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 ` on the mean RSS in a WRSN is studied, for which it is found that the RSS scaling exponent ` is given by (3``1)/`. The results would provide useful insight into the design and deployment of large-scale WRSNs in future.