Information Theory and Reliable Communication

The detection of a fluctuating signal in the presence of noise is considered for a doubly stochastic Poisson counting system that is subject to fixed nonparalyzable detector deadtime. Explicit expressions are obtained for the likelihood-ratio detection of a modulated source of arbitrary statistics in the presence of Poisson noise counts. Receiver operating characteristics (ROC curves) are presented for an unmodulated (amplitude-stabilized) source with detector dead-time as a parameter; increasing deadtime causes a decrease in the probability of detection for a fixed false-alarm rate. Probability of error curves are presented for an amplitude-stabilized source, both in the absence of modulation and in the presence of triangular modulation, illustrating the deleterious effects of modulation, noise, and deadtime on receiver performance. Expressions for the average mutual information and channel capacity of the system are obtained and graphically presented for the simple counting receiver and for the maximum-likelihood counting receiver; the channel capacity decreases with decreasing signal level and with increasing deadtime and modulation depth. Representative examples of the appropriate counting distributions are provided. Finally, a maximum-likelihood estimate of the mean signal level is obtained for a simple image detection system with a deadtime-perturbed counting array. An expression for the statistical confidence level of the estimate is also obtained. The results are valid for an arbitrary deadtime-perturbed doubly stochastic Poisson counting system and as such are expected to find application in a broad variety of disciplines including photon counting and lightwave communications, operations research, nuclear particle counting, and neural counting and psychophysics.

Information, error, and imaging in deadtime-perturbed doubly stochastic Poisson counting systems

A principal difficulty of long dwell coherent imaging ladar is its extreme sensitivity to target or platform motion. This paper describes a motion compensated frequency modulated continuous wave 3D coherent imaging ladar method that overcomes this motion sensitivity, making it possible to work with nonstatic targets such as human faces, as well as imaging of targets through refractive turbulence. Key features of this method include scannerless imaging and high range resolution. The reduced motion sensitivity is shown with mathematical analysis and demonstration 3D images. Images of static and dynamic targets are provided demonstrating up to 600×800 pixel imaging with millimeter range resolution.

Motion compensated frequency modulated continuous wave 3D coherent imaging ladar with scannerless architecture.

A single-threshold processor is derived for a wide class of classical binary
					decision problems involving the likelihood-ratio detection of a signal embedded
					in noise. The class of problems we consider encompasses the case of multiple
					independent (but not necessarily identically distributed) observations of a
					nonnegative (nonpositive) signal, embedded in additive, independent, and
					noninterfering noise, where the range of the signal and noise is discrete. We
					show that a comparison of the sum of the observations with a unique threshold
					comprises optimum processing, if a weak condition on the noise is satisfied,
					independent of the signal. Examples of noise densities that satisfy and violate
					our condition are presented. The results are applied to a generalized
					photocounting optical communication system, and it is shown that most components
					of the system can be incorporated into our model. The continuous case is treated
					elsewhere [ IEEE Trans. Inf. TheoryIT-25, (March,
						1979)].

/pdf/single-threshold-detection-of-a-random-signal-in-noise-with-5cucvgblxb.pdf

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications.

It is shown that, for an arbitrary discrete process embedded in independent additive discrete noise, the classical binary detection problem using a likelihood-ratio test reduces to a simple comparison of the number of events with a single threshold. Only a weak condition on the noise distribution is required. Our results are appropriate for the analysis of photocounting optical communications and photocounting radar systems as well as neural counting in auditory psychophysics. We specifically apply our method to a signal-detection theory model of the human visual system and draw a comparison to the analysis of Hecht, Shlaer, and Pirenne [J. Gen. Physiol. 25, 819 (1942)].

/pdf/optimum-photon-detection-with-a-simple-counting-processor-1e0pdhm8ci.pdf

Optimum photon detection with a simple counting processor.

Photocounting distributions, the decision threshold, and the probability of error are obtained for a binary optical communication system in which both the signal and background radiation are Gaussian processes. This would be the case, for example, when the radiation source is a nonlocked multimode laser or when the received radiation is scattered from a satellite. Dark current is considered. The results indicate that when possible, counting times should be adjusted to be large in comparison with the background radiation coherence time, and optical amplification before detection should be employed.

Photocounting Receiver Performance for Detection of Multimode Laser or Scattered Radiation

Though heterodyne detection provides a valuable technique for detecting small signals, the conventional system has several inherent disadvantages. In applications such as communications and radar, obtaining a reasonably high signal-to-noise ratio (SNR) requires (1) a good knowledge of the velocity of the transmitter or target, (2) a stable yet tunable local oscillator, and (3) a target or source that presents a minimum of frequency broadening. These conditions are frequently not adhered to by real systems, particularly in the ir and optical, giving rise to detection capabilities far below optimum. Calculations are presented for the use and operation of a three-frequency nonlinear heterodyne system that eliminates many of the stringent conditions required for conventional heterodyne detection, while maintaining its near-ideal SNR. The technique, which is similar in principle to heterodyne radiometry, makes use of a two-frequency transmitter and a nonlinear second detector and is particularly useful for signal acquisition; for signals of unknown Doppler shift, in fact, performance is generally superior to that of the conventional system. Although primary emphasis is on the ir and optical because of the large Doppler shifts encountered there, application of the principle in the microwave and radiowave is also discussed. For cw radar and analog communications, the SNR, power spectral density (PSD), and minimum detectable power (MDP) are obtained and compared with the standard configuration. Both sinewave and Gaussian input signals are treated. A variety of specific cases are discussed including the optimum performance case, the typical radar case, and the AM and FM communications case. Evaluation of the technique for pulsed radar and digital communications applications (both in the absence and in the presence of the lognormal atmospheric channel) is reserved for Part 2 of this paper [Appl. Opt. 14, 680 (1975)].

/pdf/three-frequency-nonlinear-heterodyne-detection-1-cw-radar-4a3t9m6sap.pdf

Three-Frequency Nonlinear Heterodyne Detection. 1: cw Radar and Analog Communications

Part 1 of this paper [Appl. Opt. 14, 666 (1975)] dealt with the cw radar and analog communications uses of three-frequency nonlinear heterodyne detection. In this paper, we evaluate the technique for a number of specific pulsed radar and digital communications applications. Both the vacuum channel and the lognormal turbulent atmospheric channel are considered. It is found that the advantages of the technique in the pulsed/digital system are similar to those obtained in the cw/analog system. Computer generated error probability curves as a function of the input signal-to-noise ratio are presented for a variety of binary receiver parameters and configurations and for various levels of atmospheric turbulence. Orthogonal and nonorthogonal signaling schemes, as well as dependent and independent fading, are considered. When Doppler information is poor, performance is generally superior to that of the conventional heterodyne system.

Rainfield Y. Yen

Papers

Photocounting Receiver Performance for Detection of Multimode Laser or Scattered Radiation

Three-Frequency Nonlinear Heterodyne Detection. 1: cw Radar and Analog Communications

Three-frequency nonlinear heterodyne detection. 2: digital communications and pulsed radar.