As a new multiple-input multiple-output (MIMO) technique, spatial modulation (SM) is limited because it can only activate one antenna each time. Generalized spatial modulation (GSM) can activate multiple antennas, but the transmission rate is not ideal when the same information is sent at the same time. By activating multiple or even all antennas to transmit information, the fully generalized spatial modulation (FGSM) technology improves the utilization rate and transmission rate of the system's transmitting antennas, but different antenna selections lead to significant performance differences of error codes. To ensure reliability and further improve the application range of FGSM-MIMO systems, researchers have introduced different antenna selection algorithms.

We propose a Pearson coefficient selection algorithm based on the basic principle of antenna selection by the Pearson coefficient between the photodetectors and LED combinations at different locations, thus improving the performance of the FGSM system and enhancing its applicability.

For GSM, the number of active antennas at the transmitting end is two and three antennas respectively, and there are four transmitting antennas in the FGSM system. The simulation results show that the bit error rate of the GSM-MIMO system is better than that of the FGSM-MIMO system under the premise of sending the same symbol. When the bit error rate is 10^-3, FGSM-MIMO loses 4.3 dB and 9.3 dB respectively compared with the GSM-MIMO system, which is because the transmission rate of the FGSM-MIMO system is higher than that of the GSM-MIMO system in transmitting the same symbol (Fig. 4). When the modulation order of the pulse amplitude modulation (PAM) is the same, the transmission rate of the FGSM system increases with the rising number of antennas, but the error performance is sacrificed. According to Fig. 5, the actual simulation reliability of the FGSM system is higher than that of the theoretical simulation under low signal-to-noise ratio (SNR), and the two basically coincide under high SNR. When the number of transmitting antennas is set to 6 and 4 respectively, compared to the two FGSM systems, the FGSM system with 6 transmitting antennas loses 4.8 dB SNR when the bit error rate is on the order of magnitude, but the transmission rate is increased by 2 bpcu (Fig. 5). All four antennas at the transmitting end are activated with the 2-PAM modulation mode adopted, and the transmission rate is 4 bpcu. The simulation results show that the bit error rate of the FGSM-MIMO system based on the Pearson coefficient selection algorithm is better than that of the random selection algorithm and maximum norm selection algorithm. The antenna selection algorithm based on Pearson coefficient has a 5.1 dB improvement over the random selection error rate and a 0.8 dB improvement over the maximum norm error rate at the order of bit error rate. This is because the proposed algorithm selects the optimal antenna combination according to Pearson coefficient correlation without dependence on the system channel characteristics, and thus realizes the multiplexing of time domain and space domain. With the improved antenna selection algorithm, the opening degree and shape of the eye image are gradually expanded and improved, which is realized by the antenna algorithm optimization system to make the signal shape closer to the ideal square pulse (Fig. 7).

The communications technology that integrates visible light communications and SM is still a research hotspot nowadays, but the transmission rate of traditional SM is low. A scheme that integrates FGSM and visible light communications is proposed to transmit data by activating multiple or even all antennas, thus addressing the low transmission rate of traditional SM. The transmission rate is proportional to the number of transmitting antennas and is improved. Meanwhile, by adopting the antenna selection algorithm based on the Pearson coefficient, the error performance of the FGSM system has been significantly improved and is better than other schemes. Under the premise of improving the transmission rate, the space utilization rate has also been enhanced, which provides a guarantee for visible light communications. The results show that the transmission rate of the FGSM system is higher than that of the GSM system under the same number of antennas and modulation modes, but the error performance will be lost. Complete indexing of different numbers of antennas will increase the transmission rate and reduce the error performance.