## 1 Introduction
### Related Works  
Backscattering communications have traditionally found their main application field in RFID systems. In that context, cross-layer frameworks for mono-static ALOHA-based systems have been proposed to analyze and optimize the identification performance metrics, such as identification time. Refs. [15; 16; 17; 18] propose the analysis and optimization of slotted ALOHA channel access schemes in the presence of the capture effect [19]. However, in the aforementioned studies the capture probability is given as a model parameter, thus resulting in a strong abstraction of the underlying channel. Furthermore, power outage, which is a peculiar limitation for passive communication devices, is not taken into account. The capture effect and the effect of fading spatial correlation on mono-static RFID systems have been studied in [20], based on a more realistic propagation channel model. In [21] the first and second order statistics of the fading are derived for both time-invariant and time-variant channels and used to build a Markov chain model of an ALOHA-based RFID system. A theoretical analysis of throughput and bit error rate for multi-tag systems, including propagation channel statistics, has been performed in [22]. Capture effect has also been included in recent studies dealing with cross-layer performance analysis of ALOHA-type one-way communications. For instance, in [23], the combined effect of interference cancellation, packet segmentation, slot slicing and capture is analyzed by means of a theoretical framework that allows to derive capture probability in both fast and slow Rayleigh fading conditions. To overcome inherent coverage limitations of mono-static backscattering systems, multi-static architectures have been proposed, where a set of networked illuminators/readers operate either cooperatively or concurrently to identify a population of passive tags. In [24; 25] the authors deal with the derivation of a stable readers scheduling algorithm that is designed for dynamic environments, where the number of arriving tags in the illumination area changes over time. In [26] a heuristic multi-channel scheduling algorithm for coordination of multiple readers is derived with the advantage of being adaptable to existing multiple access schemes for single reader scenarios. In [27], an optimization-based distributed scheme is proposed in order to avoid unpractical centralized coordination mechanisms among readers. In [28], an approach based on readers' cooperation is proposed to handle collisions. The recent work in [29] proposes a novel reader scheduling policy that substantially outperforms state of the art solutions. Finally, a novel Code Division Multiple Access (CDMA) collaborative protocol for multi-reader RFID systems is proposed in [30], where the CDMA paradigm is exploited to combat reader-to-reader interference. Nevertheless, all the aforementioned studies focus on the derivation of scheduling policies to resolve interference among readers and do consider neither physical layer peculiarities nor cross-layer interactions. Furthermore, the reception diversity opportunity offered by the multi-static setting is not considered. The recent study in [9] proposes a framework for multi-static backscattering systems that includes accurate models for the physical layer and the propagation channel, and is not limited to RFID applications. Transmit diversity is considered in order to extend the system coverage. A comprehensive analysis is conducted,which includes the derivation of Bit Error Rate (BER) performance bounds, information and energy outage probabilities. The theoretical analysis is then corroborated by experimental demonstration of overall performance improvements of multi-static systems over the mono-static counterpart. In [31] a multi-static RFID architecture is proposed, where MAC layer operations are distributed over a set of networked Software Defined Radio (SDR) illuminators.