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This paper considers a formulation of the robust adaptive beamforming (RAB) problem based on worst-case signal-to-interference-plus-noise ratio (SINR) maximization with a nonconvex uncertainty set for the steering vectors. The uncertainty set consists of a similarity constraint and a (nonconvex) double-sided ball constraint. The worst-case SINR maximization problem is turned into a quadratic matrix inequality (QMI) problem using the strong duality of semidefinite programming. Then a linear matrix inequality (LMI) relaxation for the QMI problem is proposed, with an additional valid linear constraint. Necessary and sufficient conditions for the tightened LMI relaxation problem to have a rank-one solution are established. When the tightened LMI relaxation problem still has a high-rank solution, the LMI relaxation problem is further restricted to become a bilinear matrix inequality (BLMI) problem. We then propose an iterative algorithm to solve the BLMI problem that finds an optimal/suboptimal solution for the original RAB problem by solving the BLMI formulations. To validate our results, simulation examples are presented to demonstrate the improved array output SINR of the proposed robust beamformer.

We theoretically propose a second-order topological magnon insulator by stacking the van der Waals honeycomb ferromagnets with antiferromagnetic interlayer coupling. The system exhibits Z$_{2}$ topological phase, protected by pseudo-time-reversal symmetry (PTRS). An easy-plane anisotropy term breaks PTRS and destroys the topological phase. Nevertheless, it respects a magnetic two-fold rotational symmetry which protects a second-order topological phase with corner modes in bilayer and hinge modes along stacking direction. Moreover, an introduced staggered interlayer coupling establishes a Z$_{2}$$\times$Z topology, giving rise to gapped topological surface modes carrying non-zero Chern numbers. Consequently, chiral hinge modes propagate along the horizontal hinges in a cuboid geometry and are robust against disorders. Our work bridges the higher-order topology and magnons in van der Waals platforms, and could be used for constructing topological magnonic devices.

The robust adaptive beamforming (RAB) problem is considered via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization over distributional uncertainty sets for the random interference-plus-noise covariance (INC) matrix and desired signal steering vector. The distributional uncertainty set of the INC matrix accounts for the support and the positive semidefinite (PSD) mean of the distribution, and a similarity constraint on the mean. The distributional uncertainty set for the steering vector consists of the constraints on the known first- and second-order moments. The RAB problem is formulated as a minimization of the worst-case expected value of the SINR denominator achieved by any distribution, subject to the expected value of the numerator being greater than or equal to one for each distribution. Resorting to the strong duality of linear conic programming, such a RAB problem is rewritten as a quadratic matrix inequality problem. It is then tackled by iteratively solving a sequence of linear matrix inequality relaxation problems with the penalty term on the rank-one PSD matrix constraint. To validate the results, simulation examples are presented, and they demonstrate the improved performance of the proposed robust beamformer in terms of the array output SINR.

The robust adaptive beamforming (RAB) problem for general-rank signal model with an uncertainty set defined through a matrix induced norm is considered. The worst-case signal-to-interference-plus-noise ratio (SINR) maximization RAB problem is formulated by decomposing the presumed covariance of the desired signal into a product between a matrix and its Hermitian, and putting an error term into the matrix and its Hermitian. In the literature, the norm of the matrix errors often is the Frobenius norm in the maximization problem. Herein, the closed-form optimal value for a minimization problem of the least-squares residual over the matrix errors with an induced $l_{p,q}$-norm constraint is first derived. Then, the worst-case SINR maximization problem is reformulated into the maximization of the difference between an $l_2$-norm function and a $l_q$-norm function, subject to a convex quadratic constraint. It is shown that for any $q$ in the set of rational numbers greater than or equal to one, the maximization problem can be approximated by a sequence of second-order cone programming (SOCP) problems, with the ascent optimal values. The resultant beamvector for some $q$ in the set, corresponding to the maximal actual array output SINR, is treated as the best candidate such that the RAB design is improved the most. In addition, a generalized RAB problem of maximizing the difference between an $l_p$-norm function and an $l_q$-norm function subject to the convex quadratic constraint is studied, and the actual array output SINR is further enhanced by properly selecting $p$ and $q$. Simulation examples are presented to demonstrate the improved performance of the robust beamformers for certain matrix induced $l_{p,q}$-norms, in terms of the actual array output SINR and the CPU-time for the sequential SOCP approximation algorithm., Comment: 8 pages, 4 figures

Consider a robust multiple-input single-output downlink beamforming optimization problem in a frequency division duplexing system. The base station (BS) sends training signals to the users, and every user estimates the channel coefficients, quantizes the gain and the direction of the estimated channel and sends them back to the BS. Suppose that the channel state information at the transmitter is imperfectly known mainly due to the channel direction quantization errors, channel estimation errors and outdated channel effects. The actual channel is modeled as in an uncertainty set composed of two inequality homogeneous and one equality inhomogeneous quadratic constraints, in order to account for the aforementioned errors and effects. Then the transmit power minimization problem is formulated subject to robust signal-to-noise-plus-interference ratio constraints. Each robust constraint is transformed equivalently into a quadratic matrix inequality (QMI) constraint with respect to the beamforming vectors. The transformation is accomplished by an equivalent phase rotation process and the strong duality result for a quadratically constrained quadratic program. The minimization problem is accordingly turned into a QMI problem, and the problem is solved by a restricted linear matrix inequality relaxation with additional valid convex constraints. Simulation results are presented to demonstrate the performance of the proposed method, and show the efficiency of the restricted relaxation.

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been well studied in the literature. Different from the existing literature, herein however the original beamforming problem is tackled. Resorting to the strong duality of linear conic programming, the robust adaptive beamforming problem for general-rank signal model is reformulated into an equivalent quadratic matrix inequality (QMI) problem. By employing a linear matrix inequality (LMI) relaxation technique, the QMI problem is turned into a convex semidefinite programming problem. Using the fact that there is often a positive gap between the QMI problem and its LMI relaxation, an approximate algorithm is proposed to solve the robust adaptive beamforming in the QMI form. Besides, several sufficient optimality conditions for the nonconvex QMI problem are built. To validate our results, simulation examples are presented, which also demonstrate the improved performance of the new robust beamformer in terms of the output signal-to-interference-plus-noise ratio.

Consider a multiuser downlink beamforming optimization problem for the non-orthogonal multiple access (NOMA) transmission in a multiple-input single-output (MISO) system. The total transmission power minimization problem is formulated subject to both per-antenna power constraints and quality-of-service (QoS) constraints under the NOMA principal. The problem is a non-convex quadratically constrained quadratic program, and the conventional semidefinite program (SDP) relaxation is not tight. In order to tackle the non-convex NOMA beamforming problem, we construct a second-order cone approximation for each signal-to-interference-plus-noise ratio (SINR) constraint and form an iterative algorithm, in which a sequence of second-order cone programs (SOCPs) are solved. The optimal values of the sequence of SOCPs are non-increasing, and it converges to a locally optimal value. However, our extensive simulation results show that the locally optimal value is more or less as good as the globally optimal value. In particular, we show that the SDP relaxation is tight for two-user case if one of the SINR constraints is strict (non-binding) at the optimality. Detailed simulation results are presented to demonstrate the performance gains of the NOMA downlink beamforming with per-antenna power constraints through the proposed approximate algorithm.

The robust adaptive beamforming design problem based on estimation of the signal of interest steering vector is considered in the paper. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the signal of interest steering vector. The common criteria to find the best estimate of the steering vector are the beamformer output SINR and output power, while the constraints assume as little as possible prior inaccurate knowledge about the signal of interest, the propagation media, and the antenna array. Herein, a new beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the signal of interest is away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, the prior information required consists of some allowable error norm bounds, the approximate knowledge of the antenna array geometry, and the angular sector of the signal of interest. It turns out that the array output power maximization problem is a non-convex QCQP problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the signal of interest steering vector. The results are generalized to the case where an ellipsoidal constraint is considered, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio (SINR), incorporating a positive semidefinite constraint on the actual covariance matrix of the desired signal. In the literature, semidefinite program (SDP) techniques, together with others, have been applied to approximately solve this problem. Herein an inner second-order cone program (SOCP) approximate algorithm is proposed to solve it. In particular, a sequence of SOCPs are constructed and solved, while the SOCPs have the nondecreasing optimal values and converge to a locally optimal value (it is in fact a globally optimal value through our extensive simulations). As a result, our algorithm does not use computationally heavy SDP relaxation technique. To validate our inner approximation results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformer in terms of the averaged cpu-time (indicating how fast the algorithms converge) in a high signal-to-noise region.

The design of a set of beamformers for the multiuser multiple-input single-output (MISO) downlink that provides the receivers with prespecified levels of quality-of-service (QoS) can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the SINR meet or exceed a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. In this paper, we will develop a high quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, enables us to formulate the beamformer design problem as a convex optimization problem that can be efficiently solved. For systems in which the uncertainty size is small, a further approximation yields algorithms based on iterative evaluations of closed-form expressions that have substantially lower computational cost. Since finding the beamforming directions incurs most of the computational load of these algorithms, analogous power loading algorithms for predefined beamforming directions are developed and their performance is shown to be close to optimal. When the system contains a large number of antennas, the proposed power loading can be obtained at a computational cost that grows only linearly in the number of antennas. The proposed power loading algorithm provides an explicit relationship between the outage probability required and the power consumed, which allows us to precisely control the power consumption, and automatically identifies users who are consuming most of the power resources. The flexibility of the proposed approach is illustrated by developing a power loading technique that minimizes an average notion of outage.

The integration of renewable energy sources (RES) has facilitated efficient and sustainable resource allocation for wireless communication systems. In this paper, a novel framework is introduced to develop coordinated multicell beamforming (CMBF) design for wireless cellular networks powered by a smart microgrid, where the BSs are equipped with RES harvesting devices and can perform two-way (i.e., buying/selling) energy trading with the main grid. To this end, new models are put forth to account for the stochastic RES harvesting, two-way energy trading, and conditional value-at-risk (CVaR) based energy transaction cost. Capitalizing on these models, we propose a distributed CMBF solution to minimize the grid-wide transaction cost subject to user quality-of-service (QoS) constraints. Specifically, relying on state-of-the-art optimization tools, we show that the relevant task can be formulated as a convex problem that is well suited for development of a distributed solver. To cope with stochastic availability of the RES, the stochastic alternating direction method of multipliers (ADMM) is then leveraged to develop a novel distributed CMBF scheme. It is established that the proposed scheme is guaranteed to yield the optimal CMBF solution, with only local channel state information available at each BS and limited information exchange among the BSs. Numerical results are provided to corroborate the merits of the proposed scheme., Comment: 11 pages, 6 figures

This paper considers a $K$-user multiple-input single-output (MISO) interference channels for simultaneous wireless information and power transfer (SWIPT), where each multi-antenna transmitter serves a single-antenna receiver per user pair. All receivers perform simultaneously information processing and energy harvesting (EH) based on the receive power-splitting (PS) architectures. Assuming imperfect channel state information (CSI) at the transmitters, we develop an optimal robust transceiver design scheme that minimizes the total transmission power under the worst-case signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constraints at the receivers, by jointly optimizing transmit beamforming and receive PS ratio per receiver. When the CSI uncertainties are bounded by ellipsoidal regions, it is shown that the worst-case SINR and EH constraints per receiver can be recast into quadratic matrix inequality forms. Leveraging semidefinite relaxation technique, the intended robust beamforming and PS (BFPS) problem can be relaxed as a tractable (centralized) semidefinite program (SDP). More importantly, relying on the state-of-the-art alternating direction method of multipliers (ADMM) in convex optimization, we propose a {\em decentralized} algorithm capable of computing the optimal robust BFPS scheme with local CSI and limited information exchange among the transmitters. It is shown the proposed decentralized algorithm is guaranteed to converge to the optimal centralized solution. Numerical results are provided to demonstrate the merits of the proposed approaches., Comment: 8 pages and 7 figures

This paper considers the beamforming design for a multiuser multiple-input single-output (MISO) downlink with an arbitrary number of (context-specific) shaping constraints. In this setup, the state-of-the-art beamforming schemes cannot attain the well-known performance bound promised by the semidefinite program (SDP) relaxation technique. To close the gap, we propose a redundant-signal embedded linear beamforming (REEL-BF) scheme, where each user is assigned with one information beamformer and several shaping beamformers. It is shown that the proposed REEL-BF scheme can perform general rank-$K$ beamforming for user symbols in a low-complexity and structured manner. In addition, sufficient conditions are derived to guarantee that the REEL-BF scheme always achieves the SDP bound for linear beamforming schemes. Based on such conditions, an efficient algorithm is then developed to obtain the optimal REEL-BF solution in polynomial time. Numerical results demonstrate that the proposed scheme enjoys substantial performance gains over the existing alternatives., Comment: Accepted for publication in the IEEE Transactions on Signal Processing

Two-way relaying can improve spectral efficiency in two-user cooperative communications. It also has great potential in multiuser systems. A major problem of designing a multiuser two-way relay system (MU-TWRS) is transceiver or precoding design to suppress co-channel interference. This paper aims to study linear precoding designs for a cellular MU-TWRS where a multi-antenna base station (BS) conducts bi-directional communications with multiple mobile stations (MSs) via a multi-antenna relay station (RS) with amplify-and-forward relay strategy. The design goal is to optimize uplink performance, including total mean-square error (Total-MSE) and sum rate, while maintaining individual signal-to-interference-plus-noise ratio (SINR) requirement for downlink signals. We show that the BS precoding design with the RS precoder fixed can be converted to a standard second order cone programming (SOCP) and the optimal solution is obtained efficiently. The RS precoding design with the BS precoder fixed, on the other hand, is non-convex and we present an iterative algorithm to find a local optimal solution. Then, the joint BS-RS precoding is obtained by solving the BS precoding and the RS precoding alternately. Comprehensive simulation is conducted to demonstrate the effectiveness of the proposed precoding designs., Comment: 13 pages, 12 figures, Accepted by IEEE TWC