Abstract-We consider the problem of soft decision fusion in a bandwidth-constrained wireless sensor network (WSN). The WSN is tasked with the detection of an intruder transmitting an unknown signal over a fading channel. A binary hypothesis testing is performed using the soft decision of the sensor nodes (SNs). Using the likelihood ratio test, the optimal soft fusion rule at the fusion center (FC) has been shown to be the weighted distance from the soft decision mean under the null hypothesis. But as the optimal rule requires a-priori knowledge that is difficult to attain in practice, suboptimal fusion rules are proposed that are realizable in practice. We show how the effect of quantizing the test statistic can be mitigated by increasing the number of SN samples, i.e., bandwidth can be traded off against increased latency. The optimal power and bit allocation for the WSN is also derived. Simulation results show that SNs with good channels are allocated more bits, while SNs with poor channels are censored.
We consider distributed detection in a clustered wireless sensor network (WSN) deployed randomly in a large field for the purpose of intrusion detection. The WSN is modeled by a homogeneous Poisson point process. The sensor nodes (SNs) compute local decisions about the intruder's presence and send them to the cluster heads (CHs). A stochastic geometry framework is employed to derive the optimal cluster-based fusion rule (OCR), which is a weighted average of the local decision sum of each cluster. Interestingly, this structure reduces the effect of false alarm on the detection performance. Moreover, a generalized likelihood ratio test (GLRT) for cluster-based fusion (GCR) is developed to handle the case of unknown intruder's parameters. Simulation results show that the OCR performance is close to the Chair-Varshney rule. In fact, the latter benchmark can be reached by forming more clusters in the network without increasing the SN deployment intensity. Simulation results also show that the GCR performs very closely to the OCR when the number of clusters is large enough. The performance is further improved when the SN deployment intensity is increased.
Abstract-We address the problem of centralized detection of a binary event in the presence of falsifiable sensor nodes (SNs) (i.e., controlled by an attacker) for a bandwidth-constrained under−attack spatially uncorrelated distributed wireless sensor network (WSN). The SNs send their quantized test statistics over orthogonal channels to the fusion center (FC), which linearly combines them to reach a final decision. First (considering that the FC and the attacker do not act strategically), we derive (i) the FC optimal weight combining; (ii) the optimal SN to FC transmit power, and (iii) the test statistic quantization bits that maximize the probability of detection (P d ). We also derive an expression for the attacker strategy that causes the maximum possible FC degradation. But in these expressions, both the optimum FC strategy and the attacker strategy require a − priori knowledge that cannot be obtained in practice. The performance analysis of sub-optimum FC strategies is then characterized, and based on the (compromised) SNs willingness to collaborate, we also derive analytically the sub-optimum attacker strategies. Then, considering that the FC and the attacker now act strategically, we re-cast the problem as a minimax game between the FC and the attacker and prove that the Nash Equilibrium (NE) exists. Finally, we find this NE numerically in the simulation results and this gives insight into the detection performance of the proposed strategies.
In this paper we investigate fusion rules for distributed detection in large random clustered-wireless sensor networks (WSNs) with a three-tier hierarchy; the sensor nodes (SNs), the cluster heads (CHs) and the fusion center (FC). The CHs collect the SNs' local decisions and relay them to the FC that then fuses them to reach the ultimate decision. The SN-CH and the CH-FC channels suffer from additive white Gaussian noise (AWGN). In this context, we derive the optimal log-likelihood ratio (LLR) fusion rule, which turns out to be intractable. So, we develop a sub-optimal linear fusion rule (LFR) that weighs the cluster's data according to both its local detection performance and the quality of the communication channels. In order to implement it, we propose an approximate maximum likelihood based LFR (LFR-aML), which estimates the required parameters for the LFR. We also derive Gaussian-tail upper bounds for the detection and false alarms probabilities for the LFR. Furthermore, an optimal CH transmission power allocation strategy is developed by solving the Karush-Kuhn-Tucker (KKT) conditions for the related optimization problem. Extensive simulations show that the LFR attains a detection performance near to that of the optimal LLR and confirms the validity of the proposed upper bounds. Moreover, when compared to equal power allocation, simulations show that our proposed power allocation strategy achieves a significant power saving at the expense of a small reduction in the detection performance.
In this paper, we introduce a method to estimate the range of an intruder and track its trajectory by utilizing the received signal strength of the heat flux for pyroelectric infrared (PIR) sensors. To this end, we first develop a mathematical model of the received heat flux signal strength and the corresponding PIR signal for a moving intruder. The algorithm uses only two PIR sensors and the geometry of the field of views (FOVs) to perform the estimation and tracking process without any knowledge of the intruder's parameters. The tracking algorithm shows remarkable performance in estimating the intruder's parameters. The intruder heat flux was accurately estimated even at large separation distances as was the intruder path angle. Finally, the intruder's location was also very accurately estimated with sub-meter error for large separation distances.
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