Beampattern Design Using Riemannian Manifold for Frequency Diverse Array Considering Jammers

This paper investigates a two-dimensional range-angle beampattern synthesis method for jammer suppression using a frequency diverse array (FDA) multiple-input multiple-output (MIMO) framework, where the transmit waveform, receive filter, and frequency increment are optimized. At the problem formulation stage, the objective function is chosen as the minimization of the squared error between the devised and desired beampattern, where the beampattern response corresponding to the target region attains its maximum value, whereas the response associated with the jammer region is minimized to nulls. Moreover, the constant modulus, receive energy and spectrum bandwidth constraints are forced to ensure feasibility in practical implementations. To tackle the resultant NP-hard non-convex optimization problem, a Riemannian manifold-based gradient descent (RMGD) algorithm is developed, which reformulates the problem as an unconstrained optimization task by leveraging the geometrical structure of a Riemannian product manifold. In particular, the Euclidean gradient is projected onto the tangent space, and the decision variables are updated and retracted onto the Riemannian manifold. In this respect, the transmit waveform, receive filter, and frequency increment are iteratively obtained through an alternating optimization procedure until convergence. Additionally, the computational complexity of the proposed algorithm is analyzed. Simulation results highlight the advantages of the proposed method in deceptive jammer suppression, evidenced by significant improvements in signal-to-interference-plus-noise ratio (SINR) improvement, robustness against position errors, and detection probability.