Bounded Channel Uncertainty Research Articles

Robust transmission for multi-user OFDM-based IRS-assisted cognitive radio networks

In cognitive radio networks (CRNs) employing underlay multi-user scenarios, intelligent reflecting surface (IRS) plays a crucial function in augmenting total transmission rate for cognitive radio (CR) users, while adhering to restrictions caused by the interference from secondary users (SUs) to primary users (PUs). However, due to the passive characteristics of IRS, it operates in a non-cooperative relationship with both PU and SU network, resulting in delayed information acquisition and channel errors. Therefore, in this research, considering channel uncertainties, limited interference, and interference among SUs, we put forward a robust power and subcarrier allocation strategy for orthogonal frequency division multiplexing (OFDM) with IRS-assisted CRNs in a multi-user scenario. Formulated as a resource allocation (RA) problem in an underlay spectrum sharing mode for multi-user CR, the joint optimization problem encompasses subcarrier allocation and power allocation for SUs, a phase shift matrix for IRS, and minimum rate constraints. We transform the problem using worst-case criterion into a deterministic convex optimization problem to handle the constraints of bounded channel uncertainties. By utilizing matching theory, variable substitution, scaling methods, convex-concave programming (CCP), and alternating optimization techniques, the converted non-convex problem is transformed into a convex one. Simulation results showcase that the proposed algorithm achieves significant gains in transmission rate and exhibits robustness.

Robust Secure Resource Allocation for RIS-Aided SWIPT Communication Systems.

Aiming at the influence of channel uncertainty, user information leakage and harvested energy improvement, this paper proposes a robust resource allocation algorithm for reconfigurable intelligent reflector (RIS) multiple-input single-output systems based on imperfect channel state information. First, considering the legal user minimum secret rate constraint, the base station maximum transmit power constraint and the RIS phase shift constraint with the bounded channel uncertainty, a joint optimization of the base station active beam, energy beam and RIS phase shift is established. A multivariate coupled nonlinear resource allocation problem for matrices is addressed. Then, using S-procedure and alternating optimization methods, the original non-convex problem is transformed into a deterministic convex optimization problem and an alternating optimization algorithm based on continuous convex approximation is proposed. The simulation results show that the proposed algorithm has better fairness harvested energy compared with the traditional robust algorithm.

Robust Symbol-Level Precoding and Passive Beamforming for IRS-Aided Communications

This paper investigates a joint beamforming design in a multiuser multiple-input single-output (MISO) communication network aided with an intelligent reflecting surface (IRS) panel. The symbol-level precoding (SLP) is adopted to enhance the system performance by exploiting the multiuser interference (MUI) with consideration of bounded channel uncertainty. The joint beamforming design is formulated into a nonconvex worst-case robust programming to minimize the transmit power subject to single-to-noise ratio (SNR) requirements. To address the challenges due to the constant modulus and the coupling of the beamformers, we first study the single-user case. Specifically, we propose and compare two algorithms based on the semidefinite relaxation (SDR) and alternating optimization (AO) methods, respectively. It turns out that the AO-based algorithm has much lower computational complexity but with almost the same power to the SDR-based algorithm. Then, we apply the AO technique to the multiuser case and thereby develop an algorithm based on the proximal gradient descent (PGD) method. The algorithm can be generalized to the case of finite-resolution IRS and the scenario with direct links from the transmitter to the users. Numerical results show that the SLP can significantly improve the system performance. Meanwhile, 3-bit phase shifters can achieve near-optimal power performance.

An Efficient Algorithm for Robust Fractional QCQP and its Applications to Multiuser Beamforming With Bounded Channel Uncertainties

An Efficient Algorithm for Robust Fractional QCQP and its Applications to Multiuser Beamforming With Bounded Channel Uncertainties

Robust resource allocation for NOMA-assisted heterogeneous networks

As a promising technology to improve spectrum efficiency and transmission coverage, Heterogeneous Network (HetNet) has attracted the attention of many scholars in recent years. Additionally, with the introduction of the Non-Orthogonal Multiple Access (NOMA) technology, the NOMA-assisted HetNet cannot only improve the system capacity but also allow more users to utilize the same frequency band resource, which makes the NOMA-assisted HetNet a hot topic. However, traditional resource allocation schemes assume that base stations can exactly estimate direct link gains and cross-tier link gains, which is impractical for practical HetNets due to the impact of channel delays and random perturbation. To further improve energy utilization and system robustness, in this paper, we investigate a robust resource allocation problem to maximize the total Energy Efficiency (EE) of Small-Cell Users (SCUs) in NOMA-assisted HetNets under imperfect channel state information. By considering bounded channel uncertainties, the robust resource optimization problem is formulated as a mixed-integer and nonlinear programming problem under the constraints of the cross-tier interference power of macrocell users, the maximum transmit power of small base station, the Resource Block (RB) assignment, and the quality of service requirement of each SCU. The original problem is converted into an equivalent convex optimization problem by using Dinkelbach's method and the successive convex approximation method. A robust Dinkelbach-based iteration algorithm is designed by jointly optimizing the transmit power and the RB allocation. Simulation results verify that the proposed algorithm has better EE and robustness than the existing algorithms.

Robust Beamforming Techniques for Non-Orthogonal Multiple Access Systems with Bounded Channel Uncertainties

Robust Beamforming Techniques for Non-Orthogonal Multiple Access Systems with Bounded Channel Uncertainties

Capacity-Maximized Transmitter Precoding for MU MIMO VLC Systems With Bounded Channel Uncertainties

Considering imperfect channel state information (CSI), we study robust precoding design for multiuser multiple-input–multiple-output (MIMO) indoor visible-light communication systems, where one transmitter with several light-emitting diodes sends messages to multiple receivers each with several photodiodes. We model the imperfect CSI with bounded channel uncertainties by worst-case model, aiming to maximize the worst-case sum capacity of all receivers via optimizing the precoders at the transmitter under optical power constraints. The robust precoding problem is nonconvex and thus hard to solve. To overcome this difficulty, we first separate the logarithm function and the precoders in the objective function, then employ the sign-definiteness lemma to eliminate the channel uncertainties, and finally develop an effective iterative optimization algorithm to compute the precoders. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

Energy Efficiency Optimization for Secure Transmission in MISO Cognitive Radio Network with Energy Harvesting

In this paper, we investigate different secrecy energy efficiency (SEE) optimization problems in a multiple-input single-output underlay cognitive radio (CR) network in the presence of an energy harvesting receiver. In particular, these energy efficient designs are developed with different assumptions of channels state information (CSI) at the transmitter, namely perfect CSI, statistical CSI and imperfect CSI with bounded channel uncertainties. In particular, the overarching objective here is to design a beamforming technique maximizing the SEE while satisfying all relevant constraints linked to interference and harvested energy between transmitters and receivers. We show that the original problems are non-convex and their solutions are intractable. By using a number of techniques, such as non-linear fractional programming and difference of concave (DC) functions, we reformulate the original problems so as to render them tractable. We then combine these techniques with the Dinkelbach's algorithm to derive iterative algorithms to determine relevant beamforming vectors which lead to the SEE maximization. In doing this, we investigate the robust design with ellipsoidal bounded channel uncertainties, by mapping the original problem into a sequence of semidefinite programs by employing the semidefinite relaxation, non-linear fractional programming and S-procedure. Furthermore, we show that the maximum SEE can be achieved through a search algorithm in the single dimensional space. Numerical results, when compared with those obtained with existing techniques in the literature, show the effectiveness of the proposed designs for SEE maximization.

Robust SINR-Constrained Symbol-Level Multiuser Precoding With Imperfect Channel Knowledge

In this paper, we address robust design of symbol-level precoding for the downlink of multiuser multiple-input multiple-output wireless channels, in the presence of imperfect channel state information (CSI) at the transmitter. In particular, we consider two common uncertainty models for the CSI imperfection, namely, spherical (bounded) and stochastic (Gaussian). Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming bounded channel uncertainties, we obtain a convex CI constraint based on the worst-case robust analysis, whereas in the case of Gaussian uncertainties, we define probabilistic CI constraints in order to achieve robustness to statistically-known CSI errors. Since the probabilistic constraints of actual interest are difficult to handle, we resort to their convex approximations, yielding tractable (deterministic) robust constraints. Three convex approximations are developed based on different robust conservatism approaches, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness conditions, while both always outperform the benchmark. Using the developed CI constraints, we formulate the robust precoding optimization as a convex conic quadratic program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with existing robust precoding schemes. We also show that the robust design increases the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart.

Energy Efficiency Optimization for Secure Transmission in MISO Cognitive Radio Network With Energy Harvesting

In this paper, we investigate different secrecy energy efficiency (SEE) optimization problems in a multiple-input single-output underlay cognitive radio (CR) network in the presence of an energy harvesting receiver. In particular, these energy efficient designs are developed with different assumptions of channels state information (CSI) at the transmitter, namely perfect CSI, statistical CSI and imperfect CSI with bounded channel uncertainties. In particular, the overarching objective here is to design a beamforming technique maximizing the SEE while satisfying all relevant constraints linked to interference and harvested energy between transmitters and receivers. We show that the original problems are non-convex and their solutions are intractable. By using a number of techniques, such as non-linear fractional programming and difference of concave (DC) functions, we reformulate the original problems so as to render them tractable. We then combine these techniques with the Dinkelbach’s algorithm to derive iterative algorithms to determine relevant beamforming vectors which lead to the SEE maximization. In doing this, we investigate the robust design with ellipsoidal bounded channel uncertainties, by mapping the original problem into a sequence of semidefinite programs by employing the semidefinite relaxation, non-linear fractional programming and S-procedure. Furthermore, we show that the maximum SEE can be achieved through a search algorithm in the single dimensional space. Numerical results, when compared with those obtained with existing techniques in the literature, show the effectiveness of the proposed designs for SEE maximization.

Notice of Violation of IEEE Publication Principles: Robust Secure Precoding Design for MIMO SWIPT System With Bounded Channel Uncertainties

In this paper, we investigate the worst-case robust secure precoding design for simultaneous wireless information and power transfer in multiple-input-multiple-output wiretap system, which consists of one transmitter, one information receiver, and one energy receiver. By treating the ER as potential eavesdropper, we aim to maximize the worst-case secrecy rate by designing the transmit precoding matrix. This is a typical non-convex optimal design while the channel state information uncertainties make this problem harder to handle, thus we propose a new method to obtain the solution. Specifically, instead of approximating the logarithmic determinant as a trace, we propose to linearize the two log-det terms. After linearization, epigraph reformulation is used to deal with the bounded channel uncertainties. Then, an alternating optimization method is utilized to solve the reformulated problem. After obtaining the precoding matrix, we derive the worst-case secrecy rate by solving another optimal problem with respect to the channel uncertainty. Numerical results validate the performance of our proposed design.

Robust Beamforming Techniques for Non-Orthogonal Multiple Access Systems with Bounded Channel Uncertainties

In this letter, we propose a robust beamforming design for non-orthogonal multiple access (NOMA) based multiple-input single-output (MISO) downlink systems. In particular, the robust power minimization problem is studied with imperfect channel state information (CSI), where the beamformers are designed by incorporating norm-bounded channel uncertainties to provide the required quality of service at each user. This robust scheme is developed based on the worst-case performance optimization framework. In terms of beamforming vectors, the original robust design is not convex and therefore, the robust beamformers cannot be obtained directly. To circumvent this non-convex issue, the original intractable problem is reformulated into a convex problem, where the non-convex constraint is converted into a linear matrix inequality (LMI) by exploiting S-Procedure. Finally, simulation results are provided to demonstrate the effectiveness of the proposed robust design.

Control of networked systems with packet loss and channel uncertainty

This study considers the control problem of networked control systems (NCSs) concerning both bounded channel uncertainty and packet loss. First, the authors deal with the problems of state feedback control for NCSs concerning both bounded random packet loss and channel uncertainty. Based on a previous work which copes with packet loss only, a classic model is used to describe the NCS with both packet loss and channel uncertainty in an unified framework. The stability conditions of NCSs are given by a common quadratic Lyapunov function and an approach is given to design the dynamic feedback controller via solving linear matrix inequalities. Second, the problems of output feedback control for NCSs concerned both bounded random packet loss and channel uncertainty are considered. A new sufficient condition is developed to guarantee the exponentially mean square stability of closed-loop networked systems and by using the stability theory, the controller and observer design problem is solved. Finally, numerical simulations and practical experiments are given to show the effectiveness of both approaches.

Sum-rate maximization and robust beamforming design for MIMO two-way relay networks with reciprocal and imperfect CSI

In this paper, we investigate the robust relay beamforming design for a multi-input multi-output (MIMO) two-way relay networks (TWRN) by considering imperfect and reciprocal channel state informations (CSIs). In order to maximize the sum-rate (SR) subject to the individual relay power constraint, we first equivalently convert the objective problem into a sum of the inverse of the signal-to-residual-interference-plus-noise ratio (SI-SRINR) problem. The SI-SRINR problem can be reformulated as a biconvex semi-definite programming (SDP) which employs bounded channel uncertainties as the worst-case model. Then, we convert residual-interference-plus-noise (RIN) and relay power constraints into linear matrix inequalities (LMIs). By this way, the objective problem can be tackled by the proposed efficient iterative algorithm. The analysis demonstrates the procedures of the proposed SI-SRINR robust design.

Robust Transmit Beamforming for Parameter Estimation using Distributed Sensors

In this letter, we study the problem of estimating a complex parameter in a wireless sensor network under individual power constraints and bounded channel uncertainty, where the channel state information is assumed to be imperfect at both the sensors and the fusion center. Transmit beamformers and a linear estimator that minimize the maximum mean square error are found. Although this problem is nonconvex, it can be relaxed to become a semidefinite programming problem by re-parameterization and semidefinite relaxation. Surprisingly, we find that relaxation is tight and a global optimal solution can be found. Finally, numerical simulations are performed to evaluate the performance of the robust estimator.

Distributed Resource Allocation for Relay-Aided Device-to-Device Communication Under Channel Uncertainties: A Stable Matching Approach

Wireless device-to-device (D2D) communication underlaying cellular network is a promising concept to improve user experience and resource utilization. Unlike traditional D2D communication, where two mobile devices in the proximity establish a direct local link bypassing the base station, in this work, we focus on relay-aided D2D communication. Relay-aided transmission could enhance the performance of D2D communication when D2D user equipments (UEs) are far apart from each other and/or the quality of D2D link is not good enough for direct communication. Considering the uncertainties in wireless links, we model and analyze the performance of a relay-aided D2D communication network, where the relay nodes serve both the cellular and D2D users. In particular, we formulate the radio resource allocation problem in a two-hop network to guarantee the data rate of the UEs while protecting other receiving nodes from interference. Utilizing time sharing strategy, we provide a centralized solution under bounded channel uncertainty. With a view to reducing the computational burden at relay nodes, we propose a distributed solution approach using stable matching to allocate radio resources in an efficient and computationally inexpensive way. Numerical results show that the performance of the proposed method is close to the centralized optimal solution and there is a distance margin beyond which relaying of D2D traffic improves network performance.

Robust Beamforming for Cognitive Multi-Antenna Relay Networks with Bounded Channel Uncertainties

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.

Capacity of Compound MIMO Gaussian Channels With Additive Uncertainty

This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the compound MIMO Gaussian channel. We study the optimal transmit covariance matrix design to achieve the capacity of compound MIMO Gaussian channels, where the channel uncertainty region is characterized by the spectral norm. This design problem is a challenging nonconvex optimization problem. However, in this paper, we reveal that this problem has a hidden convexity property, which can be exploited to map the problem into a convex optimization problem. We first prove that the optimal transmit design is to diagonalize the nominal channel, and then show that the duality gap between the capacity of the compound MIMO Gaussian channel and the min-max channel capacity is zero, which proves and generalizes a conjecture of Loyka and Charalambous. The key tools for showing these results are a new matrix determinant inequality and some unitarily invariant properties.

Robust estimation in flat fading channels under bounded channel uncertainties

We investigate channel equalization problem for time-varying flat fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a time-varying flat fading channel. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into their problem formulations instead of directly using the inaccurate channel information that is available. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We illustrate the performances of the equalization methods through simulations.

Worst-case mean square error (MSE) transceiver design for imperfect estimate multi-input-multi-output communication channels

The authors consider the worst-case transceiver design problem under spectrum bounded channel uncertainty matrices. Their design aims to minimise the trace and the determinant of the estimate error covariance matrix, respectively. The authors relax the formulated problem into an optimisation problem with bilinear matrix inequality constraints (i.e. BMI problem), from which a local optimal solution is obtained by applying semi-definite programming. Furthermore, the authors consider norm bounded source symbols and extend their approach to design the worst-case transceiver with respect to both channel uncertainties and norm bounded source symbols.