We study a heterogeneous Rayleigh fading wireless sensor network (WSN) in
which densely deployed sensor nodes monitor an environment and transmit their
sensed information to base stations (BSs) using access points (APs) as relays
to facilitate the data transfer. We consider both large-scale and small-scale
propagation effects in our system model and formulate the node deployment
problem as an optimization problem aimed at minimizing the wireless
communication network's power consumption. By imposing a desired outage
probability constraint on all communication channels, we derive the necessary
conditions for the optimal deployment that not only minimize the power
consumption, but also guarantee all wireless links to have an outage
probability below the given threshold. In addition, we study the necessary
conditions for an optimal deployment given ergodic capacity constraints. We
compare our node deployment algorithms with similar algorithms in the
literature and demonstrate their efficacy and superiority