## 1 Introduction
### Review of Related Works  
Significant technological advancement has been made in the fields of optical communications regarding the optical field recovery of both the intensity and phase of light [16; 17]. The field recovery capability majorly distinguishes COH detection from direct detection transmission counterpart [13]. With a number of research efforts, some direct detection systems can offer comparable detection dimensions to that of the COH system. However, the improvement in the system performance may be at the expense of either SSBN or SE wastage. To address the challenges, Kramers-Kronig (KK)-based direct detection system and Stokes vector direct detection (SV-DD) with better performance have been presented as alternatives to the conventional Co-Rxs [9; 11; 13; 18; 19; 20; 21; 22]. These schemes have been experimentally demonstrated to be viable [11; 13; 19; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. In addition, several papers have considered the related role of DSP in different aspects such as the estimation of the carrier phase, optical transceiver design, polarization state tracking, linear transmission impairment, and mitigation [7; 10; 22]. Moreover, to improve the system performance, the concepts of COH systems have been adapted to the direct detection schemes in some research efforts. For instance, various architectures have been proposed for direct phase modulation of the transmitter lasers [32], while a variety of cost-effective Co-Rx configurations have also been proposed [33; 34]. Furthermore, a review and comparison of different optical SCOH subsystems with different channel linearization technologies and DSPs have been presented [9; 11; 12; 13; 14; 19; 26; 33; 34; 35; 36; 37; 38]. Different types and principles of the Stokes space field [11; 13; 39; 40; 41] and polarization [8; 11; 13; 23; 24; 39] recoveries have been comprehensively discussed. Similarly, the Stokes vector receiver (SVR) that can perform a 3D detection without an LO has been presented [24]. Furthermore, the system capability to offer a data rate distance product beyond 10 Tb/s-km has been considered. For instance, potential 100 G per wavelength and beyond schemes for short-reach applications have been well compared [9; 12; 24; 42]. Correspondingly, a comparative review of different potential schemes for intra- and inter-DCNs regarding the minimum required electrical bandwidth for the receivers and their support for digital chromatic dispersion compensation has been discussed [14]. Furthermore, to address the related spectral broadening of the KK algorithm that is due to nonlinear operations [18; 43; 44], some viable solutions have been presented. For instance, a modified DSP algorithm that does not require digital upsampling can be employed [18]. Similarly, mathematical approximations have also been presented to prevent the associated nonlinear operations' execution [44; 45; 46]. Likewise, a low-complexity approach for the Hilbert filter implementation, where the associated convolution can be done directly, has been considered [21]. Furthermore, the related periodic spectral repetition and time domain singularity problem of the sampled Hilbert filter have been attended to through a modified Hilbert filter [21]. Moreover, one of the stringent system requirements for the conventional KK scheme is the minimum-phase condition in which a strong CW tone is demanded to realize an accurate field reconstruction. Consequently, this condition demands a high carrier-to-signal-power ratio (CSPR) [18; 19; 21; 43; 47]. This requirement deserves further research consideration as it presents an additional sensitivity penalty [48; 49]. A number of research efforts have considered a means of reducing the required CSPR in the conventional KK system through modified KK receivers [48; 49; 50; 51]. In addition, different carrier and optical single-sideband (SSB) signal generation have been presented [12; 53; 54; 55; 56]. For instance, the optical SSB signal generation regarding the offset SSB and virtual SSB (VSSB) has been presented [12].