Manifold studies of FDA geometries for joint angle and range estimation

Abstract

Different from traditional phased-array, frequency diverse array (FDA) provides an angle-range-dependent and time-variant transmit beampattern that can be utilized for many promising applications. Since array manifold is critical in various array applications, this paper studies the FDA manifold properties including manifold surface and manifold curve for joint range and angle estimation. We prove that the shape of FDA manifold surface is either parabolic or planar, and the families of θ-curves and r-curves lying on FDA manifold surface are geodesic curves. It is shown that, for a symmetric linear array, FDA manifold curve provides longer arc length than that of a phased-array. More generally, we prove that, for an arbitrary linear array, FDA also outperforms phased-array in producing longer arc length and larger rate-of-change of the arc length in some condition. Furthermore, the Cramér-Rao lower bounds (CRLBs) for both angle and range estimation under the FDA manifold geometry framework are also derived, which indicate that FDA achieves lower CRLB than phased-array for an arbitrary linear array. All theoretical analysis are verified by numerical results.