Cancellation Error Research Articles

Performance Analysis of Antenna-relay Selection in CNOMA Systems under Practical Impairments

Selection strategies prove to be a valuable approach in mitigating complexity associated with antenna selection (AS) and relay selection (RS), optimizing signal transmission through a streamlined number of antennas/relays, and enhancing overall system performance. This paper offers a comprehensive analysis, deriving closed-form expressions for the outage probability (OP) and throughput in proposed scenarios that leverage the best relay selection (BRS) and transmit antenna selection (TAS) protocol for cooperative non-orthogonal multiple access (CNOMA), along with partial relay selection (PRS) and TAS protocol for CNOMA. The study extends to Rayleigh fading channels, considering practical impairments such as successful interference cancellation (SIC) error, channel estimation error (CEE), and feedback delay error. In comparing the proposed system to conventional CNOMA, our findings highlight the substantial impact of SIC, CEE, and feedback delay imperfections on the performance of both proposed scenarios. Notably, the application of BRS-based TAS protocol outperforms PRS-based TAS in terms of OP and throughput. The close alignment between analytical, asymptotic, and simulation results attests to the credibility of conducted analysis.

Magnetostatic analysis by BEM for multiply connected problem

PurposeThe purpose of this study is to demonstrate the novel approach in treating multiply connected problems in magnetostatic.Design/methodology/approachThe new double layer approach (DLA) to be proposed is based on the use of the exciting double layer on the cut-surface. Applying Ampere’s circuital law to the circuital path along a toroidal core of M–C model, this paper derives unified exciting potential (UEP) from the common exciting potential. The UEP is applicable to the simply or M–C analysis. To check the effectiveness of the UEP, this paper analyze typical M–C problems and compares the results with those of other benchmark problems and also those obtained by surface charge method (SCM). Because the SCM encounters a cancellation error, this paper overcomes this problem by using the concept of direct boundary element method (BEM).FindingsUsing the improved DLA, this paper analyzed a typical multiply connected model and compared the results with those of the SCM, which has been improved to overcome cancellation errors. This paper has confirmed that the results obtained by the improved DLA are the same as those obtained by the improved SCM and Steklov–Poincaré operator formulation, tested at the well-known benchmark problems given in Andjelic et al. (2010). From these results, this paper concluded that the Improved DLA works well and that the improved SCM becomes available for analyzing both the simply and multiply connected problems.Originality/valueExpanding a concept of the exciting double layer on the cut-surface, this paper improve the DLA to analyze the M–C problems. Applying Ampere’s circuital law to the full circuital path along the toroidal core of M–C problem, this paper derive UEP from the original exciting potential to get the governing BIE. The BIE is applicable to either simply or multiply connected analysis.

Improved SQP and SLSQP algorithms for feasible path-based process optimisation

Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However, existing SQP algorithms may suffer from inconsistent quadratic programming (QP) subproblems and numerical noise, especially for ill-conditioned process optimisation problems, leading to a suboptimal or infeasible solution. In this work, we propose an improved SQP algorithm (I-SQP) and an improved sequential least squares programming algorithm (I-SLSQP) that solves a least squares (LSQ) subproblem at each major iteration. A hybrid method through the combination of two existing relaxations is proposed to solve the inconsistent subproblems for better convergence and higher efficiency. We find that a certain part of the dual LSQ algorithm suffers from serious cancellation errors, resulting in an inaccurate search direction or no viable search direction generated. Therefore, the QP solver is used to solve LSQ subproblems in such a situation. The computational results indicates that I-SLSQP is more robust than fmincon in MATLAB, IPOPT, Py-SLSQP and I-SQP. It is also shown that I-SLSQP and Py-SLSQP is superior to I-SQP for ill-conditioned process optimisation problems, whilst I-SQP is more computationally efficient than I-SLSQP and Py-SLSQP for well-conditioned problems.

The first application of a numerically exact, higher-order sensitivity analysis approach for atmospheric modelling: implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2

Abstract. Sensitivity analysis in chemical transport models quantifies the response of output variables to changes in input parameters. This information is valuable for researchers engaged in data assimilation and model development. Additionally, environmental decision-makers depend upon these expected responses of concentrations to emissions when designing and justifying air pollution control strategies. Existing sensitivity analysis methods include the finite-difference method, the direct decoupled method (DDM), the complex variable method, and the adjoint method. These methods are either prone to significant numerical errors when applied to nonlinear models with complex components (e.g. finite difference and complex step methods) or difficult to maintain when the original model is updated (e.g. direct decoupled and adjoint methods). Here, we present the implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2 as CMAQ-hyd. CMAQ-hyd can be applied to compute numerically exact first- and second-order sensitivities of species concentrations with respect to emissions or concentrations. Compared to CMAQ-DDM and CMAQ-adjoint, CMAQ-hyd is more straightforward to update and maintain, while it remains free of subtractive cancellation and truncation errors, just as those augmented models do. To evaluate the accuracy of the implementation, the sensitivities computed by CMAQ-hyd are compared with those calculated with other traditional methods or a hybrid of the traditional and advanced methods. We demonstrate the capability of CMAQ-hyd with the newly implemented gas-phase chemistry and biogenic aerosol formation mechanism in CMAQ. We also explore the cross-sensitivity of monoterpene nitrate aerosol formation to its anthropogenic and biogenic precursors to show the additional sensitivity information computed by CMAQ-hyd. Compared with the traditional finite difference method, CMAQ-hyd consumes fewer computational resources when the same sensitivity coefficients are calculated. This novel method implemented in CMAQ is also computationally competitive with other existing methods and could be further optimized to reduce memory and computational time overheads.

Examination of Multiples Users MIMO-NOMA over Robust Fading Channel Conditions

The purpose of this study is to analyze the performance of the multiple-input multiple-output (MIMO) system in combination with the non-orthogonal multiple access (NOMA) system, taking into consideration the robust fading channel circumstances that are characterized by considerable variations in signal quality. This study examines the susceptibility of the system to various variables that impact channel impairments and the achievable data rate. It is assumed that the fading connections, which are independent and identically distributed (i.i.d.), adhere to Nakagami-m distributions. These links also have successive interference cancellation (SIC) errors, and the channel coefficients exhibit temporal variability. The variables examined in this research include the transmission power of the base station (BS), the presence of imprecise channel state information (CSI), the number of antennas used at the BS, and the power ratio assigned to NOMA users. To assess the efficacy of the system, the conventional time division multiple access (TDMA) approach has been chosen as a means of comparing the performance of the two users inside each beam. The results of the simulations also show that MIMO-NOMA systems have a higher channel capacity than traditional orthogonal multiple access (OMA) systems. This study utilizes a comprehensive dataset to demonstrate the congruence between the analytical findings and the simulation outcomes.

Channel reconfiguration distributed interference alignment for multi-unit over-the-air computation

Over-the-air computation (AirComp) has been widely studied as an emerging technique for efficient data aggregation. In multi-unit AirComp networks, inter-unit interference seriously affects the data aggregation performance. To solve the above problem, in this paper, a novel scheme of channel reconfiguration distributed interference alignment (CRDIA) is proposed. We virtualize several devices within a unit as one transmitting device, reconstruct the channel matrix of the system, and iterate iteratively design the pre-processing and post-processing components. Based on the above, the pre-processing matrices of AirComp devices and the post-processing matrices of fusion centers are designed. The sum rate of the system is used as a metric for interference cancellation and mean-squared error (MSE) is used as a metric for data aggregation accuracy. We evaluate the proposed scheme by simulating a network with various numbers of AirComp devices and units. The simulation results show that the CRDIA scheme can achieve accurate computation of the AirComp objective function without inter-unit interference.

A versatile implicit computational framework for continuum-kinematics-inspired peridynamics

Continuum-kinematics-inspired peridynamics (CPD) has been recently proposed as a novel reformulation of peridynamics that is characterized by one-, two- and three-neighbor interactions. CPD is geometrically exact and thermodynamically consistent and does not suffer from zero-energy modes, displacement oscillations or material interpenetration. In this manuscript, for the first time, we develop a computational framework furnished with automatic differentiation for the implementation of CPD. Thereby, otherwise tedious analytical differentiation is automatized by employing hyper-dual numbers (HDN). This differentiation method does not suffer from round-off errors, subtractive cancellation errors or truncation errors and is thereby highly stable with superb accuracy being insensitive to perturbation values. The computational framework provided here is compact and model-independent, thus once the framework is implemented, any other material model can be incorporated via modifying the potential energy solely. Finally, to illustrate the versatility of our proposed framework, various potential energies are considered and the corresponding material response is examined for different scenarios.

A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models

Accurately evaluating derivatives poses a key challenge when numerically implementing complex constitutive models. This work presents an implicit stress update algorithm that utilizes the hyper dual step derivative approximation to address derivative evaluations in elastoplastic problems. Initially, the performance of various numerical differentiation methods is discussed and compared by examining their numerical errors in the representative example. Subsequently, the hyper dual step derivative approximation, without truncation and subtractive cancellation errors, is employed to compute the Jacobian matrix and consistent tangent operator, ensuring quadratic convergence in both local and global computations. The size of the Newton search step is optimized by the line search technique, thereby enhancing the convergence in solving nonlinear stress integral equations. Finally, the proposed stress update algorithm is used to implement the non-associated Mohr–Coulomb plastic model in the ABAQUS software using the UMAT subroutine. The stress update algorithm’s performance and its practical application in geotechnical engineering problems are demonstrated using five boundary value problems.

Performance Analysis of Selective DF Cooperative NOMA in Presence of Practical Impairments

In this article, we investigate a selective decode-and-forward (DF)-aided cooperative nonorthogonal multiple access (NOMA) system performance in the presence of practical impairments using imperfect successive interference cancellation (SIC) and channel estimation error (CEE). The base station communicates directly and via a relay with the two NOMA users in two-time phases. In particular, the selective DF with synchronized direct and relay transmission relaying protocol is proposed for the considered downlink NOMA system to offer enhanced quality of service and improved data reliability compared with the conventional NOMA and DF NOMA systems. The closed-form of exact and asymptotic expressions of the average bit error rate (ABER) at both NOMA users are derived considering the impact of imperfect SIC and CEE. Furthermore, the outage probability is also obtained. Finally, the improvement in the system performance acquired by the proposed scheme over the existing methods is corroborated by Monte Carlo simulations.

Throughput performance optimization of NOMA-assisted cooperative relay system with realistic impairments

Abstract This work aims to investigate the outage and throughput performance of non-orthogonal multiple access assisted cooperative relay system (CRS-NOMA) considering the realistic impairments caused due to in-phase and quadrature-phase imbalance (IQI), channel estimation errors (CEE), and successive interference cancellation (SIC) errors. More specifically, we investigate a model in which two-phase downlink transmission is carried out in two different modes: (i) CRS-NOMA without direct links and (ii) CRS-NOMA with direct links (CRS-DLNOMA). In CRS-NOMA mode, the source broadcasts a composite NOMA signal to destination users with the assistance of a decode-and-forward (DF) relay. In contrast, in CRS-DLNOMA, direct and cooperative links are available for transmission. We derive the analytical expressions of outage probability and throughput for both the NOMA destinations to evaluate the system performance of both CRS-NOMA and CRS-DLNOMA modes of transmission. Furthermore, numerical simulations also study and validate the influence of IQI, CEE, and SIC errors on the outage and throughput performance. The simulation results verify that realistic impairments degrade the system performance, but the presence of direct link has a positive impact on outage and throughput. Additionally, we use the golden search method to optimize the power allocation factor (PAF) and transmission rate to maximize the throughput at the near user while ensuring the throughput constraint at the far user.

Arbitrary-Order Sensitivity Analysis of Eigenfrequency Problems with Hypercomplex Automatic Differentiation (HYPAD)

The calculation of accurate arbitrary-order sensitivities of eigenvalues and eigenvectors is crucial for structural analysis applications, including topology optimization, system identification, finite element model updating, damage detection, and fault diagnosis. Current approaches to obtaining sensitivities for eigenvalues and eigenvectors lack generality, are complicated to implement, prone to numerical errors, and are computationally expensive. In this work, a novel methodology is introduced that uses hypercomplex automatic differentiation (HYPAD) and semi-analytical expressions to obtain arbitrary-order sensitivities for eigenfrequency problems. The new methodology exhibits no sign of truncation nor subtractive cancellation errors regardless of the order of the sensitivity, it is general, and can obtain any high-order sensitivities with the simplicity of first-order computations. A numerical example is presented to verify the accuracy of the method, where the free vibration of a homogeneous cantilever beam is studied. For this problem, up to third-order sensitivities of the eigenvalues and eigenvectors with respect to the material and geometrical parameters were obtained, considering the cases of close and distinct eigenvalues. The results were verified using analytical equations, showing excellent agreement for the eigenvalues and the eigenvectors. The new method promises to facilitate the computation of sensitivities for eigenfrequency problems into routine practice and commercial software.

On the Exact Closed-Form ABEP Analysis of Downlink NOMA Over mmWave TWDP Fading

This paper presents the performance analysis of two users’ downlink non-orthogonal multiple access (NOMA) over a millimeter-wave two-wave with diffuse power (TWDP) fading model for successive interference cancellation errors. The new closed-form expressions of average bit error probability (ABEP) for both users are derived for quadrature phase-shift-keying and binary phase-shift-keying modulation pairs. Further, the asymptotic ABEP expressions are derived to provide better insights into the performance analysis. The diversity order of each user is also derived with the aid of asymptotic ABEP expression. The obtained expressions over TWDP fading channels are generalized ABEP expressions as it also shows ABEP expressions for both Rician and Rayleigh fading channels as special cases. Simulation results support the correctness of each analytical ABEP expression.

A robust stress update algorithm for elastoplastic models without analytical derivation of the consistent tangent operator and loading/unloading estimation

AbstractA robust and concise implicit stress integration algorithm of elastoplastic models is presented. It does not require the loading/unloading estimation and analytical derivation operation for the stress update. First, the elastoplastic stress update problem is recast into an unconstrained minimization problem by utilizing the smooth function to bypass the loading/unloading estimation. Then, the object problem is solved by the line search method instead of the Newton method for better convergence. The consistent tangent operator is evaluated by the complex step derivative approximation without the subtraction cancellation error, which provides the quadratic convergence rate of global iteration. The rationality of the numerical consistent tangent operator is validated by the one obtained by the analytical derivation. A recently developed non‐orthogonal elastoplastic (NEP) clay model is implemented using the new algorithm. The algorithm is confirmed through comparing the numerical solution and the analytical one for a cavity expansion problem. The algorithm performance is assessed based on a series of geotechnical boundary value problems. It is found that the new algorithm is more robust than the one employed by ABAQUS. The source code of the model implementation can be downloaded from https://github.com/zhouxin615.

Resource Allocation in MU-MISO Rate-Splitting Multiple Access With SIC Errors for URLLC Services

Rate-splitting multiple access (RSMA) is promising to be developed as a key enabling technology for 6G. This paper investigates the resource allocation problem in a downlink multi-user and multiple-input single-output (MU-MISO) RSMA system with successive interference cancellation (SIC) errors for ultra-reliable and low-latency communications (URLLC). The single-carrier RSMA (SC-RSMA) resource allocation scheme with URLLC is first given, where the beamforming vector and the transmission rate are optimized to maximize the effective throughput (ET). To solve the non-convex optimization problem formulated in the SC-RSMA scheme, an iterative algorithm based on block coordinate descent (BCD) and successive convex approximation (SCA) is proposed to alternately optimize the beamforming factor and the transmission rate. Furthermore, the multicarrier RSMA (MC-RSMA) scheme is developed for the URLLC access of large-scale users. Based on the results of the SC-RSMA scheme, a low-complexity three-step optimization algorithm is proposed to solve the resource allocation problem formulated in the MC-RSMA scheme. Finally, the simulation results show that the RSMA scheme and MC-RSMA scheme can respectively achieve higher ET than the non-orthogonal multiple access (NOMA) scheme and multi-carrier NOMA (MC-NOMA) scheme in the URLLC scenario, and verify that RSMA can reduce the latency and improve the reliability of the system.

Investigation of Vehicular S-LSTM NOMA Over Time Selective Nakagami-m Fading with Imperfect CSI

In this paper, the performance of a deep learning based multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) system is investigated for 5G radio communication networks. We consider independent and identically distributed (i.i.d.) Nakagami-m fading links to prove that when using MIMO with the NOMA system, the outage probability (OP) and end-to-end symbol error rate (SER) improve, even in the presence of imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. Further more, the stacked long short-term memory (S-LSTM) algorithm is employed to improve the system’s performance, even under time-selective channel conditions and in the presence of terminal’s mobility. For vehicular NOMA networks, OP, SER, and ergodic sum rate have been formulated. Simulations show that an S-LSTM-based DL-NOMA receiver outperforms least square (LS) and minimum mean square error (MMSE) receivers. Furthermore, it has been discovered that the performance of the end-to-end system degrades with the growing amount of node mobility, or if CSI knowledge remains poor. Simulated curves are in close agreement with the analytical results.

The Weak Field Approximation of General Relativity and the Problem of Precession of the Perihelion for Mercury

In this paper we represent a different approach to the calculation of the perihelion shift than the one presented in common text books. We do not rely on the Schwarzschild metric and the Hamilton–Jacobi technique to obtain our results. Instead we use a weak field approximation, with the advantage that we are not obliged to work with a definite static metric and can consider time dependent effects. Our results support the conclusion of Křížek regarding the significant influence of celestial parameters on the indeterminacy of the perihelion shift of Mercury’s orbit. This shift is thought to be one of the fundamental tests of the validity of the general theory of relativity. In the current astrophysical community, it is generally accepted that the additional relativistic perihelion shift of Mercury is the difference between its observed perihelion shift and the one predicted by Newtonian mechanics, and that this difference equals 43″ per century. However, as it results from the subtraction of two inexact numbers of almost equal magnitude, it is subject to cancellation errors. As such, the above accepted value is highly uncertain and may not correspond to reality.

Performance of CSI-Based Power Control and NOMA/OMA Switching for Uplink Underlay Networks With Imperfect SIC

In a multiuser underlay uplink network, we show that despite the fact that the transmit powers are constrained by the interference temperature limit (ITL) imposed by the primary network, allowing upto two users to concurrently transmit using non-orthogonal multiple access (NOMA) principles ensures better performance than when only a single user is picked in an orthogonal multiple access (OMA) scheme. To deal with the large variation in the link SNRs in underlay networks, an optimal channel state information (CSI) based ITL apportioning scheme is suggested for the first time in literature that carefully controls the transmit powers of the selected users to maximize throughput. CSI-based throughput-optimal strategies are evolved for user selection and NOMA/OMA switching. We analyze the throughput performance of the uplink with NOMA/OMA switching, optimal user selection, and CSI based ITL apportioning, taking successive interference cancellation (SIC) errors into account. Useful bounds on performance are also derived. It is shown that when the ITL is broadcast in every coherence interval, and the ITL can also be channel dependent, large thoughput gains accrue. Computer simulations confirm accuracy of the derived expressions.

Network-coded uplink clustered NOMA relay networks: Models and performance comparisons

In this paper, network sum-rate maximization (NSR-MAX) for network-coded (NC) uplink clustered non-orthogonal multiple-access (NOMA) relay networks is considered. In particular, the goal is to maximize network sum-rate via optimal power allocation, where the user clusters communicate with the base-station over an amplify-and-forward relay, subject to quality-of-service (QoS) constraints. Two NC-NOMA transmission models – namely NC-NOMA-I and NC-NOMA-II – are proposed, where in the first model, network-coding is applied at the relay only, while the second model applies network-coding for user clusters’ transmissions and at the relay to further minimize the transmission delay. The formulated NSR-MAX problem happens to be non-convex, and hence, is computationally-intensive. Thus, a low-complexity iterative two-layer algorithm (ITLA) is devised, which decouples the formulated problem and efficiently solves its over two-layers. Specifically, the inner-layer solves the NSR-MAX problem to obtain the optimal relay transmit power, while the outer-layer determines the optimal users’ transmit powers. Numerical results are presented, which illustrate that the proposed ITLA yields near-optimal solutions for all transmission models, in comparison to the formulated NSR-MAX problem (solved via global optimization package) as well as outperforming its OMA-based counterparts. Not only that, but the NC-NOMA-II is shown to be superior to the other NOMA and OMA schemes, while demonstrating resilience to timing offsets as well as successive interference cancellation (SIC) and channel state information (CSI) errors.

Joint Power Control and Phase Shift Design for Future PD-NOMA IRS-Assisted Drone Communications under Imperfect SIC Decoding.

Intelligent reflecting surfaces (IRS) and power-domain non-orthogonal multiple access (PD-NOMA) have recently gained significant attention for enhancing the performance of next-generation wireless communications networks. More specifically, IRS can smartly reconfigure the incident signal of the source towards the destination node, extending the wireless coverage and improving the channel capacity without consuming additional energy. On the other side, PD-NOMA can enhance the number of devices in the network without using extra spectrum resources. This paper proposes a new optimization framework for IRS-enhanced NOMA communications where multiple drones transmit data to the ground Internet of Things (IoT) devices under successive interference cancellation errors. In particular, the power budget of each drone, PD-NOMA power allocation of IoT devices, and the phase shift matrix of IRS are simultaneously optimized to enhance the total spectral efficiency of the system. Given the system model and optimization setup, the formulated problem is coupled with three variables, making it very complex and non-convex. Thus, this work first transforms and decouples the problem into subproblems and then obtains the efficient solution in two steps. In the first step, the closed-form solutions for the power budget and PD-NOMA power allocation subproblem at each drone are obtained through Karush-Kuhn-Tucker (KKT) conditions. In the second step, the subproblem of efficient phase shift design for each IRS is solved using successive convex approximation and DC programming. Numerical results demonstrate the performance of the proposed optimization scheme in comparison to the benchmark schemes.

Performance of NOMA‐assisted MRC receivers in presence of imperfect SIC and CSI errors

SummaryIn this paper, we analyze the performance of maximum‐ratio combining (MRC) receivers for single‐input multiple‐output (SIMO) non‐orthogonal multiple access (NOMA) system. We explore the aforesaid system performance in presence of impairments like imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. In general, receive diversity provides diversity gain and helps to maintain quality of service (QoS), while the NOMA system achieves higher spectral efficiency compared to orthogonal multiple access (OMA). Power‐domain NOMA system transmits superimposed‐coded signal, which utilize SIC detection method at the receiving users. Here, we derive the closed‐form expression of the average bit error rate (BER) for the MRC‐based NOMA system. We also analyze the performance of the system in high signal‐to‐noise ratio (SNR) regime through derived asymptotic expression. Furthermore, the outage probability, diversity order, and sum rate comparison between NOMA and OMA system are also presented. Simulation results also validate the derived theoretical expressions and confirm the diversity gain achieved for the considered system.