Barankin bound for range and Doppler estimation using orthogonal signal transmission

In this paper, the Barankin bound for performance evaluation of target range and Doppler estimation by an active radar (or sonar) is derived. The Barankin bound is analyzed for two signal cases: pulse train with identical (coherent) signals between pulses, and pulse train with orthogonal coded signals. At high pulse repetition frequencies (PRF's), identical signal transmission results in high sidelobes in the ambiguity function, while orthogonal signal transmissions allows to reduce the sidelobes and the ambiguity level. The Barankin bound is shown to be an efficient tool for system analysis in the presence of ambiguities. It is shown that for the identical signals case, the threshold signal-to-noise ratio (SNR) predicted by the Barankin bound is higher than the orthogonal signals case. The results are accompanied by maximum likelihood (ML) simulations which show that the Barankin bound predicts the threshold SNR with a good accuracy. It is shown that at high SNR's, the Barankin bound, the Cramér-Rao bound and the ML coincide.