The Impact of Antenna Array Calibration Errors on MIMO and Multi-Channel Synthetic Aperture Radar Imaging

In radar imaging, any lateral resolution is either attained using antenna arrays or by synthetic aperture radar (SAR) principles. Recently, the combination of both approaches to a multi-channel SAR (MCSAR) has gained increased attention. However, antenna arrays are impaired by unknown calibration errors, particularly phase errors, amplification deviations, mutual coupling, and phase center position deviation of the antenna element. Since, first, established calibration procedures are often non-ideal and, second, the calibration parameters usually vary over time due to aging and changes in temperature, calibration errors distort the measurements during the radar operation. Therefore, current research focuses on finding new practical calibration procedures. However, hardly any research has been conducted to analyze the basic effects which erroneous calibration parameters have on the reconstructed image in MCSAR or MIMO radar. In this work, we analyze the effects of multiple calibration error types on MCSAR and MIMO radar imaging. Both measurement principles lead to periodic error patterns, resulting in deterministic distortions. The derived relations can be used to precisely predict the position and number of ghost targets caused by calibration errors for known measurement setups and targets. For this, no information about the actual calibration errors is required. Furthermore, worst-case distortion levels are provided for different bounded errors allowing rough estimates of the impact of different error types on the image's distortion level. The findings are validated via measurements using a 76$\,$GHz FMCW MIMO radar.