Received signal strength in large-scale wireless relay sensor network: A stochastic ray approach

The authors consider a point percolation lattice representation of a large-scale wireless relay sensor network (WRSN) deployed in a cluttered environment. Each relay sensor corresponds to a grid point in the random lattice and the signal sent by the source is modelled as an ensemble of photons that spread in the space, which may 'hit' other sensors and are 'scattered' around. At each hit, the relay node forwards the received signal to its nearest neighbour through direction-selective relaying. The authors first derive the distribution that a relay path reaches a prescribed location after undergoing certain number of hops. Subsequently, a closed-form expression of the average received signal strength (RSS) at the destination can be computed as the summation of all signal echoes' energy. Finally, the effect of the anomalous diffusion exponent β on the mean RSS in a WRSN is studied, for which it is found that the RSS scaling exponent ε is given by (3β-1)/β. The results would provide useful insight into the design and deployment of large-scale WRSNs in future.