Optimal Secrecy Capacity-Delay Tradeoff in Large-Scale Mobile Ad Hoc Networks

In this paper, we investigate the impact of information-theoretic secrecy constraint on the capacity and delay of mobile ad hoc networks (MANETs) with mobile legitimate nodes and static eavesdroppers whose location and channel state information (CSI) are both unknown. We assume n legitimate nodes move according to the fast i.i.d. mobility pattern and each desires to communicate with one randomly selected destination node. There are also n
^ν
static eavesdroppers located uniformly in the network and we assume the number of eavesdroppers is much larger than that of legitimate nodes, i.e., ν > 1. We propose a novel simple secure communication model, i.e., the secure protocol model, and prove its equivalence to the widely accepted secure physical model under a few technical assumptions. Based on the proposed model, a framework of analyzing the secrecy capacity and delay in MANETs is established. Given a delay constraint D, we find that the optimal secrecy throughput capacity is ~Θ(W((D/n))
^(2/3)
), where W is the data rate of each link. We observe that: 1) the capacity-delay tradeoff is independent of the number of eavesdroppers, which indicates that adding more eavesdroppers will not degenerate the performance of the legitimate network as long as ν > 1; 2) the capacity-delay tradeoff of our paper outperforms the previous result Θ((1/nψe)) in , where ψe=n
^ν-1
=ω(1) is the density of the eavesdroppers. Throughout this paper, for functions f(n) and g(n), we denote f(n)=o(g(n)) if limn→∞(f(n)/g(n))=0; f(n)=ω(g(n)) if g(n)=o(f(n)); f(n)=O(g(n)) if there is a positive constant c such that f(n) ≤ cg(n) for sufficiently large n; f(n)=Ω(g(n)) if g(n)=O(f(n)); f(n)=Θ(g(n)) if both f(n)=O(g(n)) and f(n)=Ω(g(n)) hold. Besides, the order notation ~Θ omits the polylogarithmic factors for better readability.