## 3 Antenna Selection Algorithm Based on Pearson Coefficient  
Antenna selection is a key issue in MIMO technology. By selecting one or more antennas with the best performance from among multiple-transmit and receiving antennas in a MIMO system, the system error performance can be improved. Presently, conventional  
Figure 2: OGSMP-MIMO system model based on antenna selection. antenna selection algorithms mainly include random antenna selection algorithms and norm-based antenna selection algorithms [31]. The random selection algorithm is the lower limit for evaluating the performance of the antenna selection algorithm; the norm-based antenna selection algorithm must know the channel parameters; however, the actual channel is time-varying, and the transmitter cannot obtain the channel state. Accordingly, this paper proposed an antenna selection algorithm based on the Pearson coefficient. The basic idea is to adopt the Pearson coefficient correlation between the PD end and the active transmit antenna at different positions, to select the optimal antenna combination that does not depend on the accuracy of channel estimation and has better environmental adaptability. As illustrated in Figure 1, first, the installation distance of each LED was determined according to the VLC communication link model, and then the division of the positioning area was determined according to the received signal strength (RSS) value of each LED received by the receiver. Several positioning points were selected in the positioning area, the received RSS value of each LED was collected, and the actual coordinates of the reference point at the positioning point were collected and stored in the fingerprint database. The \(M\) LED is denoted as LED\({}_{m}\), \(m=1,2,\cdots,M\), and can be expressed as:  
\[LED_{m}=\{R_{m},(x_{m},y_{m},z_{m})|m=1,2,\cdots,M\} \tag{7}\]  
where \(R_{m}\) represents the central luminous intensity of the \(m\)-th LED and unit: lx; and \((x_{m},y_{m},z_{m})\) denotes the coordinate of the \(m\)-th LED (m). There are \(N\) PDs in the positioning area, denoted as PDn, \(n=1,2\cdots,N\), and the light intensity received from the LED\({}_{\rm m}\) at PDn can be denoted as \(S_{m}^{m}\). Therefore, the fingerprint library can be defined as  
\[f_{n}=\{S_{\mathbf{n}},(x_{n},y_{n},z_{n}),t_{n}|n=1,2,\cdots,N\} \tag{8}\]  
where \(S_{\mathbf{n}}=\left[S_{n}^{(1)},S_{n}^{(2)},\cdots,S_{n}^{(m)}\right]\) represents the illuminance of each LED received at PDn, \((x_{n},y_{n},z_{n})\) represent the coordinates of the PD (m), and \(t_{n}\) represents the number of times that the illumination is collected by the PD. To reduce the amount of data calculation during positioning and improve the positioning accuracy, the indoor positioning area is divided into \(k\)-positioning areas, denoted as \(f_{n,k}\), \(k\in\{1,2,\cdots,K\}\), and the partition fingerprint library can be defined as the following:  
\[f_{n,k}=\{S_{n,k},(x_{n,k},y_{n,k},z_{n,k}),t_{n,k}|n=1,2,\cdots,N_{k}\} \tag{9}\]  
In addition, the partition LED position can be obtained, which can be expressed as  
\[LED_{m,k}=\{R_{m,k},(x_{m,k},y_{m,k},z_{m,k})\big{|}m=1,2,\cdots,M_{k}\} \tag{10}\]  
where \(R_{m,k}\) represents the central luminous intensity of the \(m\)-th LED in the \(k\)-th area, unit: lx; and \((x_{n,k},y_{n,k},z_{n,k})\) represent the coordinates of the PD in the \(k\)-th area (m). In the partition fingerprint library, the Pearson correlation coefficient is used to calculate the correlation between two points. The Pearson correlation coefficient is a linear correlation coefficient that is defined as the ratio of the product of the covariance and the standard deviation of the two points. The value of the Pearson's coefficient is between \(-1\) and \(1\). The larger the value, the higher the correlation. Therefore, it can be adopted as a selection criterion for antenna combination.