Shaping Radar Ambiguity Function by $L$ -Phase Unimodular Sequence

In this paper, we discuss the ambiguity function (AF) synthesis problem for unimodular sequences, which are widely used in radar/sonar and communication systems. Notions of discrete-time ambiguity function and discrete ambiguity function (DAF) are defined, and the corresponding properties are also discussed for unimodular sequences. Depending on these properties, two algorithms are proposed to synthesize the DAF of the unimodular sequence by minimizing the squared error between a desired complex/real function and a realizable one over $L$ -phase alphabet. To break the volume invariant constraint of a single sequence’s AF, multi-sequences are also considered to be optimized simultaneously to suppress sidelobes of ambiguity surface. Numerical examples show the effectiveness of the proposed algorithms in synthesizing unimodular sequence with a desired AF, and typical polyphase sequences can be well approximated by eight-phase unimodular sequences from the viewpoint of DAF.