In this paper we consider the problem of finding the optimal sensing rate for estimating an event over shared communication links. Since the communication link is shared between several systems sending their observations, not all observations can be sent to their respective estimators. To improve the performance of the estimator, we propose to oversample the event. In particular, we derive the minimum oversampling rate such that the maximum error covariance of the estimate is kept below the desired threshold. We derive a closed form equation for this minimum sampling rate that can be used in designing estimation techniques for systems with bandwidth constraints.