  Based on the technique of generalized likelihood ratio test, we address
detection schemes for Doppler-shifted range-spread targets in Gaussian noise.
First, a detection scheme is derived by solving the maximization associated
with the estimation of unknown Doppler frequency with semi-definite
programming. To lower the computational complexity of the detector, we then
consider a simplification of the detector by adopting maximization over a
relaxed space. Both of the proposed detectors are shown to have constant false
alarm rate via numerical or theoretical analysis. The detection performance of
the proposed detector based on the semi-definite programming is shown to be
almost the same as that of the conventional detector designed for known Doppler
frequency.
