This paper presents a novel approach to the phase tracking reference signal (PTRS) design for phase noise impact compensation in the 5G NR communication systems intended to work in a new 52.6 GHz to 71 GHz frequency band. For detailed problem illustration, the phase noise compensation algorithms are discussed and explained, from the basic common phase error (CPE) compensation to the MMSE-base inter-carrier interference (ICI) filtering. Performance of the different phase noise compensation algorithms is investigated for the baseline PTRS accepted in the current 5G NR specification and compared with the newly proposed approach to the PTRS design. This approach is based on nulling the subcarriers adjacent to the reference signals to minimize influence of the ICI on the estimation process. It was shown that new nulling PTRS design outperforms currently used distributed PTRS structure. In addition, numerical results represent a trade-off between the filter size and the amount of the allocated training resources to achieve better performance. It was shown that proposed PTRS structures and processing algorithms give ICI compensation level very close to optimal scheme and thus, different approaches (such as time domain compensation) may be required for further progress.