Group-Utility Metric for Efficient Sensor Selection and Removal in LCMV Beamformers

In sensor arrays or sensor networks, tracking each sensors utility helps in excluding those which do not sufficiently contribute to the task at hand, thereby reducing energy consumption or avoiding model overfitting. In a linearly-constrained minimum variance (LCMV) beamformer, the utility of a sensor is defined as the increase in the beamformer's output noise power when the sensor would be removed and the beamformer coefficients re-optimized. An expression to efficiently compute this utility metric has been found for the case where each sensor removal corresponds to a single beamformer coefficient. However, in a filter-and-sum implementation, a single sensor is filtered by a group of beamformer coefficients. Furthermore, sometimes one wants to track the joint utility of a group of sensors. In this paper we derive a generalized expression to efficiently calculate the utility of such groups as a whole, called the group-utility. We show that the computational complexity of this generalized expression is negligible if the number of groups is larger than the group sizes, leading to a very efficient group-utility computation compared to the straightforward implementation. Furthermore, an efficient updating equation re-optimizing the LCMV beamformer when a group of G beamformer inputs is removed is found as a by-product.