Rashad Eletreby

Empowering Low-Power Wide Area Networks in Urban Settings

Low-Power Wide Area Networks (LP-WANs) are an attractive emerging platform to connect the Internet-of-things. LP-WANs enable low-cost devices with a 10-year battery to communicate at few kbps to a base station, kilometers away. But deploying LP-WANs in large urban environments is challenging, given the sheer density of nodes that causes interference, coupled with attenuation from buildings that limits signal range. Yet, state-of-the-art techniques to address these limitations demand inordinate hardware complexity at the base stations or clients, increasing their size and cost. This paper presents Choir, a system that overcomes challenges pertaining to density and range of urban LP-WANs despite the limited capabilities of base station and client hardware. First, Choir proposes a novel technique that aims to disentangle and decode large numbers of interfering transmissions at a simple, single-antenna LP-WAN base station. It does so, perhaps counter-intuitively, by taking the hardware imperfections of low-cost LP-WAN clients to its advantage. Second, Choir exploits the correlation of sensed data collected by LP-WAN nodes to collaboratively reach a faraway base station, even if individual clients are beyond its range. We implement and evaluate Choir on USRP N210 base stations serving a 10 square kilometer area surrounding Carnegie Mellon University campus. Our results reveal that Choir improves network throughput of commodity LP-WAN clients by 6.84 x and expands communication range by 2.65 x.

Node isolation of secure wireless sensor networks under a heterogeneous channel model

We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdős-Rényi graph. The former graph is naturally induced by the heterogeneous random key predistribution scheme while the latter graph constitutes a heterogeneous on/off channel model; wherein, the wireless channel between a class-i node and a class-j node is on with probability αij independently. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that it has no isolated node with high probability as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime.

Minimum node degree in inhomogeneous random key graphs with unreliable links

We consider wireless sensor networks under a heterogeneous random key predistribution scheme and an on-off channel model. The heterogeneous key predistribution scheme has recently been introduced by Yağan - as an extension to the Eschenauer and Gligor scheme - for the cases when the network consists of sensor nodes with varying level of resources and/or connectivity requirements, e.g., regular nodes vs. cluster heads. The network is modeled by the intersection of the inhomogeneous random key graph (induced by the heterogeneous scheme) with an Erdös-Rényi graph (induced by the on/off channel model). We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that with high probability all of its nodes are connected to at least k other nodes; i.e., the minimum node degree of the graph is no less than k. We also present numerical results to support our results in the finite-node regime. The numerical results suggest that the conditions that ensure k-connectivity coincide with those ensuring the minimum node degree being no less than k.

On the network reliability problem of the heterogeneous key predistribution scheme

We consider the network reliability problem in wireless sensor networks secured by the heterogeneous random key predistribution scheme. This scheme generalizes Eschenauer-Gligor scheme by considering the cases when the network comprises sensor nodes with varying level of resources; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted G(n; μ, K, P). We analyze the reliability of G(n; μ, K, P) against random link failures. Namely, we consider G(n; μ, K, P, α) formed by deleting each edge of G(n; μ, K, P) independently with probability 1-α, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions onK, P, and α such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We present numerical results to support these in the finite-node regime.

Connectivity of inhomogeneous random key graphs intersecting inhomogeneous Erdős-Rényi graphs

We study the connectivity of a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdős-Rényi graph. The former graph is naturally induced by a heterogeneous random key predistribution scheme introduced for securing wireless sensor network communications. In this scheme, nodes are divided into r classes according to a probability distribution μ = {μ<inf>1</inf>,…, μ<inf>r</inf>}, and a class-i sensor is assigned Ki cryptographic keys that are selected uniformly at random from a common pool of P keys. The latter graph represents a heterogeneous on/off channel model, where the wireless channel between a class-j node and a class-j node is on (resp. off) with probability α<inf>ij</inf> (resp. 1 − α<inf>ij</inf>) independently from others. We present conditions on how to scale the parameters of the intersection model so that it is connected with high probability as the number of nodes gets large. The result is given in the form of a zero-one law and is supported by a numerical study in the finite-node regime.

Secure and reliable connectivity in heterogeneous wireless sensor networks

We consider a wireless sensor network secured by a heterogeneous random key predistribution scheme and investigate its reliability against both link and node failures. The heterogeneous random key predistribution scheme is a lightweight security mechanism proposed to secure sensor networks that include nodes with varying levels of resources, features, or connectivity requirements; e.g., regular nodes vs. cluster heads. To capture the reliability of the network against both link and node failures, we consider the case when each link fails independently with probability 1 − α and present conditions (in the form of zero-one laws) on how to scale the parameters of the resulting network so that it is k-connected with high probability, i.e., the network remains connected even if any k − 1 nodes fail or leave the network. Collectively, we obtain a network that is reliable against the probabilistic failure of each link and against the failure of any k − 1 nodes. We present numerical results to support these conditions in the finite-node regime.