# Channel Correlation-Based Adaptive Power Transmission for Free-Space Optical Communications
## 1 Introduction  
Free-space optical (FSO) communication, as a cutting-edge technique for high-speed data transmission, is gradually becoming an important choice for solving modern communication needs [1]. It uses light waves to transmit information in free space, which can achieve high data rate transmission and also has a large bandwidth, and it is widely used in the fields of satellite communication, unmanned aerial vehicle (UAV) communication, and military security communication. Although the advantages of FSO communication are significant, many challenges are also faced, among which the effect of atmospheric turbulence is particularly noticeable [2]. The atmospheric turbulence is the irregular movement of airflow in the atmosphere, which is mainly caused by the inhomogeneity of temperature and humidity distribution [3]. The transmission optical signal attenuation, distortion, and even positional drift are caused by atmospheric turbulence [4]. Therefore, the suppression of the turbulence scintillation effect is becoming one of the critical research directions to improve the stability and reliability of FSO communication systems. Many techniques have been investigated to dampen the effects of atmospheric turbulence. The aperture averaging technique is applied to mitigate the atmospheric scintillation due to its relative simplicity and straightforwardness. Ref. [5] deployed aperture averaging receivers at the relay and destination sides to reduce the variance of intensity fluctuations. However, a larger aperture receiver is more susceptible to scattering and absorption in the atmosphere, which leads to increased signal attenuation. Also, a higher level of alignment accuracy is required. Refs. [6; 7] studied the multiple-input multiple-output (MIMO) diversity technique, and the efficiency of the system was improved with the increasein the number of transmitters and receivers. However, it is difficult to deploy multiple transmitters and receivers due to the rise in physical size and complexity of the system. Ref. [8] installed an optical spatial filter (OSF) at the focus of the receiver lens to improve the strength of the received signal and remove unwanted higher-order modes and noises. However, some of the light energy is blocked or scattered during processing, which results in an optical loss. In addition, an unstable or ineffective filtering effect may be caused if the stability of the light source is poor. Ref. [9] investigated an adaptive optics (AO) architecture that detects and corrects optical wavefront aberrations caused by atmospheric turbulence. However, AO systems usually contain multiple high-precision components, which are more complex to integrate and debug. Ref. [10] proposed a scheme for the use of an electrical equalizer on the receiver. The electrical equalizer is mainly used to compensate for distortions introduced during signal transmission. However, complex algorithms and a large amount of computational resources are required to obtain highly accurate equalization results. The fixed threshold decision (FTD) technique is utilized for its simple algorithms and faster processing of the received optical signals. The received signal is decided by setting a fixed threshold value. However, the FTD technique is unable to automatically adapt to signal fluctuations due to changing channel environments [11]. The signal is decided bit by bit with a dynamically adjusted threshold based on channel state information (CSI) in the adaptive threshold decision (ATD) technique [12]. However, it is highly dependent on the accuracy of the CSI. In recent years, the adaptive power transmission technique has been widely studied to mitigate the scintillation effect for its greater flexibility and adaptability. Moreover, a certain degree of correlation is presented between the uplink and downlink turbulence channels. The channel correlation coefficient is an important measure of the correlation between signal propagation paths in PSO communication [13; 14].