Approximate Cramer-Rao bound on Doppler error in correlation-processing relatively narrowband noise radar

Limitations on accuracy of Doppler estimation in continuous-wave noise radar with correlation processing are studied. Second-order properties of output of the correlation receiver are evaluated and an approximate Cramer-Rao bound on errors of Doppler measurement is derived. The accuracy of Doppler measurements is found to be affected by the following factors: power spectral density of noise signal, frequency response of the low-pass filter in correlator, observation time, velocity of the target and signal to noise ratio. It is shown that the random nature of the transmitted signal induces additional fluctuations at the output of correlator which limit the accuracy even in the infinite signal to noise case. Qualitative extension of the results to a case covering multiple targets and clutter is made. It is argued that the performance will decrease and that increasing transmitted power may not provide significant improvement when clutter is present.