A derivation of colocated MIMO radar equation

Radar equation is a very important tool to evaluate a radar system, and an approximate derivation of colocated multiple-input multiple-output (MIMO) radar equation is presented in this paper. Firstly, we derive the Signal-to-Noise Ratio (SNR) improvement factor MN of the colocated MIMO radar array output compare to single-input single-output (SISO) radar array output employing coherent integration, where M is the number of orthogonal transmitted signals and N is the number of receive array elements. Secondly, we derive the array output's SNR expression from radar equation perspective. With the expression, we get the colocated MIMO radar equivalent array gain via comparing the array output's SNR expressions of colocated MIMO radar and SISO radar. Then we obtain the colocated MIMO radar equation without considering the antenna electromagnetic effect.