Digital beamforming (DBF) arrays with a large number of small antennas are extensively employed in millimeter-wave (mmWave) sensing systems. Sparse arrays have been posed as an attractive solution to mmWave systems due to their capability of striking the best compromise between performance and complexity. We propose two iterative antenna selection strategies, referred to as deterministic selection and adaptive selection, to design sparse DBF arrays in this paper. The first strategy assumes a common sparse array associated with different beamforming weights for multiple switched beams, while the other exploits switching networks to adaptively change the sparse array configuration with different beams. To counteract hardware-related issues that arise in practical realizations, we then propose guided adaptive selection and regularized adaptive selection to impose additional constraints for different switching networks. The optimality of sparse DBF arrays is defined in terms of both transmit and receive patterns. Taking that into account, an iterative re-weighted $l_1$-norm is modified to promote boolean sparsity of the selection vector in this work. Simulation results validate the effectiveness of proposed antenna selection methods.

具有大量小天线的数字波束成形（DBF）阵列广泛用于毫米波（mmWave）传感系统中。稀疏阵列被认为是mmWave系统的一种有吸引力的解决方案，因为它们能够在性能和复杂性之间取得最佳折衷。本文提出了两种迭代天线选择策略，即确定性选择和自适应选择，以设计稀疏DBF阵列。第一种策略假设一个公共稀疏阵列与多个切换波束的不同波束成形权重相关联，而其他策略则利用交换网络来自适应地更改具有不同波束的稀疏阵列配置。为了解决实际实现中出现的与硬件相关的问题，然后，我们提出了引导自适应选择和正则自适应选择，以对不同的交换网络施加额外的约束。稀疏DBF阵列的最佳性是根据发送和接收模式定义的。考虑到这一点，对迭代进行重新加权${升}_{\mathrm{1个}}$-norm进行了修改，以促进这项工作中选择向量的布尔稀疏性。仿真结果验证了所提出的天线选择方法的有效性。