A Cross-Layer Approach to Decentralized Detection in Sensor Networks with Noisy Communication Links and Multiple Observations †

This paper presents a general approach to distributed detection in sensor networks in scenarios with noi sy communication links between the sensors and the fusion cent er (or access point, AP). The sensors are independent and obser v a common phenomenon. While in most of the literature the performance metrics usually considered are missed detecti on and false alarm probabilities, in this paper we follow a Bayesian approach for the evaluation of the probability of decision error at the AP. We first derive an optimized fusion rule at the AP in a scenario with ideal communication links. We then consider the presence of noisy links and model them as binary symmetri c channels (BSCs). In this case, we show that if the noise inten sity is above a critical level (i.e., the cross-over probabilityof the BSC is above a critical value), the probability of decision error at the AP reduces when the AP selectively discards the information transmitted by the sensors with noisy links. We will also sho w that use of multiple observations at the sensors can be trade for increased robustness against channel impairments in th e communication links. I. I NTRODUCTION Distributed detection has been an active research field for a long time [1]. In particular, several approaches have been proposed to study this problem, in the realms of information theory [2], target recognition [3], [4], and several other a reas. The increasing interest, over the last decade, for sensor ne tworks, has spurred a significant research activity on distri buted detection techniques in this context [5]–[8]. In recent years, wireless sensor networks are becoming more common, as, for example, in terrain monitoring applications [9]. In a wireless communication scenario, link s between sensors and the access point (AP) are likely to be faded [10]. In this case, most of the results proposed in the literature are not immediately applicable, since they are b ased on the assumption that communication links between sensors and AP are “ideal,” i.e., the information transmitted by sen sors is received correctly by the AP. The characteristics (in ter ms of capacity) of the multiple access radio channel in wireles s sensor networks are taken into account in [11], where optima l configurations for decentralized detection are studied. In this paper, we first revisit the basic principles of distributed detection with binary decisions at the sensors. In This work was supported in part by Ministero dell’Istruzion e, Università e Ricerca (MIUR), Italy, under the PRIN project “CRIMSON” (C ooperative Remote Interconnected Measurement Systems Over Networks) . order to model a scenario where some of the links between sensors and AP are non-ideal (e.g., some of links in a wireles s sensor network may be faded), we assume that a link can be modeled as a binary symmetric channel (BSC) [12]. We show that selective elimination of noisy links may lead to a performance improvement when the cross-over (or bitflipping) probability of the BSC increases. In particular, for each value of the common signal-to-noise ratio (SNR) at the sensors we determine a critical bit-flipping probability wh ich discriminates between two network operating regimes: for values of the bit-flipping probability above this value, the best performance is obtained when the AP excludes the sensors with noisy links. We will also show that the use of multiple observations at each sensor, as proposed in [13], increases the robustness of the network against impairments in the communication links. More precisely, increasing the numbe r of observations at the sensor increases the value of the crit ical bit-flipping probability discriminating for selective exc lusion of the sensors with noisy links. A strategy based on selectiv exclusion of sensors with noisy links could be obtained by using a clever medium access control (MAC) protocol at the AP. Therefore, our results suggest that the use of a cross-layer approach to the design of sensor networks with unreliable communication links (e.g., wireless sensor networks) may b e an advantage. This paper is structured as follows. In Section II, we provid e the reader with preliminaries on distributed detection pri nciples, referring to a classical distributed detection schem e, with parallel schedule. In Section III, the presence of noisy links, modeled as BSCs, is considered, and the corresponding senso r network performance, with single and multiple observation s at the sensors, is analyzed. Conclusions and future researc h directions are presented in Section IV. II. PRELIMINARIES ON DISTRIBUTED DETECTION We consider a classical sensor network scenario where all sensors are connected to a single AP [5]. Two main approaches for combining the information gathered by multiple sensors have been proposed. • The first approach is referred to as centralized: all sensors observations are transmitted to a central processor that performs a global decision. • The second approach is referred to as decentralized: each sensor makes a local decision and transmits it to a fusion processor, i.e., the AP, which makes the final decision, by applying a suitablefusion rule. In this paper, all sensors make at least oneobservation of a common binary phenomenon. In other words, we consider the binary hypothesis signal detection problem [14], with stat i ically independent observations from sensor to sensor. We wi ll refer to the two hypotheses as H1 andH0, respectively. The true hypothesis will be simply denoted as H . We will assume that the two hypotheses are equally likely. The extension of this work to the case of correlated sensors [15] is currently under investigation. We assume that there are N sensors. The discrete-time observation at thei-th sensor can be expressed as