Signal-to-noise ratio gain in multi-channel SAR with digital beamforming

The signal-to-noise ratio of a radar system is described through the well-known radar equation, which can be adapted to apply to imaging Synthetic Aperture Radar (SAR). Extension to multi-channel SAR systems utilizing digital beam-forming turns out to be treacherous; the pivotal question being, if and how to include the gain of the multiple antenna apertures. This paper puts an effort into answering this question in a simple and comprehensible, yet mathematically rigorous way.