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IEEE Transactions on Wireless Communications

Secure communication over MISO cognitive radio channels

Yiyang Pei, Ying‐Chang Liang, Lan Zhang, Kah Chan Teh, Kwok Hung Li

Published Apr 1, 2010• 208 citations
Publisher

Abstract

In this paper, we address the physical-layer security issue of a secondary user (SU) in a spectrum-sharing cognitive radio network (CRN) from an information-theoretic perspective. Specially, we consider a secure multiple-input single-output (MISO) cognitive radio channel, where a multi-antenna SU transmitter (SU-Tx) sends confidential information to a legitimate SU receiver (SU-Rx) in the presence of an eavesdropper and on the licensed band of a primary user (PU). The secrecy capacity of the channel is characterized, which is a quasiconvex optimization problem of finding the capacity-achieving transmit covariance matrix under the joint transmit power and interference power constraints. Two numerical approaches are proposed to derive the optimal transmit covariance matrix. The first approach recasts the original quasiconvex problem into a single convex semidefinite program (SDP) by exploring its inherent convexity; while the second one explores the relationship between the secure CRN and the conventional CRN and transforms the original problem into a sequence of optimization problems associated with the conventional CRN, which helps to prove that beamforming is the optimal strategy for the secure MISO CR channel. In addition, to reduce the computational complexity, three suboptimal schemes are presented, namely, scaled secret beamforming (SSB), projected secret beamforming (PSB) and projected cognitive beamforming (PCB). Lastly, computer simulation results show that the three suboptimal schemes can approach the secrecy capacity well under certain conditions.

DOI
10.1109/twc.2010.04.090746

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arXiv:0901.4830•Jan 30, 2009•1 citation
In this paper, we address the physical-layer security issue of a secondary user (SU) in a spectrum-sharing cognitive radio network (CRN) from an information-theoretic perspective. Specially, we consider a secure multiple-input single-output (MISO) cognitive radio channel, where a multi-antenna SU transmitter (SU-Tx) sends confidential information to a legitimate SU receiver (SU-Rx) in the presence of an eavesdropper and on the licensed band of a primary user (PU). The secrecy capacity of the channel is characterized, which is a quasiconvex optimization problem of finding the capacity-achieving transmit covariance matrix under the joint transmit power and interference power constraints. Two numerical approaches are proposed to derive the optimal transmit covariance matrix. The first approach recasts the original quasiconvex problem into a single convex semidefinite program (SDP) by exploring its inherent convexity; while the second one explores the relationship between the secure CRN and the conventional CRN and transforms the original problem into a sequence of optimization problems associated with the conventional CRN, which helps to prove that beamforming is the optimal strategy for the secure MISO CR channel. In addition, to reduce the computational complexity, three suboptimal schemes are presented, namely, scaled secret beamforming (SSB), projected secret beamforming (PSB) and projected cognitive beamforming (PCB). Lastly, computer simulation results show that the three suboptimal schemes can approach the secrecy capacity well under certain conditions.
In this paper, we address the issue of optimal transmitter design to achieve physical layer security for a multiple-input single-output (MISO) cognitive radio network (CRN), in which a secondary user transmitter (SU-Tx) sends confidential information to a SU receiver (SU-Rx) on the same frequency band with a primary user (PU) in the presence of an eavesdropper receiver (ED-Rx). It is assumed that all the channel state information (CSI) of the secondary, primary and eavesdropper channels is not perfectly known at the SU-Tx. The optimal transmitter design, under the restriction of Gaussian signaling without preprocessing of information, involves a nonconvex semiinfinite optimization problem which maximizes the rate of the secondary link while avoiding harmful interference to the PU and keeping the eavesdropper totally ignorant of the messages sent regardless of the uncertainties in the CSI. We propose two approaches to solve this challenging optimization problem. The first one relates the original problem to a sequence of semiinfinite capacity-achieving transmitter design problems in an auxiliary CRN without any eavesdropper, which can then be solved through transformations and using convex semidefinite programs (SDPs). The second approach explores the hidden convexity of the problem and hence transforms it into a single SDP, which significantly reduces the computational complexity. Furthermore, a few heuristic beamforming solutions for the ease of implementation are also introduced. Finally, simulation results are presented to evaluate the performance of the proposed optimal and suboptimal solutions.
In this paper, we consider multiple-input single-output multi-eavesdropper cognitive radio networks (MISOME-CRNs), where a secondary user (SU) aims to transmit confidential information to a legitimate SU receiver in the presence of a primary user (PU) and a multi-antenna passive eavesdropper in fast fading environments. For this system setting, we study beamforming with artificial noise (AN) for the SU to achieve confidential communications. We consider designing an AN-assisted optimal beamforming scheme, denoted cognitive beamforming (CB), which maximizes the ergodic secrecy rate. Moreover, we propose two suboptimal beamforming schemes, namely, scaled beamforming (SB) and projected beamforming (PB). We develop an analytical framework to assess the performance of the proposed schemes in a unified manner. First, we analyze the achievable ergodic secrecy rate of the three schemes. Second, we derive the optimal power allocation for the information and AN signals that maximizes the achievable ergodic secrecy rate in the large-antenna regime. Third, we study the performance of the three schemes in terms of the secrecy outage probability. Using numerical simulations, we validate our analytical results and show that CB achieves the best performance among the three proposed schemes. In addition, we provide insights into the effect of various system parameters on the secrecy performance. In particular, we show that the interference threshold at the PU plays an important role in the beamforming design.
In the Cognitive Radio Network (CRN) with multiple multi-antenna eavesdroppers, to make the system security rate maximum, secure communication over the physical layer that is subjected to the interference power constraints at the Primary Users (PU) is provided by designing the transmit covariance optimization of Secondary User Transmitter (SU-Tx).When?the?Channel State?Information (CSI) is known, the properties of the matrices and Charnes-Cooper transformation are used, the non-convex function is converted to a Semi-Definite Programming (SDP) to get the optimization scheme of SU-Tx. Simulation results show that compared with the existing sub-optimal transmission designs, the proposed method improves the secrecy rate and has more advantages on the complexity.
This paper studies the achievable rates of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channel with multiple single-/multi-antenna eavesdroppers. It is known that the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by existing methods. To handle this difficulty, this paper explores a new relationship between the secrecy channel and the recently developed cognitive radio (CR) channel, in which the secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called ¿interference temperature (IT)¿ constraints. By constructing an auxiliary multi-antenna CR channel that has the same channel responses as the secrecy channel, this paper shows that the optimal transmit covariance to achieve the maximum secrecy rate is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Thereby, finding the optimal complex transmit covariance matrix for the secrecy channel becomes equivalent to searching over a set of real IT constraints in the auxiliary CR channel. Based on this relationship, efficient algorithms are proposed to solve the non-convex secrecy rate maximization problem by transforming it into a sequence of convex CR spectrum sharing capacity computation problems, under various setups of the secrecy channel.
This paper presents the optimal physical-layer security scheme of both primary user (PU) and secondary user (SU) in the underlay multiple-input multiple-output cognitive-radio network (MIMO-CRN) by use of a bi-directional zero-forcing beamformer. The proposed new method enables the PU to communicate along with the SUs through a relay node without sacrificing their individual secrecy capacity, i.e., without causing interference to each other even in the presence of eavesdropper(s). In the first phase, a transmitting beamformer at the PU/SU transmitters and a receiving beamformer at the relay have been adopted to separate PU and SU data. In the second phase, a bi-directional beamformer has been applied to eradicate the necessity of involving artificial noise for preventing the active eavesdropper(s). To maximize the total secrecy capacity, a generalized non-linear optimization problem has been formulated and converted to a simplified constrained optimization problem by utilizing the beamformer and the associated subspace restriction. Then, this problem is solved by the Lagrangian method. Both theoretical and numerical analyses of the total and individual ergodic secrecy rates are provided to demonstrate the effectiveness of our proposed method. The secrecy outage probability is also derived to evaluate the performance variations of our proposed scheme when the channel-estimation error occurs.
This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty, we explore a relationship between the MIMO secrecy channel and the recently developed MIMO cognitive radio (CR) channel, in which the multi-antenna secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called ``interference temperature (IT)'' constraints. By constructing an auxiliary CR MIMO channel that has the same channel responses as the MIMO secrecy channel, we prove that the optimal transmit covariance matrix to achieve the secrecy capacity is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Based on this relationship, several algorithms are proposed to solve the non-convex secrecy capacity computation problem by transforming it into a sequence of CR spectrum sharing capacity computation problems that are convex. For the case with single-antenna eavesdroppers, the proposed algorithms obtain the exact capacity of the MIMO secrecy channel, while for the case with multi-antenna eavesdroppers, the proposed algorithms obtain both upper and lower bounds on the MIMO secrecy capacity.