Optimal and Suboptimal Detection of Gaussian Signals in Noise: Asymptotic Relative Efficiency

The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is reasonable to use the simple quadratic detector that is optimal in the case of an independent and identically distributed (i.i.d.) signal. Using the large deviations principle, the performance of this detector (which is suboptimal for non-i.i.d. signals) is compared with that of the optimal detector for correlated signals via the asymptotic relative efficiency defined as the ratio between sample sizes of two detectors required for the same performance in the large-sample-size regime. The effects of SNR on the ARE are investigated. It is shown that the asymptotic efficiency of the simple quadratic detector relative to the optimal detector converges to one as the SNR increases without bound for any bounded spectrum, and that the simple quadratic detector performs as well as the optimal detector for a wide range of the correlation values at high SNR.Comment: To appear in the Proceedings of the SPIE Conference on Advanced Signal Processing Algorithms, Architectures and Implementations XV, San Diego, CA, Jul. 1 - Aug. 4, 200

Large Deviations Analysis for the Detection of 2D Hidden Gauss-Markov Random Fields Using Sensor Networks

The detection of hidden two-dimensional Gauss-Markov random fields using sensor networks is considered. Under a conditional autoregressive model, the error exponent for the Neyman-Pearson detector satisfying a fixed level constraint is obtained using the large deviations principle. For a symmetric first order autoregressive model, the error exponent is given explicitly in terms of the SNR and an edge dependence factor (field correlation). The behavior of the error exponent as a function of correlation strength is seen to divide into two regions depending on the value of the SNR. At high SNR, uncorrelated observations maximize the error exponent for a given SNR, whereas there is non-zero optimal correlation at low SNR. Based on the error exponent, the energy efficiency (defined as the ratio of the total information gathered to the total energy required) of ad hoc sensor network for detection is examined for two sensor deployment models: an infinite area model and and infinite density model. For a fixed sensor density, the energy efficiency diminishes to zero at rate O(area^{-1/2}) as the area is increased. On the other hand, non-zero efficiency is possible for increasing density depending on the behavior of the physical correlation as a function of the link length.Comment: To appear in the Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, March 30 - April 4, 200

Information, Energy and Density for Ad Hoc Sensor Networks over Correlated Random Fields: Large Deviations Analysis

Using large deviations results that characterize the amount of information per node on a two-dimensional (2-D) lattice, asymptotic behavior of a sensor network deployed over a correlated random field for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first order conditional autoregression, the behavior of the total information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density and energy vary.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 200

Energy Scaling Laws for Distributed Inference in Random Fusion Networks

The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field (MRF) hypotheses, the scheme with minimum average energy consumption is bounded below by average energy of fusion along the minimum spanning tree, and above by a suboptimal scheme, referred to as Data Fusion for Markov Random Fields (DFMRF). Scaling laws are derived for the optimal and suboptimal fusion policies. It is shown that the average asymptotic energy of the DFMRF scheme is finite for a class of MRF models.Comment: IEEE JSAC on Stochastic Geometry and Random Graphs for Wireless Network

Sensor configuration and activation for field detection in large sensor arrays

The problems of sensor configuration for the detection of correlated random fields using large sensor arrays are considered. Using error exponents that characterize the asymptotic behavior of the optimal detector, the detection performance of different sensor configurations are analyzed and compared. The dependence of the optimal configuration on parameters such as sensor signal-to-noise ratio (SNR), field correlation, etc., is examined, yielding insights into the most effective choices for sensor selection in various operating conditions. Simulation results validate the analysis based on asymptotic results for finite sampl