Abstract
This dissertation examines the transmission of confidential messages over a wireless wiretap system with no a priori channel state information (CSI) at any terminal. The studies can be divided into two parts. The first part focuses on conventional training-based transmissions schemes and examines the tradeoff between training and data transmission in wiretap channels; the second part makes no assumption on the transmission scheme and evaluates the asymptotic performance of such a system at high SNR. More specifically, in the first part, training-based transmission schemes are considered for multi-input single-output (MISO) Rayleigh block fading wiretap channels, where each block consists of a training phase followed by a data transmission phase. By taking the cost of obtaining CSI into account, this work considers the joint design of training and data transmission in physical-layer secret communication systems, and examines the role of artificial noise (AN), a key component in many physical layer secret communication techniques, in both of these phases. In particular, AN in the training phase is used to prevent the eavesdropper from obtaining accurate CSI whereas AN in the data transmission phase can be used to mask the transmission of the confidential message. By considering AN-assisted training and secrecy beamforming schemes, upper and lower bounds on the achievable secrecy rate is derived in a closed-form approximation that is asymptotically tight at high signal-to-noise ratio (SNR). Then, by maximizing the approximate achievable secrecy rate, the optimal power allocation between signal and AN in both training and data transmission phases is obtained for both conventional and AN-assisted training based schemes. We show that the use of AN is necessary to achieve a high secrecy rate at high SNR, and its use in the training phase can be more efficient than that in the data transmission phase when the coherence time is large. However, at low SNR, the use of AN provides no advantage since CSI is difficult to obtain in this case. In fact, allocating channel resources for training is inefficient and one can actually do better without it in this case. Numerical results are presented to verify our theoretical claims. Even though training-based transmission schemes have been widely adopted in practice, the optimality of such an approach is unknown and is in fact disproved in conjunction with the secrecy beamforming scheme mentioned in the first part. Therefore, a more general and fundamental study of the wiretap channel with no CSI anywhere is considered in the second part of this dissertation. In particular, we consider a multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel where the source, the destination, and the eavesdropper have nt, nr and ne antennas, respectively. The length of the coherence interval, where the channel coefficients remain constant within each interval, but vary independently from block to block, is denoted by T. The performance at high SNR is evaluated in terms of the secure degrees of freedom (s.d.o.f.), when T ≥ 2 min(nt, nr). We show that, in this case, the s.d.o.f. is exactly equal to (min(nt, nr)−ne)(T−min(nt, nr))/T . The first multiplicative term in this expression can be interpreted as the loss of ne spatial degrees of freedom at both the transmitter and the legitimate receiver due to the ne receive antennas at the eavesdropper. The second term can be viewed as the ratio of s.d.o.f. remaining after expending resources to acquire CSI at the legitimate receiver. 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. We also show that multiple dimensions in both space and time are needed to achieve a non-zero s.d.o.f. for systems without CSI. That is, one cannot achieve a positive s.d.o.f. with either a long coherence time in a single antenna system or with multiple antennas in a very short (T = 1) coherence time channel. The techniques developed in the second part is also used to examine the performance of a noncoherent network coding system with multiple hops of intermediate relays. A relay recruitment problem is considered for the case where 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 can be modeled as a noncoherent finite-field wiretap channel. The secrecy capacity is examined and the input distribution is optimized using an efficient projection-based gradient decent algorithm. The untrusted relay recruitment problem is discussed 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. Numerical results are presented to illustrate and verify our theoretical claims.