Channel State Information Error Research Articles

A novel sum-rate maximization scheme for NOMA-VLC systems via the black widow enhanced Kepler optimization algorithm

Non-orthogonal multiple access (NOMA) is a forthcoming method to address the challenges posed by increasing device connectivity and diverse communication requirements of visible light communication (VLC) systems in the sixth generation (6G) networks. This paper integrates NOMA and VLC systems (NOMA-VLC) and concentrates on studying the problem of maximizing the sum rate in downlink systems using NOMA, considering the existence of channel state information (CSI) errors. Taking power distribution and the user's quality of service (QoS) requirement as constraints, the purpose is to maximize the total sum rate. However, because this problem is usually a nonconvex NP-hard problem, it is challenging to obtain the best solution. In this paper, a combination of the improved Kepler optimization algorithm and the black widow optimization algorithm (BWO-KOA) is provided as a solution to solve this optimization problem and get an effective solution. By comparing the properties of BWO-KOA with other existing algorithms, the simulation results demonstrate that BWO-KOA outperforms these methods in the sum rate characteristics of the NOMA-VLC system.

Low complexity beamforming design in reconfigurable intelligent surface-assisted communication systems

Due to the possibility of blockage during communication, the communication quality may be poor. Therefore, Reconfigurable Intelligent Surface (RIS) technology can effectively solve this problem. In order to increase the capacity of RIS-assisted wireless communication systems, joint optimization of beamforming design is crucial. However, the complexity of the optimization algorithm increases with the increase in the number of base station antennas and RIS elements deployed. Therefore, we propose a joint low-complexity optimization beamforming design based on fractional programming (FP) to address this issue. Specifically, we first use perfect channel state information to maximize the system's sum rate, as this problem is non-convex, we decompose the original problem into three sub-problems, and then introduce appropriate auxiliary variables. We derive optimal closed-form solutions for active and passive beamforming types, respectively. As the optimal solution obtained leads to higher computational complexity with an increase in the number of base station antennas and RIS elements, we reduce the computational complexity of obtaining the optimal solution based on the Woodbury transformation and scalar transformation. The proposed algorithm is also extended to the case where there is channel state information error. Finally, simulation results show that the proposed algorithm has certain advantages over other algorithms.

Joint Hybrid Beamforming Design for Millimeter Wave Amplify-and-Forward Relay Communication Systems

Hybrid beamforming (HBF) has been regarded as one of the most promising technologies in millimeter Wave (mmWave) communication systems. In order to guarantee the communication quality in non-line-of-sight (NLOS) scenarios, joint HBF design for the mmWave amplify-and-forward (AF) relay communication system is studied in this paper. The ideal case is first considered where the mmWave half-duplex (HD) AF relay system operates with channel state information (CSI) accurately known. In order to tackle the non-convex problem, a manifold optimization (MO)-based alternating optimization algorithm is proposed, where an optimization problem containing only constant modulus constraints in Euclidean space can be converted to an unconstrained optimization problem in a Riemann manifold. Furthermore, considering more practical cases with estimation errors of CSI, we investigate the robust joint HBF design with the system operating in full-duplex (FD) mode to obtain higher spectral efficiency (SE). A null-space projection (NP) based self-interference cancellation (SIC) algorithm is developed to attenuate the self-interference (SI). Different from the traditional SI suppression algorithm, there’s no limit on the number of RF chains. Numerical results reveal that our proposed algorithms has a good convergence and can effectively deal with the influence of different CSI estimation errors. A significant performance improvement can be achieved in contrast with other approaches.

Robust Beamforming for Downlink Multi-Cell Systems: A Bilevel Optimization Perspective

Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming technique that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.

Robust Transceiver Design for Correlated MIMO Interference Channels in the Presence of CSI Errors under General Power Constraints

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Outage constrained transmission design for NOMA-based integrated sensing and communication systems

This paper investigates a framework for integrated sensing and communication (ISAC) based on non-orthogonal multiple access (NOMA). In this framework, a dual-function base station (BS) utilizes NOMA technology to send superimposed signals to various users, and this superimposed signal also acts on target sensing simultaneously. Considering the channel estimation error, ensuring the communication performance, and sensing performance requirements, a transmit power optimization problem of ISAC system using NOMA is studied. Specifically, in the statistical channel state information (CSI) error model, the total system communicate power is minimized while ensuring all single users' rate outage probability (OP) constraints and the requirements for the beampattern gains of all single radar targets. Unfortunately, the proposed problem is challenging to solve and non-convex. But we have devised a feasible way to deal with this problem. First, we use Bernstein inequality to transform the rate OP constraint, and this challenging non-convex problem is then successfully solved using a method based on semi-definite relaxation (SDR). The numerical outcomes demonstrate that the system's overall transmission power will increase due to the channel estimation error. The numerical findings also show that the ISAC system performs better with NOMA assistance than with OMA when comparing the NOMA and OMA schemes.

Performance assessment of full-duplex two-way Internet-of-vehicles relay networks under practical imperfect conditions

Contemporary Internet-of-Things (IoT) devices in general and Internet-of-Vehicles (IoV) networks in specific are taking the benefits from using full-duplex (FD) communication with the help of relay nodes to facilitate data transmission. However, self-interference between transmit and receive antennas at the relay node may cause big trouble if self-interference cancellation (SIC) is not applied. In this paper, a rigorous analysis on the performance of FD two-way relay networks (FDTWRNs) for IoV applications under imperfect conditions is provided. Different from earlier studies on the performance of FDTWRNs where one or two imperfect factors were considered, this work simultaneously takes into account many practical issues in the implementation of the IoV networks at the physical layer, including errors in channel state information at all channel links, imperfect SIC and transceiver hardware impairment at all nodes. For relaying protocol, we consider amplify-and-forward with both fixed-gain (FG) and variable-gain (VG) protocols. The exact closed-form expressions (in terms of the system parameters) of key performance factors such as signal-to-interference-plus-noise-distortion-and-error ratio (SINER), outage probability (OP), achievable data rate (ADR), and average symbol error probabilities (ASEP) of the considered system over Rayleigh fading channels and under the combined effect of imperfect CSI, SIC, and transceiver hardware are derived mathematically using probabilistic model analysis. The correctness of the analysis is then verified by Monte Carlo simulations. Drawing upon both analytical and numerical findings, the efficacy of the FDTWRNs under consideration is meticulously and comprehensively assessed in comparison to its performance in ideal conditions characterized by one or multiple critical factors. The disparity between perfect and imperfect scenarios serves as a valuable metric for appraising the practical viability of the considered FDTWRNs when deployed in practical IoV networks.

Joint Beamforming Design in Reconfigurable Intelligent Surface-Assisted Rate Splitting Networks

Reconfigurable Intelligent Surface (RIS) is an emerging technology that can improve the spectrum and energy efficiency of next-generation wireless networks. However, attaining accurate channel state information (CSI) for the cascaded RIS channel is particularly challenging. Imperfect CSI is a major bottleneck to achieving the spectral efficiency benefit of RIS-assisted networks. Rate splitting (RS), a promising multiple access technology, has been shown to be able to achieve an improved spectrum efficiency and be robust to channel uncertainties. This paper investigates the interplay between RIS and RS by considering a RIS-assisted RS beamforming problem. Active beamforming at the base station (BS) and passive beamforming at the RIS are jointly considered to maximize the minimum user rate under both the perfect CSI case and the imperfect CSI case. A block coordinate descent (BCD) algorithm is developed to solve this non-convex problem. Compared with the conventional semi-definite relaxation (SDR) approach, the proposed method does not require that the covariance matrix of the common beamforming vector be rank-one. Moreover, we present theoretical results to help reveal the impact of the system parameters and explain the performance gain resulting from the integration of RIS and RS. Extensive simulation results are also provided to show that RIS-assisted RS can improve the max-min rate performance significantly compared with conventional multiple access technologies, such as non-orthogonal multiple access (NOMA) and space division multiple access (SDMA) with/without RIS, especially in overloaded systems. With the proposed method, RS shows great potential in combating realistic CSI errors in RIS-assisted networks.

Design and Performance Analysis of Massive MIMO Modeling with Reflected Intelligent Surface to Enhance the Capacity of 6G Networks

Reflected Intelligent Surface (RIS) can establish a virtual line-of-sight link to enhance system performance while consuming less power in non-line-of-sight. RIS technique is utilized to minimize the spreading of electromagnetic signals by modifying the surface's electric and magnetic field characteristics. RIS can be adopted with the existing environment to effectively increase efficiency by modifying the radio channel characteristics. The signals are steered to the receiver using an RIS thus improving the link quality. The radio channel is viewed in traditional wireless systems as an uncontrollable entity that typically tampers with transmitted signals. This paper suggests an alternate theoretical model after examining the prevalent models and potential issues. Security of the wireless communication physical layer can be improved with an RIS by just changing the phase of the reflective unit. In this work, the massive Multiple Input Multiple Outputs (MIMO)-based iterative modeling technique is used to build the transmitter, channel, and receiver section. This will simultaneously optimize the RIS passive beamforming pre-coding matrix and thus avoid multi-user interference. At the base station cyclic programming is adopted, it iteratively calculates the active and passive beam-forming RIS matrices. The simulation results demonstrate that the combined pre-coding technique used in this work improves the weighted sum rate, efficiency, and coverage ratio. The results show that MIMO with continuous phase shift RIS achieves a higher Weighted Sum Ratio (WSR) and minimum Channel State Information (CSI) error in comparison with the random phase shift RIS. The performance metrics sum rate, signal-to-interference plus noise ratio (SINR), energy efficiency, and transmit power are analyzed and compared.

Robust Secure Transmission for Active RIS Enabled Symbiotic Radio Multicast Communications

In this paper, we propose a robust secure transmission scheme for an active reconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system in the presence of multiple eavesdroppers (Eves). In the considered system, the active RIS is adopted to enable the secure transmission of primary signals from the primary transmitter to multiple primary users in a multicasting manner, and simultaneously achieve its own information delivery to the secondary user by riding over the primary signals. Taking into account the imperfect channel state information (CSI) related with Eves, we formulate the system power consumption minimization problem by optimizing the transmit beamforming and reflection beamforming for the bounded and statistical CSI error models, taking the worst-case SNR constraints and the SNR outage probability constraints at the Eves into considerations, respectively. Specifically, the S-Procedure and the Bernstein-Type Inequality are implemented to approximately transform the worst-case SNR and the SNR outage probability constraints into tractable forms, respectively. After that, the formulated problems can be solved by the proposed alternating optimization (AO) algorithm with the semi-definite relaxation and sequential rank-one constraint relaxation techniques. Numerical results show that the proposed active RIS scheme can reduce up to 27.0% system power consumption compared to the passive RIS.

Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems

The large overhead arising from conventional channel estimations in reconfigurable intelligent surface (RIS) aided millimeter-wave communication systems, may offset the performance gain brought by the RIS. To tackle this issue, we propose a location information assisted beamforming design without the requirement of the channel training process. First, we establish the geometrical relationship between the channel model and the user location, and mathematically derive an approximate channel state information (CSI) error bound based on the user location error region. Then, for combating the negative impact of the location error on the communication performance, we formulate a worst-case robust beamforming optimization problem to optimize the beamformer at the base station (BS) and the phase-shift matrix at the RIS. To solve this non-convex problem, we develop a novel relaxed alternating optimization process (RAOP) by utilizing various optimization tools, such as the Lagrange multiplier, the matrix inversion lemma, the semidefinite relaxation (SDR), as well as the branch-and-bound (BnB). Additionally, we prove sufficient conditions for the SDR to yield rank-one solutions, and modify the BnB to acquire the phase-shift solution under an arbitrary constraint of possible phase-shift values. Finally, we analyse the convergence and complexity of the proposed RAOP, and carry out simulations for performance evaluations. Compared to the conventional non-robust beamforming, our method performs better and shows strong robustness against the location-error-related CSI uncertainty. Compared to the robust beamforming based on the S-procedure and penalty convex-concave procedure (CCP), our method with BnB shows the advantages of being able to converge faster and handle arbitrary phase-shift argument sets.

User fairness-enhanced beamforming for IRS-assisted cognitive radio networks based on prior judgment mechanism

This research proposes a novel approach, namely the user fairness-enhanced beamforming (UFEB) scheme, to improve the user fairness in intelligent reflecting surface (IRS) assisted multiuser cognitive radio networks (CRNs). The proposed scheme takes into account the bounded channel state information (CSI) error of the primary user (PU) related channel and establishes a sum α-fair utility maximization problem, where α denotes the fairness adjustment index. This problem optimizes the system for fairness and rate, subject to constraints, such as the quality-of-service requirement of secondary users (SUs), limited interference on PUs, maximum transmit power of cognitive base station (CBS), and unit modulus of the IRS. Firstly, we design a prior judgment mechanism that makes preliminary assessments of the optimized requirements of the system in terms of fairness and rate, whose rationality can be proved in the simulation results. Then, with the prior selection of α, by exploiting the successive convex approximation and Taylor series expansion, we present an alternating iterative algorithm to solve the α-fair utility maximization problem. Simulation results show that the prior selection of α can accurately reflect the difference in the optimization requirements for sum rate and fairness of the system after the beamforming of CBS and the phase of IRS are determined, and validate the effectiveness and superiority of our proposed UFEB scheme in improving the fairness among SUs.

Robust Design of IRS-Aided Multi-Group Multicast System With Imperfect CSI

In this paper, the robust design for the intelligent reflective surface (IRS) assisted wireless multi-group multicast system is considered, in which two optimization design problems under two different channel state information (CSI) error models are separately discussed, i.e., the fairness-based problems and the quality-of-service (QoS)-based problems for both the bounded CSI error model and the statistical CSI error model. In order to deal with the non-convex constraints of the considered problems, i.e., bounded CSI error based constraint and statistical CSI error based constraint, S-procedure is adopted to convert the non-convex SINR constraint with bounded CSI error into linear matrix inequalities (LMIs), and the Bernstein-type inequality is utilized to transform the outage probability constraint with statistical CSI error into a second-order cone (SOC) constraint and linear inequalities. Following that, two efficient algorithms based on alternate optimization (AO) are proposed to solve the fairness problems and QoS problems, wherein the semi-definite programming (SDP), penalty convex-concave procedure (CCP) and semi-definite relaxation (SDR) are utilized. Furthermore, we analyze the complexity of the proposed algorithms. Finally, some numerical simulation results are presented to verify the effectiveness of the proposed algorithms, and the impacts of the CSI error and the discrete precision of IRS reflection phase shift on the system performance are analyzed, which provides some insights for the IRS deployment and system robust design.

Mutated Beamforming for Cognitive Radio 5G Relay Network

In fifth-generation (5G) relay networks, the network blockage situation upsurges owing to inadequate penetration capability of the radio waves or interruption due to tall buildings and obstacles. To improve the network coverage and spectrum efficiency, a cooperative cognitive relay network with mutated beamforming is proposed. This work introduces mutation and replacement-strategy-based beamforming to enhance the opportunistic throughput and spectral efficiency. The proposed model employs imperfect channel state information (CSI) with consideration of the CSI error due to interfering signal. The mutated beamforming technique is implemented for the cognitive radio environment postefficient spectrum sensing. The proposed mutated beamforming mitigates CSI error via performing beamforming with minimized sidelobes and placing nulls in the desired direction. The mutated beamforming in 5G relay network achieves a spectral efficiency of 30 b/s/Hz at SNR = 20 dB.

Robust Transmit Beamforming for Secure Integrated Sensing and Communication

This paper studies a downlink secure integrated sensing and communication (ISAC) system, in which a multi-antenna base station (BS) transmits confidential messages to a single-antenna communication user (CU) while performing sensing on targets that may act as suspicious eavesdroppers. To ensure the quality of target sensing while preventing their potential eavesdropping, the BS combines the transmit confidential information signals with additional dedicated sensing signals, which play a dual role of artificial noise (AN) for degrading the qualities of eavesdropping channels. Under this setup, we jointly design the transmit information and sensing beamforming, with the objective of minimizing the weighted sum of beampattern matching errors and cross-correlation patterns for sensing subject to secure communication constraints. The robust design takes into account the channel state information (CSI) imperfectness of the eavesdroppers in two practical CSI error scenarios. First, we consider the scenario with bounded CSI errors of eavesdroppers, in which the worst-case secrecy rate constraint is adopted to ensure secure communication performance. In this scenario, we present the optimal solution to the worst-case secrecy rate constrained sensing beampattern optimization problem, by adopting the techniques of S-procedure, semi-definite relaxation (SDR), and a one-dimensional (1D) search, for which the tightness of the SDR is rigorously proved. Next, we consider the scenario with Gaussian CSI errors of eavesdroppers, in which the secrecy outage probability constraint is adopted. In this scenario, we present an efficient algorithm to solve the more challenging secrecy outage-constrained sensing beampattern optimization problem, by exploiting the convex restriction technique based on the Bernstein-type inequality, together with the SDR and 1D search. Finally, numerical results show that the proposed designs can properly adjust the information and sensing beams to balance the tradeoffs among communicating with CU, sensing targets, and confusing eavesdroppers, so as to achieve desirable sensing transmit beampatterns while ensuring the CU’s secrecy requirements for the two scenarios.

Performance of Cell-Free Massive MIMO Under Imperfect Channel State Information and Reciprocity Calibration

This article studies the downlink performance of a cell-free massive multiple-input–multiple-output (MIMO) system with imperfect channel estimation and reciprocity calibration. We present the statistical characteristics of the calibration error with the Argos algorithm and a relay-based calibration algorithm to obtain the calibration parameters of the whole network. Then, we derive approximate expressions of the downlink spectral efficiency for a cell-free massive MIMO system with imperfect channel state information and calibration error. The numerical results show the advantage of the proposed calibration algorithm and validate the accuracy of the theoretical expressions.

Robust beamforming for dual‐function radar‐communication with imperfect channel state information

AbstractDual‐function radar and communication (DFRC) have recently received significant attention as an effective way to alleviate spectrum congestion and reduce system costs. Joint transmit beamforming plays a critical role in DFRC systems, as it can effectively reduce mutual interference and improve the performance of both the radar and communication systems. This paper investigates the problem of robust beamforming design with imperfect channel state information (CSI) to ensure communication performance while optimizing radar performance. Considering elliptically bounded CSI errors, the objective function is designed to minimize the radar loss function, which is related to the radar transmit beam pattern, subject to worst‐case signal‐to‐interference‐plus‐noise ratio constraints at each user, which ensure fairness between users. An efficient algorithm based on semidefinite relaxation and the S‐procedure is proposed to solve the non‐convex problem. Simulation results are presented to illustrate the effectiveness of the proposed robust beamforming scheme, which can reduce the impact of channel errors.

Robust Joint Precoding/Combining Design for Multiuser MIMO Systems With Calibration Errors

We consider the downlink of a multiuser system operating in the time-division duplexing mode, for which base station (BS) and users are equipped with multiple antennas, and provide a robust precoding/combining design against imperfect channel state information (CSI) and calibration errors due to hardware mismatch. Towards this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean squared error optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and the user sides. We also provide asymptotic closed-form expressions for the mean squared error (MSE) and the achievable sum-rate in the massive MIMO regime. The results indicate that while the MSE linearly increases with the calibration errors at the user side, the sum-rate is asymptotically independent of them. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions while having the same order of complexity. Moreover, when the BS sends a quantized version of the combining coefficients to the users, it is observed that the proposed solution is more robust to the quantization errors than the existing algorithms.

Robust Power Allocation for Integrated Visible Light Positioning and Communication Networks

Integrated visible light positioning and communication (VLPC), capable of combining advantages of visible light communications (VLC) and visible light positioning (VLP), is a promising key technology for the future Internet of Things. In VLPC networks, positioning and communications are inherently coupled, which has not been sufficiently explored in the literature. We propose a robust power allocation scheme for integrated VLPC Networks by exploiting the intrinsic relationship between positioning and communications. Specifically, we derive explicit relationships between random positioning errors, following both a Gaussian distribution and an arbitrary distribution, and channel state information errors. Then, we minimize the Cramer-Rao lower bound (CRLB) of positioning errors, subject to the rate outage constraint and the power constraints, which is a chance-constrained optimization problem and generally computationally intractable. To circumvent the nonconvex challenge, we conservatively transform the chance constraints to deterministic forms by using the Bernstein-type inequality and the conditional value-at-risk for the Gaussian and arbitrary distributed positioning errors, respectively, and then approximate them as convex semidefinite programs. Finally, simulation results verify the robustness and effectiveness of our proposed integrated VLPC design schemes.

Robust Beamforming Design for RIS-Aided Cell-Free Systems With CSI Uncertainties and Capacity-Limited Backhaul

In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering the channel state information (CSI) uncertainties of both the direct channels and cascaded channels at the transmitter with capacity-limited backhaul. We jointly optimize the precoding at the access points (APs) and the phase shifts at multiple RISs to maximize the worst-case sum rate of the CF system subject to the constraints of maximum transmit power of APs, unit-modulus phase shifts, limited backhaul capacity, and bounded CSI errors. By applying a series of transformations, the non-smoothness and semi-infinite constraints are tackled in a low-complexity manner that facilitates the design of an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides the considered problem into two subproblems. For the RIS phase shifts optimization subproblem, we exploit the penalty convex-concave procedure (P-CCP) to obtain a stationary solution and achieve effective initialization. For precoding optimization subproblem, successive convex approximation (SCA) is adopted with a convergence guarantee to a Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate the effectiveness of the proposed robust beamforming design, which achieves superior performance with low complexity. Moreover, the importance of RIS phase shift optimization for robustness and the advantages of distributed RISs in the CF system are further highlighted.