Gaussian Randomization Research Articles

IRS assisted anti jamming and beamforming technique

Recently, the emerging intelligent reflecting surfaces (IRS) has been leveraged to establish a smart and controllable wireless environment. This paper addresses the challenge of maximizing spectral efficiency in an IRS-aided downlink multi-user system while facing jammer attacks. The optimization problem focuses on improving the available transmission rate and limiting the impact of malicious jammer signals. The efficiency of the IRS in anti-jamming communications is achieved by determining the optimal phase shifts of the IRS elements and the optimal beamforming at the base station (BS). The optimization problem is non-convex. To tackle this non-convexity, an alternating optimization algorithm is proposed, dividing the main problem into two sub-problems which are solved using the semi-definite relaxation (SDR) and Gaussian randomization techniques. The simulation results confirm the enhanced spectral efficiency achieved by the proposed anti-jamming method in an IRS-assisted system. The optimal adjustment of the phase shifts in the IRS elements has resulted in a significant enhancement of about 25% in spectral efficiency compared to the random IRS phase case.

A low-complexity ADMM-based secure beamforming for IRS-assisted uplink cognitive radio networks with NOMA

Intelligent reflecting surface (IRS) and non-orthogonal multiple access (NOMA) are both powerful means to improve the spectrum efficiency and can assist the cognitive radio network (CRN) in achieving more effective spectrum allocation. However, spectrum sharing in CRNs and the utilization of the scarce bandwidth in NOMA make it vulnerable to security threats. The secure beamforming design in IRS-assisted CRNs with NOMA is complicated and non-convex. Traditional semidefinite relaxation along with Gaussian randomization (SDR-GR) algorithm can solve the non-convex problem, however a high computational complexity. This paper proposes an alternating direction method of multipliers (ADMM)-based sum secrecy rate maximization (A-SSRM) scheme to achieve secure transmission with low computation complexity in IRS-assisted uplink CRNs with NOMA. Specifically, we derive an appropriate transformation of the original problem based on the ADMM framework and decompose it into multiple sub-problems, which are carefully designed to have closed-form solutions. Furthermore, an eavesdropper zero forcing (EZF)-based sub-optimal scheme is presented. Simulation results reveal that our proposed A-SSRM scheme outperforms other benchmarks in terms of sum secrecy rate and reduces the average running time by 6 times compared with the traditional SDR-GR algorithm. This is attributed to our effective decoupling and decomposing of the original problem, which enables each sub-problem to obtain a simple closed-form solution through derivation.

Randomized algorithm: An advanced algorithm for modern video games

Nowadays, video games are more and more popular, and the variety of games is also growing. Under intense competition, developers need to make their games replayable without being mediocre. Randomized algorithms would be helpful. The randomized algorithm generally refers to employing randomness to create different possible solutions. This review paper focuses on the use of randomized algorithms in modern video games. It analyzes different types of randomized algorithms, such as Gaussian Randomness and Filtered Randomness. It also outlines their general principles, advantages and disadvantages. Moreover, this paper discusses the applications of randomized algorithms in several mainstream popular types of video games, including Rogue-like, Sandbox, and Multiplayer Online Battle Arena (MOBA) games. This study will contribute to the application of stochastic algorithms in modern video games, but there are still many limitations and further research is needed.

Joint Phase Shift and Beamforming Design in a Multi-User MISO STAR-RIS Assisted Downlink NOMA Network

Simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has gradually been considered as a promising technology in the wireless communication networks. Besides, non-orthogonal multiple access (NOMA) is also the key technology in the sixth-generation (6 G) wireless communication system. In this work, we study a multiple input single output (MISO) STAR-RIS assisted NOMA downlink network and investigate the energy efficiency (EE) maximization to achieve the tradeoff between the sum rate and the power consumption. The original formulated problem is non-convex due to the coupled beamforming vectors of the users and phase shifts of the STAR-RIS. To efficiently solve the problem, we split the original non-convex problem into the phase shift and beamforming optimization problems and then solve them alternatively. In the phase shift optimization, fractional programming (FP) is applied to transform the sum rate maximum problem to convex semidefinite relaxation (SDR) one with the rank-one constraint. After this, a novel sequential rank-one constraint relaxation (SROCR) is proposed to convert the rank-one constraint into a convex one, which can effectively overcome the inadequacy of Gaussian randomization, i.e., quality of the solutions and computational complexity. Similarly, FP is applied to solve the beamforming problem by transforming it to SDR problem. It turns out that the optimal solution of the SDR beamforming optimization problem can be guaranteed to be rank-one by the mathematical proof and experiments. The simulation results demonstrate the STAR-RIS NOMA system can achieve the superior performance in EE.

UKF-Based Channel Tracking Method for IRS-Aided mmWave MISO Systems

In this paper, we propose an unscented Kalman filtering (UKF)-based method to track the channel parameters of the intelligent reflecting surface (IRS) aided millimeter wave (mmWave) multi-input single-output (MISO) systems. To minimize the mean squared error (MSE) of the tracking parameters, the beamforming vector of the base station (BS) and the reflecting vector of the IRS are designed iteratively, considering the transmit power constraint of the BS and the unit module constraint of the IRS. The resulting sub-problems can be transformed into quadratic constraint quadratic problems (QCQPs), which are solved by the semidefinite relaxation (SDR) method and Gaussian randomization. Simulation results demonstrate that the proposed method outperforms existing benchmark methods.

Fair multigroup multicast precoding design based on traffic demands for multibeam satellite systems

Onboard resources are limited for multibeam satellite communication systems, while differences exist in traffic demands among users. Since conventional multigroup multicast precoding methods do not take traffic demands for users into consideration, it is difficult to flexibly adjust the offered throughput to users’ demands. Users with higher demand may obtain lower throughput while users with lower demand may be over-satisfied, which results in the requested-offered throughput mismatch and resource waste. This paper proposes a fair multigroup multicast precoding design based on traffic demands. To obtain the precoding design, the optimization problem aimed at maximizing the minimum throughput satisfaction ratio, which is defined as the ratio of the offered throughput to the traffic demand, is formulated, so as to provide fair service for all users while satisfying per-feed power constraints and traffic demand constraints. To address this problem, an auxiliary variable is first introduced to equivalently simplify it. Then, the semidefinite relaxation and the bisection search strategies are adopted to further handle the problem. Finally, the optimal precoding vectors are obtained by employing eigenvalue decomposition or Gaussian randomization. Simulation results indicate the effectiveness of the proposed precoding algorithm and demonstrate that it can better adapt to the scenarios with different traffic demands.

Joint Active and Passive Beamforming Design for IRS-Aided Radar-Communication

In this paper, we study an intelligent reflecting surface (IRS)-aided radar-communication (Radcom) system, where the IRS is leveraged to help Radcom base station (BS) transmit the joint of communication signals and radar signals for serving communication users and tracking targets simultaneously. The objective of this paper is to minimize the total transmit power at the Radcom BS by jointly optimizing the active beamformers, including communication beamformers and radar beamformers, at the Radcom BS and the phase shifts at the IRS, subject to the minimum signal-to-interference-plus-noise ratio (SINR) required by communication users, the minimum SINR required by the radar, and the cross-correlation pattern design. In particular, we consider two cases, namely, case I and case II, based on the presence or absence of the radar cross-correlation design and the interference introduced by the IRS on the Radcom BS. For case I where the cross-correlation design and the interference are not considered, we prove that the dedicated radar signals are not needed, which significantly reduces implementation complexity and simplifies algorithm design. Then, a penalty-based algorithm is proposed to solve the resulting non-convex optimization problem. Whereas for case II considering the cross-correlation design and the interference, we unveil that the dedicated radar signals are needed in general to enhance the system performance. Since the resulting optimization problem is more challenging to solve as compared with the case I, the semidefinite relaxation (SDR) based alternating optimization (AO) algorithm is proposed. Particularly, instead of relying on the Gaussian randomization technique to obtain an approximate solution by reconstructing rank-one solution, the tightness is achieved by our proposed reconstruction strategy. Simulation results demonstrate the effectiveness of proposed algorithms and also show the superiority of the proposed scheme over various benchmark schemes.

Achieving Multi-Beam Gain in Intelligent Reflecting Surface Assisted Wireless Energy Transfer

Intelligent reflecting surface (IRS) is a promising technology to boost the efficiency of wireless energy transfer (WET) systems. However, for a multiuser WET system, simultaneous multi-beam energy transmission is generally required to achieve the maximum performance, which may not be implemented by using the IRS having only a single set of coefficients. As a result, it remains unknown how to exploit the IRS to approach such a performance upper bound. To answer this question, we aim to maximize the total harvested energy of a multiuser WET system subject to the user fairness constraints and the non-linear energy harvesting model. We first consider the static IRS beamforming scheme, which shows that the optimal IRS reflection matrix obtained by applying semidefinite relaxation is indeed of high rank in general as the number of energy receivers (ERs) increases, due to which the resulting rank-one solution by applying Gaussian Randomization may lead to significant loss. To achieve the multi-beam gain, we then propose a general time-division based novel framework by exploiting the IRS's dynamic passive beamforming. Moreover, it is able to achieve a good balance between the system performance and complexity by controlling the number of IRS shift patterns. Finally, we also propose a time-division multiple access (TDMA) based passive beamforming design for performance comparison. Simulation results demonstrate the necessity of multi-beam transmission and the superiority of the proposed dynamic IRS beamforming scheme over existing schemes.

Robust Beamforming Design With Finite Blocklength for URLLC

Ultra-reliable and low-latency communications (URLLC) are essential for mission-critical applications, such as telemedicine, automatic drive, etc. In the design of URLLC, the robustness of multi-user beamforming transmission scheme is critical and challenging. To this end, we consider a robust beamforming design in the finite blocklength regime for a multi-user multi-antenna downlink system in the case of imperfect channel state information at the transmitter. A transmission power minimization problem is formulated to optimize the beamforming vectors under the premise of guaranteeing the requirements on transmission latency, reliability and the target user rates, which is non-convex. To solve it, we first reformulate the problem into a tractable form by using the convexity and concavity of asymptotic capacity in the finite blocklength regime, then adopt S-Procedure to convert the infinite constraints into finite ones. Finally, the Gaussian randomization method and the penalty function method are utilized to generate a feasible solution to the original optimization problem and to provide a good rank-one approximation, respectively. The simulation results confirm the robustness and effectiveness of the beamforming design.

Total and Minimum Energy Efficiency Tradeoff in Robust Multigroup Multicast Satellite Communications

Satellite communication is an indispensable part of future wireless communications given its global coverage and long-distance propagation. In satellite communication systems, channel acquisition and energy consumption are two critical issues. To this end, we investigate the tradeoff between the total energy efficiency (TEE) and minimum EE (MEE) for robust multigroup multicast satellite communication systems in this paper. Specifically, under the total power constraint, we investigate the robust beamforming aimed at balancing the TEE-MEE, so as to achieve the balance between the fairness and total performance on the system EE. For this optimization problem, we first model the balancing problem as a nonconvex problem while deriving its approximate closed-form average user rate. Then, the nonconvex problem is handled by solving convex programs sequentially with the help of the semidefinite relaxation and the concave-convex procedure. In addition, depending on the solution rank value, Gaussian randomization and eigenvalue decomposition method are applied to generate the feasible solutions. Finally, simulation results illustrate that the proposed approach can effectively achieve the balance between the TEE and MEE, thus realizing a tradeoff between fairness and system EE performance. It is also indicated that the proposed robust approach outperforms the conventional baselines in terms of EE performance.

A TRUNCATED GAUSSIAN RANDOM FIELD METHOD FOR MODELING THE POROSITY DEFECT IN COMPOSITE STRUCTURES

Reducing the cost of manufacturing of primary structures can be achieved by better control of the manufacturing tolerances and acceptable levels of variability. Predicting the effect of defects can also help clear quality concerns that affect the amount of parts that require repairs or need to be scrapped. In this paper, a numerical method is presented for the assessment of the effect of a variable distribution of porosity defects in composite structures at the macroscale. A numerical method is first implemented to simulate random porous zones over the 3-D surface of the composite part. Two or more material configurations can be considered: the sane one and the porous ones. In the numerical model, each element of the part mesh is assigned one of the materials. The random choice between the materials for each element is based on the simulation of a truncated Gaussian random field over the 3-D surface. A Monte Carlo simulation method is used to study the effect of the random spatial distribution of porosity on the mechanical performance of the structure. To illustrate this approach, the case of a curved stiffened panel with a compression load case is considered, and the mechanical performance is evaluated. By taking all the samples of random porosity distributions that have high values for displacement and stress, the critical zones of the structure are identified. Based on these predictive methods, a methodology could further be defined to select more critical areas for inspection and potentially reduce time required for quality controls.

UNCERTAINTY QUANTIFICATION BY GAUSSIAN RANDOM FIELDS FOR POINT-LIKE EMISSIONS FROM SATELLITE OBSERVATIONS

We propose a statistical approach to estimate emissions of isolated pointlike sources by NO<sub>2</sub> tropospheric column concentrations satellite observations. The approach is data driven; in addition to the satellite measurements it only uses available wind data and a rudimentary model for the NO<sub>x</sub> chemistry. We construct interpolated fields of the satellite observations using Gaussian random fields, which allows for a more flexible fitting of data than the more standard Gaussian plume regressions. They enable producing uncertainty quantification, even with partly obscured or missing observations. The Gaussian random field surfaces provide continuous surfaces of the satellite observations along which flux integrals are computed to simplify the problem from two-dimensional satellite observations to one-dimensional fluxes. The emission estimates are then obtained by a simple model that combines the flux and chemistry. Extensive uncertainty quantification is implemented at every step of the estimation procedure by using Markov chain Monte Carlo sampling methods. The method is verified by simulated observations and applied to a Copernicus Sentinel-5 Precursor TROPOspheric Monitoring Instrument (TROPOMI) data to estimate industrial nitrogen oxide emissions from the power plants of Belchatow, Poland and Yangluo, Wuhan, China. With Belchatow, we compare the obtained emission rates against reported emissions using annually reported total emissions and available power generation data.

Groundwater level modeling using Augmented Artificial Ecosystem Optimization

Nature-inspired optimization is an active area of research in the artificial intelligence (AI) field and has recently been adopted in hydrology for the calibration (training) of both process-based and statistical models. This study proposes an improved AI model, Augmented Artificial Ecosystem Optimization-based Multi-Layer Perceptron (AAEO-MLP), to build a monthly groundwater level (GWL) forecasting model. AAEO-MLP model is built on the novel Augmented version of Artificial Ecosystem Optimization and traditional MLP network. In AAEO, Levy-flight trajectory and Gaussian random are utilized in exploration and exploitation to improve the optimizing ability. The AAEO-MLP model is tested on two time-series (1989–2012) datasets collected at two wells in India. Various explanatory variables such as monthly cumulative precipitation, mean temperature, tidal height, and previous measurements of GWL were considered for predicting 1-month ahead of GWL. The performance of AAEO-MLP was benchmarked against 17 different models (original AEO, 3 different variants of AEO, and 13 well-known models) in terms of forecasting accuracy based on six metrics (e.g., mean absolute error, root mean square error, Kling–Gupta efficiency, normalized Nash–Sutcliffe efficiency, Pearson’s correlation index, a20 index). Furthermore, convergence analysis and model stability are employed to indicate the effectiveness of AAEO-MLP. The compared results express that the AAEO-MLP is superior to other models in terms of prediction accuracy, convergence, and stability. Overall, the results depict that the AAEO is a promising approach for optimizing machine learning models (e.g., MLP) and should be explored for other hydrological forecasting applications (e.g., streamflow, rainfall) to further assess its strengths over existing methods.

Multi-Level Over-the-Air Aggregation of Mobile Edge Computing Over D2D Wireless Networks

In this paper, we consider a wireless multihop device-to-device (D2D) based mobile edge computing (MEC) system, where the destination wireless device (WD) is scheduled to compute nomographic functions. Under the MapReduce framework and motivated by reducing communication resource overhead, we propose a new multi-level over-the-air (OTA) aggregation scheme for the destination WD to collect the individual partially aggregated intermediate values (IVAs) for reduction from multiple source WDs in the data shuffling phase. For OTA aggregation per level, the source WDs employ a truncated channel-inverse structure multiplied by their individual transmit coefficients in transmission over the same time-frequency resource blocks, and the destination WD finally uses a receive filtering factor to construct the aggregated IVA. Under this setup, we develop a unified transceiver design framework that minimizes the mean squared error (MSE) of the aggregated IVA at the destination WD subject to the source WDs’ individual power constraints, by jointly optimizing the individual transmit coefficients of the source WDs and the receive filtering factor of the destination WD. The formulated power-constrained MSE minimization problem is non-convex. First, based on the primal decomposition method, we derive the closed-form solution under the special case of a common transmit coefficient. This shows that the common transmit coefficient of the source WDs is determined by the minimal transmit power budget among them. Next, for the general case, we transform the original problem into a quadratic fractional programming problem, and then develop a low-complexity algorithm to obtain the (near-) optimal solution by leveraging Dinkelbach’s algorithm along with the Gaussian randomization method. Numerical results are provided to demonstrate the significant performance gains achieved by the proposed multi-level OTA aggregation scheme over various existing schemes.

Statistical CSI-Based Design for RIS-Assisted Communication Systems

Reconfigurable intelligent surfaces (RISs) have attracted considerable attention over the past years. A RIS can smartly adjust the phase of incident wavefronts and create anomalous reflections towards desired directions. In this letter, we consider a RIS-assisted large antenna system and investigate the ergodic spectral efficiency (SE). By considering a finite dimensional channel, we derive an upper bound on the ergodic SE. Based on this upper bound, we propose an optimal phase shift design by exploiting statistical channel state information. Specifically, we develop a semidefinite relaxation technique and Gaussian randomization procedure for continous phase shift design. Furthermore, an alternating optimization algorithm is applied to the discrete case. Numerical results verify the tightness of the upper bound and the effectiveness of our phase shift design. Considering hardware limitations, we find that a RIS of 2-bit phase adjustable elements achieves the same ergodic SE as the continous phase shift architecture.

Reflect Beamforming Optimization for Reconfigurable Intelligent Surface Assisted Cooperative Jamming

In this letter, we propose to deploy a reconfigurable intelligent surface (RIS) along with a jammer to interfere with an illegal wireless network in a cooperative manner, where an illegal station transmits information signals to an illegal receiver. Specifically, the RIS is used to help perform jamming by reflecting the signal from the jammer and that from the illegal station, respectively. Aiming to destroy the illegal wireless transmission without being detected, we propose to optimize the RIS reflection coefficients for the sake of minimizing the signal-to-interference-plus-noise ratio (SINR) at the illegal receiver, with the constraint that the jamming power received at the illegal receiver is lower than the detection threshold. Since the formulated problem is non-convex, we propose to obtain a high-quality sub-optimal solution by applying semidefinite relaxation (SDR) followed by the Gaussian randomization method. Our numerical results show that our proposed RIS-assisted cooperative jamming (RCJ) scheme with the proposed algorithm significantly outperforms the benchmarks in terms of its SINR and computational complexity.

Sum Rate Optimization of IRS-Aided Uplink Muliantenna NOMA with Practical Reflection.

Recently, intelligent reflecting surfaces (IRSs) have drawn huge attention as a promising solution for 6G networks to enhance diverse performance metrics in a cost-effective way. For massive connectivity toward a higher spectral efficiency, we address an intelligent reflecting surface (IRS) to an uplink nonorthogonal multiple access (NOMA) network supported by a multiantenna receiver. We maximize the sum rate of the IRS-aided NOMA network by optimizing the IRS reflection pattern under unit modulus and practical reflection. For a moderate-sized IRS, we obtain an upper bound on the optimal sum rate by solving a determinant maximization (max-det) problem after rank relaxation, which also leads to a feasible solution through Gaussian randomization. For a large number of IRS elements, we apply the iterative algorithms relying on the gradient, such as Broyden–Fletcher–Goldfarb–Shanno (BFGS) and limited-memory BFGS algorithms for which the gradient of the sum rate is derived in a computationally efficient form. The results show that the max-det approach provides a near-optimal performance under unit modulus reflection, while the gradient-based iterative algorithms exhibit merits in performance and complexity for a large-sized IRS with practical reflection.

Joint Beamforming Design and Power Splitting Optimization in IRS-Assisted SWIPT NOMA Networks

This paper proposes a novel network framework of intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) non-orthogonal multiple access (NOMA) networks, where IRS is used to enhance the NOMA performance and the wireless power transfer (WPT) efficiency of SWIPT. We formulate a problem of minimizing base station (BS) transmit power by jointly optimizing successive interference cancellation (SIC) decoding order, BS transmit beamforming vector, power splitting (PS) ratio and IRS phase shift while taking into account the quality-of-service (QoS) requirement and energy harvested threshold of each user. The formulated problem is non-convex optimization problem, which is difficult to solve it directly. Hence, a two-stage algorithm is proposed to solve the above-mentioned problem by applying semidefinite relaxation (SDR), Gaussian randomization and successive convex approximation (SCA). Specifically, after determining SIC decoding order by designing IRS phase shift in the first stage, we alternately optimize BS transmit beamforming vector, PS ratio, and IRS phase shift to minimize the BS transmit power. Numerical results validate the effectiveness of our proposed optimization algorithm in reducing BS transmit power compared to other baseline algorithms. Meanwhile, compared with non-IRS-assisted network, the IRS-assisted SWIPT NOMA network can decrease BS transmit power by 51.13%.

A Multicarrier Phase‐Coded Waveform Design Scheme for Joint Radar and Communication System

A Multicarrier phase-coded (MCPC) waveform design scheme with two steps for Joint radar and communication (JRC) system is developed. Firstly, an integrated MCPC waveform design method is addressed by simultaneously maximizing the Signal-to-clutter-to-noise ratio (SCNR) and the Shannon capacity, subject to both the Integrated sidelobe level ratio (ISLR) constraint and the energy constraint. This model is theoretically proved to be a convex optimization problem with respect to the absolute squares of the transmit weights corresponding to different subcarriers, of which the analytical result is also discussed. Subsequently, by further optimizing the phases of the transmit weights, minimizing the Peak to average power ratio (PAPR) for JRC system is recast as a Semidefinite programming (SDP) problem, which can be effectively solved with the Semidefinite relaxation (SDR) technique via Eigenvalue decomposition (EVD) or Complex Gaussian randomization (CGR). Numerical examples are provided to verify the effectiveness of the proposed scheme.

Novel stochastic approach to predict the energy demand and thermal comfort in the office buildings considering materials and human-related Gaussian uncertainties

In the decision-making process during the office buildings' design or management, a significant problem arises from the necessity of simultaneous satisfaction of the users’ thermal comfort and minimization of the energy demand. Since the features of the materials, the comfort perception and the number of people are uncertain quantities, the energy demand and parameters describing thermal comfort should be treated as random variables as well. The parameters, which influence mostly the energy demand and thermal comfort are gathered in two groups: the material properties of façade and the human-related factors. The thermal transmittance, solar heat gain coefficient of the transparent façade, number of people and internal temperature are Gaussian uncertainties, but meanwhile they should fulfil the specific requirements concerning health and safety. In the proposed framework, the perturbation theory and approaches based on the transformed random variables method, which enable to determine the probability density function of the energy demand and predicted thermal comfort, are employed and compared. The proposed approach is applied to investigate the uncertainty propagation considering the reference office building unit. The results show that the Gaussian randomness extends into the non-symmetrical uncertainty of energy demand and predicted thermal comfort. In comparison with the Monte Carlo method, the introduced methodology provides the explicit form of the probability density function of analysed random variables at a much lower computational cost.