A THREE-STATE MARKOV CHANNEL MODEL WITH ACTIVE JAMMING FOR EVALUATING THE RESILIENCE OF ADAPTIVE COMMUNICATION PROTOCOLS

Abstract

The paper proposes a three-state Markov model of a wireless communication channel that explicitly accounts for active radio-electronic jamming (electronic warfare, EW). Classical channel models such as Gilbert–Elliott and Fritchman describe impulsive noise but do not reproduce long periodic blackouts caused by deliberate wideband jamming, which makes them inadequate for evaluating protocols in conditions of active EW. The proposed Gilbert–Elliott–Jamming (GEJ) model adds an explicit third state with near-unity packet-loss probability and its own transition sub-graph, while remaining analytically tractable. Closed-form expressions are derived for the stationary distribution as the principal left eigenvector of the transition matrix, for the mean recurrence time of the jamming state, and for the expected blackout duration. The model is calibrated on publicly available CRAWDAD/MERLIN-WiFi wireless traces using the Kolmogorov–Smirnov criterion: the GEJ approximation error is 0.07 versus 0.21 for the classical Gilbert–Elliott model that omits the jamming state, a three-fold reduction in approximation error that supports the position that an explicit jamming state is necessary for modelling channels under active EW. A comparative analysis with the Gilbert–Elliott, Fritchman, and hidden Markov channel models identifies the application domain of each and places GEJ at a useful design point that combines blackout reproduction with closed-form analytical convenience. The practical applicability of the model is demonstrated by deriving applicability bounds for Reed–Solomon codes RS(255, 231) and RS(255, 191) under four typical operating scenarios – stable Wi-Fi, mobile 4G, tactical channel, and active jamming. A sensitivity analysis of the stationary distribution with respect to the inter-state transition probabilities is provided, which is useful for protocol designers calibrating the model to a specific physical channel.

Keywords: active jamming, channel modelling, electronic warfare, Gilbert–Elliott model, Markov chain, stationary distribution, wireless communication