Frequency Diverse Coprime Arrays With Coprime Frequency Offsets for Multitarget Localization

Different from conventional phased-array radars, the frequency diverse array (FDA) radar offers a range-dependent beampattern capability that is attractive in various applications. The spatial and range resolutions of an FDA radar are fundamentally limited by the array geometry and the frequency offset. In this paper, we overcome this limitation by introducing a novel sparsity-based multitarget localization approach incorporating both coprime arrays and coprime frequency offsets. The covariance matrix of the received signals corresponding to all sensors and employed frequencies is formulated to generate a space-frequency virtual difference coarrays. By using <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(M+N)$</tex-math></inline-formula> antennas and <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(M+N)$</tex-math></inline-formula> frequencies, the proposed coprime arrays with coprime frequency offsets enables the localization of up to <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(M^2N^2)$</tex-math></inline-formula> targets with a resolution of <inline-formula><tex-math notation="LaTeX"> $\mathcal {O}(1/(MN))$</tex-math></inline-formula> in angle and range domains, where <inline-formula> <tex-math notation="LaTeX">$M$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$N$</tex-math> </inline-formula> are coprime integers. The joint direction-of-arrival (DOA) and range estimation is cast as a two-dimensional sparse reconstruction problem and is solved within the Bayesian compressive sensing framework. We also develop a fast algorithm with a lower computational complexity based on the multitask Bayesian compressive sensing approach. Simulations results demonstrate the superiority of the proposed approach in terms of DOA-range resolution, localization accuracy, and the number of resolvable targets.