Impact of Secrecy on Capacity in Large-Scale Wireless Networks

Since wireless channel is vulnerable to eavesdroppers, the secrecy during message delivery is a major concern in many applications such as commercial, governmental and military networks. This paper investigates information-theoretic secrecy in large-scale networks and studies how capacity is affected by the secrecy constraint where the locations and channel state information (CSI) of eavesdroppers are both unknown. We consider two scenarios: 1) non-colluding case where eavesdroppers can only decode messages individually; and 2) colluding case where eavesdroppers can collude to decode a message. For the non-colluding case, we show that the network secrecy capacity is not affected in order-sense by the presence of eavesdroppers. For the colluding case, the per-node secrecy capacity of Theta(1/root n) can be achieved when the eavesdropper density psi(e)(n) is O(n(-beta)), for any constant beta > 0 and decreases monotonously as the density of eavesdroppers increases. The upper bounds on network secrecy capacity are derived for both cases and shown to be achievable by our scheme when psi(e)(n) = O(n(-beta)) or psi(e)(n) = beta(log(alpha-2/alpha)n), where alpha is the path loss gain. We show that there is a clear tradeoff between the security constraints and the achievable capacity.