## 1 Introduction  
Unrepeated transmission systems provide a low-complexity and cost-effective solution for point-to-point connections on the order of a few hundred kilometers. The main objective for these systems is to achieve a single-span system between the points of interest without any in-line active elements between the terminals. Recently, high-order modulation formats and coherent detection using digital signal processing (DSP) have been introduced to increase the transport capacity. In these systems, the distributed Raman fiber amplifier (DFRA) is an attractive alternative to the conventional lumped erbium-doped fiber amplifier (EDFA). The DRFA ensures a relatively constant power distribution of the optical signals along the link and thereby improves the optical signal-to-noise ratio (OSNR) and the fiber nonlinearity tolerance [1; 2; 3; 4; 5; 6; 7]. Using DRFA with a large effective area fiber, unrepeated transmission of a 30 Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) over 444 km [2] and a 28 Gbaud DP-16 quadrature amplitude modulation (DP-16 QAM) over 240 km [3; 4] have been demonstrated. Unrepeated transmission of a 40 \(\times\) 256 Gb/s DP-16 QAM signal over an ultra-low loss fiber with a very large effective area was demonstrated by using a first-order backward-pumped DRFA combined with a discrete EDFA at the receiver [5]. Transmission performance analysis was performed for differential phase shift keying (DPSK) transmission using standard fiber and second-order Raman amplification in [6], showcasing the different balance between impairments for different transmission lengths and higher-order distributed amplification. Recently, an unrepeated Nyquist PDM-16 QAMtransmission over 364 km was demonstrated using Raman amplification and multi-channel digital back-propagation [7]. In DRFAs, the intensity fluctuations of the pump will induce both intensity and phase noise of the received signal. This is known as relative intensity noise (RIN) transfer which deteriorates the system performance and limits the system reach. The effect of RIN transfer on the intensity noise of the received signal has been intensively investigated in intensity modulation direct-detection systems [8; 9; 10]. The results show that the characteristics of the RIN transferred to the signal are strongly affected by different aspects, for example fiber dispersion, pumping configuration, and polarization-dependent gain [11; 12; 13; 14; 15]. The RIN transfer to both the amplitude and phase noise of multilevel coherent optical communication systems using DRFA has been studied using numerical analysis and system simulations, and evaluated with both unrepeatered and repeated transmission experiments [16; 17; 18; 19; 20; 21]. The stochastic intensity fluctuations of the Raman pump laser induce extra phase noise of the signal due to the pump signal cross-phase modulation. This is known as relative phase noise (RPN) and it degrades the system performance of phase-sensitive detection schemes. For example, the analytical model for the statistical property of RPN in first- and higher-order distributed Raman amplifiers [15] indicates that the impairments dependent on the Raman pumping order and RIN tolerance are different for each configuration. The study also shows that for the multi-level modulation format, in addition to RIN and RPN, Raman pump RIN will also induce polarization crosstalk through the cross-polarization modulation effect which has about the same impact on the performance as the RPN. A comprehensive theoretical and simulation study of the RPN was presented for M-ary phase shift keying (PSK) and 16 QAM modulation formats in Reference [18]. The RPN-induced impairment was evaluated and compared for QPSK, 8 PSK, 16 PSK, and 16 QAM signals.