Richard L. Mitchell

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.

Matched-Filter Responses of the Linear FM Waveform

Although the properties of the linear FM signal have been studied previously in considerable detail, such studies have involved rather narrow aspects of the theory. This paper extends the work in several respects. By presenting three-dimensional projections of the conventional ambiguity function of the linear FM signal in more detail than was available before, we can study the sidelobe behavior off as well as on the axes, without weighting, with unilateral weighting in the receiver, and with bilateral weighting. These plots reveal interesting properties related to the signal symmetry in time and frequency. The matched-filter response is then extended to include Doppler distortions of the modulation function. The results show that Woodwards ambiguity function is valid only for signals with relatively modest sophistication, even though in most practical situations one is interested only in those undistorted parts of the matched-filter response in the vicinity of the delay axis. Plots of the response are presented for various degrees of distortion, for signals with and without weighting. Lastly, we consider the effects of a mismatch in range acceleration, again for the various cases of interest. The results convey a thorough insight into the properties of chirp radar under a broad range of operational conditions.

Attenuation of the 5-mm wavelength band in a variable atmosphere

Effects of atmospheric changes on attenuation in the atmosphere are examined for the 5-mm wavelength region of the electromagnetic spectrum (48 to 72 GHz). Attenuation versus frequency and altitude for vertical transmission through the atmosphere, caused by oxygen absorption, are tabulated for geographical and seasonal model atmospheres. The attenuation effects of atmospheric water formations are discussed and compared to oxygen attenuation.

Effect of a Turbulent Medium on the Power Pattern of a Wavefront-Tracking Circular Aperture*

The angular power pattern, or equivalently the image-plane intensity distribution, is obtained for a circular aperture receiving a plane wave perturbed in transmission through a turbulent atmosphere. The aperture is assumed always to be aligned so as to maximize the received power. This alignment is shown to be that effected by a conventional angle-tracking servomechanism. Homogeneous, isotropic turbulence is assumed, and the aperture is taken to be of moderate size so that the 5/3-power law phase-structure function predicted by use of the Obukhov–Kolmogorov theory of turbulence applies adequately over its full extent. It is assumed also that the departure of the incident wavefronts from planarity everywhere on the aperture is small relative to a wavelength. This condition is shown to be met for relatively large deviation of phase from that of an unperturbed plane wave. Power patterns for tracking and nontracking apertures are compared.

Single-Slit Fresnel Diffraction Patterns: Comparison of Experimental and Theoretical Results*†

Experimental work at the University of Utah has produced high-resolution optical diffraction patterns by slit apertures, 20 m from source and 30 m from photomultiplier receiver slit. The slit widths varied in 26 values from 0.5 to 32 mm with 4358- and 5461-A light, corresponding to a Fresnel-variable difference ranging from 0.271 to 19.396. The receiver-slit width was 0.2 mm. A versatile program developed at The Aerospace Corporation for calculation of Fresnel integrals has been used for comparison with experiment, including averaging to give the effect of integration by the photomultiplier slit. Experimental and theoretical diffraction curves are compared for various slit widths. One double-slit-pattern comparison is also given. A high degree of symmetry is found in the measured curves. Even the very fine fluctuations of irradiance in the experimental and theoretical curves match. Three-dimensional theoretical projections of diffraction patterns show the continuous change of pattern from near-Fraunhofer to Fresnel diffraction.

Power pattern degradation for weighted circular apertures in a turbulent atmosphere

Abstract : Average power patterns are calculated for weighted circular apertures in a turbulent medium. The turbulence is assumed to be locally homogeneous and the aperture diameters treated are such that they fall within the inertial subrange of the Obukhov-Kolmogorov theory of turbulence. Calculations are performed both for fixed apertures and for apertures which track wavefront tilt in such a manner that alignment with the direction of maximum power is maintained. They are based on supporting analyses which treat only phase perturbations due to the atmosphere, but have wide applicability because of the validity of ray optics in turbulent medium propagation where small perturbation theory is applicable to both phase and amplitude fluctuations. Curves showing percent half-power beambroadening and gain reduction as a function of degree of turbulence are also presented. The results show that pattern degradation is significantly less for tracking apertures than for fixed apertures. (Author)