Second-Order Characterization of Micro Doppler Radar Signatures of Drone Swarms

We propose an analytic model for the second-order characteristics of the radar return signal from a swarm of rotor drones. We consider the case of a swarm of identical drones, with each a number of rotors comprised of a number of rotor blades. By considering the orientation and speed of each rotor as stochastic variables, we derive expressions for the autocorrelation function (ACF) and power spectral density (PSD). The ACF and PSD are in the form of an infinite series with coefficients that drop to zero at a predictable limit. Thus in practical applications, the series may be truncated. As a special case, we show that for deterministic rotor speed, the ACF can be expressed in closed form. We further investigate how system parameters (Blade length, Rotor speed, number of blades, and number of drones) influence the derived expressions for the ACF and PSD.