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.
@cite_13
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We bound the number of sensors required to achieve a desired level of sensing accuracy in a discrete sensor network application (e.g. distributed detection). We model the state of nature being sensed as a discrete vector, and the sensor network as an encoder. Our model assumes that each sensor observes only a subset of the state of nature, that sensor observations are localized and dependent, and that sensor network output across different states of nature is neither identical nor independently distributed. Using a random coding argument we prove a lower bound on the 'sensing capacity' of a sensor network, which characterizes the ability of a sensor network to distinguish among all states of nature. We compute this lower bound for sensors of varying range, noise models, and sensing functions. We compare this lower bound to the empirical performance of a belief propagation based sensor network decoder for a simple seismic sensor network scenario. The key contribution of this paper is to introduce the idea of a sharp cut-off function in the number of required sensors, to the sensor network community. In wireless sensor networks that consist of a large number of low-power, short-lived, unreliable sensors, one of the main design challenges is to obtain long system lifetime without sacrificing system original performances (sensing coverage and sensing reliability). In this paper, we propose a node-scheduling scheme, which can reduce system overall energy consumption, therefore increasing system lifetime, by identifying redundant nodes in respect of sensing coverage and then assigning them an off-duty operation mode that has lower energy consumption than the normal on-duty one. Our scheme aims to completely preserve original sensing coverage theoretically. Practically, sensing coverage degradation caused by location error, packet loss and node failure is very limited, not more than 1 as shown by our experimental results. In addition, the experimental results illustrate that certain redundancy is still guaranteed after node-scheduling, which we believe can provide enough sensing reliability in many applications. We implement the proposed scheme in NS-2 as an extension of the LEACH protocol and compare its energy consumption with the original LEACH. Simulation results exhibit noticeably longer system lifetime after introducing our scheme than before. Copyright © 2003 John Wiley & Sons, Ltd. Assume that n sensors with identical range r = f(n) 2n, for some f(n) > 1 for all n, are thrown randomly and independently with the uniform distribution in the unit interval [0,1]. They are required to move to new positions so as to cover the entire unit interval in the sense that every point in the interval is within the range of a sensor. We obtain tradeoffs between the expected sum and maximum of displacements of the sensors and their range required to accomplish this task. In particular, when f(n) = 1 the expected total displacement is shown to be Θ(√n). For sensors with larger ranges we present two algorithms that prove the upper bound for the sum drops sharply as f(n) increases. The first of these holds for f(n) ≥ 6 and shows the total movement of the sensors is O ( √In n (n)) while the second holds for 12 ≤ f(n) ≤ In n - 2 In In n and gives an upper bound of O(ln n f(n)ef(n) 2 ). Note that the second algorithm improves upon the first for f(n) δ In In n - In In Inn. Further we show a lower bound, for any 1 ω f(n) 0. For the case of the expected maximum displacement of a sensor when f(n) = 1 our bounds are (n -1 2) and for any e > 0, O(n-1 2+e). For larger sensor ranges (up to (1 - e)ln n n e > O) the expected maximum displacement is shown to be Θ(ln n n). We also obtain similar sum and maximum displacement and range tradeoffs for area coverage for sensors thrown at random in a unit square. In this case, for the expected maximum displacement our bounds are tight and for the expected sum they are within a factor of √ln n. Finally, we investigate the related problem of the expected total and maximum displacement for perimeter coverage (whereby only the perimeter of the region need be covered) of a unit square. For example, when n sensors of radius > 2 n are thrown randomly and independently with the uniform distribution in the interior of a unit square, we can show the total expected displacement required to cover the perimeter is n 12 + o(n). © 2013 ACM. This paper considers the problem of blindly calibrating sensor response using routine sensor network measurements. We show that as long as the sensors slightly oversample the signals of interest, then unknown sensor gains can be perfectly recovered. Remarkably, neither a controlled stimulus nor a dense deployment is required. We also characterize necessary and sufficient conditions for the identification of unknown sensor offsets. Our results exploit incoherence conditions between the basis for the signals and the canonical or natural basis for the sensor measurements. Practical algorithms for gain and offset identification are proposed based on the singular value decomposition and standard least squares techniques. We investigate the robustness of the proposed algorithms to model mismatch and noise on both simulated data and on data from current sensor network deployments.