Decentralized Detection in Wireless Sensor Networks with Channel Fading Statistics

EURASIP Journal on Wireless Communications and Networking Hindawi Publishing Corporation Decentralized Detection in Wireless Sensor Networks with Channel Fading Statistics Bin Liu 0 Biao Chen 0 Recommended by C. C. Ko 0 Department of Electrical Engineering and Computer Science (EECS), Syracuse University , 223 Link Hall, Syracuse, NY 13244-1240 , USA Existing channel aware signal processing design for decentralized detection in wireless sensor networks typically assumes the clairvoyant case, that is, global channel state information (CSI) is known at the design stage. In this paper, we consider the distributed detection problem where only the channel fading statistics, instead of the instantaneous CSI, are available to the designer. We investigate the design of local decision rules for the following two cases: (1) fusion center has access to the instantaneous CSI; (2) fusion center does not have access to the instantaneous CSI. As expected, in both cases, the optimal local decision rules that minimize the error probability at the fusion center amount to a likelihood ratio test (LRT). Numerical analysis reveals that the detection performance appears to be more sensitive to the knowledge of CSI at the fusion center. The proposed design framework that utilizes only partial channel knowledge will enable distributed design of a decentralized detection wireless sensor system. 1. INTRODUCTION While study of decentralized decision making can be traced back to the early 1960s in the context of team decision problems (see, e.g., [1]), the effort significantly intensified since the seminal work of [2]. Classical distributed detection [3– 7], however, typically assumes error-free transmission between the local sensors and the fusion center. This is overly idealistic in the emerging systems with stringent resource and delay constraints, such as the wireless sensor network (WSN) with geographically dispersed lower-power low-cost sensor nodes. Accounting for nonideal transmission channels, channel aware signal processing for distributed detection problem has been developed in [8–10]. The optimal local decision rule was still shown to be a monotone likelihood ratio partition of its observation space, provided the observations were conditionally independent across the sensors. It was noted recently that such optimality is preserved for a more general setting [11]. The work in [8–10] assumed a clairvoyant case, that is, global information regarding the transmission channels between the local sensors and the fusion center is available at the design stage. This approach is theoretically significant as it provides the best achievable detection performance to which any suboptimal approach needs to be compared. However, its implementation requires the exact knowledge of global channel state information (CSI) which may be costly to acquire. In the case of fast fading channel, the sensor decision rules need to be synchronously updated for different channel states; this adds considerable overhead which may not be affordable in resource constrained systems. To make the channel aware design more practical, the requirement of the global CSI in the distributed signaling design needs to be relaxed. In the present work, only partial channel knowledge instead of the global CSI is assumed to be available. In the context of WSN, a reasonable assumption is the availability of channel fading statistics, which may remain stationary for a sufficiently long period of time. Therefore, the updating rate of the decision rules is more realistic. In this paper, we consider the distributed detection problem where the designer only has the channel fading statistics instead of the instantaneous CSI. In this case, a sensible performance measure is to use the average error probability at the fusion center where the averaging is performed with respect to the channel state. We restrict ourselves to binary local sensor outputs and derive the necessary conditions for optimal local decision rules that minimize the average error probability at the fusion center for the following two H0/H1 X1 XK Sensor 1 γ1 ... Sensor K γK U1 UK Channel g1 ... Channel gK Y1 YK Fusion center γ0 U0 cases: ( 1 ) CSIF: the fusion center has access to the instantaneous CSI. ( 2 ) NOCSIF: the fusion center does not have access to the instantaneous CSI. We note here that for the CSIF case, the design of sensor decision rules does not require CSI; the CSI is only used in the fusion rule design, which is reasonable due to the typical generous resource constraint at the fusion center. Its computation, however, is very involved and has to resort to exhaustive search. On the other hand, as to be elaborated, the NOCSIF case can be reduced to the channel aware design where one averages the channel transition probability with respect to the fading channel using the known fading statistics. We show that the sensor decision rules amount to local LRTs for both cases. Compared w (...truncated)