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In multichannel signal processing with distributed sensors, choosing the optimal subset of observed sensor signals to be exploited is crucial in order to maximize algorithmic performance and reduce computational load, ideally both at the same time. In the acoustic domain, signal cross-correlation is a natural choice to quantify the usefulness of microphone signals, i.e., microphone utility, for array processing, but its estimation requires that the uncoded signals are synchronized and transmitted between nodes. In resource-constrained environments like acoustic sensor networks, low data transmission rates often make transmission of all observed signals to the centralized location infeasible, thus discouraging direct estimation of signal cross-correlation. Instead, we employ characteristic features of the recorded signals to estimate the usefulness of individual microphone signals. In this contribution, we provide a comprehensive analysis of model-based microphone utility estimation approaches that use signal features and, as an alternative, also propose machine learning-based estimation methods that identify optimal sensor signal utility features. The performance of both approaches is validated experimentally using both simulated and recorded acoustic data, comprising a variety of realistic and practically relevant acoustic scenarios including moving and static sources.