A Time-Space Multigrid Method for Efficient Solution of the Harmonic Balance Equation System

In this paper, an efficient time-space multigrid (TS-MG) method for solving a harmonic balance (HB) equation system is proposed. The principle of the time-space multigrid method is to coarsen grids in both space and time dimensions simultaneously when coarse grids are formed. The inclusion of time in the time-space multigrid is to address the instability issue or diminished convergence speedup of the spatial multigrid (S-MG) due to larger grid reduced frequencies on coarse grids. With the proposed method, the unsteady governing equation will be solved on all grid levels. Comparing to the finest grid, fewer harmonics and thus fewer equations will be solved consequently on coarse grids. Discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT) are used to achieve solution prolongation and restriction between different time grid levels. Results from the proposed method are compared with those obtained from the traditional spatial multigrid and time domain methods. It is found that the TS-MG method can increase solution stability, reduce analysis time cost required for convergence, save memory usage and has no adverse effect on solution accuracy.

Clipping Noise Compensation with Neural Networks in OFDM Systems

The application of deep learning (DL) to solve physical layer issues has emerged as a prominent topic. In this paper, the mitigation of clipping effects for orthogonal frequency division multiplexing (OFDM) systems with the help of a Neural Network (NN) is investigated. Unlike conventional clipping recovery algorithms, which involve costly iterative procedures, the DL-based method learns to directly reconstruct the clipped part of the signal while the unclipped part is protected. Furthermore, an interpretation of the learned weight matrices of the neural network is presented. It is observed that parts of the network, in effect, implement transformations very similar to the (Inverse) Discrete Fourier Transform (DFT/IDFT) to provide information in both the time and frequency domains. The simulation results show that the proposed method outperforms existing algorithms for recovering clipped OFDM signals in terms of both mean square error (MSE) and Bit Error Rate (BER).

The impact of the inverse chirp z-transform on breast microwave radar image reconstruction

This work examines the impact of the inverse chirp z-transform (ICZT) for frequency-to-time-domain conversion during image reconstruction of a pre-clinical radar-based breast microwave imaging system operating over 1–8 GHz. Two anthropomorphic breast phantoms were scanned with this system, and the delay-multiply-and-sum beamformer was used to reconstruct images of the phantoms, after using either the ICZT or the inverse discrete Fourier transform (IDFT) for frequency-to-time domain conversion. The contrast, localization error, and presence of artifacts in the reconstructions were compared. The use of the IDFT resulted in prominent ring artifacts that were not present when using the ICZT, and the use of the ICZT resulted in higher contrast between the tumor and clutter responses. In one of the phantoms, the tumor response was only visible in reconstructions that used the ICZT. The use of the ICZT evaluated with a time-step size of 11 ps resulted in the reduction of prominent artifacts present when using the IDFT and the successful identification of the tumor response in the reconstructed images.

Marching On-In-Time Unstructured PEEC Method for Electrically Large Structures with Conductive, Dielectric, and Magnetic Media

The Marching On-In-Time (MOT) unstructured Partial Element Equivalent Circuit (PEEC) method for time domain electromagnetic problems is presented. The method allows the transient analysis of electrically large electromagnetic devices consisting of conductive, dielectric, and magnetic media coupled with external lumped circuits. By re-formulating PEEC following the Coulombian interpretation of magnetization phenomena and by using electric and magnetic vector potentials, the proposed approach allows for a completely equivalent treatment of electric and magnetic media and inhomogeneous and anisotropic materials are accounted for as well. With respect to the recently proposed Marching On-In-Time PEEC approach, based on the standard (structured) discretization of PEEC, the method presented in this paper uses a different space and time MOT discretization, which allows for a reduction in the number of the unknowns. Analytical and industrial test cases consisting in electrically large devices are considered (e.g., the model of a Neutral Beam Injector adopted in thermonuclear fusion applications). Results obtained from the simulations show that the proposed method is accurate and yields good performances. Moreover, when rich harmonic content transient phenomena are considered, the unstructured MOT–PEEC method allows for a significant reduction of the memory and computation time when compared to techniques based on Inverse Discrete Fourier Transform applied to the frequency domain unstructured PEEC approach.

Desarrollo Y Simulación De Un Modelo De Transceptor Basado En Prime Para Simulación Sobre Canal PLC

The choice of modification technique for a communications system depends to a large extent on the nature and characteristics of the medium in which it must operate (Hrasnica et al., 2005). In a PLC (Power Line Communications) system, the first applications in the LDR band (oriented to the control of devices) operated with monocarrier modulations, such as ASK, BPSK, and FSK. This allows for low implementation costs, provided that it operates at low data rates and with an error correction system. It is clear that applications require a higher data rate. The modulation technique must overcome challenges such as the necessary equalization for the cause of the non-linearity of the channel, or avoid the propagation delays and the multipath caused by the impedance differences in the branches. Likewise, it must offer flexibility and avoid the use of certain frequencies if they are altered or assigned to another service and, therefore, cannot be used in PLC. In this scenario, one of the techniques that have been imposed in the most used developments in NB-PLC as in BB-PLC has been Orthogonal Frequency Division Multiplexing (OFDM). One of its most attractive aspects from the point of view of its complexity is the possibility of implementing the structure of its multifrequency modulation and demodulation scheme through a simple Inverse Discrete Fourier Transform (IDFT) and its corresponding direct transform, Fast Fourier Transform (FFT). Based on this technique, an appropriate transceiver scheme for operating on a PLC channel model was presented. This development implements the error correction technique proposed for NB-PLC.

Denoising controlled-source electromagnetic data using least-squares inversion

Strong noise is one of the toughest problems in the controlled-source electromagnetic (CSEM) method, which highly affects the quality of recorded data. The three main types of noise existing in CSEM data are periodic noise, Gaussian white noise, and nonperiodic noise, among which the nonperiodic noise is thought to be the most difficult to remove. We have developed a novel and effective method for removing such nonperiodic noise by formulating an inverse problem that is based on inverse discrete Fourier transform and several time windows in which only Gaussian white noise exists. These critical locations, which we call reconstruction locations, can be found by taking advantage of the continuous wavelet transform (CWT) and the temporal derivative of the scalogram generated by CWT. The coefficients of the nonperiodic noise are first estimated using the new least-squares method, and then they are subtracted from the coefficients of the raw data to produce denoised data. Together with the nonperiodic noise, we also remove Gaussian noise using the proposed method. We validate the methodology using real-world CSEM data.