Millimeter-wave (mmWave) communications and cell densification are the key techniques for the future evolution of cellular systems beyond 5G. Although the current mmWave radio designs are focused on hybrid digital and analog receiver array architectures, the fully digital architecture is an appealing option due to its flexibility and support for multi-user multipleinput multiple-output (MIMO). In order to achieve reasonable power consumption and hardware cost, the specifications of analog circuits are expected to be compromised, including the resolution of analog-to-digital converter (ADC) and the linearity of radio-frequency (RF) front end. Although the state-of-theart studies focus on the ADC, the nonlinearity can also lead to severe system performance degradation when strong input signals introduce inter-modulation distortion (IMD). The impact of RF nonlinearity becomes more severe with densely deployed mmWave cells since signal sources closer to the receiver array are more likely to occur. In this work, we design and analyze the digital IMD compensation algorithm, and study the relaxation of the required linearity in the RF-chain. We propose novel algorithms that jointly process digitized samples to recover amplifier saturation, and relies on beam space operation which reduces the computational complexity as compared to perantenna IMD compensation.