Cancellation Error Research Articles

Secure Transmission Design in HARQ Assisted Cognitive NOMA Networks

In this paper, we design a secure transmission scheme in hybrid automatic repeat request (HARQ) assisted cognitive non-orthogonal multiple access (NOMA) networks, where a security-required user (SRU) is paired with a quality of service (QoS)-sensitive user (QSU) to perform NOMA. To elaborate, the QoS requirement of the QSU is guaranteed by a cognitive power allocation scheme, while the HARQ technique is employed to mitigate the successive interference cancellation (SIC) errors and improve the secrecy performance of the SRU. For reducing information leakage, a randomized retransmission NOMA (RR-NOMA) scheme is designed, where the retransmitted signals are generated from independent randomized codebooks. In this scheme, the closed-form expressions for the connection outage probability (COP), the average number of transmission (ANT), the secrecy outage probability (SOP), and effective secrecy throughput (EST) of the SRU are derived. In addition, as benchmarks, the performance analyses for the fixed retransmission (FR-NOMA) scheme and the randomized retransmission orthogonal multiple access (RR-OMA) scheme are also provided. Results show a trade-off between SOP and COP or EST, which is denoted by security-reliability trade-off (SRT) or security-efficiency trade-off (SET). Furthermore, simulation results show that the HARQ technique improves SRT and the RR-NOMA scheme achieves better SET than the FR-NOMA scheme in the low SOP region. We further conduct asymptotic analysis in the RR-NOMA, FR-NOMA and RR-OMA schemes. Asymptotic results demonstrate that the three schemes achieve the same ANT and the RR-NOMA scheme obtains better secrecy performance than the RR-OMA scheme and equal secrecy performance to the FR-NOMA scheme in terms of both EST and SOP.

A Robust Hybrid of a Feedback Linearization Technique and an Interval Type-2 Fuzzy Control System for the Flapping Angle Dynamics of a Biomimetic Aircraft

We introduce a new configuration of a robust and adaptive autopilot system for a model-scale flapping-wing aircraft. The system is specifically designed to achieve high performance flapping angle tracking in the face of large uncertainties. To describe the dynamics of the system, we leverage the benefits of both first principle modeling and data-driven approach (system identification technique). We introduce a high-performance robust and adaptive nonlinear control system by means of a feedback linearization (FL) technique, supported with an interval Type-2 fuzzy system due to its ability to accommodate the footprint-of-uncertainties (FoUs). While the first stage of our nonlinear control system is to cancel some predictable nonlinearities using an FL technique, the second phase of control is to accommodate the existing uncertainties in the system by way of an interval Type-2 fuzzy control technique, e.g., due to imperfect cancelation and modeling errors. This way, the stability and the robustness of the closed-loop control system can be guaranteed. We quantify the relative merit of our hybrid control system with respect to an FL technique, supported with a fixed gain state feedback controller and a Type-1 fuzzy system. Lastly, we also conduct stability analysis of the overall closed-loop control system.

Performance analysis at far and near user in NOMA based system in presence of SIC error

Non-orthogonal multiple access (NOMA) scheme is an emerging 5G technology to improve upon the spectral efficiency. It can support more users than the number of available frequency-,time-, and code-domain resources. The innovation behind NOMA technology is to exploit non-orthogonal resource allocation at the cost of receiver complexity to mitigate the inter-user interference arising due to non-orthogonal signals. In this paper, we present performance analysis of downlink NOMA (DL-NOMA) system in presence of successive interference cancellation (SIC) error over Rayleigh fading channels. In particular, we derive the exact closed-form expressions of bit error rate (BER) at near-user (U1) and far-user (U2) for the considered DL-NOMA system. Besides, we also present the achievable rate analysis of the considered NOMA system and it is observed that its achievable rate is higher as compared to conventional orthogonal multiple access (OMA) schemes. Further, we also determine the optimized power allocation coefficient for the NOMA system. The analytical results are corroborated with the Monte-Carlo simulations. The simulation results are presented for different modulation schemes and for different NOMA scenarios. A close argument between the analytical and simulation results validate our analysis.

TOA positioning for uplink cooperative NOMA in 5G networks

Wireless geolocation considering Non-Orthogonal Multiple Access (NOMA) is particular of interest for enabling high precision location based services (LBSs) in 5G networks. In this paper, we study the fundamental limits of Time-of-arrival (TOA) positioning for uplink cooperative NOMA in the power domain under different 5G network conditions with special emphasis on the user fairness. The theoretical analysis is conducted in terms of Cramer–Rao Lower Bound (CRLB) expressions. More specifically, the CRLB of TOA positioning for uplink cooperative NOMA and OMA are obtained considering Amplify-and-Forward (AF) and Decode-and-Forward (DF) relaying strategies. Then, the numerical results of both TOA positioning for uplink cooperative NOMA and OMA are obtained and compared under different 5G network scenarios. In particular, the effects of successive interference cancellation (SIC) error, bandwidth, number of relays, and number of UEs and relaying strategy type on the performance of position accuracy are investigated. The results reveal that the cooperative NOMA outperforms cooperative OMA in terms of location estimation accuracy under different network conditions. Furthermore, the results suggest that TOA positioning of cooperative NOMA is a promising choice for supporting high precision LBSs in 5G networks.

Computation of High-Order Electromagnetic Field Sensitivities With FDTD and the Complex-Step Derivative Approximation

This paper introduces a new approach for the computation of electromagnetic field derivatives, up to any order, with respect to the material and geometric parameters of a given geometry, in a single Finite-Difference Time-Domain (FDTD) simulation. The proposed method is based on embedding the complex-step derivative (CSD) approximation into the standard FDTD update equations. Being finite-difference free, CSD provides accurate derivative approximations even for very small perturbations of the design parameters, unlike finite-difference approximations that are prone to subtractive cancellation errors. The availability of accurate approximations of field derivatives with respect to design parameters enables studies such as sensitivity analysis of multiple objective functions (as derivatives of those can be derived from field derivatives via the chain rule), uncertainty quantification, as well as multi-parametric modeling and optimization of electromagnetic structures. The theory, FDTD implementation and applications of this technique are presented.

New BEM/BEM and BEM/FEM scalar potential formulations for magnetostatic problems

The majority of the numerical methods applied so far for the simulation of a magnetostatic problem is based either on reduced and total scalar or vector potential formulations. The first one suffers from cancellation errors, the second one from the difficulty of defining the jump condition for potential on the surface of a magnet. Furthermore, the vector potential introduces three Degrees of Freedom per node increasing the computational effort for the solution of a three dimensional problem. Mayergoyz et al. (1987) proposed an alternative formulation, which is based on scalar potentials and is free of the aforementioned problems. The present work implements this formulation for the solution of magnetostatic problems by utilizing either Boundary Element Method (BEM) or its combination with Finite Element Method (FEM). Both numerical schemes are explained for two dimensional and linear problems. Two representative magnetostatic problems are solved and their solutions are compared to the corresponding ones taken by well-known commercial package.

Computationally advantageous expressions for 3-D MHD stability

Numerically accurate expressions are critical for the evaluation of 3-D MHD plasma stability, as the conventional formulas generally suffer from large numerical problems. In this work, we present new expressions for the quantities of interest, namely the parallel current density σ, the local shear S and the normal and geodesic components of the curvature κ.High accuracy is achieved in these expressions by employing strategies such as avoiding as much as possible the computation of derivatives in the direction normal to the flux surfaces, and avoiding cancellation errors by subtracting large numbers. The result is a set of equations that have been found to be important for the calculation of MHD stability of axisymmetric equilibria, and essential for the assessment of 3-D ones.

Full/Half Duplex Cooperative NOMA Under Imperfect Successive Interference Cancellation and Channel State Estimation Errors

This paper investigates the application of non-orthogonal multiple access (NOMA) in a coordinated direct and relay transmission (CDRT) system, where the base station (BS) directly communicates with the near (i.e., cell-centric) user, while it requires the help of a dedicated full duplex (FD) relay to communicate with the far (i.e., cell-edge) user. For the considered NOMA-FD-CDRT system, we derive closed-form expressions for the outage probabilities and ergodic rates experienced by the downlink users, under the realistic assumptions of imperfect channel state information (I-CSI) and imperfect successive interference cancellation (I-SIC). Expressions for system outage probability and ergodic sum rate are also presented. The links are assumed to experience independent, non-identically distributed Nakagami-m fading. The analysis of outage probabilities are carried out for both integer and non-integer values of the fading severity index. Extensive simulation results are described to validate the accuracy of analytical results, and to illustrate the performance gain of the considered system, as compared to NOMA-HD-CDRT system and the orthogonal multiple access (OMA) based CDRT system. Our results show that, both channel estimation error variance and I-SIC factor have significant impact on the performance of the considered NOMA-FD/HD-CDRT system. Further, to ensure fairness in terms of outage, we numerically determine the power allocation coefficient at the BS that provides equal outage performance for both the near and the far users in the presence of I-CSI and I-SIC. Furthermore, we derive closed-form expression for the optimal power allocation (OPA) coefficient at the BS that minimizes the system outage probability of the NOMA-FD/HD-CDRT network under I-CSI. With the help of numerical and simulation investigations, we establish that the proposed OPA significantly reduces the system outage probability, as compared to random (i.e., non-optimal) power allocation at the BS.

Adaptive Digital Self-Interference Cancellation for Millimeter-Wave Full-Duplex Backhaul Systems

This paper addresses self-interference (SI) cancellation for millimeter-wave (mmWave) based full-duplex backhaul systems, which involves not only the near-end cross talk due to antenna leakage, but also the far-end cross talk due to reflections from obstacles around the transmission path. The SI channel is with a long response, particularly for mmWave systems where the bandwidth is large. In order to manage the SI comprehensively, we put forward an adaptive multi-segment frequency-domain cancellation (MSFDC) scheme based on the frequency-domain block least-mean-square algorithm, which can cover the long SI channel with low complexity. In addition, we introduce an output branch on the traditional adaptive training loop and perform tap selection, so that the cancellation error decreases while the convergence and tracking abilities are maintained. To demonstrate the effectiveness of the proposed tap-selection based MSFDC, comprehensive evaluations are carried out in an E-band full-duplex backhaul scenario. It is shown that the number of multiplication operations can be greatly reduced by dividing the SI channel into multiple segments. Meanwhile, in a wide range of cases, the proposed scheme can cancel the SI to the degree below the noise floor, and significantly outperforms the traditional method without tap selection.

NOMA‐based multiple‐antenna and multiple‐relay networks over Nakagami‐ m fading channels with imperfect CSI and SIC error

In this study, non-orthogonal multiple access (NOMA)-based multiple-antenna and multiple-relay networks over Nakagami- m fading channels with imperfect channel state information (CSI) and successive interference cancellation (SIC) error are investigated. In order to measure the performance of the system, the exact outage probability and the ergodic sum rate of the system are explored. By analysing the impact of the partial relay selection scheme, it is shown that the performance gain can be achieved significantly by increasing the number of relays from one to two, but when the number of relays is equal to or greater than three, the increment of the performance gain becomes smaller and smaller, and finally saturated as the number of relays increases. Furthermore, due to the complexity of the derivation process for the ergodic sum rate, an upper bound of the ergodic sum rate is taken into account. Finally, by carrying out a series of experimental simulations, the authors prove the correctness of the theoretical derivations above, and from the comparison of NOMA and orthogonal multiple access (OMA), it is found that NOMA can provide better spectral efficiency and user fairness than OMA.

Efficient and robust recurrence relations for the Zernike circle polynomials and their derivatives in Cartesian coordinates.

For some time it has been known and recommended that the calculation of Zernike polynomials to radial orders higher than 8 to 10 should be performed using recurrence relations rather than explicit expressions due increasingly large cancellation errors. This paper presents a set of simple recurrence relations that can be used for the unit-normalized Zernike polynomials in polar coordinates and easily adapted to Cartesian coordinates as well. The recurrence relations are also well suited for the calculation of the Cartesian derivatives of the Zernike polynomials. The recurrence relations are easily extended to arbitrarily high orders. Assessments of the precision achievable with standard 64-bit floating point arithmetic show that Zernike polynomials up to radial order 30 can be calculated over the unit disc with errors not exceeding 5E-14, and up to radial order 50 with errors not exceeding 1.2E-13. Comparison with the Zernike capability in OpticStudio (Zemax) shows that the recurrence relations are superior in performance (both speed and precision) over the existing algorithm implemented in the software. General pseudo-code for the calculation of Zernike polynomials and their derivatives is also presented.

Outage-Constrained Resource Allocation in Uplink NOMA for Critical Applications

In this paper, we consider the resource allocation problem for uplink non-orthogonal multiple access (NOMA) networks whose users represent power-restricted but high priority devices, such as those used in sensor networks supporting health and public safety applications. Such systems require high reliability and robust resource allocation techniques are needed to ensure performance. We examine the impact on system and user performance due to residual cancellation errors resulting from imperfect successive interference cancellation (SIC) and apply the chance-constrained robust optimization approach to tackle this type of error. In particular, we derive an expression for the user outage probability as a function of SIC error variance. This result is used to formulate a robust joint resource allocation problem that minimizes user transmit power subject to rate and outage constraints of critical applications. As the proposed optimization problem is inherently non-convex and NP-hard, we apply the techniques of variable relaxation and complementary geometric programming to develop a computationally tractable two-step iterative algorithm based on successive convex approximation. Simulation results demonstrate that, even for high levels of SIC error, the proposed robust algorithm for NOMA outperforms the traditional orthogonal multiple access case in terms of user transmit power and overall system density, i.e., serving more users over fewer sub-carriers. The chance-constrained approach necessitates a power-robustness tradeoff compared with non-robust NOMA but effectively enforces maximum user outage and can result in transmit power savings when users can accept a higher probability of outage.

A Current Control Scheme With Back EMF Cancellation and Tracking Error Adapted Commutation Shift for Switched-Reluctance Motor Drive

In this paper, an improved winding current control scheme for switched-reluctance motor drive is developed and evaluated. The current feedback controller (CFBC) is augmented with an observed back electromotive force (EMF) current feedforward controller (CFFC) and a current tracking error adapted dynamic commutation shift controller (DCSC). In the proposed DCSC, the rising winding current tracking errors of all phases are extracted, synthesized, and processed to generate the suitable advanced commutation shift angle. The effects of motor back EMF and nonlinear winding inductance can be reduced to yield improved winding current tracking waveforms under a wide operation range. The gradual improvements in current responses and efficiencies by augmenting the CFBC with the CFFC and then the DCSC are verified experimentally. Then, the robust speed control scheme is properly designed to achieve good acceleration/deceleration, reversible running, and dynamic characteristics.

Adaptive Combination of Proportionate NSAF with the Tap-Weights Feedback for Acoustic Echo Cancellation

To obtain fast convergence rate and low steady-state error in acoustic echo cancellation, a convex combination scheme of the improved proportionate normalized subband adaptive filter algorithm is proposed. Instead of the gradient method in the conventional combination theory, the mixing parameter is adapted by using the normalized gradient method which makes it more robust to the variations of subband error signals. Also, to implement a smooth transition from the fast filter to the accurate filter, a cyclic feedback of the overall tap-weights giving to all component filters is applied.

Modelling a Bathtub-Shaped Failure Rate by a Coxian Distribution

We build a Coxian random variable model to describe characterizations of a bathtub-shaped failure rate and present a perturbation to the Coxian random variable. In the perturbation, the corresponding probability density function is a linear combination of exponentials, and weights may be negative. The clear mechanism of the perturbation reveals that numerical error of the computation includes cancellation error. By studying weights in a perturbation, we can control absolute errors of all intermediate results. As the involving probability density function is a summation, the total absolute error of the final result is not larger than the sum of absolute errors of intermediate results. Hence, we can suggest the level of numerical precision to control errors. With an accurate likelihood function, some algorithms of maximum likelihood estimates can be established. We evaluate proposed algorithms through simulation examples and empirical data.

Assessment of the performance of commonly used DFT functionals vs. MP2 in the study of IL-Water, IL-Ethanol and IL-(H2O)3 clusters

We present a comparative study of the accuracy of different DFT approaches vs. MP2 for evaluating ionic liquids (ILs)+cosolvent. Namely, we are interested in [XBmim]+cosolvent (X being Cl−, BF4−, PF6−, and CH3SO3− anions and cosolvent being water or ethanol) and [XBmim]+(H2O)3 clusters. In this study the B3LYP, B3LYP-D3, M06, M06-2X and M06-HF functionals with Pople and Dunning basis sets are considered. We find that the influence of the basis sets is a factor to take into consideration. As already seen for weakly bonded systems when the basis set quality is low the uncorrected counterpoise (unCP) or averaging counterpoise (averCP) energies must be used due to cancellation errors. Besides, the inclusion of extra diffuse functions and polarization is also required specially in the case of ILs interacting with water clusters. The B3LYP functional does not reproduce either the structure or the interaction energies for ILs+H2O and ILs+EtOH aggregates, the energetic discrepancies being more significant than the structural ones. Among the dispersive corrected functionals, M06-2X results resemble to a great extent the reference data when the unCP interaction energies are considered for both water and ethanol. In turn, M06 and B3LYP-D3 functionals are the best option for ILs containing polar and non-polar anions, respectively, whether the averCP interactions energies are taking into consideration. From the structural point of view, B3LYP and M06 functionals describe more open structures whereas B3LYP-D3, M06-2X and M06-HF structures resemble quite well MP2 results. When the number of water molecules increases the H bonding motif gains importance and the effect depends on the underlying functional. Only M06-2X and M06-HF behaviour is similar to that observed for one water molecule. This is important because to describe ILs-cosolvent solutions is not only necessary to take into account the ILs-cosolvent interactions but also the cosolvent-cosolvent ones in the ensemble of the system.

Magnetostatic Shield Analysis by Double-Layer Charge Formulation Using Difference Field Concept

This paper proposes a novel accuracy improvement technique for the double-layer charge (DLC) formulation in shielding problems. Although the DLC formulation has advantages over the direct methods from the viewpoint of computational cost, the calculation accuracy can be worse because of cancellation errors. In order to improve the accuracy, we apply a new technique based on the difference field concept. Numerical results, which verify the effectiveness of the proposed method, are presented.

Computing multi-mode shock-induced compressible turbulent mixing at late times

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems.We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as “physically conservative voxelization.”At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain.We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.

Fast Evaluation of Far-Field Signals for Time-Domain Wave Propagation

Time-domain simulation of wave phenomena on a finite computational domain often requires a fictitious outer boundary. An important practical issue is the specification of appropriate boundary conditions on this boundary, often conditions of complete transparency. Attention to this issue has been paid elsewhere, and here we consider a different, although related, issue: far-field signal recovery. Namely, from smooth data recorded on the outer boundary we wish to recover the far-field signal which would reach arbitrarily large distances. These signals encode information about interior scatterers and often correspond to actual measurements. This article expresses far-field signal recovery in terms of time-domain convolutions, each between a solution multipole moment recorded at the boundary and a sum-of-exponentials kernel. Each exponential corresponds to a pole term in the Laplace transform of the kernel, a finite sum of simple poles. Greengard, Hagstrom, and Jiang have derived the large-$$\ell $$l (spherical-harmonic index) asymptotic expansion for the pole residues, and their analysis shows that, when expressed in terms of the exact sum-of-exponentials, large-$$\ell $$l signal recovery is plagued by cancellation errors. Nevertheless, through an alternative integral representation of the kernel and its subsequent approximation by a smaller number of exponential terms (kernel compression), we are able to alleviate these errors and achieve accurate signal recovery. We empirically examine scaling relations between the parameters which determine a compressed kernel, and perform numerical tests of signal teleportation from one radial value $$r_1$$r1 to another $$r_2$$r2, including the case $$r_2=\infty $$r2=?. We conclude with a brief discussion on application to other hyperbolic equations posed on non-flat geometries where waves undergo backscatter.