## 1 Introduction
### Development of OSC System  
The European Space Agency (ESA) demonstrated the first OSC link at 50 Mbps between ARTEMIS and SPOT-4 [17]. In [18], an LSO-based 5500 km OSC link between NFIRE and SAR-X at 5.5 Gbps was reported in [18] in 2008. The data rate was increased to 5.6 Gbps in TerraSAR-X satellites using binary shift keying (BPSK) and covered 6000 km of link length [19]. In 2012, a multilevel quadrature phase shift keying (QPSK) modulation was first demonstrated over a 9352 km OSC link distance for the binary data speed of 100 Gbps [20]. QPSK has capacity doubling advantages because of using two binary bits per symbol and hence reduces the strain on the electronic binary data generator. Non-return to zero (NRZ) and return to zero (RZ) are the primary modulation formats and are widely incorporated in the OSC system due to their simple architecture and reasonable cost [21; 22; 23; 24; 25; 26; 27; 28]. However, these formats are not bandwidth and power efficient for optical communication systems. Carrier spectrum efficiency improvement is reported by the emergence of three different advanced pulse formats (APF), such as carrier spectrum RZ (CSRZ), modified duo-binary (MDRZ), and DRZ [29]. Despite the higher spectral efficiency, these APFs failed to support data rates higher than 40 Gbps per channel. As a result, differential phase shift keying (DPSK) was investigated in the OSC systems to eliminate the need for fixed thresholding at the receiver, as opposed to NRZ/RZ, and to provide better power efficiency [30]. DPSK has a higher probability of errors in the received bits because it  
Figure 1: General representation of OSC link. requires a pair of two bits for decoding, and sometimes an error in the first bit also causes an error in the second bit. Phase shifting in the data offers higher tolerance to pulse broadening and reduces interchannel interference (ISI). Differential quadrature PSK is also investigated in 50,000 km OSC systems at 200 Gbps and has 0, \(\pi\), +\(\pi\)/2, and \(-\pi\)/2 phase shifts [31]. High noise and phase errors make DQPSK less popular in OSC systems. For the MSO and HSO communications, multilevel modulations play a remarkable role in the OSC system due to their high power efficiency, improved receiver sensitivity, narrow spectrum, and prolonged distances. Some of the most widely used multilevel modulations are orthogonal frequency division multiplexing (OFDM), QPSK, and quadrature amplitude modulation (QAM). OFDM has improved resistance to ISI and high spectral efficiency but has the limitation of a high peak-to-average noise ratio (PAPR). In [32], a radio frequency-enabled 35,000 km OSC system with OFDM and 4-QAM at 20 Gbps was presented. In [33], 4-QAM in OFDM was replaced with DPSK encoding, and it was perceived that the OSC system covered 20,000 km at 10 Gbps. Coherent optical QPSK is also an attractive spectral-efficient and highly noise-resistant modulation for OSC systems. An OSC distance of 42,500 km has been achieved by incorporating CO-QPSK and digital signal processing at 40 Gbps [34]. The third multilevel modulation is QAM, and it comes in different variants, such as 8-QAM to 512-QAM. It has greater power efficiency than QPSK due to the higher number of bits per symbol. CO-16-QAM was investigated in the OSC system and offered 45,000 km at 1 Tbps capacity operating in the conventional band (C-Band) [35]. The polarization dimension is an important property of light among other dimensions such as frequency, space, and time, but it has yet to be extensively explored to obtain ultra-high data rates. The hybridization of multilevel modulations with different states of polarizations (SOPs) has opened a new window for high-capacity optical systems [36]. In the literature, the hybridization of OFDM, QAM, and QPSK has been reported with different SOPs, termed PDM, allowing lower-speed electronics, high receiver sensitivity, and long-range OSC links. However, these systems are vulnerable to pulse width broadening (PWB), phase errors, nonlinear effects, other noises, etc.