Visualization of Large Wireless Network Behavior Using Random Matrix Theory

Recent works on the universality of Empirical Spectral Density (E.S.D) of Random Matrices have provided a framework to study the asymptotic behavior of random network data. In this paper, the behavior of a wireless campus network with low received base-station transmit power is investigated. Mobile users are organized into 10 clusters of 25 mobile users each and wireless IMT-Advanced Macro channel standard is used for the channel model. The network is simulated using Optimized Network Engineering Tools (OPNET) Modeler 17.5 platform and packet drop data is collected to form the entries of a non-hermittian random matrix. Data is collected for a duration of 400s during downlink transmission and analyzed for three scenarios namely. static mobile users with shadowing vs no shadowing, and network interference from a stealth jamming source. The result shows that for static nodes with shadowing and no-shadowing, the spectral density of packet drop covariance matrix follows Mareenko and Pastur (NIP) distribution and the Ring law accurately, but deviates considerably from MP distribution when the network is jammed using a pulsed jamming source. Outliers are also observed in the Ring-Law together with a shrinkage of eigenvalue distribution towards the center of the inner-circle of the Ring-Law when jammers are introduced into the network.