A physical layer average consensus algorithm for wireless sensor networks

We propose a consensus algorithm for distributed average computation in a decentralized wireless network. In contrast to gossip-based schemes that operate on the network layer, our scheme is performed on the physical layer and exploits the broadcast character of the wireless channel. For the proposed scheme the sensor nodes in the network are partitioned into two groups of nodes. The nodes of each group transmit their information simultaneously in a given time slot while the nodes of the opposite group process the received superposition of signals. Each node´s transmitted signal is constructed as a weighted sum of its received signals and its own data. The proposed scheme is energy efficient and associated with a moderate requirement in system overhead, e.g., associated with the acquisition of channel state information. Further, it offers fast convergence to the true mean of the sensor data in the network in a fully distributed manner.