The problem to be considered is a phase-modulated waveform design for detection of extended targets contaminated by signal-dependent clutter returns and additive channel noise in practical radar systems. We first introduce an optimal waveform design algorithm for extended target detection in a band-limited radar system by maximizing the signal-to-clutter-and-noise ratio (SCNR) at the output of the receiver, and give the analytical solution of the optimal signal energy spectral density (ESD). In order to make full use of the transmission power, a phase iterative algorithm to design the phase-modulated waveform with constant envelop is proposed, which is proven to be able to achieve a small SCNR loss by minimizing the mean-square spectral distance between the optimal waveform and the designed one. The results of extensive simulations illustrate that our approach provides less than 1 dB SCNR loss when the signal duration is greater than 1 μs.
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