Robust Rank-Two Multicast Beamforming Under a Unified CSI Uncertainty Model

The design problem associated with robust downlink beamforming in multicast, multigroup, multicell wireless systems is addressed. The channel state information (CSI) of users is assumed to be imperfect and the uncertainty of CSI is modelled using the Frobenius norm. The objective is to optimise the signal-to-interference-plus-noise ratio over all users with a constraint on the maximum total transmitted power. This was achieved through a robust solution using the successive convex approximation (SCA) method. The beamforming problem is treated as a bi-convex problem, which is solved using the iterate-alternative convex technique. Here, the CSI uncertainty is addressed using a convex package through the non-monotone spectral projected gradient method and the beamforming vector is extracted using the SCA method. Also, the authors offer the required condition to extract the beamform vector using the SCA method through a suboptimal solution that always addressed before using different beamforming methods. Their simulation results examine all proposed system parameters in order to show convergence and feasibility of the solution. They also compare the solution with a suboptimal solution and the quality of service method for imperfect CSI in downlink beamforming. Numerical results show that the robust solution achieves the best power efficiency for practical solutions.

We consider the multiuser beamforming problem for a multi-input single-output downlink channel that takes into account the errors in the channel state information at the transmitter side (CSIT). By modeling the CSIT errors as elliptically bounded uncertainty regions, this problem can be formulated as minimizing the transmission power subject to the worst-case signal-to-interference-plus-noise ratio constraints. Several methods have been proposed to solve this nonconvex optimization problem, but none can guarantee a global optimal solution. In this article, we consider a semidefinite relaxation (SDR) for this multiuser beamforming problem, and prove that the SDR method actually solves the robust beamforming problem to global optimality as long as the channel uncertainty bound is sufficiently small or when the transmitter is equipped with at most two antennas. Numerical examples show that the proposed SDR approach significantly outperforms the existing methods in terms of the average required power consumption at the transmitter.

In cognitive relay networks, the interferences from secondary users (SUs) and relays to primary users are constrained to be lower than a threshold. The interference constraints are difficult to satisfy when the channel state information (CSI) is imperfect. In this paper, we propose a robust beamforming scheme for the multi-antenna non-regenerative cognitive relay network where the multi-antenna relay with imperfect CSIs helps the communication of single-antenna SU. Our objective is to design a robust beamforming scheme which maximizes the system capacity subject to transmit power constraint and interference constraints. The bounded channel uncertainties are modeled using the worst-case model. The robust beamforming problem, neglecting the correlation of channel uncertainties, is reformulated as a convex semidefinite programming (SDP) by rank-one relaxation. This convex SDP is related with the worst-case relay transmit power minimization problem, which is further reformulated as a convex SDP, whose rank-one solution is proved to exist. Thus, we propose the suboptimal solution to the robust beamforming problem which is found effectively by solving two convex SDPs. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

Considering that wireless unidirectional full-duplex (FD) transmission is one of the FD transmissions over 5G mobile wireless networks, this paper proposes a joint receive and transmit relay beamformer design for systems consisting of a source, a FD relay, an intended destination, and an eavesdropper. The source and destination are single-antenna nodes, whereas the FD relay is a multi-antenna node. Assuming that full channel state information (CSI) is available and the eavesdropper processes two blocks of received data at a time, the joint optimization problem is reformulated as a semidefinite relaxation (SDR) problem (in terms of relay transmit beamformer), which is tight in the sense that the rank-one beamformer can always be recovered from the SDR solution. In order to significantly minimize the computational cost of the SDR implementation, a novel semi-analytical approach based on dual optimization is proposed to obtain the optimum transmit beamformer. When the number of data blocks is arbitrary, we propose a successive convex approximation approach for solving the original non-convex optimization problem and show that a stationary solution can be efficiently obtained. We then propose a distributionally robust beamformer design for the case of an arbitrary number of blocks, assuming that the means and covariance matrices of the eavesdropper's channels are known. Computer simulations show that the proposed semi-analytical solution matches with that obtained from numerical optimization of the SDR problem, the FD scheme significantly outperforms its half-duplex counterpart, and the proposed robust design provides robustness against CSI uncertainty.

Consider an optimal design problem of robust adaptive beamforming of minimum variance distortionless response, based on estimation of steering vector. The optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the desired signal steering vector. The common criteria to select a best estimate include high performance in terms of output signal-to-noise-plus-interference ratio (SINR) and array output power, but less prior knowledge. However there is often a trade-off between the two criteria. Herein, in order to find an optimal steering vector estimate, a beamformer output power maximization problem is formulated subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint to guarantee the desired source direction-of-arrival (DOA) to get away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, all the prior information includes some allowable error norm bounds, besides the antenna array geometry and angular sector of the desired signal. It turns out that the optimization problem is a non-convex quadratically constrained quadratic program with inhomogeneous constraints, but we show that it is still solvable, and propose how to efficiently get an optimal estimate, via a semidefinite programming relaxation technique. To validate our results, simulation examples are presented to demonstrate the improved performance of the new robust beamformer in terms of the output SINR as well as the output power.

A multi-user multiple-input single-output simultaneous wireless information and power transfer full-duplex system with imperfect channel state information is considered. Under the assumption that the unknown channel estimation error is within a certain range, the self-interference cannot be suppressed completely at the base station and at the multi-user nodes. The proposed design problem is formulated as maximizing the average harvested energy of multi-user nodes and maintaining the signal-to-interference-plus-noise ratio requirement, which is proved to be non-convex. Utilizing semidefinite relaxation and S-procedure methods, a convex optimization problem of optimal beamforming vector for the multi-antenna transmitter is obtained. Moreover, semidefinite relaxation is proved to be tight by showing the existence of rank-one optimal solutions. Simulation results are presented to verify the robustness and effectiveness of the proposed algorithm compared with the non-robust design.

The future of mobile communication systems is evolving rapidly toward being more intelligent, while also having the ability to interconnect with everything and be aware of the current wireless environment. For complex scenarios, the asymmetry features of channel state information (CSI) will seriously restrict the performance of the communication system. With its accurate positioning technology and high-speed communication rate, ultra-wideband (UWB) has a promising future as a solution to integrate communication and positioning functions. The traditional CSI channel estimation usually requires channel training, which will greatly increase the overhead of the system. This paper proposes a location information-assisted beamforming to replace the traditional channel training process. First, we use the user location parameter information to reconstruct the channel model and derive the CSI error distribution based on the location distribution. Second, considering the uncertainty of the user positioning error, we model the robust beamforming optimization problem that minimizes the total transmit power. To solve this non-convex problem effectively, we design a new beamforming algorithm by using semidefinite relaxation (SDR) and Bernstein-type inequalities. Finally, simulation results verify the robustness of the proposed robust beamforming compared to the worst-case robust beamforming.

We propose a novel restriction and relaxation (RAR) method for robust relay beamforming design in cognitive two-way relay networks with imperfect channel state information (CSI). Due to the uncertainty in CSI, the self-interference cannot be completely canceled. Hence, both channel uncertainties and residual self-interference should be considered. The proposed RAR method aims to minimize the transmit power of relay nodes while guaranteeing the worst-case signal-to-interference plus noise ratio (SINR) of secondary users (SUs) as well as satisfying the interference temperature (IT) constraints. Specifically, in the restriction step of RAR, infinite number of complicated constraints are reformulated into a finite number of linear matrix inequalities (LMIs). In the relaxation step of RAR, the nonconvex robust design problem is transformed into a convex semidefinite program (SDP), which can be efficiently solved by interior-point methods. Simulation results verify the effectiveness and robustness of the proposed method.

A Gaussian multiple-input single-output (MISO) secrecy channel is considered, where a transmitter is equipped with multiple antennas, and an intended receiver and an eavesdropper each equipped with a single antenna. This paper studies the robust beamforming design in the presence of uncertainty of channel state information (CSI) on the eavesdropper channel. Under the assumption that all possible states of the eavesdropper channel are in a given set, the problem of optimizing the transmit covariance for the worst-case secrecy capacity which is the maximum transmission rate at which the eavesdropper is unable to decode under any channel realization in the set, is cast as a max-min optimization problem. We propose to transfer the max-min problem into a convex optimization problem that can be solved efficiently. The optimal secrecy rate and transmit covariance are expressed in the form of the generalized eigenvalue and eigenvector, the same form as the conventional case of the perfect eavesdropper's CSI, which indicates our results is the generalization of the conventional case.

Rate-splitting multiple access (RSMA) and the intelligent reflecting surface (IRS) are novel technologies to improve spectrum and energy efficiencies in multi-antenna networks. In this paper, we investigate a multi-user multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system assisted with an IRS and using RSMA. In particular, the IRS assists with data and energy transmission from the base station (BS) to power-splitting (PS) users under a non-linear energy harvesting (EH) model. Our objective is to minimize the transmission power subject to rate and EH requirements at the users. To solve the non-convex problem, we propose a bilevel programming problem in which a genetic algorithm is used to solve the outer optimization problem, and the inner optimization problem is addressed with the semidefinite relaxation (SDR) method. In addition, to study a practical scenario of imperfect channel state information (CSI), we consider a robust beamforming design based on imperfect cascade channels at the BS. Then, we propose a solution based on the S-procedure with the SDR technique. Simulation results show that our proposed RSMA-based scheme provides a significant reduction in transmission power compared to the space-division multiple access (SDMA) and non-orthogonal multiple access (NOMA) methods under perfect and imperfect CSI.

Joint Beamforming and power allocation schemes are considered for cognitive radio (CR) multiple input single output (MISO) system in this paper. We considered the robust downlink beamforming and power allocation problem with per-antenna power constraints which is more realistic in practice, instead of sum-power constraint, under the imperfect channel state information (CSI). Since the given optimization problem is a non-convex problem which is difficult to handle, we transformed it into second order cone program (SOCP) problem, which can be solved efficiently. Simulation shows that the proposed scheme indeed has a better performance in CR system.

Terahertz (THz) communication has been regarded as one promising technology to enhance the transmission capacity of future Internet-of-Things (IoT) users due to its ultrawide bandwidth. Nonetheless, one major obstacle that prevents the actual deployment of THz lies in its inherent huge attenuation. Intelligent reflecting surface (IRS) and multiple-input-multiple-output (MIMO) represent two effective solutions for compensating the large path loss in THz systems. In this article, we consider an IRS-aided multiuser THz MIMO system with orthogonal frequency-division multiple (OFDM) access, where the sparse radio frequency chain antenna structure is adopted for reducing the power consumption. The objective is to maximize the weighted sum rate via jointly optimizing the hybrid analog/digital beamforming at the base station (BS) and reflection matrix at the IRS. Since the analog beamforming and reflection matrix need to cater all users and subcarriers, it is difficult to directly solve the formulated problem, and thus, an alternatively iterative optimization algorithm is proposed. Specifically, the analog beamforming is designed by solving a MIMO capacity maximization problem, while the digital beamforming and reflection matrix optimization are both tackled using semidefinite relaxation (SDR) technique. Considering that obtaining perfect channel state information (CSI) is a challenging task in IRS-based systems, we further explore the case with the imperfect CSI for the channels from the IRS to users. Under this setup, we propose a robust beamforming and reflection matrix design scheme for the originally formulated nonconvex optimization problem. Finally, simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

This paper addresses channel state information (CSI) estimation in a wireless relay network, which consists of a base station (BS), a relay station (RS), and a mobile station (MS). We propose a method for the BS to obtain the instantaneous CSIs of the three links (BS-RS, BS-MS, and RS-MS links) with minimized overhead. The CSI availability plays an important role for the BS to adapt its transmission strategies to the given channel conditions. Our proposed method exploits the fact that the link condition between fixed BS and fixed RS tends to be stable, and the frequent CSI update is not necessary for this link. In order for the BS to obtain the CSI of the distant link (i.e. RS-MS link), RS amplifies a pilot signal received from MS with a pre-defined amplification factor, and forwards it to BS. This enables the BS to obtain the CSI of the RS-MS link based on the received pilot signal and pre-knowledge on the CSI of BS-RS link. We show by computer simulation that our proposed method can reduce the required overhead for CSI estimation with little degradation on the accuracy of the obtained CSI.

In this letter, we investigate a robust beamforming problem for localization-aided millimeter wave (mmWave) communication systems. To handle this problem, we propose a novel restriction and relaxation (R&R) method. The proposed R&R method aims at minimizing the total transmit power while the positioning error follows a Gaussian distribution. Specifically, in the restriction phase of R&R, the probabilistic constraint is transformed into the deterministic form by using the Bernstein-type inequality. In the relaxation phase of R&R, the non-convex optimization problem is reformulated into a convex semidefinite program (SDP) by using semidefinite relaxation (SDR) and first-order Taylor expansion methods. To the best of our knowledge, we first consider the impact of the distribution of the positioning error on the channel state information (CSI), which further influences the data rate. Numerical results present the trade-off of the beamforming between the communication and positioning.

In this letter, we study the robust beamforming design for the reconfigurable intelligent surface (RIS)-assisted communication systems from a multi-antenna access point (AP) to a single-antenna user under imperfect channel state information (CSI), where the RIS has only a finite number of phase shifts at each element. In particular, considering the cascaded AP-RIS-user channel estimation error, we aim to jointly optimize the transmit beamforming at the AP and discrete phase shifts of RIS to minimize the transmission power of AP, subject to a signal-to-noise ratio constraint at the user. To tackle the non-convex optimization problem, we decouple it into two subproblems and propose a novel alternative optimization framework. More specifically, the robust beamforming of AP is first obtained through S-Procedure and semidefinite relaxation. Then we recast the discrete phase shift constraint at RIS into an equivalent convex one, and propose an efficient algorithm to obtain a near optimal solution. Finally, the two subproblems are iteratively optimized to obtain joint robust beamforming. Simulation results show that the proposed scheme can approach the performance of the perfect CSI counterpart and substantially outperform traditional non-robust methods.