Decision Fusion Rules in Ambient Backscatter Wireless Sensor Networks Domenico Ciuonzo, 1 Giacinto Gelli, 1 Antonio Pescapé, 1,2 and Francesco Verde 1 1 University of Naples Federico II (Italy) and 2 NM2 s.r.l. (Italy) {domenico.ciuonzo, gelli, pescape, f.verde}@unina.it Abstract—Ambient backscatter (AmBC) communications cap- italize on ambient radio-frequency (RF) signals to enable com- munications among ultra-low-power devices, thus representing a promising cost-effective solution for wireless sensor networks in the Internet of Things. In this paper, we study the scenario where single-antenna AmBC sensors are employed to perform decision fusion over multiple-access fading channels. Specifically, AmBC sensors detect the presence/absence of a phenomenon of interest and transmit their decisions to a multiple-antenna fusion center reader (FCR), by reflecting part of an incident RF ambient signal. In this scenario, we derive fusion rules at the FCR by considering both the cases of instantaneous and statistical channel state information, as well as their corresponding low- complexity alternatives. Numerical simulation results are provided to compare the proposed fusion rules and highlight the relevant trends. I. I NTRODUCTION With the advent of the Internet of Things (IoT) paradigm, billions of tiny devices with sensing, computation, and commu- nicating capabilities are expected to be used in numerous areas of everyday life [1], such as connected industry, smart cities and homes, smart-energy, connected car, smart-agriculture, healthcare, etc. In many of these domains, such devices are required not only to use existing Internet standards to pro- vide services for information transfer, analytics, applications, and communications, but also to sense information from the environment by interacting with the physical world. In these applications, spatially separated devices, referred to as sensors, are used to form a wireless sensor network (WSN), whose aim is usually to distinguish between two hypotheses, such as the absence or presence of a certain phenomenon of interest (POI) [2]. Specifically, each sensor performs a local observation of the POI and, after a limited processing, transmits the result to a fusion center (FC), which combines the received signals to calculate a global decision: the overall process is known as decision (or information) fusion [2]. Decision fusion has been mainly studied assuming that sensors are active [3, 4, 5, 6] units, i.e., they are equipped with active radio-frequency (RF) components and other signal conditioning units. In these applications, sensors can directly radiate their outputs to the FC through parallel [3, 6] or multiple access channels [4, 5], by using either digital [3, 4, 6] or This work ha been partially funded by GRISIS project (CUP: B63D180002800079), DD MIUR prot.368 of 24/10/2018, Programma Opera- tivo FESR Campania 2014-2020. analog processing methods [5]. Also, to counteract the adverse effects of channel fading and, hence, improve decision fusion performance, multiple antennas have been employed at the FC [4, 5], thus creating a virtual multiple-input multiple-output (MIMO) channel between the single-antenna sensors and the multiple-antenna FC. However, in many applications, active sensors have a limited lifetime since they use a small battery as an internal power source, leading to high maintenance costs. The lifetime of battery-powered active sensors can be in- creased by minimizing network power consumption [7, 8] or using an energy harvester at the sensor nodes to convert RF power into direct current (DC) power [6]. In the former approaches, whose aim is to minimize the WSN energy expen- diture, network lifetime remains bounded and finite and, also, such solutions cannot be used in situations where recharging or replacement of sensors’ batteries is too costly. Differently, harvesting energy from external sources can be a solution to improve WSN lifetime. However, since active sensors are power consuming and, thus, quickly waste the harvested RF energy, their duty cycle might be significantly lowered. Unlike conventional WSNs, which employ active radio de- vices, backscatter networks [9] are emerging as an interesting solution to support massive low-power IoT applications, since they modulate information by reflecting RF signals, without requiring power-consuming and expensive radio analog com- ponents. Recently, a novel transmission paradigm, referred to as ambient backscatter (AmBC) communication, has been attracting much attention [10, 11, 12, 13]. AmBC techniques work by exploiting ambient or legacy RF signals (such as TV, radio, cellular, or Wi-Fi systems) and, since signal reflection consumes only a very-small power [9], they have the potential to design lifespan-unlimited ultra-low-power WSNs. To the best of our knowledge, the problem of the fusion of local decisions in WSN employing AmBC sensors has not been studied yet. To fill this gap, the objective of this work is to extend the classical decision fusion framework for active devices [2, 3] to a multiple-access WSN composed of AmBC single-antenna sensors that simultaneously transmit to a multiple-antenna FC reader (FCR). Specifically, we consider two relevant scenarios: in the former one, referred to as full channel state information (F-CSI) scenario, the FCR has perfect knowledge of the instantaneous values of all the relevant channels; in the latter one, referred to as statistical channel