This letter considers a scenario in which the Terahertz (THz) transmitter equipped with a linear antenna array wishes to focus its beam to a desired spatial region in the array near-field. The goal is to compute the achievable spatial region and determine how the system parameters such as the carrier frequency, the array dimension and the user’s location affect its beam focusing performance. First, based on a theorem from analytic geometry, we show that the achievable focusing spatial region constitutes a rotated ellipse, with the x{x} and y{y} coordinates denoting the range and angle, respectively. In this way, the determination of the spatial region is reduced to a problem of deriving the coverage of an ellipse. The achievable coverage is then obtained in closed form, and the construction of carrier frequency offsets that can analytically control the beam focusing performance is provided. Numerical results validate the theoretical findings and demonstrate the performance of the proposed method.

中文翻译：

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太赫兹线性天线阵列的分析范围与角度相关的光束聚焦模型


这封信考虑了一种场景，其中配备线性天线阵列的太赫兹（THz）发射器希望将其波束聚焦到阵列近场中的所需空间区域。目标是计算可实现的空间区域，并确定系统参数（例如载波频率、阵列尺寸和用户位置）如何影响其波束聚焦性能。首先，基于解析几何定理，我们证明可实现的聚焦空间区域构成一个旋转椭圆，其中 x{x} 和 y{y} 坐标分别表示范围和角度。这样，空间区域的确定就简化为推导椭圆的覆盖范围的问题。然后以封闭形式获得可实现的覆盖范围，并提供可以分析控制波束聚焦性能的载波频率偏移的构造。数值结果验证了理论结果并证明了所提出方法的性能。