Optimal preprocessing for source localization by fewer receivers than sensors

In many source detection and localization applications, the number of receivers is smaller than the number of sensors, where the receivers are connected to the sensors via a preprocessing device. The preprocessing device can easily be implemented in hardware by linear transformation of the measured signals at the sensors. In this paper, the Cramer-Rao lower bound for this problem is developed and it is shown that by judicious choice of the preprocessing matrix, it is possible to reduce the bound on direction of arrival estimation errors. The results demonstrate the trade-off between azimuth and elevation estimation errors using a planar array divided to subarrays.