Coherent Integration Loss Due to Nonstationary Phase Noise in High-Resolution Millimeter-Wave Radars

Phase noise refers to the instability of an oscillator, which is the cause of instantaneous phase and frequency deviations in the carrier wave. This unavoidable instability adversely affects the performance of range–velocity radar systems, including synthetic aperture radars (SARs) and ground-moving target indicator (GMTI) radars. Phase noise effects should be considered in high-resolution radar designs, operating in millimeter wavelengths and terahertz frequencies, due to their role in radar capability during the reliable identification of target location and velocity. In general, phase noise is a random process consisting of nonstationary terms. It has been shown that in order to optimize the coherent detection of stealthy, fast-moving targets with a low radar cross-section (RCS), it is required to evaluate the integration gain and to determine the incoherent noise effects for resolving target location and velocity. Here, we present an analytical expression for the coherent integration loss when a nonstationary phase noise is considered. A Wigner distribution was employed to derive the time–frequency expression for the coherent loss when nonstationary conditions were considered. Up to now, no analytical expressions have been developed for coherent integration loss when dealing with real nonstationary phase noise mathematical models. The proposed expression will help radar systems estimate the nonstationary integration loss and adjust the decision threshold value in order to maximize the probability of detection. The effect of nonstationary phase noise is demonstrated for studying coherent integration loss of high-resolution radar operating in the W-band. The investigation indicates that major degradation in the time-frequency coherent integration due to short-term, nonstationary phase noise instabilities arises for targets moving at low velocities and increases with range. Opposed to the conventional model, which assumes stationarity, a significant difference of up to 25 dB is revealed in the integration loss for radars operating in the millimeter wave regime. Moreover, for supersonic moving targets, the loss peaks at intermediate distances and then reduces as the target moves away.