An important characteristic of a cognitive radar is the capability to adjust its transmitted waveform to adapt to the\nradar environment. The adaptation of the transmit waveform requires an effective framework to synthesize\nwave forms sharing a desired ambiguity function (AF). With the volume-invariant property of AF, the integrated\nsidelobe level (ISL) can only be minimized in a certain area on the time delay and Doppler frequency shift plane. In this\npaper, we propose a new algorithm for unimodular sequence to minimize the ISL of an AF in a certain area based on\nthe phase-only conjugate gradient and phase-only Newton�s method. For improving detection performance of a\nmoving target detecting (MTD) radar system, slow-time ambiguity function (STAF) is defined, and the proposed\nalgorithm is presented to optimize the range-Doppler response. We also devise a cognitive approach for a MTD radar\nby adaptively altering its sidelobe distribution of STAF. At the simulation stage, the performance of the proposed\nalgorithm is assessed to show their capability to properly shape the AF and STAF of the transmitted waveform.
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