Bruce R. Davis

A review of stochastic resonance: circuits and measurement

Noise in dynamical systems is usually considered a nuisance. However, in certain nonlinear systems, including electronic circuits and biological sensory systems, the presence of noise can enhance the detection of weak signals. The phenomenon is termed stochastic resonance and is of great interest for electronic instrumentation. We review and investigate the stochastic resonance of several bistable circuits. A new type of S characteristic circuit is demonstrated using simple nonlinear elements with an operational amplifier. Using this circuit, the effects on stochastic resonance were determined as the slope of the S shaped characteristic curve was varied.

An Improved Importance Sampling Method for Digital Communication System Simulations

The use of importance sampling techniques can substantially reduce the variance of probability of error estimates obtained by Monte Carlo type simulations of digital communication systems. However, the advantages of importance sampling diminish as the memory length of the system becomes greater. This paper presents a modified importance sampling method which achieves substantial variance reduction for systems with memory.

FM Noise With Fading Channels and Diversity

The response of an FM discriminator to a fading signal is derived, taking into account the below-threshold noise and the effect of various diversity techniques. The effect of muting the discriminator output at low signal levels is considered and shown to achieve only marginal improvement. The diversity techniques considered are maximal-ratio combining, selection diversity, and equalgain combining. Only predetection combining is considered for the maximal-ratio and equal-gain techniques. The average SNR at the discriminator output is derived for each form of diversity, assuming that each diversity branch is independent of the others and subject to fading with a Rayleigh envelope distribution. Curves of average SNR plotted against the mean CNR in one branch are presented for various numbers of diversity branches and ratios of IF bandwidth and baseband bandwidth. The curves presented are for maximal-ratio combining only, but it is shown that the results for selection diversity and equal-gain combining may be obtained from these curves by simply applying a correction to the mean CNR. The theoretical results are supported by experimental measurements that show very close agreement with theory.

Delay Analysis for a TDMA Channel with Contiguous Output and Poisson Message Arrival

An analysis of the exact delay of a TDMA or a loop communication system with a contiguous output and a Poisson message arrival process is presented. The nonlinear relationship of a contiguous output with arbitrary arrival process can be expressed by an infinite series. In the case of a Poisson message arrival process, the series can be summed to a closed form. The derived result, which is validated by simulation, is a vast improvement over the previously used approximate model of multiple frames with single output.

Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums

A simple theoretical derivation for obtaining the Johnson thermal noise formula using window-limited Fourier transforms is presented in detail for the first time, utilizing the well-known energy theorems. In the literature, a diverse range of alternative methods already exist, and the pedagogical value of the Fourier transform approach illustrates useful mathematical principles, taught at the undergraduate level, naturally highlighting a number of physical assumptions that are not always clearly dealt with. We also proceed to survey a number of misconceptions, problems, surprises, and conundrums concerning thermal noise.

A Systemized View of Superluminal Wave Propagation

This paper reviews earlier studies on superluminal wave propagation in anomalously dispersive media that have been carried out in the electronic, microwave, and optical regimes. Those studies are relevant to observation of modulated Gaussian pulses transmitted through various media at speeds apparently faster than c without distortion. This paper also presents the condition for superluminal propagation that is established based on the magnitude-phase relation of a causal and minimum-phase filter. Since the condition is modeled on the basis of filter theory, it is applicable to all types of media. A terahertz experiment with a periodic bandgap structure is also included to illustrate superluminal propagation.

Random FM in Mobile Radio with Diversity

The probability density function and autocorrelation function of random FM in a mobile radio system are derived for the case where postdetection selection diversity is used. Closed-form solutions for the autocorrelation function have been found for no diversity and two-branch diversity and infinite series expansions for higher orders. The use of two-branch selection diversity is shown to reduce the random FM by 13.5 dB in a typical case, with a further 2.5-dB reduction when three branches are used. The effect of other forms of diversity on random FM is briefly assessed, but not pursued in detail.

REVERSE AUCTION: THE LOWEST UNIQUE POSITIVE INTEGER GAME

A reverse auction can be likened to a tendering process where a contract is awarded to the lowest bidder. This is in contrast to a conventional forward auction where the highest bidder wins. In this paper we analyze a minority game version of the reverse auction where an extra condition is imposed that, namely, the bid must be unique. In other words, the bidder with the lowest positive unique integer (LUPI) wins. We examine and compare two extrema, namely, the case when all players are rational and the case when all players make random selections.

The problem of detailed balance for the Feynman-Smoluchowski Engine (FSE) and the Multiple Pawl Paradox

The Feynman-Smoluchowski Engine (FSE) is simply a ratchet and pawl device, connected by a shaft to a vane, that is small enough to rectify the effect of random bombardment of gas molecules on the vane. The significance of the FSE is that it has inspired much activity in the area of Brownian ratchets. There is considerable interest in both the FSE and Brownian ratchets as these models are finding increasing use in a wide range of multidisciplinary applications from stochastic signal processing to econophysics to biology and even sociological processes. In this paper we examine the problem of detailed balance of the FSE and we introduce a new problem that considers a ratchet wheel with multiple pawls.

Error probability estimator structures based on analysis of the receiver decision variable

The paper presents schemes for rapid on-line error probability estimation of digital communications links. Several estimator structures are proposed based on the assumption of sample independence, including weighted least squares (WLS) and maximum likelihood (ML) forms. The continuous-form ML estimator is shown to lie on the Rao-Cramer bound, making it a most efficient estimator of probability of error. The design, performance, implementation complexity and behavior of these estimators is described for AWGN. >