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.
The problem of estimating a continuous field using a sensor network is an active area of research. @cite_2 considers the relationship of transport capacity and the rate distortion function of a continuous random processes. @cite_15 proves limits on the estimation of an inhomogeneous random fields using sensor that collect noisy point samples. Other work on the problem of estimating a continuous random field includes @cite_12 , @cite_5 , @cite_21 , @cite_26 . @cite_33 considers the estimation of continuous parameters of a set of underlying random processes through a noisy communications channel. The results presented in this paper consider the detection of a discrete state of an environment. We do not consider extensions to environments with a continuous state.
@cite_26 @cite_33 @cite_21 @cite_2 @cite_5 @cite_15 @cite_12
2962919833 2111224874 2167484620 2109914635
In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints is an important problem in this context. Here we study the estimation of correlation functions between sensors using compressed acquisition and one-bit-quantization. The estimation is achieved directly using compressed samples, without considering any reconstruction of the signals. We show that if the signals of interest are far from white noise, estimation of the correlation using @math compressed samples out of @math can be more advantageous than estimation of the correlation using @math consecutive samples. The analysis consists of studying the asymptotic performance of the estimators at a fixed compression rate. We provide the analysis when the compression is realized by a random projection matrix composed of independent and identically distributed entries. The framework includes widely used random projection matrices, such as Gaussian and Bernoulli matrices, and it also includes very sparse matrices. However, it does not include subsampling without replacement, for which a separate analysis is provided. When considering one-bit-quantization as well, the theoretical analysis is not tractable. However, empirical evidence allows the conclusion that in practical situations, compressed and quantized estimators behave sufficiently correctly to be useful in, for example, time-delay estimation and model estimation. We consider a problem of broadcast communication in sensor networks, in which samples of a random field are collected at each node, and the goal is for all nodes to obtain an estimate of the entire field within a prescribed distortion value. The main idea we explore in this paper is that of jointly compressing the data generated by different nodes as this information travels over multiple hops, to eliminate correlations in the representation of the sampled field. Our main contributions are: (a) we obtain, using simple network flow concepts, conditions on the rate distortion function of the random field, so as to guarantee that any node can obtain the measurements collected at every other node in the network, quantized to within any prescribed distortion value; and (b) we construct a large class of physically-motivated stochastic models for sensor data, for which we are able to prove that the joint rate distortion function of all the data generated by the whole network grows slower than the bounds found in (a). A truly novel aspect of our work is the tight coupling between routing and source coding, explicitly formulated in a simple and analytically tractable model - to the best of our knowledge, this connection had not been studied before. Sensing, processing and communication must be jointly optimized for efficient operation of resource-limited wireless sensor networks. We propose a novel source-channel matching approach for distributed field estimation that naturally integrates these basic operations and facilitates a unified analysis of the impact of key parameters (number of nodes, power, field complexity) on estimation accuracy. At the heart of our approach is a distributed source-channel communication architecture that matches the spatial scale of field coherence with the spatial scale of node synchronization for phase-coherent communication: the sensor field is uniformly partitioned into multiple cells and the nodes in each cell coherently communicate simple statistics of their measurements to the destination via a dedicated noisy multiple access channel (MAC). Essentially, the optimal field estimate in each cell is implicitly computed at the destination via the coherent spatial averaging inherent in the MAC, resulting in optimal power-distortion scaling with the number of nodes. In general, smoother fields demand lower per-node power but require node synchronization over larger scales for optimal estimation. In particular, optimal mean-square distortion scaling can be achieved with sub-linear power scaling. Our results also reveal a remarkable power-density tradeoff inherent in our approach: increasing the sensor density reduces the total power required to achieve a desired distortion. A direct consequence is that consistent field estimation is possible, in principle, even with vanishing total power in the limit of high sensor density. We consider the problem of obtaining a high quality estimates of band-limited sensor fields when sensor measurements are noisy and the nodes are irregularly deployed and subject to random motion. We consider the mean square error (MSE) of the estimate and we analytically derive the performance of several reconstruction estimation techniques based on linear filtering. For each technique, we obtain the mean value of the MSE, as well as its asymptotic expression in the case where the field bandwidth and the number of sensors grow to infinity, while their ratio is kept constant. Our results provide useful guidelines for the design of sensor networks when many system parameters have to be traded off.