IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. *, NO. *, MONTH YYYY 1 Quantizer Design for Generalized Locally-Optimum Detectors in Wireless Sensor Networks D. Ciuonzo, Senior Member, IEEE, and P. Salvo Rossi, Senior Member, IEEE Abstract—We tackle distributed detection of a non-cooperative (i.e. whose emitted power is unknown) target with a Wireless Sensor Network (WSN). When the target is present, sensors observe an (unknown) randomly-fluctuating signal with atten- uation depending on the distance between the sensor and the (unknown) target positions, embedded in Gaussian noise. The Fusion Center (FC) receives (only) sensor decisions through error-prone Binary Symmetric Channels (BSCs) and is in charge of performing a more-accurate global inference. The resulting test is one-sided with nuisance parameters (i.e. the target position) present only under the hypothesis H1. To reduce the complexity of Generalized Likelihood Ratio Test (GLRT), a generalized locally-optimum detection test (based on Davies’ framework) is investigated and a corresponding sensor threshold optimization (based on a semi-theoretical criterion) is developed and verified through simulations. Index Terms—Decentralized detection, threshold optimization, WSN, GLRT, locally-optimum detection, data fusion. I. I NTRODUCTION W IRELESS Sensor Networks (WSNs) have drawn huge interest given their applicability to several fields, with distributed detection being one key task [1]. Due to strict band- width and energy constraints, each sensor usually sends one bit about the estimated hypothesis to the Fusion Center (FC). In this case, the optimal per-sensor test (under Bayesian/Neyman- Pearson frameworks) is a one-bit quantization of the local Likelihood-Ratio Test (LRT) [2], [3]. However, the search for quantization thresholds is exponentially complex and lack of knowledge of the parameters of the target to be detected precludes LRT sensor computation [4]. Thus the bit sent is either the result of a “dumb” quantization [5], [6] or embodies the estimated binary event, based on a sub-optimal rule [7]. In both cases, sensors bits are collected by the FC and fused via an intelligently-designed rule to improve individ- ual detection rates; the optimum strategy, under conditional independence assumption, is a weighted sum, with weights depending on unknown target parameters [1]. Then, simple fusion approaches, based on the “counting rule” or simplified sensor assumptions, have been proposed to overcome such unavailability [8]–[11]. Indeed, the FC is faced to tackle a composite hypothesis test and the Generalized LRT (GLRT) is commonly employed [12]. To this end, GLRT-based fusion of Manuscript received 18th September 2017, accepted 9th October 2017. D. Ciuonzo is with Network Measurement and Monitoring (NM2) s.r.l., Naples, Italy. P. Salvo Rossi is with Kongsberg Digital, Trondheim, Norway. E-mail: {domenico.ciuonzo, salvorossi}@ieee.org. quantized data was studied in [5], [13], [14] for detecting: (i)a known source with unknown location, (ii) an unknown source with known observation coefficients, and (iii) an unknown source with unknown location. The latter case (i.e. the unco- operative target scenario) represents the most challenging, as it requires the least knowledge and one of the most interesting, given its applicability to surveillance [13], [14]. Also, to the best of our knowledge, only a few recent works have dealt with it. In [14], a GLRT was derived for this scenario and compared to the counting rule, the optimum rule and a “power- clairvoyant” GLRT, showing a marginal loss of GLRT with respect to the latter rule. Nevertheless, the GLRT requires a grid search on both the target location and emitted power domains, thus motivating the search for simpler fusion rules. Also, the test considered is one-sided with nuisance parameters present only under the alternative hypothesis, precluding the application of the usual Locally-Optimum Detection (LOD) test [12]. Hence, as a computationally simpler solution (i.e. not requiring a grid search for the target power), a Generalized LOD (G-LOD) test has been proposed in [15] and evaluated by simulations for a fixed value of local sensor thresholds. In this letter, we tackle the decentralized detection of a non-cooperative target with a spatially-dependent fluctu- ating signature, with emitted power modeled as unknown and deterministic [15]. Specifically, each sensor observes a measurement on the target absence/presence, whose received signal is buried in additive Gaussian noise and experiences an Amplitude Attenuation Function (AAF) depending on the sensor-target distance. Each node forwards a sensor-optimal decision to a FC, over imperfect reporting channels (modelled as Binary Symmetric Channels, BSCs), being in charge of providing a more accurate global decision. The FC adopts the G-LOD test in [15] as an appealing alternative to GLRT and a novel threshold optimization is here proposed, based on a semi–theoretical rationale obtained from (asymptotic) Position-Clairvoyant (PC) LOD performance, not obtained in [15]. The resulting optimization is per-sensor, accounts for sensor-FC channel status, and requires neither the target power nor its position, so it can be computed offline. Simulation re- sults are provided to compare the considered rules (and assess performance loss w.r.t. PC LOD) versus the local thresholds and verify the proposed design in a practical scenario. The letter is organized as follows: Sec. II describes the sys- tem model; Sec. III recalls GLR and G-LOD tests, whereas in Sec. IV we focus on quantizer optimization; finally simulation results and concluding remarks are given in Sec. V.