Bandwidth-efficient Decentralized Detection For Wireless Sensor Networks

We consider a decentralized detection problem in which a number of sensor nodescollaborate to detect the presence of an unknown deterministic signal. To cope with thepower/bandwidth constraints inherent in wireless sensor networks (WSNs), eachsensor node needs to locally process its observations in order to reduce the amount ofinformation being transmitted. The local processed messages are then transmitted tothe fusion center (FC) via wireless channel, where a global decision is made byresorting to a generalized likelihood ratio test (GLRT) based on the received signal.Two local processing methods are introduced in this paper, namely, linear precodingmethod and quantization method.For linear precoding method, the aim is to develop effective linear precodingstrategies and GLRT detector based on precoding scheme, then study their detectionperformance under the asymptotic regime where the number of sensors tends to infinity,i.e., N π. Two precoding strategies are introduced in this paper: a randomprecoding scheme which generates its precoding vectors following a Gaussiandistribution, and a sign-assisted random precoding scheme which assumes theknowledge of the plus/minus signs of the signal components and designs its precodingvectors with the aid of this prior knowledge. The multidimensional observations arecompressed into a dimension signal using a linear precoder, thus dimension reductionand precoding are treated the same in this paper.Performance analysis shows that utilizing the sign information can radicallyimprove the detection performance. Also, it is found that precoding-based schemes aremore effective than the energy detector in detecting weak signals that are buried innoise. Specifically, the sign-assisted random precoding scheme achieves a significantperformance advantage over the energy detector when the observation signal-to-noiseratio (SNR) is less than1π/2. Numerical results are conducted to corroborate ourtheoretical analysis and to illustrate the effectiveness of the proposed algorithms. For quantization method, a one-bit quantization method is introduced. Each sensornode quantizes its local observations into one bit of information. The binary data aresent to the fusion center, where a GLRT detector is employed to make a global decision.In this context, we study one-bit quantizer design, and analyze the asymptoticperformance of the one-bit GLRT detector for cases where the quantized data are sentto the FC via perfect or imperfect channels.Our theoretical analysis and simulation experiments indicate that the proposedone-bit GLRT scheme can achieve the same detection performance as a clairvoyantdetector by slightly increase the number of sensors by a factor of π/2. The one-bitscheme only needs to transmit a total number of πN/2bits, while the clairvoyantdetector requires sending N real-valued messages to the FC.