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.