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Consider a decode‐and‐forward wireless relay system assisted by an intelligent reflection surface (IRS), where a robust design on receive beamforming at the relay and reflection coefficients at the IRS is studied. The worst‐case signal‐to‐noise ratio maximization problem is formulated, subject to the reflection coefficients (with either continuous or discrete phases) constraints, under the assumption of imperfect channel state information for all channels. To cope with the hard problem, an equivalent nonconvex quadratic optimization problem with a simpler form is derived, and then the Cauchy‐Schwarz inequality is applied to update the beamforming and a cyclic process is proposed to update the reflection coefficients, where a closed‐form optimal solution is computed in each step. It turns out that the proposed algorithm achieves a locally optimal solution for the robust design problem. Simulation results show that the proposed robust design outperforms an existing non‐robust design and two robust designs via semidefinite relaxation technique. [ABSTRACT FROM AUTHOR]

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transmitter is imperfectly known mainly due to the channel direction quantization errors, channel estimation errors and outdated channel effects.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. [ABSTRACT FROM AUTHOR]

The design of beamformers for the multi-user multiple-input single-output downlink that provide prespecified levels of quality-of-service can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the signal-to-interference-and-noise ratio (SINR) satisfy a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. We develop a high-quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, enables us to formulate the robust beamformer design problem for Gaussian channel estimation errors as a convex optimization problem that can be efficiently solved. For systems with small uncertainties, further approximations yield design algorithms based on iterative evaluations of closed-form expressions that have substantially lower computational cost. Since finding the beamforming directions incurs most of that cost, 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. [ABSTRACT FROM AUTHOR]

The availability of renewable energy sources (RES) has facilitated efficient and sustainable resource allocation for wireless communication systems. In this paper, a novel framework is proposed to implement coordinated multicell beamforming (CMBF) scheme for cellular networks powered by a smart microgrid, where the BSs are equipped with RES harvesting devices and can buy/sell energy from/to the main grid. New models are developed to capture the stochastic energy harvesting, dynamic electricity prices, and energy transaction cost gauged by the conditional value-at-risk (CVaR) function. Based upon these models, a distributed CMBF scheme is put forth to minimize the grid-wide transaction cost under user quality-of-service (QoS) constraints. Specifically, it is shown that the relevant task can be cast into a convex program to be tackled in a distributed fashion, leveraging the state of the art optimization tools. To deal with the unpredictable nature of the renewable energy, the stochastic alternating direction method of multipliers is then employed to develop a novel distributed CMBF scheme. It is established that the proposed scheme can guarantee optimality of the obtained CMBF solution, using only local channel state information at each BS and limited information exchange among the BSs. Merits of the proposed scheme are corroborated by extensive numerical results. [ABSTRACT FROM AUTHOR]

This paper considers the beamforming design for a multiuser multiple-input single-output 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. [ABSTRACT FROM PUBLISHER]

This letter considers a downlink multi-input single-out (MISO) system where each user performs simultaneous wireless information and power transfer (SWIPT) based on a power splitting receiver architecture. Assuming imperfect channel state information (CSI) at the base station, we develop two robust joint beamforming and power splitting (BFPS) designs that minimize the transmission power under both the signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constraints per user. In the first design, we consider the worst-case (WC) SINR and EH constraints, and show that the WC-BFPS problem can be relaxed as a semidefinite program (SDP) through a linear matrix inequality representation for (infinitely many) robust quadratic matrix inequality constraints. In the second design, we consider the chance constraints (CCs) for SINR and EH, and resort to both semidefinite relaxation and Bernstein-type inequality restriction to transform the CC-BFPS problem into another convex SDP. Based on these convex reformulations, the (near-)optimal robust BFPS designs can be efficiently solved. Numerical results are provided to demonstrate the merit of the proposed robust designs. [ABSTRACT FROM AUTHOR]

We consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple-input multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. The minimization of transmit power is formulated subject to both quality-of-service (QoS) constraints on the secondary receivers and interference temperature constraints on the primary users, under the assumption of imperfect channel state information (CSI). The problem is a nonconvex quadratically constrained quadratic program (QCQP), and in general it is hard to achieve the global optimality. As a compromise, we present two randomized approximation algorithms for the problem via convex optimization techniques. Apart from the general setting of the robust beamforming problem, we identify one interesting special case, the robust problem of which can be solved efficiently. Simulation results are presented to demonstrate the performance gains of the proposed algorithms over an existing robust design. [ABSTRACT FROM PUBLISHER]

• A robust adaptive beamforming problem for general-rank signal model is considered. • The worst-case SINR maximization formulation is established. • The closed-form optimal value of the minimization problem of the least-squares residual over the matrix errors with an induced norm constraint is derived. • With the closed-form result, the worst-case SINR maximization problem is approximated by a sequence of SOCPs. 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. First, 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 derived. Then, the maximization problem is reformulated into the maximization of the difference between an l 2 -norm function and an l q -norm function, with a convex quadratic constraint. It is shown that for any q ≥ 1 in the set of rational numbers, the maximization problem can be approximated by a sequence of second-order cone programming problems, with the ascent optimal values. The resultant beamvector for some q in the set with the maximal actual array output SINR, is treated as the candidate making the RAB design 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 with 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. [ABSTRACT FROM AUTHOR]

Consider a multiuser downlink beamforming optimization problem for the non-orthogonal multiple access (NOMA) transmission in a multiple-input single-output (MISO) system with a general number of users. The total transmission power minimization problem is formulated subject to both quality-of-service (QoS) constraints under the NOMA principal and per-antenna power constraints, which are more realistic since each antenna has its own power amplifier and is limited individually by the linearity of the power amplifier. The problem is a nonconvex quadratically constrained quadratic program, and the conventional semidefinite program (SDP) relaxation is not tight. In order to tackle the non-convex problem, we construct second-order cone program (SOCP) approximation for each signal-to-interference-plus-noise ratio (SINR) constraint and form an iterative algorithm, in which a sequence of SOCPs are solved. The optimal values of SOCPs in the sequence are proved to be non-increasing, and converging to a locally 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 algorithm, which is compared with some state-of-the-art methods. [ABSTRACT FROM AUTHOR]