Gaussian Noise Generator Research Articles

FPGA-based experimental board for error control codes

This paper proposed an experimental device that emulates and facilitates teaching the theoretical concepts of error-control coding (ECC) techniques. Two prototypes laboratory boards were designed and implemented. The first board simulates the transmitter side of a typical digital communication system. It mainly contains a data source, (7,4) Hamming encoder, cyclic redundancy check encoder (CRC), and Gaussian noise generator. The second board has two types of Hamming decoders, a syndrome decoder, and a maximum likelihood (ML) decoder that accepts the received soft signals at the channel output. Each board has several control switches so that the trainee can change the code variables, noise power, user ID, in addition to display tools such as light-emitting diodes (LEDs), and test points for the oscilloscope that help the user to observe the results. Moreover, results and setting variables can also be displayed on a PC’s screen connected through a USB port and organic light emitting diodes (OLED) display that is attached to the receiver board. The pipelining architecture of the field programmable gate array (FPGA) device was exploited in this proposed system to reduce the processing delay and hence increase the data throughput. Furthermore, we proved that both theoretical and experimental tests are identical.

Inhibitory effect induced by fractional Gaussian noise in neuronal system

We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly, essential properties of fractional Brownian motion (fBm) and generation of fractional Gaussian noise (fGn) are presented, and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes. Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of fGn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance (ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals (ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.

Discrete time domain analysis of radiation detector noise

In this paper, the analysis of radiation detector noise is carried out based on digital signal processing in the discrete time domain. To generate accurate noise models, detector noise sources are analyzed and modeled in the discrete region. Poisson noise generator was used for shot noise, and White Gaussian Noise Generator was used for Johnson Noise and Channel Thermal Noise. For flicker noise, White Gaussian Noise Generator with 1/f filter was applied. The output noise was calculated by convolution sum of the system impulse function and noise input. In order to improve the accuracy noise analysis, the time domain equation was derived based on the advanced model compared to the existing noise model. CSA model is based on a realistic limited-bandwidth OP-AMP. For the realistic detector model, Laplace transformed function of CSA and shaper out signal for parallel and series noise were derived and inversed for time domain signal. The results of the existing frequency domain analysis match well with the discrete time domain analysis. The discrete time domain analysis can increase the accuracy of noise investigation because it can visualize results of existing frequency domain models and provide different representation methods for the same results.

Generation of Geiger-Muller detector dataset for simulation of radioactive source localization algorithm

Detector dataset in digital data is required to simulate and evaluate a particle filter (PF) algorithm. The PF is used to estimate the position and intensity of unknown hotspots within a region of interest (ROI) from sparse sampling points around the ROI. The dataset will emulate GM measured data at these sampling points. GM radiation detection model, Poisson random variable generator, and Gaussian noise generator were implemented to generate the datasets. Next, using the datasets as input to the PF code, the corresponding output is evaluated for various configuration of hotspot locations and radiation intensities. The resulting detector datasets and the particle filter output were analyzed; and the results are presented in the paper.

Generation of homogeneous 3D Gaussian noise with spherically symmetric covariance.

In this paper, an approach for 3D noise generation is presented. The proposed algorithm might be a useful tool for the generation of correlated phase screens. These phase screens can be used for the simulation and modeling of optical wave propagation through atmospheric turbulence. Arbitrary user-defined covariance functions between voxel pairs can be achieved. Correlated 3D noise is formed by superposition of multiple uncorrelated 3D Gaussian noise patterns. These uncorrelated input noise patterns are of different dimensions. They are upsampled to the same target dimensions by linear interpolation. Each input pattern then contributes to total covariance on different spatial scales. The covariances between different voxels are expressed analytically by propagation of error. For a subset of randomly chosen voxels in the entire voxel space, relative deviations between the analytical and user-defined covariances are calculated. A sum of squares of these relative deviations is then minimized by machine learning methods. The optimized parameters are the weighting factors of individual uncorrelated 3D noise patterns. Corresponding covariance functions are numerically evaluated for two current atmospheric turbulence spectra. The first one is the generalized modified atmospheric spectrum. The second one is the generalized modified von Karman spectrum. Based on these covariance functions, optimal superpositions are calculated. Finally, statistical properties of these patterns are validated by ensemble sample covariance analysis.

Fractal behaviour of distances between consecutive aftershocks: the examples of Landers, Northridge and Hector Mine Southern California mainshocks

Distances between consecutive aftershocks are analysed by means of mono- and multifractal theory with the aim of quantifying the complexity of the physical mechanism governing them, as well as their predictability and predictive instability. Hausdorff, Ha, and Hurst, H, exponents are determined by semivariograms and rescaled analysis, respectively. The exponent β of the power law describing power spectral contents is also quantified. These three parameters permit a generation of fractional Gaussian noise, fGn, simulating distances. The complexity and predictive instability of physical mechanism generating the series of distances is quantified by means of the correlation dimension, μ*, the Kolmogorov entropy, κ, and the Lyapunov exponents, λi, which are based on the reconstruction theorem formulation. Additionally, the multifractal detrended fluctuation analysis, MF-DFA, contributes with a different point of view to quantify the complexity of the series, in terms of fractal spectral width, W, spectral asymmetry, B, and the critical Holder exponent, a0. By one hand, the MF-DFA is applied to the complete set of distances characterising the whole aftershock process. By the other hand, the MF-DFA is applied to segments of the series of distances with the aim of determining the evolution of the complexity since the mainshock up to the end of the stress relaxation process. Finally, an ARIMA multilinear regression process is applied to obtain some improvements, in comparison with fGn simulations, on the prediction of distances. The database for this analysis is obtained from the Southern California Seismic Network (SCSN) catalogue. Three series of aftershocks equalling to or exceeding magnitudes of 2.0, assuring seismic catalogue completeness, and associated with Landers (06/28/1992), Northridge (01/17/1994) and Hector Mine (10/16/1999) mainshocks are obtained. It is worth mentioning that common mono-multifractal behaviour for the three aftershocks series is not detected, whatever aftershock periods or segments of them are considered.

Compact digital implementation of a non‐coherent IR‐UWB transmitter and receiver

Non-coherent impulse-radio ultra-wideband (IR-UWB) transceivers are attractive candidates for applications where the silicon area and power consumption are relatively limited. This study presents the compact digital architecture design and implementation of a non-coherent IR-UWB transmitter and receiver based on the energy detection scheme, including the synchroniser module. The software models of the designed transceiver are simulated and verified in both floating-point and fixed-point numerical representations. The synthesisable Verilog description of the transmitter and receiver architectures is simulated and verified against their fixed-point simulation model. The transmitter and receiver are implemented in the authors custom-developed field-programmable gate array (FPGA) board. The bit error rate performance of the transmitter and receiver is measured in real-time on the FPGA, utilising an accurate on-chip Gaussian noise generator. The characteristics and implementation results of the transmitter and receiver architecture on the FPGA are presented. An application-specific integrated circuit (ASIC) architecture of the IR-UWB transceiver is estimated to occupy 0.0227 mm 2 and dissipate 760 mW from a 1.0 V supply while operating at 82 MHz in a standard 32 nm complementary metal-oxide-semiconductor technology.

Design and Implementation of a Digital Secure Code-Shifted Reference UWB Transmitter and Receiver

This paper presents the first compact hardware implementation of a digital code-shifted reference (CSR) ultra-wideband (UWB) transceiver. The security of the transmission is based on changing the physical properties of the transmission without the use of higher level security options. The software models of the designed transceiver are simulated and verified in both floating-point and fixed-point numerical representations. The synthesizable Verilog description of the transceiver architecture is simulated and verified against its fixed-point simulation model. The secure transceiver is implemented on our custom-developed field-programmable gate array (FPGA) board. The characteristic and implementation results of the secure transceiver architecture on the FPGA are presented. The bit error rate performance of the transceiver is measured in real time on the FPGA using an accurate on-chip Gaussian noise generator and is compared with that of the software simulation model. An ASIC architecture of the CSR-UWB transceiver is estimated to occupy 0.019 mm2 and dissipate 0.63 mW from a 1.0 V supply while operating at 82 MHz in a standard 32-nm CMOS technology.

Modular design and implementation of field-programmable-gate-array-based Gaussian noise generator

ABSTRACTThe modular design of a Gaussian noise generator (GNG) based on field-programmable gate array (FPGA) technology was studied. A new range reduction architecture was included in a series of elementary function evaluation modules and was integrated into the GNG system. The approximation and quantisation errors for the square root module with a first polynomial approximation were high; therefore, we used the central limit theorem (CLT) to improve the noise quality. This resulted in an output rate of one sample per clock cycle. We subsequently applied Newton's method for the square root module, thus eliminating the need for the use of the CLT because applying the CLT resulted in an output rate of two samples per clock cycle (>200 million samples per second). Two statistical tests confirmed that our GNG is of high quality. Furthermore, the range reduction, which is used to solve a limited interval of the function approximation algorithms of the System Generator platform using Xilinx FPGAs, appeared to have a higher numerical accuracy, was operated at >350 MHz, and can be suitably applied for any function evaluation.

FPGA-Based Bit Error Rate Performancemeasuring of Wireless Systems

The bit error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. The proposed BER tester (BERT) integrates fundamental baseband signal processing modules of a typical wireless communication system along with a realistic fading channel simulator and an accurate Gaussian noise generator onto a single FPGA to provide an accelerated and repeatable test environment. Using a developed graphical user interface, the error rate performance of single- and multiple-antenna systems over a wide range of parameters can be rapidly evaluated. The FPGA-based BERT should reduce the need for time-consuming software based simulations, hence increasing the productivity. The BERT modules were developed using deviceindependent HDL, and no specific features of the FPGAs, such as built-in soft processors, were utilized. Therefore, the system is portable and can easily be synthesized onto larger and faster new FPGAs for the rapid prototyping of increasingly complex emerging wireless communication systems. FPGA solutions offer significant cost reduction compared to commercially available solutions.

Bit Error Rate Performance Measurement of Wireless MIMO System Based on FPGA

To measure the bit error rate (BER) performance validation of digital baseband communication systems on a field-programmable gate array (FPGA). The proposed BER tester (BERT) integrates fundamental baseband signal processing modules of a typical wireless communication system along with a realistic fading channel simulator and an accurate Gaussian noise generator onto a single FPGA to provide an accelerated and repeatable test environment in a laboratory setting. Using a developed graphical user interface, the error rate performance of single- and multiple-antenna systems over a wide range of parameters can be rapidly evaluated. The FPGA-based BERT should reduce the need for time-consuming software-based simulations, hence increasing the productivity. This FPGA-based solution is significantly more cost effective than conventional performance measurements made using expensive commercially available test equipment and channel simulators.

Variable Correlation Digital Noise Source on FPGA — A Versatile Tool for Debugging Radio Telescope Backends

Contemporary wideband radio telescope backends are generally developed on Field Programmable Gate Arrays (FPGA) or hybrid (FPGA+GPU) platforms. One of the challenges faced while developing such instruments is the functional verification of the signal processing backend at various stages of development. In the case of an interferometer or pulsar backend, the typical requirement is for one independent noise source per input, with provision for a common, correlated signal component across all the inputs, with controllable level of correlation. This paper describes the design of a FPGA-based variable correlation Digital Noise Source (DNS), and its applications to built-in testing and debugging of correlators and beamformers. This DNS uses the Central Limit Theorem-based approach for generation of Gaussian noise, and the architecture is optimized for resource requirements and ease of integration with existing signal processing blocks on FPGA.

FPGA-Based Bit Error Rate Performance Measurement of Wireless Systems

This paper presents the bit error rate (BER) performance validation of digital baseband communication systems on a field-programmable gate array (FPGA). The proposed BER tester (BERT) integrates fundamental baseband signal processing modules of a typical wireless communication system along with a realistic fading channel simulator and an accurate Gaussian noise generator onto a single FPGA to provide an accelerated and repeatable test environment in a laboratory setting. Using a developed graphical user interface, the error rate performance of single- and multiple-antenna systems over a wide range of parameters can be rapidly evaluated. The FPGA-based BERT should reduce the need for time-consuming software-based simulations, hence increasing the productivity. This FPGA-based solution is significantly more cost effective than conventional performance measurements made using expensive commercially available test equipment and channel simulators.

Evaluation of Vibration References with Equivalent Kurtosis and Dissimilar Amplitude Probability Densities

The generation of Gaussian noise with a specific auto spectral density (ASD) is a well-documented process employed in drive signal generation in vibration control applications. In recent years, vibration control system vendors have introduced the ability to modify the probability density function (PDF) characteristics associated with the reference ASD, yielding a non-Gaussian drive. The specific parameter defining this process is kurtosis. This paper will discuss concerns with this practice in terms of synthesizing a time history with dissimilar PDF characteristics to that of the measured data upon which the original ASD and kurtosis characteristics were based. An example is discussed from both statistical and fatigue perspectives.

Physical AWGN Channel Emulator for Bit Error Rate Test of Digital Baseband Communication

This paper presents a physical channel emulator solution for applications such as Bit Error Rate Testing of Error Correcting Codes. The solution relies on an analog White Gaussian Noise Generator coupled additively with an analog data signal to emulate the communication channel. This is interfaced to a computer through a USB connection, allowing the use of programs in different environments, such as Matlab and Labview. This solution can allow different types of channels to be emulated and with different noise sources. A software-based method to measure Signal to Noise Ratio and to characterize the channel is also presented. The system has been validated using a Matlab interface implementing multiple error correcting codes and showed good agreement with the theoretical model.

Hardware Architecture of a Gaussian Noise Generator Based on the Inversion Method

In this brief, we present a hardware-based Gaussian noise generator (GNG) with low hardware cost, high generation rate, and high Gaussian tail accuracy. The proposed generator is based on a piecewise polynomial approximation of the inverse cumulative distribution function (ICDF). We propose to avoid the area-demanding barrel-shifter of the ICDF approximation by means of creating a new uniform random sequence from the uniform random number generator output. The GNG architecture has been implemented in field-programmable gate array devices, and the implementation results are compared with other published designs, achieving a higher deviation with fewer hardware resources. Our GNG generates 242 Msps of random noise and achieves a tail of 13.1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $\sigma$</tex></formula> with 442 slices, two multipliers, and two Block-RAM of a Virtex-II device. The generator output successfully passed commonly used statistical tests.

A Programmable Look-Up Table-Based Interpolator with Nonuniform Sampling Scheme

Interpolation is a useful technique for storage of complex functions on limited memory space: some few sampling values are stored on a memory bank, and the function values in between are calculated by interpolation. This paper presents a programmable Look-Up Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can also be reconfigured to minimize the approximation error on specific portions of the interpolated function’s domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a study case, the proposed interpolator was used as the core of a programmable noise generator—output signals drawn from different Probability Density Functions were produced for testing FPGA implementations of chaotic encryption algorithms. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518.

Design and implementation of an optical Gaussian noise generator

A design of a fast and accurate optical Gaussian noise generator is proposed and demonstrated. The noise sample generation is based on the Box-Muller algorithm. The functions implementation was performed on a high-speed Altera Stratix EP1S25 field-programmable gate array (FPGA) development kit. It enabled the generation of 150 million 16-bit noise samples per second. The Gaussian noise generator required only 7.4% of the FPGA logic elements, 1.2% of the RAM memory, 0.04% of the ROM memory, and a laser source. The optical pulses were generated by a laser source externally modulated by the data bit samples using the frequency-shift keying technique. The accuracy of the noise samples was evaluated for different sequences size and confidence intervals. The noise sample pattern was validated by the Bhattacharyya distance (Bd) and the autocorrelation function. The results showed that the proposed design of the optical Gaussian noise generator is very promising to evaluate the performance of optical communications channels with very low bit-error-rate values.

The coherent detection method of gravitational wave bursts for spherical antennas

We provide a comprehensive theoretical framework and a quantitative test of the method we recently proposed for processing data from a spherical detector with five or six transducers. Our algorithm is a trigger event generator performing a coherent analysis of the sphere channels. In order to test our pipeline we first built a detailed numerical model of the detector, including deviations from the ideal case such as quadrupole modes splitting, and non-identical transducer readout chains. This model, coupled with a Gaussian noise generator, has then been used to produce six time series, corresponding to the outputs of the six transducers attached to the sphere. We finally injected gravitational wave burst signals into the data stream, as well as bursts of non-gravitational origin in order to mimic the presence of non-Gaussian noise, and then processed the mock data. We report quantitative results for the detection efficiency versus the false alarm rate and for the affordability of the reconstruction of the direction of arrival. In particular, the combination of the two direction reconstruction methods can reduce by a factor of 10 the number of false alarms due to the non-Gaussian noise.

Validation of CT dose‐reduction simulation

The objective of this research was to develop and validate a custom computed tomography dose-reduction simulation technique for producing images that have an appearance consistent with the same scan performed at a lower mAs (with fixed kVp, rotation time, and collimation). Synthetic noise is added to projection (sinogram) data, incorporating a stochastic noise model that includes energy-integrating detectors, tube-current modulation, bowtie beam filtering, and electronic system noise. Experimental methods were developed to determine the parameters required for each component of the noise model. As a validation, the outputs of the simulations were compared to measurements with cadavers in the image domain and with phantoms in both the sinogram and image domain, using an unbiased root-mean-square relative error metric to quantify agreement in noise processes. Four-alternative forced-choice (4AFC) observer studies were conducted to confirm the realistic appearance of simulated noise, and the effects of various system model components on visual noise were studied. The "just noticeable difference (JND)" in noise levels was analyzed to determine the sensitivity of observers to changes in noise level. Individual detector measurements were shown to be normally distributed (p > 0.54), justifying the use of a Gaussian random noise generator for simulations. Phantom tests showed the ability to match original and simulated noise variance in the sinogram domain to within 5.6% +/- 1.6% (standard deviation), which was then propagated into the image domain with errors less than 4.1% +/- 1.6%. Cadaver measurements indicated that image noise was matched to within 2.6% +/- 2.0%. More importantly, the 4AFC observer studies indicated that the simulated images were realistic, i.e., no detectable difference between simulated and original images (p = 0.86) was observed. JND studies indicated that observers' sensitivity to change in noise levels corresponded to a 25% difference in dose, which is far larger than the noise accuracy achieved by simulation. In summary, the dose-reduction simulation tool demonstrated excellent accuracy in providing realistic images. The methodology promises to be a useful tool for researchers and radiologists to explore dose reduction protocols in an effort to produce diagnostic images with radiation dose "as low as reasonably achievable".