This paper is a study of the Gaussian weak interference channel in which two single-antenna sources aim to send their messages to legitimate destinations such that all messages are kept confidential from non-intended receivers. Under the Gaussian codebook assumption, the problem of secrecy rate balancing with the objective of exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. It is shown that at the optimal point, the two secrecy rates are equal; hence, the problem is abstracted to maximize the secrecy rate associated with one destination, while the other is restricted to having the same secrecy rate. The optimum secrecy rate associated with the investigated max-min problem is analytically derived, leading to the solution of the secrecy rate balancing problem. An additional scenario is considered in which sources can transmit artificial noise in addition to their signals. In this case, the max-min problem is solved and a suboptimal solution is provided. Numerical results show that the proposed solution is near-optimal and can be used as a suitable alternative.
This paper is a study of the Gaussian weak interference channel in which two single-antenna sources aim to send their messages to legitimate destinations such that all messages are kept confidential from non-intended receivers. Under the Gaussian codebook assumption, the problem of secrecy rate balancing with the objective of exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. It is shown that at the optimal point, the two secrecy rates are equal; hence, the problem is abstracted to maximize the secrecy rate associated with one destination, while the other is restricted to having the same secrecy rate. The optimum secrecy rate associated with the investigated max-min problem is analytically derived, leading to the solution of the secrecy rate balancing problem. An additional scenario is considered in which sources can transmit artificial noise in addition to their signals. In this case, the max-min problem is solved and a suboptimal solution is provided. Numerical results show that the proposed solution is near-optimal and can be used as a suitable alternative.
This paper studies a two-user Gaussian interference channel in which two single-antenna sources aim at sending their confidential messages to the legitimate destinations such that each message should be kept confidential from non-intended receiver. Also, it is assumed that the direct channel gains are stronger than the interference channel gains and the noise variances at two destinations are equal. In this regard, under Gaussian code book assumption, the problem of secrecy rate balancing which aims at exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. To this end, it is shown that at the optimal point, two secrecy rates are equal, hence, the problem is abstracted to maximizing the secrecy rate associated with one of destinations while the other destination is restricted to have the same secrecy rate. Accordingly, the optimum secrecy rate associated with the investigated max-min problem is analytically derived leading to the solution of secrecy rate balancing problem.
We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates.
Multi-user Gaussian MIMO wiretap channel is considered under interference power constraints (IPC), in addition to the total transmit power constraint (TPC). Algorithms for global maximization of its secrecy rate are proposed. Their convergence to the secrecy capacity is rigorously proved and a number of properties are established analytically. Unlike known algorithms, the proposed ones are not limited to the MISO case and are proved to converge to a global rather than local optimum in the general MIMO case, even when the channel is not degraded. In practice, the convergence is fast as only a small to moderate number of Newton steps is required to achieve a high precision level. The interplay of TPC and IPC is shown to result in an unusual property when an optimal point of the max-min problem does not provide an optimal transmit covariance matrix in some (singular) cases. To address this issue, an algorithm is developed to compute an optimal transmit covariance matrix in those singular cases. It is shown that this algorithm also solves the dual (nonconvex) problems of globally minimizing the total transmit power subject to the secrecy and interference constraints; it provides the minimum transmit power and respective signaling strategy needed to achieve the secrecy capacity, hence allowing power savings.
This thesis examines the challenges of information-theoretic secret communication that exploits the temporal and spatial variations of the wireless medium to improve secret communication rates. We first examine the secrecy capacity of a system consisting of independent parallel channels with one transmitter, one intended receiver and one eavesdropper. We show that the secrecy capacity of the system is the sum of the secrecy capacities of the individual subchannels. We further derive the optimal power allocation strategy for a system of parallel AWGN channels subject to a total power constraint, and also extend the results to random fading channels with additive Gaussian noise. We then study the achievable secrecy rate with Gaussian random codes for the situation where the channel of the intended receiver is a constant AWGN channel, while the eavesdropper's channel is fast Rayleigh fading with unknown realizations but known statistics to the transmitter. The proposed method with artificial noise and bursting provides ways to achieve positive secrecy rate even when Bob's channel is worse than Eve's channel on average. We also examine the achievable secrecy rate for a multiple antenna system, and the optimal input structure needed to achieve this rate. For the multiple input single output case, an analytical solution is derived. Multiple antenna systems provide extra degrees of freedom to the transmitter so that a beamforming-like approach can be used to provide advantage to the intended receiver against the eavesdropper. Next we derive a secrecy capacity outer bound region for a class of one-sided interference channels. The outer bound is shown to be tight for a class of binary deterministic one-sided interference channels, and can be achieved within one bit for some Gaussian one-sided interference channels.Finally, as Gaussian random codes are impractical, we evaluate achievable secrecy rates with discrete signaling. We observe that with discrete signaling, there exists an optimal power that maximizes the achievable secrecy rate. For the AWGN channel, larger constellation is always better. While for fading channel, the optimal constellation size varies with the power constraint, and discrete signaling can perform better than random Gaussian coding.
A secure communication game is considered for the two-user MISO Gaussian interference channel with confidential messages, where each transmitter aims to maximize the difference between its secrecy rate and the secrecy rate of the other transmitter. In this novel problem, the weaker link tries to minimize the extra secret information obtained by its adversary, while the stronger link attempts to maximize it. We provide an information theoretic formulation for this non-cooperative zero-sum game scenario and determine that, under the assumption of Gaussian signaling at the transmitters, there exists a unique Nash equilibrium solution for the proposed problem. Moreover, we obtain in closed-form the optimal strategies (beamformers) at the transmitters that result in the Nash equilibrium. While the NE strategies are achievable in one shot when full channel state information is available at the transmitters (CSIT), we also propose an iterative step-by-step algorithm that converges to the NE point, but only requires limited CSIT. Numerical results are presented to illustrate the analytical findings and to study the role of different channel parameters on the NE strategies.
With the rapid development of wireless communications, security becomes extremely important. In many applications, each transmitter desires to send independent and confidential message to its intended receiver while ensuring mutual information-theoretic secrecy. In this dissertation, I study strategies for enhanced secrecy in wireless communication systems with limited rate feedback and transmitter cooperation. The two-user Gaussian channel model is considered under different scenarios. The transmitters both require channel state information (CSI), which is quantized at the receiver and fed back through the sum-rate-limited feedback channels. The quantization errors reduce the beamforming gain from the direct transmitter, and cause interference leakage from the cross transmitter. In the first scenario, I introduce the wiretap channel model where one receiver is a known eavesdropper, and a second transmitter is used to send a cooperative jamming signal to degrade the eavesdropper's channel. I consider two cases, one where no information about the eavesdroppers is available, and one where statistical CSI is available. With no information about the eavesdroppers, I show how to choose the allocation of feedback bits to the transmitters in order to maximize the amount of jamming power available to interfere with the eavesdroppers, subject to maintaining the lower bound on the rate at a minimum quality-of-service level. For the case of statistical CSI, I derive an approximate lower bound on the average secrecy rate, and optimize the bound to find a suitable bit allocation and the transmit power allocated to the transmitters. In the second scenario, I consider the interference channel model where the two transmitters are amenable to cooperation for improving the overall secrecy performance of the system. I derive an approximation for the average secrecy rate of each link, and optimize the sum secrecy rate over the transmit power and feedback bits allocated to the transmitters. Interestingly, increasing the transmit power beyond a certain point decreases the secrecy performance. When the transmitters have the same number of antennas, I derive the results in closed form. Simulations validate the theoretical analysis and demonstrate the significant performance gains that result from the use of optimal transmit power control and intelligent feedback bit allocation.