Beampattern Optimization for Frequency Diverse Array With Sparse Frequency Waveforms

Multiple-input multiple-output (MIMO) radar equipped with a frequency diverse array (FDA) can produce a range-dependent beampattern and increase the degrees-of-freedom of the antenna array. In this paper, a new method of designing the MIMO radar beampattern with sparse frequency waveforms is proposed for the FDA, which randomly samples multiple distance points such that the MIMO radar beampattern with the both sparse frequency spectrum and constant modulus constraints are realized by the proposed beampattern design framework. The main steps are as follows. We first obtain the covariance matrix of the transmitted signal by a given ideal beampattern, and formulate the problem of designing the realizable beampattern as a nonconvex optimization problem, which includes the constraints of the both constant modulus of transmitted signals and sparse frequency spectrum. Then, a cyclic optimization algorithm is proposed, which guarantees the monotonic decrease of the objective function as the algorithm proceeds. The simulation results illustrate that the proposed method can achieve smaller errors than the traditional method, which does not consider the frequency diversity.