This work proposes a distributed sampling design for the signal detection application in the cluster-based wireless sensor networks (WSNs). Considering the energy saving require- ment in the cluster-based WSNs, a linear weighting data fusion scheme for data reduction at the cluster head is also developed in this paper. Both the distributed sampling and the data reduction schemes are designed based on Ali-Silvey distance measures. The objective functions are derived in a closed form and two numerical examples are presented to illustrate our distributed sampling design and data reduction scheme. Numerical results show that our sampling design outperforms the uniform sampling and is insensitive to the sampling jitter. The results also show that the performance loss caused by the data reduction is quiet small. Therefore, the proposed schemes are very suitable for the detection applications in battery-powered WSNs. Index Terms—Distributed sampling, Ali-Silvey distance, detec- tion, data fusion, sensor networks This work studies the distributed sampling design for the detection application in wireless sensor networks (WSNs). WSNs should be energy efficient due to the use of battery- powered sensor nodes. Cluster-based mechanism has been proposed to conserve the energy consumption in WSNs (1). In the cluster-based WSNs, nodes are organized into a number of clusters and the nodes within a cluster collaboratively sense the environment and the cluster head relays the sensing information to the destination or other cluster heads. In this topology, the distance between the nodes and their associated cluster head is much shorter than that between the cluster head and the destination or other cluster heads. Therefore, to conserve the communication energy, it is better for the cluster head to fuse the sensing messages collected from sensor nodes and reduce the amount of sensing information before transmitting the messages. In most situations, sensor observations are continuous-time in nature and need to be sampled into discrete-time samples. Sampling design for the Gaussian detection problem has been studied in (2)-(5), where the received signals under hypotheses H1 and H0 were Gaussian random processes. Both random and deterministic sampling schemes for the detection of known signals in Gaussian noise were considered in (2). Using the decision statistic based on the sampled data, instead of the continuous-time detector (matched filter or correlation receiver), naturally results in a degradation of performance. Deterministic and random sampling schemes were designed so as to minimize the degradation in the performance of the detector. In (3), an asymptotically optimal periodic sampling design for the Gaussian hypothesis testing problem was pre- sented. Under very general conditions, the probabilities of error decrease exponentially with increasing sample size. For this problem, an asymptotically optimal periodic sampling scheme was designed by maximizing the rate of exponential decrease. In (4), a universal approach based on the Ali-Silvey distance measure (ASDM) for the design of sampling schemes for Gaussian hypothesis testing problems was presented. In the strong signal case, sampling points were determined that max- imize the distance measures between the conditional densities. In the weak signal case, a new member of the class of ASDMs suitable for the weak Gaussian signal detection problem was developed. The sampling scheme was designed by maximizing the distance measure. A sampling design for weak signal detection in additive spherically invariant random process (SIRP) noise was also presented in (5). A new member of the class of ASDMs suitable for this problem was developed. It was also numerically shown that the sampling design is insensitive to the statistics (the characteristic PDF) of the SIRP noise samples.
['Tsang-Yi Wang', 'Yu Cj', 'Chih-Hao Tai']
Distributed Sampling Design and Data Fusion for Signal Detection in Cluster-Based Sensor Networks