## 2 Operation Principle  
Figure 1 shows the block diagram of the proposed MLA-based CP-OOK signal detection. A laser diode (LD) of 1550 nm wavelength is directly modulated with an OOK signal. A linear polarizer is deployed to obtain a polarized OOK signal, and the state of polarization (SOP) is set at 45\({}^{\circ}\) to the fast axis of QWP. The linearly polarized OOK signal is converted into right circular polarization (RCP) by QWP. Thus, the CP-OOK format signal \(s(t)\) is obtained by the combination of LP and QWP. A laser beam with a CP-OOK signal suffers the turbulence effect in the FSO links. The turbulence-induced scintillation effect, which causes received signal intensity variation, is the major issue in the IM/DD FSO system [3]. In addition, the SOP of CP-OOK remains stable in the FSO links [11; 12]. Thus, the scintillation effect is studied in this turbulence channel. The degree of turbulence effect is assessed by the scintillation index \(\sigma_{I}^{2}\), which is expressed by  
\[\sigma_{I}^{2}=\left\langle I^{2}\right\rangle/\left\langle I\right\rangle^{2}-1, \tag{1}\]  
where \(I\) is the optical intensity of the received CP-OOK signal, and \(\left\langle.\right\rangle\) is the ensemble average [13; 14]. In the receiver terminal, the RCP of CP-OOK is recovered into linear polarization by QWP without the aligning procedure of polarization coordinates between the transmitter and receiver. Linearly polarized CP-OOK passes through LP before the photodiode (PD), and the non-polarized background noises are blocked without CP-OOK signal distortion. The CP-OOK signal after LP \(r_{LP}(t)\) is given by  
\[r_{LP}(t)=I(t)s(t)+N_{BG}(t)/\sqrt{2}, \tag{2}\]  
where \(N_{BG}(t)\) is the background noise. The PD-received signal is converted into a digital signal \(r_{PD}[k]\) via an analog-to-digital conversion (ADC). Figure 2 depicts the amplification curves of different LAs. LA has the characteristics of gain nonlinearity, and the degree of nonlinearity increases with the increase of input values and base numbers of the logarithm. The turbulence effect is reduced through the intensity variation decreasing using nonlinear gains from LA, i.e., the high and low signal intensity obtain large and small gains from LA, respectively. The received signal from a stronger turbulence channel requires a much larger degree of nonlinearity to equalize the received signal intensity variation. However, the issue of CP-OOK signal ER distortion accompanies the process of scintillation mitigation. Bit '1' and bit '0' also obtain different gains from LA, and it is serious in the peak power part of the signal stream in the case of LA with high gain nonlinearity, as shown in Figure 3. Besides, the ER distortion issue increases as the turbulence degree increases. Therefore, a single LA is only capable of equalizing the signal intensity variation in the case of bit '0' blocking [9]. MLAs are applied in this work to cope with ER distortion issues by using cascaded LAs. Multiple stages of logarithmic amplification processes are employed to assign different gains into the intensity variated CP-OOK signal under each LA works in a low gain nonlinearity condition instead of using a single LA in a high gain nonlinearity condition. Therefore, ER degradation effect is reduced by this proposed MLAs method. The process of MLAs application is described as  
\[ \begin{split} r_{LA1}[k]&=\log_{a}^{(r_{PD}[k]+b)}= \log_{a}^{(t[k]s[k]+N_{BG}[k]/\sqrt{2}+N_{PD}[k]+b)}\\ &\vdots\\ r_{LAn}[k]&=\log_{a}^{(r_{LA(n-1)}[k]+b)},\end{split}  \tag{3}\]  
where \(r_{LAn}[k]\) is the signal after log amplification, n is the levels of LA, \(N_{PD}[k]\) is the PD noises. Parameters a, b, and n adjust to effectively mitigate the scintillation effect to realize an FTD without ER distortion, and this process is defined as an optimization process in this work. Consequently, the turbulence effect is effectively mitigated by the CP-OOK transmission FSO communication links. Figure 1: Block diagram of the proposed MLA-based CP-OOK signal detection.