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 the knowledge of the wireless path-loss model, and given that the distance to the sink node is exponentially distributed with known mean. As a precursor to the formulation of the deploy-as-you-go problem, 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 for the fixed source-sink distance case suggests 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. 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.