## 2 Operating Principle  
Figure 1 shows the block diagram of the proposed technique. At the transmitter end, the multilevel linear SOPs are modulated into the OOK signal. A laser diode (LD) with a continuous wavelength (CW) is polarized into the linear SOP of 45\({}^{\circ}\) using a polarization controller (PC). The polarized laser beam is split into two orthogonal \(x\)- and \(y\)-polarizations using a polarization beam splitter (PBS). The \(s\_1[t]\) and \(s\_2[t]\) signals are modulated using MZMs with electrical signals \(d\_1[t]\) and \(d\_2[t]\), respectively. This is represented by the following:  
\[\left\{\begin{array}{l}d\_1[t]=[1,\quad 0,\quad 0,\quad 0,\ \cdots]\\ d\_2[t]=[0,\quad 1,\ \cos(\alpha),\ \cos(\beta),\ \cdots]\\ \end{array}\right. \tag{1}\] \[\left\{\begin{array}{l}s\_1[t]=\left[p_{s\_1[t]\_1},\ p_{s\_1[t]\_0 },\ p_{s\_1[t]\_0},\ p_{s\_1[t]\_0},\ p_{s\_1[t]\_0},\ \cdots\right]\\ s\_2[t]=\left[p_{s\_2[t]\_0},p_{s\_2[t]\_1},p_{s\_2[t]\_1},p_{s\_2[t]\_\cos( \alpha)},p_{s\_2[t]\_\cos(\beta)},\ \cdots\right]\\ \end{array}\right.,\]  
where \(p_{s\_1[t]\_1}\) and \(p_{s\_1[t]\_0}\) are the bit powers of \(s\_1[t]\), and \(p_{s\_2[t]\_0}\), \(p_{s\_2[t]\_1}\), \(p_{s\_2[t]\_\cos(\alpha)}\), and \(p_{s\_2[t]\_\cos(\beta)}\) are the bit powers of \(s\_2[t]\). The signal \(s\_2[t]\) is attenuated using a variable optical attenuator (VOA). \(s\_1[t]\) and the attenuated \(s\_2^{\prime}[t]\) are combined using a polarization beam combiner (PBC) to generate the MPS-OOK signal \(s[t]\). The SOPs of \(s[t]\) were determined by the power ratio between \(s\_1[t]\) and \(s\_2^{\prime}[t]\), which is given by the following [3]:  
\[SOP_{s[t]}=\arctan(s\_1[t]/s\_2^{\prime}[t])\times 180^{\circ}/\pi=\arctan(s\_1[t]/ (s\_2[t]/G_{VOA}))\times 180^{\circ}/\pi, \tag{2}\]  
where \(G_{VOA}\) is the degree of attenuation from the VOA. Therefore, the MPS-OOK signal is modulated with a constant SOP at the high-intensity level and various SOPs at the low-intensity level with the transmitted power efficiency. The ER of the MPS-OOK is determined by \(G_{VOA}\), and the SOPs of the MPS-OOK are dependent on \(d\_2[t]\), the ER of the MZM, and \(G_{VOA}\). The MPS-OOK signal suffers the scintillation effect in the turbulence channel. At the receiver end, the polarization-independent SOA is deployed to mitigate the scintillation effect and equalize the intensities of the various SOPs in the deep gain saturation state without the distortion of the SOPs. The scintillation effect is effectively mitigated by the nonlinear gains from the SOA since the high dynamic gain frequency (around 10 GHz) of the SOA is much higher than the scintillation effect (less than a few kHz) [1, 11]. Then, the intensities of the various SOPs are equalized by the high dynamic gains in a much deeper gain saturation state. An LP is applied after the SOA to transform the knowledge of the SOPs into various intensity levels. The intensity spacing of the transformed MPS-OOK signal is determined by the degree of the SOPs. The MPS-OOK signal is detected via a single PD and decided using an M-FTD. Consequently, the various SOPs are detected under effective scintillation mitigation using the proposed technique.