Unbiased consensus in wireless networks via collisional random broadcast and its application on distributed optimization

•Unbiased consensus is achieved via random broadcast gossip in any connected topology.•Consider the possible collisions on receivers in a shared wireless channel.•Propose a distributed optimization algorithm by combining random broadcast gossip and local gradient descent.

We first propose an unbiased consensus algorithm in wireless networks via random broadcast, by which all the nodes tend to the initial average in mean almost surely. The innovation of the algorithm lies in that it can work in any connected topology, in spite of the possible collisions from simultaneous data arriving at receivers in a shared channel. Based on the consensus algorithm, we propose a distributed optimization algorithm for a sum of convex objective functions, which is the fundamental model for many applications on signal processing in network. Simulation results show that our algorithms provide an appealing performance with lower communicational complexity compared with existing algorithms.