In this project, we investigate channel estimation and robust detection for uplink massive multi input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with in-phase and quadrature-phase imbalances (IQI). We represent the received signal with a real-valued model, where the combination of the IQI and the wireless channel is treated as the effective channel. Based on the real-valued model, we then perform the minimum mean square error (MMSE) criterion based estimation for the effective channel. We use adjustable phase shift pilots (APSPs) to reduce the pilot overhead and verify that the MSE of the effective channel estimation can be minimized by scheduling the pilot phase shifts properly. We propose a pilot phase shift scheduling algorithm based on the covariance matrices of the effective channels. Since the channel estimation performance might be degraded due to using APSPs, we develop an MMSE criterion based data detection scheme which is robust to the channel estimation error. Using operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed detection scheme. The performance of the channel estimation with APSPs and the robust data detection is demonstrated via extensive numerical results.