Deploy-As-You-Go Wireless Relay Placement: An Optimal Sequential Decision Approach using the Multi-Relay Channel Model

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of as-you-go deployment of relay nodes. The achievable rate formulas are for full-duplex radios at the relays and for decode-and-forward relaying. Deployment is done along the straight line joining a source node and a sink node at an unknown distance from the source. The problem is for a deployment agent to walk from the source to the sink, deploying relays as he walks, given that the distance to the sink is exponentially distributed with known mean. As a precursor, we apply the multi-relay channel achievable rate formula to obtain the optimal power allocation to relays placed along a line, at fixed locations. This permits us to obtain the optimal placement of a given number of nodes when the distance between the source and sink is given. Numerical work suggests that, at low attenuation, the relays are mostly clustered near the source in order to be able to cooperate, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that the effect of path-loss can be entirely mitigated if a large enough number of relays are placed uniformly between the source and the sink. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of as-you-go placement of relays along a line of exponentially distributed length, and with the exponential path-loss model, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, establish results for the value function, and provide insights into the placement policy and the performance of the deployed network via numerical exploration.Comment: 21 pages. arXiv admin note: substantial text overlap with arXiv:1204.432

Impromptu Deployment of Wireless Relay Networks: Experiences Along a Forest Trail

We are motivated by the problem of impromptu or as- you-go deployment of wireless sensor networks. As an application example, a person, starting from a sink node, walks along a forest trail, makes link quality measurements (with the previously placed nodes) at equally spaced locations, and deploys relays at some of these locations, so as to connect a sensor placed at some a priori unknown point on the trail with the sink node. In this paper, we report our experimental experiences with some as-you-go deployment algorithms. Two algorithms are based on Markov decision process (MDP) formulations; these require a radio propagation model. We also study purely measurement based strategies: one heuristic that is motivated by our MDP formulations, one asymptotically optimal learning algorithm, and one inspired by a popular heuristic. We extract a statistical model of the propagation along a forest trail from raw measurement data, implement the algorithms experimentally in the forest, and compare them. The results provide useful insights regarding the choice of the deployment algorithm and its parameters, and also demonstrate the necessity of a proper theoretical formulation.Comment: 7 pages, accepted in IEEE MASS 201

Sequential Decision Algorithms for Measurement-Based Impromptu Deployment of a Wireless Relay Network along a Line

We are motivated by the need, in some applications, for impromptu or as-you-go deployment of wireless sensor networks. A person walks along a line, starting from a sink node (e.g., a base-station), and proceeds towards a source node (e.g., a sensor) which is at an a priori unknown location. At equally spaced locations, he makes link quality measurements to the previous relay, and deploys relays at some of these locations, with the aim to connect the source to the sink by a multihop wireless path. In this paper, we consider two approaches for impromptu deployment: (i) the deployment agent can only move forward (which we call a pure as-you-go approach), and (ii) the deployment agent can make measurements over several consecutive steps before selecting a placement location among them (which we call an explore-forward approach). We consider a light traffic regime, and formulate the problem as a Markov decision process, where the trade-off is among the power used by the nodes, the outage probabilities in the links, and the number of relays placed per unit distance. We obtain the structures of the optimal policies for the pure as-you-go approach as well as for the explore-forward approach. We also consider natural heuristic algorithms, for comparison. Numerical examples show that the explore-forward approach significantly outperforms the pure as-you-go approach. Next, we propose two learning algorithms for the explore-forward approach, based on Stochastic Approximation, which asymptotically converge to the set of optimal policies, without using any knowledge of the radio propagation model. We demonstrate numerically that the learning algorithms can converge (as deployment progresses) to the set of optimal policies reasonably fast and, hence, can be practical, model-free algorithms for deployment over large regions.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1308.068

Optimal Capacity Relay Node Placement in a Multi-hop Wireless Network on a Line

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a sink node. The achievable rate formulas that we use are for full-duplex radios at the relays and decode- and-forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of impromptu ("as-you-go") placement of relays along a line of exponentially distributed length, with exponential path- loss, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, for which we prove results for the value function, and provide insights into the placement policy via numerical exploration.Comment: 22 pages, 12 figures; the initial version of this work was accepted in RAWNET 2012 (an workshop of WiOpt 2012); this is a substantial extension of the workshop pape

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs

Coverage Optimization with a Dynamic Network of Drone Relays

The integration of aerial base stations carried by drones in cellular networks offers promising opportunities to enhance the connectivity enjoyed by ground users. In this paper, we propose an optimization framework for the 3-D placement and repositioning of a fleet of drones with a realistic inter-drone interference model and drone connectivity constraints. We show how to maximize network coverage by means of an extremal-optimization algorithm. The design of our algorithm is based on a mixed-integer non-convex program formulation for a coverage problem that is NP-Complete, as we prove in the paper. We not only optimize drone positions in a 3-D space in polynomial time, but also assign flight routes solving an assignment problem and using a strong geometrical tool, namely Bézier curves, which are extremely useful for non-uniform and realistic topologies. Specifically, we propose to fly drones following Bézier curves to seek the chance of approaching to clusters of ground users. This enhances coverage over time while users and drones move. We assess the performance of our proposal for synthetic scenarios as well as realistic maps extracted from the topology of a capital city. We demonstrate that our framework is near-optimal and using Bézier curves increases coverage up to 47 percent while drones move