Noise Enhancement Factor Research Articles

Eliminating intrinsic interference in GFDM systems: Design of a complex-valued prototype filter

Prototype filter design is a critical challenge in generalized frequency division multiplexing (GFDM) systems. Poorly designed filters can result in inherent and out-of-band (OOB) interferences, severely impacting system performance. This paper proposes a novel solution to this problem by introducing an optimal prototype filter that mitigates the adverse effects of intrinsic interferences in GFDM systems. Our approach involves using a complex-valued prototype filter, which resembles a single-sideband (SSB) modulation scheme and significantly enhances bandwidth efficiency compared to conventional GFDM. To design the optimal filter, we formulate an optimization problem that eliminates inband and adjacent subcarriers intrinsic interferences. We also provide analytical expressions for evaluating the system’s bit error rate (BER) and demonstrate the superiority of our optimized prototype filter over its current counterparts. To validate the design of the proposed prototype filter, we assess the noise enhancement factor (NEF). Our results indicate that our proposed filter improves system performance and reduces BER in GFDM systems.

Multi-User Scheduling for 6G V2X Ultra-Massive MIMO System.

6G vehicle-to-everything (V2X) communication will be combined with vehicle automatic driving technology and play an important role in automatic driving. However, in 6G V2X systems, vehicle users have the characteristics of high-speed movement. Therefore, how to provide stable and reliable wireless link quality and improve channel gain has become a problem that must be solved. To solve this problem, a new multi-user scheduling algorithm based on block diagonalization (BD) precoding for 6G ultra-massive multiple-input multiple-output (MIMO) systems is proposed in this paper. The algorithm takes advantage of the sensitive nature of BD precoding to channel correlation, uses the Pearson coefficient after matrix vectorization to measure the channel correlation between users, defines the scheduling factor to measure the channel quality according to the user noise enhancement factor, and jointly considers the influence of the correlation between user channels and channel quality, ensuring the selection of high-quality channels while minimizing channel correlation. Simulation results show that compared with the multi-user scheduling algorithm based on subspace correlation, condition number, and geometric angle, the proposed algorithm can obtain higher user channel gain, effectively reduce the system bit error rate, and can be applied to 6G V2X communication.

On the Noise Enhancement of GFDM

Generalized frequency division multiplexing (GFDM) is a multicarrier system employing well-localized prototype filters to form the transmitted signal. However, because of the non-orthogonality of the waveform, the demodulation process of GFDM inherits a noise enhancement, which leads to the performance degradation. Eigenvalues of the GFDM matrix determine the level of noise enhancement. In this letter, by defining the condition number of the GFDM matrix as the noise enhancement factor (NEF), we derive a closed-form presentation of NEF criterion based on the prototype filter shape. We show that the value of NEF is independent of the number of subsymbols and subchannels, if they are even; contrarily, for odd numbers, a larger NEF is resulted as the number grows up.

A Simple and Accurate Modeling Method of Channel Thermal Noise Using BSIM4 Noise Models

This article presents a method for extracting a channel thermal noise ( ${S} _{\mathrm{ id}}$ ) using analytical equations and measured noise parameters. Among the four noise parameters considered ( $R_{n}$ , G opt, B opt, and NF min), the equations of $R_{n}$ and NF min were used to extract ${S} _{\mathrm{ id}}$ , since the ${S} _{\mathrm{ id}}$ extracted from G opt and B opt was affected more by measurement variations. NTNOI, the noise enhancement factor of the charge-based thermal model of a Berkeley short-channel IGFET model 4 (BSIM4), was modeled as a gate-bias-dependent function to reproduce ${S} _{\mathrm{ id}}$ extracted from the measured noise parameters. Regarding the accuracy of the proposed model, while the error rate was found to vary slightly depending on the device dimensions (finger number), the new model showed only 4% error for $r_{n}$ , compared to the default model’s error of 41% obtained with NTNOI fixed at 1. In addition, the accuracy of G opt, B opt, and NF min is substantially higher than that of the default model. Finally, the modeling technique using the holistic model, another BSIM4 thermal noise model, was briefly discussed.

Minimum BER Power Allocation for Space-Time Coded Generalized Frequency Division Multiplexing Systems

In this letter, we propose a minimum BER (MBER) power allocation (PA) method for generalized frequency division multiplexing (GFDM) systems with zero forcing receiver. The MBER PA of GFDM systems is solved through minimizing noise enhancement factor at the receiver. Additionally, theoretical BER and achievable rate (AR) expressions are derived with the proposed PA strategy. Furthermore, we also generalize the MBER PA strategy in space-time coded (STC) GFDM systems. Simulation results show that, no matter GFDM or STC GFDM systems, the proposed PA strategy could improve BER and AR performances simultaneously.

BER Analysis for GFDM Systems With Gabor MMSE Receiver

In this letter, we investigate theoretical BER performances of generalized frequency division multiplexing (GFDM) systems with receivers based on Gabor window. Considering relationships between zero forcing and minimum mean square error (MMSE) receivers, theoretical BER expressions of GFDM systems with an MMSE receiver are derived over AWGN and fading channels through calculating noise enhancement factor at the receiver. To demonstrate the generality of proposed methods, analytical BER expressions of DFT and weighted-type fractional Fourier transform precoded GFDM systems are also given and verified by simulation results.

BER Analysis of WFRFT Precoded OFDM and GFDM Waveforms With an Integer Time Offset

In this paper, we investigate bit error rate (BER) performances of weighted-type fractional Fourier transform (WFRFT) precoded orthogonal frequency-division multiplexing (OFDM) and generalized frequency-division multiplexing (GFDM) waveforms with an integer time offset (TO) over additive white Gaussian noise and fading channels. First of all, theoretical BER expressions of hybrid carrier systems with TO are derived according to the linear combination characteristic of WFRFT. In addition, the fusion mechanism is also employed to calculate noise enhancement factor (NEF) of WFRFT precoded GFDM waveforms, and then analytical BER expressions are derived, including the cases with TO. Basically, analytical BER expressions of WFRFT precoded OFDM and GFDM waveforms are under the same framework, and BER of the latter could be simplified to the former when GFDM systems are reduced to OFDM systems. Through WFRFT precoding, the BER performance of GFDM waveforms could be improved by about 2 dB over fading channels with timing errors. Furthermore, using derived NEF of WFRFT precoded GFDM waveforms, theoretical BER expressions could be easily extended to space-time coded systems. Finally, when interblock interference and intercarrier interference are generated due to insufficient cyclic prefix and timing errors, BER performances of WFRFT precoded OFDM and GFDM waveforms also surpass their two special cases, i.e., nonprecoded and discrete Fourier transform precoded ones.

Optimal Radix-2 FFT Compatible Filters for GFDM

For a linear waveform, a finite condition number of the corresponding modulation matrix is necessary for the waveform to convey the message without ambiguity. Based on the Zak transform, this letter presents an analytical approach to compute the condition number of the modulation matrix for the multi-carrier waveform generalized frequency division multiplexing (GFDM). On top, we further propose a filter design that yields non-singular modulation matrices for an even number of subcarriers and subsymbols, which is not achievable for any previous work. Such new design has significant impact on implementation complexity, as the radix-2 FFT operations for conventional multicarrier waveforms can readily be employed for GFDM. Additionally, we analytically derive the optimal filter that minimizes the condition number.We further numerically evaluate the signal-to-interference ratio (SIR) and noise-enhancement factor (NEF) for matched filter (MF) and zero-forcing (ZF) GFDM receivers for such design, respectively.

Detailed modeling of the statistical uncertainty of Thomson scattering measurements

The uncertainty of electron density and temperature fluctuation measurements is determined by statistical uncertainty introduced by multiple noise sources. In order to quantify these uncertainties precisely, a simple but comprehensive model was made of the noise sources in the MST Thomson scattering system and of the resulting variance in the integrated scattered signals. The model agrees well with experimental and simulated results. The signal uncertainties are then used by our existing Bayesian analysis routine to find the most likely electron temperature and density, with confidence intervals.In the model, photonic noise from scattered light and plasma background light is multiplied by the noise enhancement factor (F) of the avalanche photodiode (APD). Electronic noise from the amplifier and digitizer is added. The amplifier response function shapes the signal and induces correlation in the noise. The data analysis routine fits a characteristic pulse to the digitized signals from the amplifier, giving the integrated scattered signals. A finite digitization rate loses information and can cause numerical integration error.We find a formula for the variance of the scattered signals in terms of the background and pulse amplitudes, and three calibration constants. The constants are measured easily under operating conditions, resulting in accurate estimation of the scattered signals' uncertainty. We measure F ≈ 3 for our APDs, in agreement with other measurements for similar APDs. This value is wavelength-independent, simplifying analysis. The correlated noise we observe is reproduced well using a Gaussian response function. Numerical integration error can be made negligible by using an interpolated characteristic pulse, allowing digitization rates as low as the detector bandwidth. The effect of background noise is also determined.

Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems

We derive closed-form expressions for nonlinear transmission performance of dual-polarization closely spaced coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. We find that the fiber nonlinear noise exhibits a signature of the flicker noise or 1/f noisebeyond the corner frequency that is inversely proportional to the total participating bandwidth. We derive a noise enhancement factor that captures the interference effect of nonlinear noises among different spans. For a 10 t 100-km standard single-mode-fiber (SSMF) link with no dispersion compensation at an optimal launch power density of - 15.9 dBm/GHz, the spectral efficiency of 9.90 b/s/Hz can be achieved for dual-polarization transmission, which is about 93% increase over single-polarization transmission. The closed-form expressions are also applicable to the closely spaced coherent single-carrier systems where the symbol rate is much larger than the dispersion walk-off bandwidth, and the optical dispersion is uncompensated.

A new model for electromigration grain boundary noise based on free volume

Grain boundary plays a key role in electromigration process of polycrystal interconnection. We take a free volume to represent a ‘vacancy–ion complex’ as a function of grain boundary specific resistivity, and develop a new characterisation model for grain boundary noise. This model reveals the internal relation between the boundary scattering section and electromigration noise. Comparing the simulation result with our experimental result, we find the source as well as the form of noise change in the electromigration process. In order to describe the noise enhancement at grain boundary quantitatively, we propose a new parameter—grain boundary noise enhancement factor, which reflects that the grain boundary noise can characterise the electromigration damage sensitively.

Quantifying an iterative clipping and filtering technique for reducing PAR in OFDM

In Orthogonal Frequency Division Multiplexing, a simple clipping method is widely used in order to reduce the peak-to-average power ratio since it is easy to implement. The performance analysis of the clipping approach has been previously introduced in the literature. Clipping, however, is a nonlinear process and may cause two major undesirable effects: (i) spectral regrowth, which causes unacceptable out-of-band radiation; and (ii) distortion of the desired signal, which increases bit-error-rate (BER). The out-of-band radiation can and often is suppressed by filtering, which leads to peak regrowth. Therefore, iterative clipping and filtering is required until the desired clipping level is achieved. However, this iterative process makes BER estimation difficult. This letter provides expressions and analytical techniques for estimating the attenuation factor, error vector magnitude, and BER, using a noise enhancement factor that is obtained by simulation. Simulation results show strong agreement with our semi-analytical results for 1024 subcarriers.

Elastic‐impedance analysis constrained by rock‐physics bounds†

ABSTRACTBy applying seismic inversion, we can derive rock impedance from seismic data. Since it is an interval property, impedance is valuable for reservoir characterization. Furthermore, the decomposition of the impedance into two fundamental properties, i.e. velocity and density, provides a link to the currently available rock‐physics applications to derive quantitative reservoir properties. However, the decomposition is a challenging task due to the strong influence of noise, especially for seismic data with a maximum offset angle of less than 30°. We present a method of impedance decomposition using three elastic impedance data derived from the seismic inversion of angle stacks, where the far‐stack angle is 23.5°. We discuss the effect of noise on the analysis as being the most significant cause of making the decomposition difficult. As the result, the offset‐consistent component of noise mostly affects the determination of density but not the velocities (P‐ and S‐wave), whereas the effect of the random component of noise occurs equally in the determination of the velocities and density. The effect is controlled by the noise enhancement factor 1/A, which is determined by a combination of stack angles. Based on the results of the analysis, we show an innovative method of decomposition incorporating rock‐physics bounds as constraints for the analysis. The method is applied to an actual data set from an offshore oilfield; we demonstrate the result of analysis for sandbody detection.

On the search for good aperiodic binary invertible sequences

For an aperiodic invertible sequence of length L, the optimality criterion is chosen to be the minimum noise enhancement factor of the corresponding aperiodic inverse filter. The noise enhancement factor is defined as the ratio of the noise energies at the outputs of the aperiodic inverse and the normalized matched filters of the sequence due to white noise at the filter inputs. Optimal binary sequences of length L/spl les/32 and optimal binary skew symmetric sequences of length 33/spl les/L/spl les/59 were found by exhaustive search. The search for near-optimal sequences is shown to have strong connections to the search for sequences with large products of Golay (1977) merit factor times the minimum of the energy density spectrum. Based on Legendre sequences and on Kronecker product sequences, long near-optimal binary sequences are found that have associated noise enhancement factors close to 1 dB.

Peak locater for multicomponent spectra

A sliding pivot technique capable of locating component peak maxima of multicomponent spectra is presented. The locations of peak maxima obtained in this way are shown to be the same as those of the minima in the second derivative. A major advantage over the second-derivative test is simply that derivative spectra are not needed. The sliding pivot technique requires only the original spectrum to locate the component peak maxima and consequently reduces the noise enhancement factor. The deconvuluted Fourier transform infrared spectrum of purple membrane is analyzed and compared to a Gaussian analysis and a second-derivative analysis. The sliding pivot technique identifies a band missed by second-derivative analysis.

Effect of doping on the optical gain and the spontaneous noise enhancement factor in quantum well amplifiers and lasers studied by simple analytical expressions

The maximum optical gain and the spontaneous noise enhancement factor in quantum well structures are expressed as extremely simple functions that are accurate over a wide range of carrier densities. These expressions are used to study the effect of doping on the optical gain and the noise enhancement factor in a 100 Å InGaAs/InP quantum well structure. n-type doping is most effective in reducing the transparency excitation level (laser threshold) and the noise enhancement factor (amplifier noise figure), whereas p-type doping enables increased gain at a given excitation level.

Noise enhancement in laser amplifiers caused by gain nonuniformity

We have calculated the noise-enhancement factor of a semiconductor laser amplifier with a very thin active region. This (somewhat academic) model exhibits large Petermann's K-factors. However, the calculated noise-enhancement factor K´ is only about half the K-value. The reason for the discrepancy is that in evaluating K´ the radiation modes of the guiding structure have been taken into account. Similar conclusions have been reached for realistic laser models. These theoretical considerations show that gain-guided laser amplifiers are not as noisy as was originally thought.