On the representation of continuous parameter processes by a sequence of random variables

This paper examines the question of representing a continuous parameter random process{ x_t, t in T }by a sequence of random variables "without loss of information." The principal result is that such a representation by expansion coefficients relative to a basis{ phi_i }ofmathcal{L}_2(T)is always possible, regardless of the orthogonality of{ phi_i }and of the boundedness of the time intervalT, provided only that the process is continuous in probability and almost every sample path has finite energy.     

On Poisson contention resolution problem with feedback based onconflict intensity

Communication over a random multiple-access, time-slotted, packet-switched, collision-type, broadcast channel with feedback is considered under a Poisson infinite-user model. The feedback generated by the channel provides some information about the intensity of conflicts. Two conflict-resolution algorithms are discussed for the above channel; they achieve throughputs of 0.334 and 0.369, respectively. The modification technique used to arrive at the second algorithm is emphasized. It is pointed out that the modification technique could be helpful in improving the performance of the conflict-resolution algorithms operating under other types of feedback     

Renewal approximations of the doubly stochastic Poisson processes

In this paper, we analyze two approaches to approximate a doubly stochastic Poisson (DSP) process by a renewal process. A DSP process consists of Poisson processes whose rates alternate between two levels. Each rate remains for renewal times forming an alternating renewal process. Such processes can be used to model situations in reliability, inventory, queueing and production systems. We develop two expressions for the Laplace-Stieltjes transforms of the interrenewal time distributions of the renewal processes that approximate a DSP process. We then use these approximations to develop expressions for the stationary loss probability in a G/M/1/0 system. We evaluate the quality of these approximations by comparing them against exact results. Our approximations should be of significant use in several practical applications.     

Reduction of shot noise with light emitting diodes

The authors find that the optical shot noise and the electrical shot noise in light emitting diodes have the identical fluctuation due to spontaneous emission as far as the quantum efficiency is unity. The 0.45-dB reduction of noise below the standard shot-noise limit is achieved by using such correlation between the two kinds of shot noise     

Analytical model of shot noise in double-barrier resonant-tunnelingdiodes

The shot noise in double-barrier diodes is analyzed using the stationary-state approach to resonant tunneling through the first quasi-bound level. Significant deviations from full shot noise are predicted. Significant shot noise suppression occurs in the entire positive differential resistance region below the current peak, and shot noise enhancement occurs in the negative differential resistance region above the peak. The physical basis for these effects is assumed to be the modulation of the double-barrier transmission probability by charge stored in the first quasi-bound level in the quantum well. The analysis confirms microwave noise measurements of high-speed double-barrier diodes     

Timing estimation for a filtered Poisson process in Gaussian noise

The problem of estimation of time shift of an inhomogeneous casually filtered Poisson process in the presence of additive Gaussian noise is discussed. Approximate expressions for the likelihood function, the MAP estimator, and the MMSE estimator that becomes increasingly accurate as the per-unit-time density of superimposed filter responses becomes small are obtained. The optimal MAP estimator takes the form of a cascade of linear and memoryless nonlinear components. For smooth point process intensities, the performance of the MAP estimator is studied via local bias and local variance. A rate distortion type lower bound on the MSE of any estimator of time delay is then derived by identification of a communications channel that accounts for the mapping from time delay to observation process. Results of numerical studies of estimator performance are presented. Based on the examples considered it is concluded: (1) the small-error MSE of the nonlinear MAP estimator can be significantly better than the small-error MSE of the optimal linear estimator: (2) the rate distortion lower bound can be significantly tighter than the Poisson limited bounds determined in previous studies     

An approximation for the distribution of shot noise (Corresp.)

If a shot noise distribution is conditioned on the number of Poisson events before it is expanded in Edgeworth's series, the resulting approximation may be more accurate than the usual direct expansion. We investigate the error of such an approximation, both asymptotically and for a particular example, and give an application to laser communication. We also give a general recurrence relation for determining the successive terms of Edgeworth's series.     

Predicting dynamic range and intensity discrimination for electrical pulse-train stimuli using a stochastic auditory nerve model: the effects of stimulus noise

This work investigates dynamic range and intensity discrimination for electrical pulse-train stimuli that are modulated by noise using a stochastic auditory nerve model. Based on a hypothesized monotonic relationship between loudness and the number of spikes elicited by a stimulus, theoretical prediction of the uncomfortable level has previously been determined by comparing spike counts to a fixed threshold, Nucl. However, no specific rule for determining Nucl has been suggested. Our work determines the uncomfortable level based on the excitation pattern of the neural response in a normal ear. The number of fibers corresponding to the portion of the basilar membrane driven by a stimulus at an uncomfortable level in a normal ear is related to Nucl at an uncomfortable level of the electrical stimulus. Intensity discrimination limens are predicted using signal detection theory via the probability mass function of the neural response and via experimental simulations. The results show that the uncomfortable level for pulse-train stimuli increases slightly as noise level increases. Combining this with our previous threshold predictions, we hypothesize that the dynamic range for noise-modulated pulse-train stimuli should increase with additive noise. However, since our predictions indicate that intensity discrimination under noise degrades, overall intensity coding performance may not improve significantly.     

Fast total variation deconvolution for blurred image contaminated by Poisson noise

In this paper, we present a fast non-blind deconvolution method for restoring blurred images contaminated by Poisson noise. The problem is formulated by finding the minimizer of the negative logarithmic Poisson log-likelihood combined with the total variation (TV). To attack the challenging task, we adopt the well-known variable splitting and penalty technique to convert the problem into two easier sub-problems: one is a modified TV regularized deconvolution and the other is a simple convex optimization problem. Experimental results show that the proposed method runs very fast and the quality of the restored image is comparable with that of some state of the art methods.     

On the quantum limit of intensity and phase noise in negativefrequency feedback lasers

The quantum limit of intensity and phase noise in negative frequency feedback semiconductor lasers is calculated. It is shown that under some conditions the number-phase uncertainty can be reduced to the ultimate Heisenberg uncertainty limit     

On improving the representation of a region achieved by a sensor network

This paper considers the class of applications of sensor networks in which each sensor node makes measurements, such as temperature or humidity, at the precise location of the node. Such spot-sensing applications approximate the physical condition of the entire region of interest by the measurements made at only the points where the sensor nodes are located. Given a certain density of nodes in a region, a more spatially uniform distribution of the nodes leads to a better approximation of the physical condition of the region in the sensed data. This paper considers the error in this approximation and seeks to improve the quality of representation of the physical condition of the points in the region in the data collected by the sensor network. We develop two essential metrics which together allow a rigorous quantitative assessment of the quality of representation achieved: the average representation error and the unevenness of representation error, the latter based on a well-accepted measure of inequality used in economics. We present the rationale behind the use of these metrics and derive relevant theoretical bounds on them in the common scenario of a planar region of arbitrary shape covered by a sensor network deployment. A simple new heuristic algorithm is presented for each node to determine if and when it should sense or sleep to conserve energy while also preserving the quality of representation. Simulation results show that it achieves a significant improvement in the quality of representation compared to other related distributed algorithms. Interestingly, our results also show that improved and consistent spatial uniformity has the welcome side-effect of a significant increase in the network lifetime.     

Poisson intensity estimation for tomographic data using a wavelet shrinkage approach

We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.     

Analytic alpha-stable noise modeling in a Poisson field ofinterferers or scatterers

This paper addresses non-Gaussian statistical modeling of interference as a superposition of a large number of small effects from terminals/scatterers distributed in the plane/volume according to a Poisson point process. This problem is relevant to multiple access communication systems without power control and radar. Assuming that the signal strength is attenuated over distance r as 1/r/m, we show that the interference/clutter could be modeled as a spherically symmetric α-stable noise. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted, such as the finite number of interferers and nonhomogeneous Poisson fields of interferers. In addition, the formulas derived allow us to predict noise statistics in environments with lognormal shadowing and Rayleigh fading. The results obtained are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws. Computer simulations are provided to demonstrate the efficiency of the α-stable noise model in multiuser communication systems. The analysis presented will be important in the performance evaluation of complex communication systems and in the design of efficient interference suppression techniques     

Reduction of optical shot noise from light emitting diodes

The mechanism responsible for the reduction of optical shot noise from high impedance driven light-emitting diodes is addressed. It is shown that the electronic feedback mechanism is the same as that for laser diodes with spontaneous recombination. Quantum noise reduction below the optical shot noise level is due to the effect of negative feedback on the recombination rate that occurs when the junction voltage and carrier number are permitted to respond to the underlying (Poisson) stochastic recombination process as in a light-emitting diode or laser diode driven by a high impedance source. Extensive measurements on light-emitting diodes confirm the magnitude of the noise suppression predicted from semiclassical theory     

The estimation of a probability density function from measurements corrupted by Poisson noise (Corresp.)

The estimation of a probability density function from measurements corrupted by independent additive Poisson noise is considered. An estimate is derived that is asymptotically unbiased and consistent in the quadratic mean. Also, a practical realization of the estimator is given.     

Tests for positive jumps in the intensity of a Poisson process: apower study

Tests are considered for the hypothesis of a constant intensity against the alternative of an intensity which increases with time in a nonhomogeneous Poisson process. Attention is focused on step-function alternatives and tests designed for such alternatives. One application is testing for abrupt changes in equipment following scheduled overhauls. The authors recommend the order-restricted likelihood-ratio test over an ordered chi-square test for such situations, provided the points at which jumps can occur are known. Otherwise, they recommend the test based on the Laplace statistic. The performance of these tests is evaluated for smooth alternatives, with the result that the smallest relative power of the order-restricted likelihood-ratio test is 73%, while for the Laplace test it is 82%. A numerical example based on failure times for a main-propulsion diesel engine is presented. The result is that the order-restricted likelihood-ratio test corresponds to the lowest statistical significance level     

Relative intensity noise of laser-diode arrays

Relative intensity noise in GaAs-GaAlAs semiconductor laser arrays was measured, compared with that in single-stripe lasers, and reviewed in the context of laser noise theory. When all the light is gathered and back reflections removed, all the arrays tested show comparable noise levels. Good agreement between theory and experiment is obtained for low drive currents where mode competition noise is relatively small. For low drive currents the noise is limited by the quantum noise, whereas for higher currents the noise saturates at about -145 dB/Hz under the best conditions, 10 dB below the level for a comparable single-stripe laser but 10 dB worse than for a single-mode distributed-feedback laser. The low noise in the array is explained quantitatively by considering the multiple transverse modes and the longer cavity length of the array.<>     

Relative intensity noise measurements of a widely tunablesampled-grating DBR laser

The intensity noise of a sampled-grating distributed Bragg reflector laser with 50-nm tuning range and 45-dB side-mode suppression ratio has been measured. The resonance frequency, damping factor, and modified Schawlow-Townes linewidth are extracted from the noise spectra. At high output power, the relative intensity noise (RIN) of the laser is below the photodiode shot noise limit, which is -160 dB/Hz. The laser has uniform shot noise limited RIN properties along the whole tuning range. The maximum resonance frequency is 5.4 GHz at a bias current of 120 mA and the K factor is 0.58 ns     

Shaping filter representation of nonstationary colored noise

The problem of determining a shaping filter for nonstationary colored noise is considered. The shaping filter transforms white noise into a possibly nonstationary random process (having no white noise component) with a specified covariance function. A set of conditions to be satisfied by the covariance function leads to the determination of a shaping filter. The shaping filter coefficients are simply related to the solution of a matrix Riccati equation. In order to formulate the Riccati equation, basic results concerning the mean-square differentiability of a random process are developed. If the Riccati equation can not be defined, an autonomous (zero-input) shaping filter may be easily determined.     

Analytical noise model with the influence of shot noise induced bythe gate leakage current for submicrometer gate-lengthhigh-electron-mobility transistors

A new high-frequency noise model which takes into account the influence of shot noise induced by the gate leakage current is introduced; the model accurately explains the observed minimum noise figure of submicrometer gate-length HEMT's as a function of frequency. Based on the steady-state Nyquist theorem for multiterminal devices recently reported, the minimum noise figure and the corresponding optimum source impedance of the microwave field effect transistors are expressed as functions of the measurable device parameters including noise spectral intensities and small-signal circuit parameters. The derived minimum noise figure can be shown to reduce to a simple form, i.e., an empirical relation with two fitting constant. The simple form and the derived formulas for the optimum source impedance can explain very well the experimental findings of the submicrometer gate-length high electron mobility transistors over the extended microwave frequency range and also provide the informations needed for the design of microwave low noise amplifiers