Rate Allocation for Decentralized Detection in Wireless Sensor Networks

We consider the problem of decentralized detection where peripheral nodes make noisy observations of a phenomenon and send quantized information about the phenomenon towards a fusion center over a sum-rate constrained multiple access channel. The fusion center then makes a decision about the state of the phenomenon based on the aggregate received data. Using the Chernoff information as a performance metric, Chamberland and Veeravalli previously studied the structure of optimal rate allocation strategies for this scenario under the assumption of an unlimited number of sensors. Our key contribution is to extend these result to the case where there is a constraint on the maximum number of active sensors. In particular, we find sufficient conditions under which the uniform rate allocation is an optimal strategy, and then numerically verify that these conditions are satisfied for some relevant sensor design rules under a Gaussian observation model.Comment: Accepted at SPAWC 201

Distributed M-ary hypothesis testing for decision fusion in multiple-input multiple output wireless sensor networks

In this study, the authors study binary decision fusion over a shared Rayleigh fading channel with multiple antennas at the decision fusion centre (DFC) in wireless sensor networks. Three fusion rules are derived for the DFC in the case of distributed M-ary hypothesis testing, where M is the number of hypothesis to be classified. Namely, the optimum maximum a posteriori (MAP) rule, the augmented quadratic discriminant analysis (A-QDA) rule and MAP observation bound. A comparative simulation study is carried out between the proposed fusion rules in-terms of detection performance and receiver operating characteristic (ROC) curves, where several parameters are taken into account such as the number of antennas, number of local detectors, number of hypothesis and signal-to-noise ratio. Simulation results show that the optimum (MAP) rule has better detection performance than A-QDA rule. In addition, increasing the number of antennas will improve the detection performance up to a saturation level, while increasing the number of the hypothesis will deteriorate the detection performance

Massive MIMO for Wireless Sensing with a Coherent Multiple Access Channel

We consider the detection and estimation of a zero-mean Gaussian signal in a wireless sensor network with a coherent multiple access channel, when the fusion center (FC) is configured with a large number of antennas and the wireless channels between the sensor nodes and FC experience Rayleigh fading. For the detection problem, we study the Neyman-Pearson (NP) Detector and Energy Detector (ED), and find optimal values for the sensor transmission gains. For the NP detector which requires channel state information (CSI), we show that detection performance remains asymptotically constant with the number of FC antennas if the sensor transmit power decreases proportionally with the increase in the number of antennas. Performance bounds show that the benefit of multiple antennas at the FC disappears as the transmit power grows. The results of the NP detector are also generalized to the linear minimum mean squared error estimator. For the ED which does not require CSI, we derive optimal gains that maximize the deflection coefficient of the detector, and we show that a constant deflection can be asymptotically achieved if the sensor transmit power scales as the inverse square root of the number of FC antennas. Unlike the NP detector, for high sensor power the multi-antenna ED is observed to empirically have significantly better performance than the single-antenna implementation. A number of simulation results are included to validate the analysis.Comment: 32 pages, 6 figures, accepted by IEEE Transactions on Signal Processing, Feb. 201

Distributed Detection over Gaussian Multiple Access Channels with Constant Modulus Signaling

A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic function of the sensing noise and the error exponent for the system is derived using large deviation theory. Optimization of the deflection coefficient and error exponent are considered with respect to a transmission phase parameter for a variety of sensing noise distributions including impulsive ones. The proposed scheme is also favorably compared with existing amplify-and-forward and detect-and-forward schemes. The effect of fading is shown to be detrimental to the detection performance through a reduction in the deflection coefficient depending on the fading statistics. Simulations corroborate that the deflection coefficient and error exponent can be effectively used to optimize the error probability for a wide variety of sensing noise distributions.Comment: 30 pages, 12 figure

Distributed Detection over Fading MACs with Multiple Antennas at the Fusion Center

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean channels between the sensors and the fusion center when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the fusion center. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be no more than a factor of (8/pi) for Rayleigh fading channels between the sensors and the fusion center, independent of the number of antennas at the fusion center, or correlation among noise samples across sensors. Scaling laws for such gains are also provided when both sensors and antennas are increased simultaneously. Simple practical schemes and a numerical method using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.Comment: 21 pages, 9 figures, submitted to the IEEE Transactions on Signal Processin

Performance Analysis and Design of Maximum Ratio Combining in Channel-Aware MIMO Decision Fusion

In this paper we present a theoretical performance analysis of the maximum ratio combining (MRC) rule for channel-aware decision fusion over multiple-input multiple-output (MIMO) channels for (conditionally) dependent and independent local decisions. The system probabilities of false alarm and detection conditioned on the channel realization are derived in closed form and an approximated threshold choice is given. Furthermore, the channel-averaged (CA) performances are evaluated in terms of the CA system probabilities of false alarm and detection and the area under the receiver operating characteristic (ROC) through the closed form of the conditional moment generating function (MGF) of the MRC statistic, along with Gauss-Chebyshev (GC) quadrature rules. Furthermore, we derive the deflection coefficients in closed form, which are used for sensor threshold design. Finally, all the results are confirmed through Monte Carlo simulations.Comment: To appear in IEEE Transactions on Wireless Communication

Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors

In this paper, we design an optimal sensor collaboration strategy among neighboring nodes while tracking a time-varying parameter using wireless sensor networks in the presence of imperfect communication channels. The sensor network is assumed to be self-powered, where sensors are equipped with energy harvesters that replenish energy from the environment. In order to minimize the mean square estimation error of parameter tracking, we propose an online sensor collaboration policy subject to real-time energy harvesting constraints. The proposed energy allocation strategy is computationally light and only relies on the second-order statistics of the system parameters. For this, we first consider an offline non-convex optimization problem, which is solved exactly using semidefinite programming. Based on the offline solution, we design an online power allocation policy that requires minimal online computation and satisfies the dynamics of energy flow at each sensor. We prove that the proposed online policy is asymptotically equivalent to the optimal offline solution and show its convergence rate and robustness. We empirically show that the estimation performance of the proposed online scheme is better than that of the online scheme when channel state information about the dynamical system is available in the low SNR regime. Numerical results are conducted to demonstrate the effectiveness of our approach