Secrecy Capacity Scaling in Large 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 nl legitimate nodes, ne eavesdroppers, and path loss exponent α ≥ 2. As long as n
_e
²
(log(n
_e
))
^γ
= o(n
_l
), for some positive γ, we show that 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: 1) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays and 2) 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
^α/2+1
(log(n
_e
))
^{γ +δ(α/2+1)}
= o(n
_l
) holds, for some positive γ, δ. Finally, we study the improvement (to the detriment of legitimate nodes) that the eavesdroppers achieve in terms of the information leakage rate in a large cooperative network in the case of collusion. We show that again the zero-cost secure communication is possible, if n
_e
^(2+2/α)
(log n
_e
)
^γ
= o(n
_l
) holds, e for some positive γ; that is, in the case of collusion slightly fewer eavesdroppers can be tolerated compared with the non-colluding case.