Velocity Estimation beyond Nyquist Limit for Pulse Doppler Radars Using Pulse-Compressed Signals Correlated with Divided Reference Signals

Abstract

We propose seven velocity-estimation methods for fast moving targets beyond the Nyquist-limit velocity for pulse Doppler radars. The Doppler-shift frequency beyond the Nyquist limit, which equals one-half the pulse-repetition frequency, cannot be correctly measured as the frequency is folded back within the Nyquist interval. Our methods use pulse compression with divided reference signals of varying center frequencies to detect the difference among the Doppler-shift frequencies of the pulse-compressed signals and increase sensitivity through signal integration, all without modifying the transmitted signals. These methods are either grid-search-type or Newton-type methods, each possessing distinct characteristics. The Cramér-Rao lower bounds on the variance of estimated velocity are derived, and the upper bounds on the probability of correct ambiguity resolution are shown. The results of our numerical simulation indicate that our methods can estimate target velocity beyond the Nyquist-limit velocity and that the method of independently estimating the Doppler frequencies at both end parts of the signal bandwidth and estimating the target velocity from the difference exhibits a lower decrease than the other methods regarding the success probability of Doppler ambiguity resolution even for high target velocities. We also confirmed that the upper bounds closely match the probability of corresponding methods for when the target velocity is lower than several times the Nyquist velocity and the signal-to-noise ratio on the range-Doppler map is above approximately 20 dB.