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58
Mutual information and minimum meansquare error in Gaussian channels
 IEEE TRANS. INFORM. THEORY
, 2005
"... This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given the out ..."
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Cited by 285 (32 self)
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This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signaltonoise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discretetime and continuoustime noncausal MMSE estimation. This fundamental informationtheoretic result has an unexpected consequence in continuoustime nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signaltonoise ratio is chosen uniformly distributed between 0 and SNR.
On the Complexity of Sphere Decoding in Digital Communications
 IN DIGITAL COMMUNICATIONS,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, TO APPEAR
, 2005
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Fundamental limits on detection in low SNR under noise uncertainty
 in WirelessCom 2005, Maui, HI
, 2005
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NeymanPearson detection of GaussMarkov signals in noise: Closedform error exponent and properties,” preprint
, 2004
"... Abstract — The performance of NeymanPearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the statespace structure of the signal and observation model, a closedform expression for the er ..."
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Cited by 36 (17 self)
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Abstract — The performance of NeymanPearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the statespace structure of the signal and observation model, a closedform expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signaltonoise ratio (SNR)> 1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR < 1 there is an optimal correlation that maximizes the error exponent for a given SNR. I.
Detection of GaussMarkov Random Fields with NearestNeighbor Dependency
, 2008
"... The problem of hypothesis testing against independence for a GaussMarkov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the loglikelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uni ..."
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Cited by 27 (11 self)
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The problem of hypothesis testing against independence for a GaussMarkov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the loglikelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uniform distribution and nearestneighbor dependency graph, the error exponent of the NeymanPearson detector is derived using largedeviations theory. The error exponent is expressed as a dependencygraph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio.
Sensor configuration and activation for field detection in large sensor arrays
 in Proc. 2005 Information Processing in Sensor Networks (IPSN
, 2005
"... 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 ..."
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Cited by 15 (8 self)
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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 signaltonoise 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 sample
DETECTION OF GAUSSMARKOV RANDOM FIELD ON NEARESTNEIGHBOR GRAPH
"... The problem of hypothesis testing against independence for a GaussMarkov random field (GMRF) with nearestneighbor dependency graph is analyzed. The sensors measuring samples from the signal field are placed IID according to the uniform distribution. The asymptotic performance of NeymanPearson det ..."
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Cited by 10 (0 self)
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The problem of hypothesis testing against independence for a GaussMarkov random field (GMRF) with nearestneighbor dependency graph is analyzed. The sensors measuring samples from the signal field are placed IID according to the uniform distribution. The asymptotic performance of NeymanPearson detection is characterized through the largedeviation theory. An expression for the error exponent is derived using a special law of large numbers for graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent (improved detection performance) at low values of the variance ratio, whereas the opposite is true at high values of the ratio.
Regression in sensor networks: training distributively with alternating projections
 In Advanced Signal Processing Algorithms, Architectures, and Implementations XV, Volume SPIE 5910  1
, 2005
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Optimal Node Density for Detection in Energy Constrained Random Networks
"... The problem of optimal node density maximizing the NeymanPearson detection error exponent subject to a constraint on average (per node) energy consumption is analyzed. The spatial correlation among the sensor measurements is incorporated through a GaussMarkov random field model with Euclidean nea ..."
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Cited by 9 (8 self)
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The problem of optimal node density maximizing the NeymanPearson detection error exponent subject to a constraint on average (per node) energy consumption is analyzed. The spatial correlation among the sensor measurements is incorporated through a GaussMarkov random field model with Euclidean nearestneighbor dependency graph. A constant density deployment of sensors under the uniform or Poisson distribution is assumed. It is shown that the optimal node density crucially depends on the ratio between the measurement variances under the two hypotheses and displays a threshold behavior. Below the threshold value of the variance ratio, the optimal node density tends to infinity under any feasible average energy constraint. On the other hand, when the variance ratio is above the threshold, the optimal node density is the minimum value at which it is feasible to process and deliver the likelihood ratio (sufficient statistic) of the sensor measurements to the fusion center. In this regime of the variance ratio, an upper bound on the optimal node density based on a proposed 2approximation fusion scheme and a lower bound based on the minimum spanning tree are established. Under an alternative formulation where the energy consumption per unit area is constrained, the optimal node density is shown to be strictly finite for all values of the variance ratio and bounds on this optimal node density are provided.