Synthetic aperture radar (SAR) systems have become an important tool for fine-resolution mapping and other remote sensing operations. The multi-channel SAR ground moving-target indication (GMTI) must process its data to produce not only the image of surveillance area but also the information of the ground moving-targets. The topic of moving-target detection in clutter has been extensively studied, and there are many methods that are used to detect moving targets, such as displaced phase center antenna (DPCA) method, along-track interfero-metric (ATI) phase, space-time adaptive processing (STAP), or some other metrics. A canonical framework is proposed that encompasses all the multi-channel SAR-GMT methods, namely, DPCA and ATI. The statistical test metric for multi-channel SAR-GMTI is established in a simple form, via the definition of the complex central Wishart distribution, to deduce the statistics of the test metric, and the probability distribution of the test metric for multi-channel SAR-GMTI has the complex central Wishart distribution of 1×1 case, namely the χ2 distribution. The theory foundation offers the possibility to construct the united multi-channel SAR-GMTI detector, and derives the constant false alarm rate (CFAR) detector tests for separating moving targets from clutter. Synthetic aperture radar (SAR) systems have become an important tool for fine-resolution mapping and other remote sensing operations. The multi-channel SAR ground moving-target indication (GMTI) must process its data to produce not only the image of surveillance area but also the information of the ground moving-targets. The topic of moving-target detection in clutter has been extensively studied, and there are many methods that are used to detect moving targets, such as displaced phase center antenna (DPCA) method, along- track interfero-metric (ATI) phase, space-time adaptive processing (STAP), or some other metrics. A canonical framework is proposed that encompasses all the multi-channel SAR-GMT methods, namely, DPCA and ATI. for multi-channel SAR-GMTI is established in a simple form, via the definition of the complex central Wishart distribution, to deduce the statistics of the test metric, and the probability distribution of the test metric for multi-cha nnel SAR-GMTI has the complex central Wishart distribution of 1 × 1 case, namely the χ2 distribution. The theory foundation offers the possibility to construct the united multi-channel SAR-GMTI detector, and derives the constant false alarm rate (CFAR) detector tests for separating moving targets from clutter.