Analytical Derivation of Outage Correlation in Random Media Access with Application to Average Consensus in Wireless Networks: Extended Paper Version

Abstract: We study a finite and fixed relative formation of possibly mobile wireless networked nodes. The nodes apply average consensus to agree on a common value like the formation's center. %Performance of consensus in terms of convergence speed is affected by message losses due path loss and interference. We assume framed slotted ALOHA based broadcast communication. Our work has two contributions. First, we analyze outage correlation of random media access in wireless networks under Nakagami fading. Second, the correlation terms are applied to the so called L2-joint spectral and numerical radii to analyze convergence speed of average consensus under wireless broadcast communication. This yields a unified framework for studying joint optimization of control and network parameters for consensus subject to message losses in wireless communications. Exemplary we show in this work how far outage correlation in wireless broadcast communication positively affects convergence speed of average consensus compared to consensus in the uncorrelated case.