Scaling Laws for Secrecy Capacity in Cooperative Wireless Networks

We investigate large wireless networks subject to security constraints. In contrast to point-to-point, interference-limited communications considered in prior works, we propose active cooperative relaying based schemes. We consider a network with $n_l$ legitimate nodes, $n_e$ eavesdroppers, and path loss exponent $\alpha\geq 2$. As long as $n_e^2(\log(n_e))^{\gamma}=o(n_l)$, for some positive $\gamma$, we show one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given fixed total power constraint for the entire network. We achieve this result through (i) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays and (ii) the relays acting as a virtual multi-antenna to apply beamforming against the eavesdroppers. Our simpler parallel (two-stage) relaying scheme can achieve the same unbounded secure aggregate rate when $n_e^{\frac{\alpha}{2}+1}(\log(n_e))^{\gamma+\delta(\frac{\alpha}{2}+1)}=o(n_l)$ holds, for some positive $\gamma,\delta$.