Abstract
This letter provides a Cramer-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.
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