Cross-Layer MAC Protocol for Unbiased Average Consensus Under Random Interference

Wireless Sensor Networks have been revealed as a powerful technology to solve many different problems through sensor nodes cooperation. One important cooperative process is the so-called average gossip algorithm, which constitutes a building block to perform many inference tasks in an efficient and distributed manner. From the theoretical designs proposed in most previous work, this algorithm requires instantaneous symmetric links in order to reach average consensus. However, in a realistic scenario wireless communications are subject to interferences and other environmental factors, which results in random instantaneous topologies that are, in general, asymmetric. Consequently, the estimation of the average obtained by the gossip algorithm is a random variable, which its realizations may significantly differ from the average value. In the present paper, we first derive a sufficient conditions for any MAC protocol to guarantee that the expected value of the obtained consensus random variable is the average of the initial values (unbiased estimator), while the variance of the estimator is minimum. Then, we propose a cross-layer and distributed link scheduling protocol based on carrier sense, which besides avoiding collisions, ensures both an unbiased estimation and close to minimum variance values. Extensive numerical results are presented to show the validity and efficiency of the proposed approach.