Jamming-Resilient Physical-to-Virtual Communications in Digital Twin Edge Networks

As an integration of digital twin and edge computing, the digital twin edge networks (DITENs) have been proposed in recent years to fill the gap between physical edge networks and digital systems. Meanwhile, the multi-access wireless environments in edge computing make it hard to provide ultra-reliable and low-latency communications for digital twin, especially when the jamming attacks can be launched by the adversaries. This paper studies the jamming-resilient physical-to-virtual communication (PTVC) problem in DITENs despite strong cooperative jamming. Note that the previous jamming models mainly focus on the jamming behaviors from individual adversaries and are restricted by the energy budget limitation and uniform jamming assumption. In this paper, we consider a more comprehensive jamming model, in which <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> adversaries can cooperatively launch their jamming attacks in totally <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> wireless channels with unlimited power budget and non-uniform jamming signals. Then, based on the new proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k,f)$ </tex-math></inline-formula>-cooperative jamming model, we show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k\gt f$ </tex-math></inline-formula> is the necessary and also sufficient condition to solve the PTVC problem. On one hand, we prove that the PTVC problem is insoluble when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f\leq k$ </tex-math></inline-formula>; on the other hand, two distributed algorithms are given as the solutions of the PTVC problem among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> physical objectives and one sink node when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k\gt f$ </tex-math></inline-formula>, the time complexity of which are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\frac {n \log n}{k (\log k-\log f)}}}\right)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\frac {n \log n}{\log k-\log f}}}\right)$ </tex-math></inline-formula> based on the communication modes with/without acknowledgement, respectively. Both of the theoretical results and empirical simulations are conducted to show the resilience of our algorithms despite such a strong cooperative jamming model.