## 1 Introduction  
Space laser communication has many advantages, such as a high communication rate, strong anti-interference ability, and high confidentiality. It has been widely used in the information transmission of various laser communication links [1; 2; 3; 4]. In the process of building a laser communication link, it has to be ensured that the beam of the transmitter and receiver are pointed (PAT), captured, and tracked, which is a prerequisite for stable communication. And the accuracy of spot position detection determines the performance of the communication system. Considering that the quadrant detector (QD) has the advantages of a fast response speed, high measurement accuracy, and simple data processing, it has developed into a core device in the space laser communication system [5; 6; 7]. In the practical system, the relationship between the output signals of QD and the real position of the spot on the detector target is complicated. Therefore, in recent years, some researchers have conducted a lot of work on how to improve the spot position detection accuracy of QD. In [8], the relationship between the spot position and the output voltage is analyzed when the spot shape and the spot energy distribution are different, and the linear measurement range of QD is extended. In [9], the relationship between the position of the spot position and the output signal of QD is obtained by combining the opposite error characteristics of the infinite integral method and Boltzmann method, which reduces the position detection error of a different spot radius. In [10], an error compensation factor and the gap size of the detector are introduced into the traditional spot position detection model. The high-precision spot position information of the QD in a complex environment is obtained by using the improved spot position detection model. In [11], the effect of the signal-to-noise ratio (SNR) on the accuracy of QD position detection is analyzed, and the cyclic cross-correlation method is used to denoise the modulated light, which improves the accuracy of spot position detection. Reference [12] used the Kalman filter to estimate the real output of four electrical signals of QD, which decrease the root-mean-square errors of detection using the improved detection method compared with the direct detection method. However, more research focuses on the traditional space laser communication system, which can no longer meet the transmission needs of space information by point-to-point mode. Therefore, the laser communication system should have the ability to communicate with multiple nodes simultaneously to form a high-speed communication network [13]. However, traditional modulation technology cannot realize one-to-many laser communication. Therefore, researchers have been exploring the application of multiplexing technology in space laser communication systems to achieve one-to-many laser communication. Reference [14] proposes the use of frequency division multiplexing technology combined with phase detection technology to achieve the simultaneous detection of multi-spot on a single position sensing detector (PSD), but the frequency of the modulation signals is low. Reference [15] proposes the use of the integral approximation method to fit the offset of distributed light spot, which is used as the initial position. The Boltzmann function is used to compensate for the calculation error to simplify the calculation of the multi-spot offset of QD, but its application has limitations. Reference [16] proposes applying a square wave signal to modulate the beacon light at the transmitter. At the receiver, the same-frequency square wave signal is used to perform a correlation operation with the PSD output photocurrent signal to calculate the spot position. However, the method needs to ensure synchronization between the signals of the transmitter and the receiver. Therefore, orthogonal frequency division multiplexing (OFDM) is a special multi-carrier modulation technology. The frequency of the modulation signals is orthogonal.