This letter provides a Cramér-Rao Bound (CRB) based analysis of compressive arrays with applications in mmWave channel sensing, where the measurements at the output of an antenna array are further compressed using a complex-valued compression matrix, in order to reduce the system complexity and power consumption. While necessary conditions for the existence of CRB for compressed arrays have been recently derived, currently no sufficient conditions exist that can guarantee the existence of the CRB in different compressive regimes, and therefore can be used to guide the design of the overall system. We overcome this drawback by deriving tight sufficient conditions (that agree with the necessary conditions) for almost all choices of the compression matrix. Our results decisively demonstrate the additional benefit gained by using sparse arrays (such as nested array) even when a compression matrix is deployed.

中文翻译：

---

压缩阵列和混合通道传感：基于 Cramr-Rao 边界的分析

这封信提供了基于 Cramér-Rao Bound (CRB) 的压缩阵列分析，在毫米波信道传感中的应用，其中天线阵列输出的测量结果使用复值压缩矩阵进一步压缩，以减少系统复杂性和功耗。虽然最近推导出了压缩阵列 CRB 存在的必要条件，但目前还没有足够的条件可以保证 CRB 在不同压缩状态下的存在，因此可以用来指导整个系统的设计。我们通过为压缩矩阵的几乎所有选择推导出严格的充分条件（与必要条件一致）来克服这个缺点。