This paper studies hybrid beamforming for active sensing applications, such as millimeter-wave or ultrasound imaging. Hybrid beamforming can substantially lower the cost and power consumption of fully digital sensor arrays by reducing the number of active front ends. Sparse arrays can be used to further reduce hardware costs. We consider phased arrays and employ linear beamforming with possibly sparse array configurations at both the transmitter and receiver. The quality of the acquired images is improved by adding together several component images corresponding to different transmissions and receptions. In order to limit the acquisition time of an image, we formulate an optimization problem for minimizing the number of component images subject to achieving a desired point spread function. Since this problem is not convex, we propose algorithms for finding approximate solutions in the fully digital beamforming case, as well as in the more challenging hybrid and analog beamforming cases that employ quantized phase shifters. We also determine upper bounds on the number of component images needed for achieving the fully digital solution using fully analog and hybrid architectures, and derive closed-form expressions for the beamforming weights in these cases. Simulations demonstrate that a hybrid sparse array with very few elements, and even fewer front ends, can achieve the resolution of a fully digital uniform array at the expense of a longer image acquisition time.

中文翻译：

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使用稀疏阵列进行主动传感的混合波束成形

本文研究了用于主动传感应用的混合波束成形，例如毫米波或超声成像。通过减少有源前端的数量，混合波束成形可以显着降低全数字传感器阵列的成本和功耗。稀疏阵列可用于进一步降低硬件成本。我们考虑相控阵，并在发射器和接收器处采用可能具有稀疏阵列配置的线性波束成形。通过将对应于不同传输和接收的多个分量图像相加在一起，可以提高所获取图像的质量。为了限制图像的获取时间，我们制定了一个优化问题，以最小化组件图像的数量以实现所需的点扩散函数。由于这个问题不是凸的，我们提出了在全数字波束成形情况下以及在使用量化移相器的更具挑战性的混合和模拟波束成形情况下寻找近似解的算法。我们还确定了使用全模拟和混合架构实现全数字解决方案所需的组件图像数量的上限，并在这些情况下推导出波束成形权重的封闭形式表达式。仿真表明，具有很少元素甚至更少前端的混合稀疏阵列可以实现全数字均匀阵列的分辨率，但代价是更长的图像采集时间。我们还确定了使用全模拟和混合架构实现全数字解决方案所需的组件图像数量的上限，并在这些情况下推导出波束成形权重的封闭形式表达式。仿真表明，具有很少元素甚至更少前端的混合稀疏阵列可以实现全数字均匀阵列的分辨率，但代价是更长的图像采集时间。我们还确定了使用全模拟和混合架构实现全数字解决方案所需的组件图像数量的上限，并在这些情况下推导出波束成形权重的封闭形式表达式。仿真表明，具有很少元素甚至更少前端的混合稀疏阵列可以实现全数字均匀阵列的分辨率，但代价是更长的图像采集时间。