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Robust Transmit Design for MISO Gaussian Broadcast Channel with Integrated Services

Weiqing Kong, Zhi Chen, Lingxiang Li, Chuan Zhen Huang

Published Dec 1, 2015• 1 citation
Publisher

Abstract

We consider the problem of physical layer service integration for the multiple-input single-output (MISO) Gaussian Broadcast Channel (BC). In particular, we study a scenario with two receivers and two messages: one common message intended for both receivers and one confidential message for only receiver 1 which needs to be kept perfectly secure from receiver 2. With partially known Channel state information (CSI), we aim to study the robust design of the input covariance matrices to maximize the worst-case secrecy rate region. To this end, we adopt a Quality of Service (QoS) constrained method, and we recast the original nonconvex optimization problem as a sequence of convex ones. Moreover, we study the rank of the optimal solutions. It proves that, generally, the rank of the optimal input covariance matrix associated with the confidential message is 1, while the rank of the optimal input covariance matrix associated with the common message is less than 4. Further, we prove that for the case of perfect CSI, beamforming is optimal for both common message and confidential message. Numerical results are presented to show the efficacy of the proposed method.

DOI
10.1109/glocomw.2015.7414138

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We consider the problem of physical layer service integration for the multiple-input single-output (MISO) Gaussian Broadcast Channel (BC). In particular, we study a scenario with two receivers and two messages: one common message intended for both receivers and one confidential message for only receiver 1 which needs to be kept perfectly secure from receiver 2. With partially known Channel state information (CSI), we aim to study the robust design of the input covariance matrices to maximize the worst-case secrecy rate region. To this end, we adopt a Quality of Service (QoS) constrained method, and we recast the original nonconvex optimization problem as a sequence of convex ones. Moreover, we study the rank of the optimal solutions. It proves that, generally, the rank of the optimal input covariance matrix associated with the confidential message is 1, while the rank of the optimal input covariance matrix associated with the common message is less than 4. Further, we prove that for the case of perfect CSI, beamforming is optimal for both common message and confidential message. Numerical results are presented to show the efficacy of the proposed method.
This paper considers an optimal artificial noise (AN)-aided transmit design for multi-user MISO systems in the eyes of service integration. Specifically, two sorts of services are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. This paper considers a general case of imperfect channel state information (CSI), aiming at a joint and robust design of the input covariances for the multicast message, confidential message and AN, such that the worst-case secrecy rate region is maximized subject to the sum power constraint. To this end, we reveal its hidden convexity and transform the original worst-case robust secrecy rate maximization (SRM) problem into a sequence of semidefinite programming. Numerical results are presented to show the efficacy of our proposed method.
This paper considers a two-user multiple-input single-output Gaussian broadcast channel model with two sorts of information transfer, i.e., multicasting and confidential broadcasting. Specifically, three service messages are combined at the transmitter. The transmitter sends a multicast message to both users, and a confidential message to each user which is kept perfectly secret from the other user. Our goal is to jointly design the optimal input covariances for the multicast message and the two confidential messages, such that the secrecy capacity region is maximized. This problem can be formulated as a secrecy rate maximization (SRM) problem with the quality of multicast service constraint and the quality of confidential service constraint. This SRM problem is nonconvex by nature. To solve it, we reveal its hidden convexity and transform the original SRM problem into a semidefinite programming problem. Furthermore, we prove that the optimal input covariance matrices of the multicast message and the two confidential messages are always with rank one, which implies the optimality of beamforming. Besides, we show that the arithmetic complexity of our proposed method is polynomial with regard to the dimension of the optimization variables. Numerical results are finally presented to show the efficacy of our proposed method.
This paper considers an energy-efficient transmit design in a three-node MISO wiretap channel in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for both receivers and one confidential message intended for only one authorized receiver. The confidential message must be kept perfectly secure from the unauthorized receiver. Our goal is to jointly design the input covariance matrices of the multicast message and confidential message such that the secrecy energy efficiency (SEE) is maximized, subject to the multicast rate, secrecy rate and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the feasibility of transmit beamforming to achieve the maximum SEE. Numerical results are finally presented to verify the efficacy of our proposed method.
This letter considers a two-receiver multiple-input single-output Gaussian broadcast channel model with integrated services. Specifically, two sorts of service messages are combined and served simultaneously: one multicast message intended for both receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from the unauthorized receiver. Our goal is to jointly design the input covariances for the multicast message and confidential message, such that the secrecy capacity region is maximized. This secrecy capacity region maximization (SCRM) problem is a nonconvex vector maximization problem. To deal with this issue, we reformulate the SCRM problem into a provably equivalent scalar optimization problem and propose a searching method to find its overall Pareto optimal points. Further, for implementation efficiency, transmit beamforming is proved to be Pareto optimal. However, since the two service messages are coupled in our optimization problem, it is difficult to deduce closed-form expressions of the Pareto optimal beamformers. A suboptimal transmit design is accordingly proposed to analytically obtain beamformers for both service messages. Numerical results illustrate that the performance gap between the Pareto optimal design and our proposal is negligible.
This paper considers artificial noise (AN) aided transmit designs for multiuser MISO systems in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. Our goal is to jointly design the optimal input covariances for the multicast message, confidential message, and AN, such that the achievable secrecy rate region is maximized subject to the sum power constraint. This secrecy rate region maximization (SRRM) problem is a nonconvex vector maximization problem. To handle it, we reformulate the SRRM problem into a provably equivalent scalar optimization problem and propose a searching method to find all of its Pareto optimal points. The equivalent scalar optimization problem is identified as a secrecy rate maximization (SRM) problem with the quality of multicast service (QoMS) constraints. Further, we show that this equivalent QoMS-constrained SRM problem, albeit nonconvex, can be efficiently handled based on a two-stage optimization approach, including solving a sequence of semidefinite programs (SDPs). Moreover, we also extend the SRRM problem to an imperfect channel state information (CSI) case where a worst case robust formulation is considered. In particular, while transmit beamforming is generally a suboptimal technique to the SRRM problem, we prove that it is optimal for the confidential message transmission whether in the perfect CSI scenario or in the imperfect CSI scenario. For implementation efficiency, we also analyze the computational complexity of our proposed methods and put forward two suboptimal schemes and two possible extensions. Finally, numerical results demonstrate that the AN-aided transmit designs are effective in expanding the achievable secrecy rate regions, and that the suboptimal strategies can achieve near-optimal performance.
This paper considers an optimal artificial noise (AN)-aided transmit design for multi-user MISO systems in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. Our goal is to jointly design the optimal input covariances for the multicast message, confidential message and AN, such that the achievable secrecy rate region is maximized subject to the sum power constraint. To this end, we exploit its hidden convexity and transform the original secrecy rate maximization (SRM) problem into a semidefinite programming. Furthermore, we prove that the optimal input covariance matrix of confidential message is always with rank one, which implies the optimality of beamforming. Numerical results are presented to show the efficacy of our proposed method.