High spectral efficiency modulation format based unrepeatered transmission systems using distributed Raman amplifier (DRA) have attracted much attention recently. To enhance the reach and optimize system performance, careful design of DRA is required based on the analysis of various types of impairments and their balance. In this paper, we study various pump RIN induced distortions on high spectral efficiency modulation formats. The vector theory of both 1st and higher-order stimulated Raman scattering (SRS) effect using Jones-matrix formalism is presented. The pump RIN will induce three types of distortion on high spectral efficiency signals: intensity noise stemming from SRS, phase noise stemming from cross phase modulation (XPM), and polarization crosstalk stemming from cross polarization modulation (XPolM). An analytical model for the statistical property of relative phase noise (RPN) in higher order DRA without dealing with complex vector theory is derived. The impact of pump RIN induced impairments are analyzed in polarization-multiplexed (PM)-QPSK and PM-16QAM-based unrepeatered systems simulations using 1st, 2nd and 3rd-order forward pumped Raman amplifier. It is shown that at realistic RIN levels, negligible impairments will be induced to PM-QPSK signals in 1st and 2nd order DRA, while non-negligible impairments will occur in 3rd order case. PM-16QAM signals suffer more penalties compared to PM-QPSK with the same on-off gain where both 2nd and 3rd order DRA will cause non-negligible performance degradations. We also investigate the performance of digital signal processing (DSP) algorithms to mitigate such impairments.