Delay estimation using narrow-band processes

Array processing of narrow-band Gaussian signals is studied with emphasis on delay estimation. The Barankin bound is used to examine the effect of ambiguity on mean-square measurement error. When the bound is plotted as a function of signal-to-noise ratio one observes a distinct threshold. Above the critical signal-to-noise ratio the lower bound on mean-square error is given by the Cramér-Rao inequality, which is approached by the Barankin inequality under these conditions. Below the threshold the Barankin bound can exceed the Cramér-Rao bound by large factors. The relative magnitude of the bounds in that region depends critically on the ratio of signal center frequency to signal bandwidth.