The rapid development of 5G New Radio (NR) and millimeter-wave (mmWave) communication systems highlights the critical importance of maintaining accurate phase synchronization to ensure reliable and efficient communication. This study focuses on evaluating phase noise models and implementing Minimum Mean Square Error (MMSE) algorithms for Common Phase Error (CPE) compensation. Through extensive simulations, we demonstrate that CPE compensation significantly enhances signal quality by reducing Error Vector Magnitude (EVM) and Bit Error Rate (BER) across various Signal-to-Noise Ratio (SNR) levels and antenna configurations. Results indicate that implementing MMSE-based CPE estimation and compensation in 5G-NR mmWave systems reduced EVM from 7.4\% to 4.6\% for 64QAM and from 5.4\% to 4.3\% for 256QAM, while also decreasing BER from $5.5 \times 10^{-3}$ to $5.2 \times 10^{-5}$ for 64QAM, demonstrating significant improvements in signal quality and reliability across various SNR levels and antenna configurations. Our findings provide valuable insights for optimizing phase noise mitigation strategies in 5G-NR mmWave systems, contributing to the development of more robust and efficient next-generation wireless networks.