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In this paper, we study the optimal training design for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay systems in the presence of interference. In order to address the interference issue while accurately estimating the channels, we minimize the total transmit power consumed by two source nodes and a relay subject to the constraint on mean square error (MSE) of the channel estimation, which is a nonconvex problem. To solve this challenging problem, we first derive the optimal structure of the training signals, and then, we convert the original problem into a tractable convex form, from which the optimal training scheme is designed efficiently. We further consider a practical special case, for which the optimal training scheme is designed with a lower complexity and the useful insights into the optimal training design are obtained. Also, to reduce the computational complexity of the optimal training design, we propose an asymptotically optimal training scheme in the high signal-to-interference-plus-noise ratio (SINR) regime with a low complexity. Simulation results demonstrate that the proposed schemes significantly outperform the existing schemes. [ABSTRACT FROM AUTHOR]

This paper studies a cognitive radio network (CRN), in which a multiple-input single-output (MISO) secondary transmitter (SU-Tx) aims to send confidential messages to its receiver (SU-Rx) in the presence of unknown eavesdroppers, while having to control its generated interference to the primary users (PUs) under a given threshold. Because the eavesdroppers are unknown, this paper considers the artificial noise (AN) approach or masked beamforming to provide the information secrecy. The objective of this paper is to maximize the power of AN in order to degrade the eavesdroppers, subject to the signal-to-interference-plus-noise ratio (SINR) constraint at the SU-Rx, as well as the interference temperature limits (ITLs) for the PUs. In the case of perfect channel state information (CSI), we reveal that the optimal strategy for the information-bearing signal is beamforming. Imperfect CSI cases of bounded and stochastic uncertainties are investigated. In the case of ellipsoid-bounded errors, we derive the equivalent forms for the SINR and ITL constraints and then transform the optimization problem into a form of semidefinite programming (SDP). For the case of probabilistic CSI uncertainties, we propose an outage-constrained robust formulation where the CSI errors are Gaussian distributed. With the aid of two kinds of Bernstein-type inequalities, we reexpress the probabilistic constraints into deterministic forms, which results in a safe approximate solution. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the sum-rate maximization problem in multiple-input multiple-output interference channels. We design the transmit covariance matrix, associated with each transmitter to maximize the sum-rate of the network when the number of data symbols is unknown. The design problem is nonconvex and then hard to be solved. We devise a semidistributed design methodology according to majorization–minimization technique to deal with the optimization problem. This leads us to a convex quadratically constrained quadratic program at each iteration with a semiclosed form solution. The proposed method is computationally efficient and converges to stationary points of the problem. The fact that the method is based on a distributed processing framework along with relatively low computational burden ( $\mathcal{O}(\max \lbrace M,N\rbrace ^{2.3})$ per iteration with $M$ and $N$ being the number of antennas at the transmitter and receiver, respectively) for the user terminals can make it a potential candidate for practical implementations. Finally, we extend the proposed method for the case with channel estimation errors. Simulation results verify the efficiency of the proposed method, and in a typical scenario we have around 60 times lower run-time when compared to the counterparts of the method. [ABSTRACT FROM AUTHOR]

Two-stage beamforming is a transmit strategy that uses two types of beamformers to reduce the feedback overhead of frequency-division-duplexing massive multiple-input multiple-output systems that are spatially correlated. In this paper, we present large system analysis of two-stage beamforming when a transmitter has limited channel information from feedback and when regularized-zero-forcing (RZF) is used as a second-stage beamformer. We consider two random-vector-quantization-based feedback schemes that can be respectively applied when users have perfect channel information or perfect effective channel information. For each feedback method, we analyze both expected signal-to-interference-plus-noise ratio (SINR) and expected rate loss and then characterize their bounds as a function of the number of feedback bits. From the characterization, we reveal that the sum rate of two-stage beamforming is very sensitive to the regularization parameter of RZF, especially when the number of feedback bits is limited. Motivated by this, we derive the optimal regularization parameter that maximizes the SINR of two-stage beamforming with limited feedback. Using simulations, we verify the tightness of the characterized bounds and quantify how the use of the optimal regularization parameter improves the sum rate of two-stage beamforming. [ABSTRACT FROM AUTHOR]

This paper investigates an outage-constrained secrecy rate maximization (OC-SRM) problem based on the statistical channel uncertainty assumption in an underlay multiple-input multiple-output (MIMO) cognitive radio network, where the secondary transmitter provides simultaneous wireless information and power transfer to receivers. Our objective is to design the transmit covariance matrix and artificial noise aided covariance matrix through maximizing the secrecy rate of the secondary user while satisfying the given outage probability requirements. The designed problem is nonconvex and challenging. We employ the existing theory to reformulate the original problem into two equivalent subproblems by introducing auxiliary variables in order to overcome the difficulty arising from the Shannon capacity expression. The Bernstein-type inequality approach is resorted to conservatively approximate the probabilistic constraints. The merit of the transformation and conversion is that the tractable solutions of the original OC-SRM problem can be easily obtained through solving two convex conic subproblems alternately. Furthermore, we extend the proposed algorithm to solve full uncertainty model design. Numerical results demonstrate the efficacy of the proposed designs. [ABSTRACT FROM AUTHOR]

In this paper, the feasibility of a new downlink transmission mode in massive multi-input multi-output (MIMO) systems is investigated with two types of users, i.e., the users with only statistical channel state information (CSI) and the users with imperfect instantaneous CSI. The problem of downlink precoding design with mixed utilization of statistical and imperfect instantaneous CSI is addressed. We first theoretically analyze the impact of the mutual interference between the two types of users on their achievable rate. Then, considering the mutual interference suppression, we propose an extended zero forcing and an extended maximum ratio transmission precoding methods to minimize the total transmit power of base station and to maximize the received signal power of users, respectively. Thanks to the exploitation of statistical CSI, pilot-based channel estimation is avoided enabling more active users, higher system sum rate, and shorter transmission delay. Finally, simulations are performed to validate the accuracy of the theoretical analysis and the advantages of the proposed precoding methods. [ABSTRACT FROM PUBLISHER]