Detection rate optimization in radar systems with unknown disturbance power

In this work, we study the fundamental tradeoff between integration time and scan rate in radar systems. The contrasting needs for a large probability of detection and a short scan time are carefully balanced by optimizing the detection rate, defined as the average number of detections from a target per unit of time. A closed-form solution for the optimum pulse train length is provided in the relevant case of Gaussian observations with unknown noise variance. Some examples are given to show the possible tradeoffs among the principal system parameters