# Bidirectional Atmospheric Channel Reciprocity-Based Adaptive Power Transmission
## 2 Theoretical Analysis
### Adaptive Power Transfer System  
In this research, we present an adaptive power transfer technique based on bidirectional atmospheric channel reciprocity. We discuss a point-to-point FSO communication system employing intensity modulation/direct detection On-Off Keying (OOK) modulation across turbulent channels in this approach due to the high complexity of phase or frequency modulation. The system block diagram of the proposed adaptive power transfer approach is shown in Figure 2. In the bidirectional atmospheric channel, because the forward-transmission and reverse-transmission channel turbulence intensity are related, the CSI of the forward transmission channel can be extracted, and the signal power can be adjusted according to the known CSI in the reverse transmission, so as to achieve the purpose of suppressing turbulence and enhancing the communication quality. The specific process is as follows: at the transmitting end of the forward transmission, an amplitude 0 or 1 random pulse sequence is generated and sent into the turbulent channel after OOK modulation. At the receiving end, the state information of the channel is estimated based on the received signal, and the CSI reflecting the noise level of the channel is obtained; at this time, the receiving end of the forward transmission becomes the transmitting end of the reverse transmission. The OOK signal power is changed according to the known CSI, increasing the signal power at the poorer channel quality and decreasing the signal power at the better channel quality. After receiving the signal at the receiving end of the reverse transmission, the CSI estimation is performed again and the result is fed back to the transceiver. This can form a closed-loop control system so that the power of the transmitted signal can be dynamically adjusted according to the actual communication situation to improve communication quality. While in the communication process, the received optical signals are converted into electrical signals under the influence of the noise generated during the detection process, which consists of thermal noise, dark current, and scattered particle noise. The noise produced by the photodetector can be characterized in the FSO communication system simulation engineering as additive white Gaussian noise (AWGN), whose noise amplitude  
Figure 2: Block diagram of adaptive power transfer system. is expressed in terms of the signal-to-noise ratio (SNR). The formula for SNR can be expressed as Equation (6), where \(P_{s}\) and \(P_{n}\) represent the effective power of the signal and noise, respectively. \[SNR=10\lg(\frac{P_{s}}{P_{n}}) \tag{6}\]  
An analog-to-digital converter subsequently transforms the signal from current to digital signal. In order to acquire the digital received signal, the current is sampled at kT moments at k-bit intervals. The signal is split into two parts after sampling is complete, and the first portion can be used to determine the CSI of the forward transmission channel based on the amplitude shift brought on by turbulence. The second stage completes the demodulation before completing the CSI-based signal power modification. At this time, OOK signal has had their power adjusted, and the transmitting end serves as the receiving end for forward transmission while the receiving end serves as the transmitting end for inverse transmission. To demonstrate the effectiveness of the adaptive transmission technique in terms of the magnitude of the BER, the OOK signals are transmitted into the turbulent channel with background noise and are identified at the receiving end. The formula for BER is as follows [27]:  
\[BER=\int\limits_{0}^{\infty}f(r)Q(\frac{r}{\sqrt{2(N_{C}+N_{PD})}})dr \tag{7}\]  
where \(f(r)\) is the probability density function (PDF) that obeys a normal distribution under turbulent conditions, \(Q(\cdot)\) denotes the Gaussian function, \(N_{C}\) denotes the noise present in the channel, and \(N_{PD}\) denotes the noise generated by the photodetector in Equation (7).