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Manifold studies of FDA geometries for joint angle and range estimation

机译:FDA几何形状的流形研究,用于关节角度和范围估计

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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 Cramer-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.
机译:与传统的相控阵不同,频率分集​​阵列(FDA)提供了一种角度范围相关且随时间变化的发射波束图,可用于许多有希望的应用中。由于阵列流形对于各种阵列应用至关重要。包括歧管表面和用于连接范围和角度估计的歧管曲线的歧管特性。我们证明FDA歧管表面的形状是抛物线形或平面形,并且FDA歧管表面上的θ曲线和r曲线族是测地曲线。结果表明,对于对称线性阵列,FDA流形曲线提供的弧长比相控阵更长,更普遍地,我们证明了对于任意线性阵列,FDA在产生更长的弧长方面也胜过相控阵此外,在FDA歧管几何框架下,用于角度和范围估计的Cramer-Rao下界(CRLB)也得到了确定。结果表明,对于任意线性阵列,FDA的CRLB均低于相控阵。所有理论分析均通过数值结果验证。

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