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We consider the problem of multicasting information from a source to a destination over a multihop network of intermediate relays. However, some of the relays are untrustworthy and may be subject to eavesdropping. The source wishes to enlist their help while keeping the message secret against the eavesdropper. By employing random linear network coding at the relays, the problem is modeled as a noncoherent wiretap channel and is examined in terms of its secrecy capacity. The input distribution is optimized using an efficient projection-based gradient decent algorithm. The untrusted relay recruitment problem is also examined based on the derived secrecy capacity. An interesting scenario is analyzed where each potentially insecure relay may be randomly eavesdropped with a certain probability. Our asymptotic analysis reveals that, with enough untrusted relays, there exists a threshold on the eavesdropping probability below which all untrusted relays should be recruited.

Discriminatory channel estimation (DCE) is a secrecy-enhancing training and channel estimation technique previously proposed in the literature to enhance the effective channel quality difference between the main and the eavesdropper channels (i.e., the channels experienced by the legitimate receiver and the eavesdropper, respectively) in the channel estimation phase. In the past, this was achieved by developing techniques to first provide the transmitter with preliminary estimates of the main channel and by then emitting training signals that embed AN in the null space of the estimated main channel to disrupt the channel estimation at the eavesdropper. Extending upon previous works on DCE, this work proposes a general AN design that does not rely on the availability of the null space of the estimated main channel and, thus, does not require the transmitter to have more antennas than the receiver. In particular, the AN covariance matrix, the pilot signal power, and the linear estimator are jointly determined to minimize the channel estimation error at the receiver subject to a constraint below on the channel estimation error at the eavesdropper. The design is obtained by adopting an alternating optimization approach where the AN and pilot signals at the transmitter and the estimator at the receiver are optimized in turn until no further decrease in channel estimation error is observed. The effectiveness of the proposed scheme is demonstrated through computer simulations.

We consider the block Rayleigh fading multiple-input multiple-output (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant in a coherence time of T symbols, and then change to another independent realization. The transmitter, the legitimate receiver and the eavesdropper have n t , n r and n e antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2 min(n t , n r ). We show that, in this case, the s.d.o.f. is exactly (min(n t , n r ) - n e ) + (T - min(n t , n r ))/T. The first term can be interpreted as the eavesdropper with n e antennas taking away n e antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(n t , n r )/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.

In this paper, we consider the joint design of training and data transmission signals for wiretap channels where the transmitter is to send a secrect massage to the receiver without being intercepted by the eavesdropper. The celebrated secrecy beamforming scheme, which may or may not be assisted by artificial-noise (AN), is adopted in the data transmission phase to achieve this task. The achievable secrecy rate for practical systems with channel estimation error is first derived. Based on the achievable secrecy rate, we find the optimal tradeoff between the energy used for training and data signals. The optimal solutions in the low and high energy regimes are characterized analytically. We show that AN does not provide any advantages in the low energy regime, while it may have significant impact in the high energy regime. Numerical results are presented to verify our theoretical claims.