This paper demonstrates fundamental limits of sensor networks for detection problems where the number of hypotheses is exponentially large. Such problems characterize many important applications including detection and classification of targets in a geographical area using a network of seismic sensors, and detecting complex substances with a chemical sensor array. We refer to such applications as large-scale detection problems. Using the insight that these problems share fundamental similarities with the problem of communicating over a noisy channel, we define the “sensing capacity” and lower bound it for a number of sensor network models. The sensing capacity expression differs significantly from the channel capacity due to the fact that for a fixed sensor configuration, codewords are dependent and nonidentically distributed. The sensing capacity provides a bound on the minimal number of sensors required to detect the state of an environment to within a desired accuracy. The results differ significantly from classical detection theory, and provide an intriguing connection between sensor networks and communications. In addition, we discuss the insight that sensing capacity provides for the problem of sensor selection.
We review the main theoretical results presented in this paper. In Section we introduce a simple but useful sensor network model that can be used to model sensing applications such as chemical sensing applications and computer network monitoring. For this model, we define and bound the sensing capacity. The sensing capacity bound differs significantly from the standard channel capacity results, and requires novel arguments to account for the constrained encoding of a sensor network. This is an important observation due to the use of mutual information as a sensor selection heuristic @cite_13 . Our result shows that this is not the correct metric for large-scale detection applications. Extensions are presented to account for non-binary target vectors, target sparsity, and heterogeneous sensors. Plotting the sensing capacity bound, we demonstrate interesting sensing tradeoffs. For example, perhaps counter-intuitively, sensors of shorter range can achieve a desired detection accuracy with fewer measurements than sensors of longer range. Finally, we also compare our sensing capacity bound to simulated sensor network performance.
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