  Cooperative relaying is often deployed to enhance the communication
reliability (i.e., diversity order) and consequently the end-to-end achievable
rate. However, this raises several security concerns when the relays are
untrusted since they may have access to the relayed message. In this paper, we
study the achievable secrecy diversity order of cooperative networks with
untrusted relays. In particular, we consider a network with an N-antenna
transmitter (Alice), K single-antenna relays, and a single-antenna destination
(Bob). We consider the general scenario where there is no relation between N
and K, and therefore K can be larger than N. Alice and Bob are assumed to be
far away from each other, and all communication is done through the relays,
i.e., there is no direct link. Providing secure communication while enhancing
the diversity order has been shown to be very challenging. In fact, it has been
shown in the literature that the maximum achievable secrecy diversity order for
the adopted system model is one (while using artificial noise jamming). In this
paper, we adopt a nonlinear interference alignment scheme that we have proposed
recently to transmit the signals from Alice to Bob. We analyze the proposed
scheme in terms of the achievable secrecy rate and secrecy diversity order.
Assuming Gaussian inputs, we derive an explicit expression for the achievable
secrecy rate and show analytically that a secrecy diversity order of up to
min(N,K)-1 can be achieved using the proposed technique. We provide several
numerical examples to validate the obtained analytical results and demonstrate
the superiority of the proposed technique to its counterparts that exist in the
literature.
