Signal Processing and Communications Group (SPCOM)

In this paper we study the convergence of consensus algo-rithms in wireless sensor networks with random topologies and instantaneous symmetric links which exist with different probabilities independently in time but correlated in space. Aiming at minimizing the convergence time of the algorithm, we adopt an optimization criterion based on the spectral ra-dius of a positive semidefinite matrix for which we derive a closed-form expression, and propose a general formulation for the spatial correlation among the links that allows us to compute the optimum parameters ensuring almost sure con-vergence. We show that our general formulation can be par-ticularized for existing protocols found in literature, and de-rive additionally closed-form expressions for the optimal pa-rameters in two particular cases of equal probability of con-nection for all the links. 1