The Range-Doppler SRL of Two Close Targets for Active Sensor in the GLRT Context

In this text we bring in the generalized likelihood radio test (GLRT) theory to resolve two-dimensional resolution problem of two close targets, naming the range-Doppler statistical resolution limit (SRL), which is put forwarded for the first time. We utilize the first-order Taylor expansion of the return signals to get an approximate linear model w.r.t. the range and Doppler parameters to be tested, then apply the detection theory to get a closed-form expression of the SRL. From the expression one can see the SRL is linear trade-off between the range and Doppler SRL, with their sum fixed. The two-dimension SRL is inversely proportional to the difference of their power. We have considered both cases with noise variance known or unknown. The numerical simulations have demonstrated the validity of our theoretical results.