# Research Progress on Carrier-Free Phase-Retrieval Receivers
For ASCD receivers, optical bandpass filters (OBPF) with sharp responses are required to eliminate the SSBI, which places strict requirements on receiver hardware. Generally, the carrier-to-signal-power ratio (CSPR) is defined as the power ratio between the CW carrier and the modulated signal, determining the SSBI mitigation capability. At least 6, 7, and 10 dB CSPR for KK, CADD and ASCD receivers are needed to guarantee the optimal performance. However, due to the saturation of erbium-doped fiber amplifiers (EDFAs), the aforementioned high CSPR will limit the number of wavelength division multiplexing (WDM) channels. More details about the comparison of these self-coherence detection schemes can be found in [24; 25]. The polarization division multiplexing (PDM) can double the capacity and spectral efficiency (SE) of a single-polarization direct-detection system [26]. For PDM coherence detection, the signal can be divided into two orthogonal polarization state outputs using the polarization beam splitter (PBS). On the other hand, the local oscillator (LO) at the Rx allows for the state of polarization (SOP) to be well aligned with the PBS and equally split. Thus, reconstructing a replica of both polarized signals is possible and polarization demultiplexing can be accomplished in the digital domain, whereas in the self-coherent systems described above, the optical CW carrier is added at the transmitter, acting as the equivalent of LO, and undergoes random polarization rotation in the fiber link [27; 28; 29; 30; 31; 32]. Therefore, evenly splitting the CW carrier using PBS without active polarization control is no longer guaranteed. The above random carrier splitting phenomenon is called carrier fading, which is different from the power fading effect caused by the CD in IM/DD systems [32]. One solution to avoid carrier fading [33; 34; 35; 36; 37; 38; 39] is to add two spaced orthogonal carriers on either side of the signal, but during polarization demultiplexing, OBPFs with sharp edges are needed to remove the unwanted orthogonal carriers [33]. In addition, polarization multiplexing quadrature amplitude modulation (QAM) signals can be received using the Jones space scheme [40], but polarization recovery needs to be performed after signal field recovery (SFR). However, under unpredictable polarization changes, the SFR of the signal cannot operate stably. In order to improve the stability, a joint polarization multiplexing self-coherent detection and reception scheme combining SVR and KK is proposed [41; 42]. The CSPR of this scheme is about 10 dB, and at least six single-ended PDs and one optical hybrid are needed at the Rx. The high sampling rate also brings higher requirements of the devices. Recently, carrier-free phase-retrieval (CF-PR) receivers [43; 44; 45; 46; 47] have been widely studied to circumvent the requirement of a strong CW optical carrier, and the full optical field information of DSB signal can be reconstructed by the multiple intensity measurements after PD detection by running an iterative PR algorithm. The most obvious advantage of utilizing CF-PR is that there is no need to insert a strong CW carrier to co-propagate with the information-bearing signal at the transmitter, which usually means a higher spectral efficiency (a guard band is essential for the insertion of the optical CW carrier) and simplified transmitter configuration. In this paper, we provide an overview of the principles and challenges of CF-PR receivers, with special attention on the advances in reducing the complexity of the iterative PR algorithm, reducing receiver-side sampling rate, and recovering polarization/space division multiplexed QAM signals. In Section 2, we briefly introduce the principle and challenges of the CF-PR scheme, and in Section 3, we present various performance-enhanced CF-PR receivers in detail. Finally, we summarize the results and look forward to the future development of CF-PR receiver systems.