Cooperation and Competition in MIMO Multi-User Networks with Confidential Message

The broadcast nature of a wireless medium makes it very susceptible to eavesdropping, where the transmitted message is decoded by unintended receiver(s). Recent information theoretic research on secure communication has moved towards optimizing the confidentiality at the physical layer of multi-user wireless networks, mainly by exploiting the advanced capabilities of multiple-input multiple-out (MIMO) signal processing methods. MIMO communications that are secure at the physical layer without depending upon network-layer encryption are achieved by redirecting jamming or multi-user interference to unauthorized receivers, while minimizing that to legitimate receivers.;In this thesis, we revisit some basic scenarios like MIMO Gaussian wiretap channel, two-user broadcast channel, and two-user interference channel with confidential messages, where each receiver is also an eavesdropper for the other link. To study the optimal transmit strategies, we considered (non)convex optimization problems or information theoretic zero-sum games. We start with a general MIMO Gaussian wiretap channel, where transmitter, intended receiver and eavesdropper are all equipped with arbitrary number of antennas. Determining the secrecy capacity of a general MIMO Gaussian wiretap channel is in general a difficult non-convex optimization problem, and still an open problem. We first investigate the rank property of the optimal input covariance matrix under the average power constraint and next we obtain necessary and sufficient conditions under which the optimal transmit covariance matrix is full rank. When the solution is full-rank, we characterize the optimal input covariance in closed form.;Next we consider the secure communication problem in a general MIMO Gaussian wiretap channel with a multi-antenna external helper. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal.;This dissertation considers the optimality of linear precoding for the two-receiver MIMO Gaussian broadcast channel (BC) with confidential messages. Secret dirty paper coding (S-DPC) is optimal under an input covariance constraint, but there is no computable secrecy capacity expression for the general MIMO case under an average power constraint. We prove that for a two-user MIMO Gaussian BC under an input covariance constraint, linear precoding is optimal and achieves the same secrecy rate region as S-DPC if the input covariance constraint satisfies a specific condition, and we characterize the corresponding optimal linear precoders. We then use this result to derive a closed-form sub-optimal algorithm based on linear precoding for an average power constraint.;Two user interference channel, where each receiver is assumed to be an eavesdropper for the other link, is an interesting scenario which can be considered from a game-theoretic perspective. In this thesis, we study the achievable rate regions of the MIMO interference channel with independent confidential messages sent to two receivers, assuming the transmitters use linear precoding. We define different game scenarios where transmitters use cooperative or non-cooperative strategies for Gaussian interference channel, and derive their achievable secrecy rate regions. For a special case where transmitters have arbitrary number of antennas and receivers are single antenna, Nash Equilibrium (NE) strategies at transmitters are characterized in closed-form. For the general MIMO scenario, a game-theoretic formulation of the problem is adopted to allow the transmitters to find an operating point that balances network performance and fairness. The benefit of cooperation between transmitters is demonstrated via several numerical examples. Through this thesis, we show that by exploiting the advanced capabilities of multiple-input multiple-out (MIMO) signal processing methods, the secrecy rate can be significantly improved at the physical layer.