Robust Beamforming Research Articles

Rate-Splitting Multiple Access in a MISO SWIPT System Assisted by an Intelligent Reflecting Surface

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.

Digital adaptive wideband beamforming without pre-steering delay processing

Compared with the traditional frost space-time beamformer (STB) with a pre-steering delay processing (PSDP), the method without the PSDP is able to provide a more intuitive observation of the space-frequency response (SFR) for both the desired signal and interference in the beam pattern. In this paper, a new SFR constraint is proposed to guarantee the same time delay for all different frequency components in the desired signal by analyzing the desired signal process of the digital STB. Specifically, in order to make all frequencies in the desired bandwidth meet the SFR constraint, we propose a method to obtain the number of the sample frequency points of the new constraint. After that, the equivalent beamformer with lower complexity is acquired via transforming the SFR constraints into a part of the optimization objectives. On this basis, a robust wideband beamformer against the direction of arrival (DOA) mismatch of the desired signal is established. To be more concretely, in the proposed robust beamformer, the covariance matrix of the interference plus noise and the covariance matrix of the desired signal are reconstructed with the observed data containing the desired signal. Additionally, the reconstructed two matrices are used to estimate the actual desired signal steering vector by considering a maximization of the desired signal output power. Numerical results verify the effectiveness of those proposed algorithms.

Robust transmission design for artificial noise aided multiuser broadcast system in inaccurate channel state information scenario with users of different importance

In this article, robust beamforming (BF) and artificial noise (AN) design method is proposed for multiuser broadcast secure transmission under secrecy outage probability (SOP) constraints. A special scenario is assumed that the transmitter cannot obtain the accurate channel state information (CSI) of the users' channel, and different users have different priorities and importance. This special scenario makes traditional BF algorithms and AN design methods unable to guarantee the effective and secure transmission of information. To deal with intractable non-convex problems in this new design, a series of optimization methods like Bernstein-type inequality (BTI) and S-Procedure are employed to transform these problems into solvable functions. Moreover, a search algorithm is explored for simplifying the computational complexity of the optimization algorithm. After that, the new robust algorithm is compared with former methods in inaccurate CSI scenarios by numerical simulation, which shows the advantages of our algorithm.

Outage Constrained Robust Secure Beamforming in Integrated Sensing and Communication Systems

In this letter, we consider the secure multi-user downlink communication scheme against eavesdroppers in Integrated Sensing and Communication (ISAC) systems, where the ISAC base station (BS) transmits ISAC waveform to serve communication users and sense targets, and artificial noise (AN) is employed to guarantee the transmission secrecy. In particular, we study the robust ISAC beamforming design under the assumption of imperfect legitimate users’ and eavesdroppers’ channel state information (CSI). Specifically, we aim to minimize the squared error between designed and desired beampatterns under the probabilistic outage constraints concerning the secrecy performance as well as power budget constraint. To deal with the non-convex problem, we utilize the semidefinite relaxation (SDR) technique and Bernstein-type inequality to convert the problem to a tractable form. Numerical results show that the proposed robust beamforming design algorithm is able to approach the performance under perfect CSI, and illustrates the trade-off between sensing and secrecy performances.

Cooperative Beamforming for Reconfigurable Intelligent Surface-Assisted Symbiotic Radios

In this paper, we study a novel reconfigurable intelligent surface (RIS) enabled symbiotic radio system, where a RIS is used to enhance the communication between the primary transmitter (PTx) and the primary receiver (PRx), and concurrently transmit its information (e.g., environmental monitoring information) to the PRx by varying the phase shifts. The objective is to cooperatively optimize the active transmit beamforming at the PTx and passive reflecting beamforming at the RIS to minimize the PTx's transmit power, subject to the signal-to-noise ratio constraints of primary and RIS transmissions. A new optimization problem is formulated where the RIS phase shifts are not only related to the channel state information (CSI), but also related to its message. First, we consider the perfect CSI setup to draw useful insights into the cooperative beamforming design between the PTx and RIS. Then, the worst-case robust beamforming design is carried out under the imperfect CSI setup. In particular, we take into account the imperfect successive interference cancellation at the PRx. Finally, simulation results show the effectiveness of the RIS information transfer and the integration of RIS into a symbiotic radio system can significantly improve the performance.

CSI-Impaired Beamforming Optimization for Dense MIMO Communication Networks

This paper studied the robust beamforming for dense transmission systems with imperfect channel state information (CSI). The objective was to maximize the minimum signal to interference plus noise ratio (SINR) in the constraint of the per base station (BS) power. By performing the uplink–downlink duality theory, the referred non-convex optimization problem can be changed into the equivalent uplink decoupling optimization problem. Then, we proposed the instantaneous updating uplink–downlink power algorithm, which relies on instantaneous CSI for the finite system. For the massive MIMO system, to obtain the solution to the problem required for power to instantaneously update, we proposed the updating uplink–downlink power algorithm, which only requires statistical CSI, by applying the random matrix theory. The simulation results show the feasibility and effectiveness of our proposed algorithms.

Robust Beamforming and Power Allocation for Secure Communication in Systems With Imperfect Channel and Hardware Impairments

In practice, hardware impairments (HIs) of communication systems are inevitable. In addition, perfect channel state information (CSI) is difficult to get due to channel estimation errors. In this letter, we design the power allocation strategy (PAS) at transmitters to optimize the worst-case secrecy rate for the wireless communication system with both norm-bounded channel uncertainty and HIs. The proposed problem is non-convex and difficult to solve. To solve this thorny problem, we use S-procedure, conservative approximation (CA), robust beamforming, and sequential convex approximation (SCA) to effectively convert the non-convex problem into a series of convex problems that are easy to solve. The numerical results demonstrate that the proposed PAS and robust beamforming method can offset the performance loss caused by HIs to a large extent.

Robust Beamforming for Active Reconfigurable Intelligent Omni-Surface in Vehicular Communications

Two key impediments to reconfigurable intelligent surface (RIS)-aided vehicular communications are, respectively, the double fading experienced by the signal on RIS-aided cascaded links and the high-mobility-induced intractability of acquiring channel state information (CSI). To overcome these challenges, a novel kind of RIS is presented in this paper, namely active reconfigurable intelligent omni-surface (RIOS), each element of which is supported by active loads, that concurrently transmits and reflects the incident signal amplified rather than just reflecting it as compared to the case of a passive reflecting-only RIS. We consider the use of an active RIOS to a vehicular communication system for mitigating double fading effect. Specifically, the active RIOS is mounted on the vehicle window to enhance transmission for users in the vehicle and for adjacent vehicles. We aim to jointly optimize the transmit precoding matrix at the base station (BS) and RIOS coefficient matrices to minimize the BS’s transmit power relying exclusively upon the imperfect knowledge of the large-scale CSI. To significantly relax the frequency of channel information updates, initially an efficient transmission protocol is put forward to reap the high active RIOS beamforming gain with low channel training overhead by appropriately tailoring the time-scale of CSI acquisition. Then, two algorithms, namely an alternating optimization (AO)-based algorithm and a constrained stochastic successive convex approximation (CSSCA)-based algorithm, are developed to tackle with the investigated resource allocation problem, whose pros and cons are elaborated, respectively. Simulation results substantiate the significant performance improvement of active RIOS as well as determine the validity and robustness of our proposed algorithms over various benchmark schemes.

Flexible Null Broadening Robust Beamforming Based on JADE

In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method.

A penalized inequality-constrained approach for robust beamforming with DoF limitation

A well-known challenge in beamforming is how to optimally utilize the degrees of freedom (DoF) of the array to design a robust beamformer, especially when the array DoF is limited. In this paper, we leverage the tool of constrained convex optimization and propose a penalized inequality-constrained minimum variance (P-ICMV) beamformer to address this challenge. Specifically, a well-targeted objective function and inequality constraints are proposed to achieve the design goals. By penalizing the maximum gain of the beamformer at any interfering directions, the total interference power can be efficiently mitigated with limited DoF. Multiple robust constraints on the target protection and interference suppression can be introduced to increase the robustness of the beamformer against steering vector mismatch. By integrating the noise reduction, interference suppression, and target protection, the proposed formulation can efficiently obtain a robust beamformer design while optimally trading off various design goals. To numerically solve this problem, we formulate the P-ICMV beamformer design as a convex second-order cone program (SOCP) and propose a low complexity iterative algorithm based on the alternating direction method of multipliers (ADMM). Three applications are simulated to demonstrate the effectiveness of the proposed beamformer.

Robust Multiuser Beamforming for IRS-Enhanced Near-Space Downlink Communications Coexisting With Satellite System

To the best of our knowledge, this article represents the first attempt toward robust beamforming design for multiuser downlink communications in intelligent reflecting surface (IRS)-enhanced satellite (SAT) and high altitude platform (HAP) integrated network. Such network configuration is mainly composed of a single-antenna SAT, a multiple-antenna HAP, multiple single-antenna SAT and HAP terminals and an IRS. Although sharing the same spectrum resource with the SAT, the HAP suspended in the near-space intends to offer temporary higher-speed and lower-delay multiuser communication connections than the SAT. Therefore, the power budget should be carefully tuned at the HAP. Toward this end, we first formally formulate the transmit power minimization problem at the HAP under the constraints of signal-to-interference-plus-noise-ratio-outage-probability (SINR-OP) at each SAT and HAP terminal by taking into account the imperfect channel state informations and their Gaussian channel estimation errors. Note that the complicated superposition of direct SAT/HAP links and cascaded IRS links, makes the optimization problem rather challenging. Specifically, we transform the probabilistic constraints into approximate deterministic ones, by performing rank relaxation. Based on this, we are able to solve the optimization problem by alternately optimizing the two ensuring subproblems. As verified by extensive simulation results, the proposed IRS-enhanced beamforming schemes can substantially diminish the transmit power at the HAP compared to the beamforming counterparts without IRS.

Outage Constrained Robust Beamforming Optimization for Multiuser IRS-Assisted Anti-Jamming Communications With Incomplete Information

Malicious jamming attacks have been regarded as a serious threat to Internet of Things (IoT) networks, which can significantly degrade the Quality of Service (QoS) of users. This article utilizes an intelligent reflecting surface (IRS) to enhance anti-jamming performance due to its capability in reconfiguring the wireless propagation environment via dynamically adjusting each IRS reflecting elements. To enhance the communication performance against jamming attacks, a robust beamforming optimization problem is formulated in a multiuser IRS-assisted anti-jamming communications scenario with or without imperfect jammer’s channel state information (CSI). In addition, we further consider the fact that the jammer’s transmit beamforming can not be known at BS. Specifically, with no knowledge of jammers transmit beamforming, the total transmit power minimization problems are formulated subject to the outage probability requirements of legitimate users with the jammer’s statistical CSI, and signal-to-interference-plus-noise ratio requirements of legitimate users without the jammer’s CSI, respectively. By applying the decomposition-based large deviation inequality, Bernstein-type inequality, Cauchy–Schwarz inequality, and penalty nonsmooth optimization method, we efficiently solve the initial intractable and nonconvex problems. Numerical simulations demonstrate that the proposed anti-jamming approaches achieve superior anti-jamming performance and lower power-consumption compared to the non-IRS scheme and reveal the impact of key parameters on the achievable system performance.

Robust transmit beamforming design for multi‐cell multiuser MIMO NOMA

This paper focuses on the robust beamforming design for downlink multi-cell multiple-input multiple-output (MIMO) nonorthogonal multiple access (NOMA) systems without having any restrictions on the number of users and cells. The beamforming matrices are designed by solving a sum rate maximization problem under imperfect channel state information (CSI) while satisfying transmission power constraints. In order to solve the proposed non-convex optimization problem with infinite-dimensional robust constraints, an iterative algorithm is provided to transform this problem into a convex form by utilizing diagonalization theory and introducing some auxiliary variables. Numerical results demonstrate that the proposed algorithm converges quickly, and the proposed robust NOMA design achieves strong robustness and acceptable performance.

Robust Secure Energy Efficient Beamforming for mmWave UAV Communications With Jittering

This letter proposes a robust secure and energy efficient beamforming (BF) scheme for a millimeter-wave unmanned aerial vehicle (UAV) communication system with imperfect angle-of-departure (AoD) estimation of air-to-ground channel caused by jittering. Specifically, an optimization problem is formulated to maximize the worst-case secrecy energy efficiency (SEE), defined as the ratio of the sum achievable secrecy rate (ASR) to the total power consumption, subject to the UAV transmit power constraint. Due to the difficulty in solving this problem arisen from the AoD uncertainties and the non-convex structures of SEE and ASR, we first adopt the discretization method to simplify AoD uncertainties to a deterministic form and then exploit the successive convex approximation approach with auxiliary variables to convert the original problem into a convex one. Finally, an iterative algorithm is designed to obtain the suboptimal solution. Numerical results are provided to confirm the effectiveness and superiority of the proposed robust BF scheme compared to some benchmark schemes.

Location Information-Assisted Robust Beamforming Design for Ultra-Wideband Communication Systems

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.

Robust Beamforming Optimization for Self-Sustainable Intelligent Reflecting Surface Assisted Wireless Networks

We focus on an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) system where the IRS sustains its operations by harvesting energy from the access point (AP) in the power splitting (PS) protocol. We aim to minimize the AP’s transmit power subject to the receivers’ signal-to-noise ratio (SNR) and the IRS’s energy budget constraints. A two-stage optimization framework is proposed to jointly optimize the AP’s active beamforming, the IRS’s passive beamforming, and the reflection amplitude. Given the reflection amplitude, we employ alternating optimization to update the beamforming strategies. Then, we determine the lower and upper bounds of the reflection amplitude in closed-form expressions, which help to update the reflection amplitude in a bisection method. We further extend our study to the robust case with uncertain channels. Our analysis reveals that the robust counterpart can be solved by the same optimization framework. Extensive simulations reveal that our algorithm is efficacy to balance the IRS’s energy budget and the receiver’s SNR performance. With uncertain channel information, a larger size of the IRS does not always ensure a higher performance improvement to information transmissions.

Robust Design for Intelligent Reflecting Surface-Assisted Secrecy SWIPT Network

This paper investigates the robust beamforming design in a secrecy multiple-input single-output (MISO) network aided by the intelligent reflecting surface (IRS) with simultaneous wireless information and power transfer (SWIPT). Specifically, by considering that the energy receivers (ERs) are potential eavesdroppers (Eves) and imperfect channel state information (CSI) of the direct and cascaded channels can be obtained, we investigate the max-min fairness robust secrecy design. The objective is to maximize the minimum robust information rate among the legitimate information receivers (IRs). To solve the formulated non-convex design problem in bounded and probabilistic CSI error models, we utilize the alternating optimization (AO) and successive convex approximation (SCA) methods to obtain an approximate problem. Then, an iteration-based algorithm framework was proposed, where the unit modulus constraint (UMC) of the IRS is handled by the penalty dual decomposition (PDD) method. Moreover, a stochastic SCA method is proposed to handle the outage constrained design with statistical CSI. Finally, simulation results validate the promising performance of the proposed design.

Robust Optimization of Instantaneous Beamforming and Quasi-Static Phase Shifts in an IRS-Assisted Multi-Cell Network

The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most existing works. In this paper, we investigate a multi-antenna base station (BS) serving a single-antenna user with the help of a multi-element IRS in a multi-cell network with inter-cell interference. We consider imperfect channel state information (CSI) at the BS, i.e., imperfect CSIT, and focus on the robust optimization of the BS’s instantaneous CSI-adaptive beamforming and the IRS’s quasi-static phase shifts in two scenarios. In the scenario of coding over many slots, we formulate a robust optimization problem to maximize the user’s ergodic rate. In the scenario of coding within each slot, we formulate a robust optimization problem to maximize the user’s average goodput under the successful transmission probability constraints. The robust optimization problems are challenging two-timescale stochastic non-convex problems. In both scenarios, we obtain closed-form robust beamforming designs for any given phase shifts and more tractable stochastic non-convex approximate problems only for the phase shifts. Besides, we propose an iterative algorithm to obtain a Karush-Kuhn-Tucker (KKT) point of each of the stochastic problems for the phase shifts. It is worth noting that the proposed methods offer closed-form robust instantaneous CSI-adaptive beamforming designs which can promptly adapt to rapid CSI changes over slots and robust quasi-static phase shift designs of low computation and phase adjustment costs in the presence of imperfect CSIT and inter-cell interference. Numerical results further demonstrate the notable gains of the proposed robust joint designs over existing ones and reveal the practical values of the proposed solutions.

Robust Beamforming for Localization-Aided Millimeter Wave Communication Systems

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.

Robust Adaptive Beamforming Algorithm for Sparse Subarray Antenna Array Based on Hierarchical Weighting

Sparse antenna arrays based on subarrays have more and more broad application prospects for the limitation of array space, real-time algorithm and hardware costs. Aiming at the beamforming technology of sparse antenna arrays based on subarrays, this paper proposes a robust adaptive beamforming algorithm based on hierarchical weighting. The algorithm performs conventional beamforming to calculate the weights of each element in the subarray, then the synthetic signals output by each subarray are used as sparse array metadata. The Interference-plus-Noise Covariance Matrix (INCM) is reconstructed by integration in two-dimensional space, and a convex optimization model of a multi-constraint array containing the signal pointing error was established to estimate the real guide vector. Finally, using the reconstructed INCM and the estimation of the guide vector, we obtain a weighted vector between the subarrays and output signal for the whole array. The simulation results show that the proposed algorithm has better Signal-to-Interference-and-Noise Ratio (SINR) and robustness compared with other algorithms for sparse subarray antenna array beamforming.