## 2 FSO Communication System
### Receiver Side
#### 2.3.3 Self-Coherent FSO Systems  
Coherent optical transmission systems facilitate efficient information encoding, resulting in improved SE and extended network reach for both digital and analog channels. These systems are especially well suited for medium-to-long-reach links. However, the practical application of full-coherent FSO systems may be limited due to their high power consumption, large physical footprint, and elevated system costs, primarily driven by optical components such as 90\({}^{\circ}\) optical hybrids, LO laser, and high-speed DSP [24; 26; 28; 33]. To tackle these challenges, several quasi-coherent approaches with reduced complexity have been proposed to strike an optimal balance between achievable bit-rate and hardware complexity. In this context, various high-capacity DD transmission techniques, which offer notable advantages such as a a smaller footprint, lower power consumption, and significantly reduced costs, have been extensively explored. Despite these benefits, DD systemsare susceptible to linear propagation impairments like chromatic dispersion. These include single-polarization intensity modulation (IM) using high-order Pulse-Amplitude Modulation (PAM), such as PAM-4, and discrete multi-tone (DMT) [34; 35; 36; 37; 38; 39]. Other techniques under investigation include Stokes vector transceivers [40; 41; 42], and Single-Sideband (SSB) DD. Notably, the SSB DD scheme employs self-coherent detection, which can be realized through Signal-Signal Beat Interference (SSBI) cancellation or Kramers-Kronig (KK) field reconstruction. Among the various DD-based transmission systems, the SSB DD scheme stands out for its superior performance in terms of network reach [25; 26; 28; 43; 44; 45]. Moreover, achieving optimal performance in DD systems necessitates intricate manipulation of the optical field at both the Tx and Rx ends. For example, SSB techniques have been investigated to capture amplitude and phase information using DD. However, SSB transmission schemes often suffer from inherent signal-to-signal beating noise (SSBN) in DD systems. Although a Stokes vector Rx could potentially address this issue, its practical use is hindered by sensitivity degradation and increased hardware complexity. A more promising and practical solution for SSB DD transmission is the self-coherent, minimum phase signal-based KK field reconstruction algorithm, which significantly reduces SSBN and enhances system performance [26]. The KK algorithm allows the employment of a single PD and ADC per polarization, while maintaining compatibility with phase-preserving Rx-side post-processing and supporting advanced modulation formats. Also, it enables the reconstruction of the complex-valued electric field at the Rx using only intensity measurements, allowing for digital compensation of propagation effects similar to those achieved with more complex coherent Rxs [26; 43]. Despite the significant complexity reduction offered by the self-coherent-based KK FSO (KK-FSO) system, several challenges remain. For example, the nonlinear operations (logarithmic and exponential) in the KK method require the DSP to operate at much higher speeds than the Nyquist sampling rate to handle spectral broadening. A potential solution to reduce the sampling rate is to bypass these nonlinear operations. For instance, an upsampling-free KK method employs a Taylor expansion approximation for these operations. However, these approximations generally require a higher carrier-to-signal power ratio (CSPR), leading to a sensitivity penalty. To meet the demands for an increased tone power and high sampling rate of both the traditional KK and the upsampling-free KK methods, a DC-Value (DC-V) method can be used [26; 27; 33]. This method leverages the SSB and DC-V properties of the minimum phase signal, offering an upsampling-free phase reconstruction process with low tone power operation.