Probability Distribution Function Of Noise Research Articles

Data-Driven Safe Control of Uncertain Linear Systems Under Aleatory Uncertainty

Safe control of constrained uncertain linear systems under aleatory uncertainty is considered. Aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF). Data-based probabilistic safe controllers are designed for the cases where the noise PDF is 1) zero-mean Gaussian with a known covariance, 2) zero-mean Gaussian with an uncertain covariance, and 3) zero-mean non-Gaussian with an unknown distribution. Easy-to-check model-based conditions for guaranteeing probabilistic safety are provided for the first case by introducing probabilistic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> -contractive sets. These results are then extended to the second and third cases by leveraging distributionally-robust probabilistic safe control and conditional value-at-risk ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CVaR</b> ) based probabilistic safe control, respectively. Data-based implementations of these probabilistic safe controllers are then considered. Moreover, an upper bound on the minimal risk level, under which the existence of a safe controller is guaranteed, is learned using collected data. A simulation example is provided to show the effectiveness of the proposed approach.

Closed-Form Bit Error Probability of ZF Detection for OFDM-M-MIMO Systems Using Effective Noise PDF

This paper derives the closed-form bit error probability (BEP) of massive multiple-input, multiple-output (M-MIMO) systems using orthogonal frequency-division multiplexing (OFDM) and zero-forcing (ZF) detection. We improve the BEP accuracy by increasing the Neumann series expansion (NSE) to second order for the system that was previously analyzed in [1] employing a derived probability distribution function (PDF) of the effective noise. The proposed PDF is then utilized to evaluate the BEP, the PDF of output signal-to-noise ratio (SNR), and the outage probability as a function of the output SNR of the system. Furthermore, a simplified closed-form expression for the effective noise PDF, in terms of the Gaussian distribution, and the noise variance are firstly derived in this paper for simplifying the performance analysis. Monte-Carlo simulation results confirm that the outcome from the derived equation and the approximation closely matched those obtained by simulation. In addition, we employ the proposed noise variance to estimate the log-likelihood ratio (LLR) instead of the approximate noise variance for the low-complexity soft-output ZF detection. The computational complexity of the proposed detection is thus significantly reduced, whereas its bit error rate (BER) is lower than that of the classical detection. Focusing on a 10 × 200 Coded-OFDM-M-MIMO system, 97.81% of multiplications, required for producing the LLR from the estimated symbol, were minimized by utilizing the proposed detection. Therefore, the derived equations can be efficiently used for analyzing the performance of OFDM-M-MIMO systems, and reducing the computational complexity of the soft-output ZF detection.

Effects of stochastic resonance for linear–quadratic detector

In this paper, the stochastic resonance (SR) effects of the fixed linear–quadratic (L–Q) detector in binary hypothesis testing problems is investigated. The effects include the improvement of the overall performance of the detector wherein the output signal-to-noise ratio (SNR) of receiver and the detection probability (PD) are increased and the false-alarm probability (PFA) is reduced at the same time. The SNR of a noise modified detector is derived. Since the improvement of the SNR does not mean the improvement of detection performance, the noise enhanced detection performance in terms of PFA and PD are discussed graphically and elaborated through an example of Gaussian background noise. Furthermore, the conditions are deduced to determine whether the overall performance of the detector can be improved or not. In addition, the form of the suitable noise probability distribution function (PDF) is determined and the PDF of noise that satisfies the conditions to improve the overall performance of detector are derived. Finally, an illustrative example is presented to verify the theoretical results.

Closed-Form Relations for Resonance Detection Error Using Statistical Analysis of Amplitude Noise

The optimization of resonance-tracking sensors relies critically on proper estimation of resonance detection error. We study this error in two common resonance detection algorithms: the absolute minimum method and the linear regression method. Closed-form relations for the error originating from additive noise are presented. The formulation accommodates the majority of lineshapes of practical interest and a wide variety of noise statistics. Lorentzian and Fano line shapes are studied here with further detail for their practical importance. It is discussed that while the performance of the absolute minimum method depends on the tail of the noise probability distribution function, for the linear regression method the total noise power is the determining characteristic of the noise. This fact is explained for the specific case of quantization noise. The results of this study enable a quantitative comparison of the performance of resonance-based sensors, which is a center piece in the optimization of their limit of detection.

OPTIMAL DIRECTED CURRENT OF A BROWNIAN MOTOR UNDER A NON-GAUSSIAN NOISE GENERATED BY A MULTIPLICATIVE PROCESS

Unidirectional motion is achieved when a particle, moving under the influence of an underlying noise source, is subjected to a ratchet asymmetric periodic potential. Here, we investigate how deviations from the Gaussian nature of the noise distribution function impacts the average particle's current. The input noise is considered to be produced by a Langevin process including both multiplicative and additive random noise sources. The resulting input random signal has a power-law amplitude distribution and a finite correlation time. These features are controlled by the average of the multiplicative noise. We show that the average particle's velocity depends non-monotonically on the degree of non-Gaussianity of the input noise. It exhibits a maximum at an intermediate value of the effective power-law exponent that characterizes the asymptotic decay of the noise probability distribution function.

Quantization Error and Resolution in Ensemble Averaged Data With Noise

We investigate the properties of ensemble averaged data from a uniform quantizer, when the quantizer input signal is noisy. An expression for the mean-square error (MSE) MSE(/spl sigma/,N) of the ensemble averaged data, accounting for an ensemble of finite length N, and noise RMS /spl sigma/, is obtained. Previously published results for N=1 and N/spl rarr//spl infin/ are recovered. For intermediate N, we show that there is an optimal noise RMS, /spl sigma//sub opt/(N), which minimizes the MSE. Such a minimum point exists regardless of the type of noise probability distribution function. Conditions on /spl sigma/ and N for achieving a smaller MSE than in the noise-free case (/spl Delta//sup 2//12) are discussed. The convergence properties of MSE(/spl sigma/,N) for increasing N, and the effect of applying uniformly distributed dither, is established.

Searching for Dark Matter Halos in the Suprime-Cam 2 Square Degree Field

We report the first result of a weak gravitational lensing survey on a 2.1 deg2 Rc-band image taken with a wide-field camera (Suprime-Cam) on the prime focus of the 8.2 m Subaru Telescope. The weak lensing mass reconstruction is applied to the data to search for dark matter halos of cluster scale M ≥ 1014 M☉. The reconstructed convergence field is divided by 1 σ noise to obtain the signal-to-noise ratio (S/N) map of the detection. Local maxima and minima are searched on the S/N map, and the probability distribution function (PDF) of the peaks is created to compare with model predictions. We found excess over noise PDF created from the randomized realization on both the positive and negative sides. Negative peaks imply the presence of voids in the dark matter distribution, and this is the first report of the detection. Positive peaks, on the other hand, represent the dark matter halos, and the number count of the halos on the 2.1 deg2 image is 4.9 ± 2.3 for S/N > 5, where the Gaussian smoothing radius of the convergence map is 1'. The result is consistent with the prediction assuming the Press-Schechter mass function and the Navarro-Frenk-White halo profile under the cluster-normalized cold dark matter cosmology. Although the present statistics are not enough because of the limited field of view, this work demonstrates that dark matter halo count via weak lensing is a promising way to test the paradigm of structure formation and the cosmological model.

船舶雑音の近似的確率分布表現と実験

船舶雑音の近似的確率分布表現と実験