Owing to the special structure of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC), the associated capacity region computation and beamforming optimization problems are typically non-convex, and thus cannot be solved directly. One feasible approach is to consider the respective dual multiple-access channel (MAC) problems, which are easier to deal with due to their convexity properties. The conventional BC-MAC duality has been established via BC-MAC signal transformation, and is applicable only for the case in which the MIMO BC is subject to a single transmit sum-power constraint. An alternative approach is based on minimax duality, which can be applied to the case of the sum-power constraint or per-antenna power constraint. In this paper, the conventional BC-MAC duality is extended to the general linear transmit covariance constraint (LTCC) case, which includes sum-power and per-antenna power constraints as special cases. The obtained general BC-MAC duality is applied to solve the capacity region computation for the MIMO BC and beamforming optimization for the multiple-input single-output (MISO) BC, respectively, with multiple LTCCs. The relationship between this new general BC-MAC duality and the minimax duality is also discussed, and it is shown that the general BC-MAC duality leads to simpler problem formulations. Moreover, the general BC-MAC duality is extended to deal with the case of nonlinear transmit covariance constraints in the MIMO BC.

This paper studies the achievable rates of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channel with multiple single-/multi-antenna eavesdroppers. By assuming Gaussian input, 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.

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.

This paper studies the robust beamforming design problem for a multiple-input single-output (MISO) secrecy channel with a single-antenna eavesdropper. Due to the illegal nature, the eavesdropper may try to hide itself from being caught; thus, it could be difficult for the secrecy transmitter (S-Tx) to obtain accurate channel state information (CSI) of the eavesdropping link between S-Tx and the eavesdropper. Assuming that the CSI of the eavesdropping link belongs to a known uncertain set, this paper designs the optimal transmit strategy for the secrecy user to maximize the transmit rate under the condition that the eavesdropper cannot decode the secrecy message for all possible channel realizations of the eavesdropping link. This robust design problem is non-convex and cannot be solved by existing algorithms in the literature. By exploiting the relationship between the secrecy MISO channel and the cognitive radio (CR) MISO channel, this problem is transformed into a robust CR beamforming design problem, which can be solved efficiently by the interior point method. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.

The conventional Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC)- multiple-access channel (MAC) duality has previously been applied to solve non-convex BC capacity computation problems. However, this conventional duality approach is applicable only to the case in which the base station (BS) of the BC is subject to a single sum-power constraint. An alternative approach is the minimax duality, established by Yu in the framework of Lagrange duality, which can be applied to solve the per-antenna power constraint case. This paper first extends the conventional BC-MAC duality to the general linear transmit covariance constraint (LTCC) case, and thereby establishes a general BC-MAC duality. This new duality is then applied to solve the BC capacity computation problem with multiple LTCCs. Moreover, the relationship between this new general BC-MAC duality and the minimax duality is also presented, and it is shown that the general BC-MAC duality has a simpler form. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

To improve the spectrum utilization efficiency, cognitive radio (CR) has been proposed by allowing a cognitive radio network (CRN) to coexist with a licensed primary network. The security issues, although critical, have been less explored in the literature of CRN. In this paper, we consider a secure CRN in which a multi-antenna secondary user (SU) transmitter sends confidential information to a SU receiver on the same frequency band with a primary user (PU) in the presence of an eavesdropper. All receive terminals are equipped with a single antenna. The capacity-achieving transmitter design is formulated as a quasiconvex optimization problem to maximize the rate of the secondary link while avoiding harmful interference to the PU and preventing the eavesdropper from decoding the messages sent. By exploring the inherent convexity, the original problem is solved efficiently by a single semidefinite program (SDP). Besides, two suboptimal algorithms are proposed to reduce the computational complexity, namely, scaled secret beamforming (SSB) and projected secret beamforming (PSB). It is shown through computer simulations that the two suboptimal algorithms can achieve close-to-optimal secrecy capacity under certain conditions.

Cognitive radio is an emerging technology that shows great promise to dramatically improve the efficiency of spectrum utilization. This paper considers a cognitive radio model, in which the secondary network is allowed to use the radio spectrum concurrently with primary users (PUs) provided that interference from the secondary users (SUs) to the PUs is constrained by certain thresholds. The weighted sum rate maximization problem is studied under interference power constraints and individual transmit power constraints, for a cognitive multiple access channel (C-MAC), in which each SU having a single transmit antenna communicates with the base station having multiple receive antennas. An iterative algorithm is developed to efficiently obtain the optimal solution of the weighted sum rate problem for the C-MAC. It is further shown that the proposed algorithm, although developed for single channel transmission, can be extended to the case of multiple channel transmission. Corroborating numerical examples illustrate the convergence behavior of the algorithm and present comparisons with other existing alternative algorithms.

This paper considers a spectrum sharing based cognitive radio (CR) communication system, which consists of a secondary user (SU) having multiple transmit antennas and a single receive antenna and a primary user (PU) having a single receive antenna. The channel state information (CSI) on the link of the SU is assumed to be perfectly known at the SU transmitter (SU-Tx). However, due to loose cooperation between the SU and the PU, only partial CSI of the link between the SU-Tx and the PU is available at the SU-Tx. With the partial CSI and a prescribed transmit power constraint, our design objective is to determine the transmit signal covariance matrix that maximizes the rate of the SU while keeping the interference power to the PU below a threshold for all the possible channel realizations within an uncertainty set. This problem, termed the robust cognitive beamforming problem, can be naturally formulated as a semi-infinite programming (SIP) problem with infinitely many constraints.We first transform this problem into a second order cone programming (SOCP) problem and then solve it via a standard interior point algorithm. Then, an analytical solution with significantly reduced complexity is developed from a geometric perspective. It is shown that both algorithms yield the same optimal solution. Simulation examples are presented to validate the effectiveness of the proposed algorithms.

In this paper, we consider a cognitive radio (CR) network, in which the unlicensed (secondary) users are allowed to concurrently access the spectrum allocated to the licensed (primary) users provided that their interference to the primary users (PUs) satisfies certain constraints. We study a weighted sum rate maximization problem for the secondary user (SU) multiple input multiple output (MIMO) broadcast channel (BC), in which the SUs are subject to not only a sum power constraint but also interference power constraints. We transform this multiconstraint maximization problem into its equivalent form, which involves a single constraint with multiple auxiliary variables. Fixing these multiple auxiliary variables, we propose a duality result for the equivalent problem. Exploiting the duality result, we develop an efficient subgradient based iterative algorithm to solve the equivalent problem and show that the developed algorithm converges to a globally optimal solution. Simulation results are provided to corroborate the effectiveness of the proposed algorithm.

In this paper, a new spectrum sharing model called sensing-based spectrum sharing is proposed for cognitive radio networks. This model consists of two phases: in the first phase, the secondary user (SU) listens to the spectrum allocated to primary user (PU) to detect the state of PU; in the second phase, SU adapts its transit power based on the sensing results. If the PU is inactive, the SU allocates the transmission power based on its own benefit. However, if the PU is active, interference power constraint is imposed in order to protect the PU. By studying the ergodic capacity of SU, we show that this spectrum sharing model can achieve a higher capacity of SU link and improve the spectrum utilization compared to conventional opportunistic spectrum access or simple spectrum sharing. Using the dual decomposition method, we find the optimal power allocation policies and the optimal sensing time for fading channels to achieve the ergodic capacity of the SU link considering both transmit and interference power constraints. Finally, the numerical results are presented to validate the analytical results.

Cognitive radio is an emerging technology improving the spectrum utilization efficiency in communication systems. In this paper, we are interested in a multiple-input single-output (MISO) based cognitive radio (CR) network where the secondary user (SU) shares the same frequency band with the primary user (PU). It is assumed that the SU transmitter (SU-Tx) has perfect channel information (CSI) from SU-Tx to SU receiver (SU-Rx), but partial CSI from SU-Tx to PU receiver. We propose a robust design method to determine the optimal transmission covariance of SU-Tx to maximize the rate of the SU while keeping the interference power to the PU less than a threshold with high probability. This problem is formulated as a semi-infinite programming (SIP) problem. Two algorithms are proposed to transform this SIP problem into a finite constraint problem, and it is shown that these algorithms obtain the optimal solution. Simulations are presented to validate the effectiveness of the proposed algorithms.

In this paper, we consider a cognitive radio (CR) network in which the unlicensed (secondary) users (SUs) are allowed to concurrently access the spectrum allocated to the licensed (primary) users provided that their interference to the primary users (PUs) satisfies certain constraints. We study a weighted sum rate maximization problem for the secondary user (SU) multiple input multiple output (MIMO) broadcast channel (BC), in which the SUs have not only the sum power constraint but also interference constraints. We first transform this multi- constraint maximization problem into its equivalent form, which involves a single constraint with multiple auxiliary variables. Fixing these multiple auxiliary variables, we establish a duality result for the equivalent problem. Our duality result can be viewed as an extension of the previously known results, which depend on either a sum power constraint or per-antenna power constraints. Furthermore, we develop an efficient sub-gradient based iterative algorithm to solve the equivalent problem and show that the developed algorithm converges to a globally optimal solution. Computer simulations are also provided to corroborate the effectiveness of the proposed algorithm.

Cognitive radio (CR) has been proposed as a strategy to enhance the spectrum utilization efficiency. In a CR network, the secondary users (SUs) share the same radio spectrum with the primary user (PU) under the constraint that the interference from the SUs to PU is below a certain threshold. In this paper, we consider the single-input multiple-output multiple access channels (SIMO-MAC) for the secondary network, and study the optimal power allocation strategy for maximizing the weighted sum rate of the SIMO-MAC under interference constraints and peak transmit power constraints. Employing decoupling techniques, we develop an iterative algorithm to obtain optimal power allocation for maximizing weighted sum rate. Simulation results are presented to verify the effectiveness of the proposed algorithm.

A cognitive radio (CR) network refers to a secondary network operating in a frequency band originally licensed/allocated to a primary network consisting of one or multiple primary users (PUs). A fundamental challenge for realizing such a system is to ensure the quality of service (QoS) of the PUs as well as to maximize the throughput or ensure the QoS, such as signal-to-interference-plus-noise ratios (SINRs), of the secondary users (SUs). In this paper, we study single-input multiple output multiple access channels (SIMO-MAC) for the CR network. Subject to interference constraints for the PUs as well as peak power constraints for the SUs, two optimization problems involving a joint beamforming and power allocation for the CR network are considered: the sum-rate maximization problem and the SINR balancing problem. For the sum-rate maximization problem, zero-forcing based decision feedback equalizers are used to decouple the SIMO-MAC, and a capped multi-level (CML) water-filling algorithm is proposed to maximize the achievable sum-rate of the SUs for the single PU case. When multiple PUs exist, a recursive decoupled power allocation algorithm is proposed to derive the optimal power allocation solution. For the SINR balancing problem, it is shown that, using linear minimum mean-square-error receivers, each of the interference constraints and peak power constraints can be completely decoupled, and thus the multi-constraint optimization problem can be solved through multiple single-constraint sub-problems. Theoretical analysis for the proposed algorithms is presented, together with numerical simulations which compare the performances of different power allocation schemes.

In this paper, we study the problem of joint admission control and power allocation for cognitive radio networks. In such a scenario, the quality of service for primary and secondary users is needed to be guaranteed, which can be translated into the following two constraints: the inference temperature constraint for primary users and the minimum signal-to-interference-plus-noise ratio (SINR) constraint for secondary users. Due to the high density or the mobility of the secondary users, not all the secondary users are supportable. The problem of our interest is to select the maximum subset of secondary users given that the above constraints are satisfied. Moreover, because different secondary users have different revenue outputs, the problem becomes how we can find a subset of the secondary users such that the total revenue output of the networks is maximized. It can be shown that finding the optimal removal set is a NP hard problem. Therefore, we transform the original problem into a smooth optimization problem, and solve it by using a gradient descent based algorithm. This algorithm solves the power allocation and admission control jointly, and its superior performance over the existing algorithms is demonstrated through simulations.