The Incidence and Cross methods for efficient radar detection

The designation of the radar system is to detect the position and velocity of targets around us. The radar transmits a waveform, which is reflected back from the targets, and echo waveform is received. In a commonly used model, the echo is a sum of a superposition of several delay-Doppler shifts of the transmitted waveform, and a noise component. The delay and Doppler parameters encode, respectively, the distances, and relative velocities, between the targets and the radar. Using standard digital-to-analog and sampling techniques, the estimation task of the delay-Doppler parameters, which involves waveforms, is reduced to a problem for complex sequences of finite length N. In these notes we introduce the Incidence and Cross methods for radar detection. One of their advantages, is robustness to inhomogeneous radar scene, i.e., for sensing small targets in the vicinity of large objects. The arithmetic complexity of the incidence and cross methods is O(N logN + r³) and O(N logN + r²); for r targets, respectively. In the case of noisy environment, these are the fastest radar detection techniques. Both methods employ chirp sequences, which are commonly used by radar systems, and hence are attractive for real world applications.