Strengths and limitations of the Fourier method for detecting accelerating targets by pulse Doppler radar

The Fourier transform method has been generally used in pulse Doppler radar for detecting targets that are moving with acceleration, despite the phenomenon known as Doppler smearing which limits the performance of the method. Examples of accelerating targets are manoeuvring aircraft and missiles. The authors quantify the effects of Doppler smearing. In using a pulse Doppler radar to detect a nonaccelerating target in additive white Gaussian noise and to estimate its radial velocity, the Fourier method provides an output signal-to-noise ratio (SNR) that increases linearly with the number of pulses. When the target is accelerating, the Fourier method may still be used to detect the target and estimate its median velocity, provided the acceleration is small enough in the sense described. For a given acceleration, when the number Of pulses is increased, the output SNR of the Fourier method varies as a concave function, increasing to a maximum and then decreasing, before the method fails catastrophically. Thus the number of pulses and the acceleration have to be matched to achieve optimum performance. Empirical formulas for the dependence of the optimum SNR and the optimum number Of Pulses on the acceleration are given. The results are shown to be relevant to the design of generalised likelihood ratio test detectors that apply a search over a grid.