5 Parameter comparison of different CSK schemes
Fig.5 Variation curve of bit error rate of different CSK schemes with signal-to-noise ratio
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