Radio Astronomy Measurements Technology and Signal Analysis

Abstract: The San Marino Scale, an analytical tool for assessing the significance of transmissions from Earth, was adopted by the IAA SETI Permanent Study Group in 2007. This additive model, which encompasses estimates of both signal strength and signal characteristics, remains a work in progress. It is statistically valid only to the extent that the two terms are assumed to be wholly independent discrete random variables. We question this assumption of independence, and, in fact, find a strong negative correlation between the two terms, though we further suspect that the interaction is nonlinear. Thus, we propose to amend the San Marino Scale, making it more statistically robust by capturing, and compensating for, this interdependence between detectability and information content.

Abstract: The investigation of sampling properties of a signal sample spectral density involves the statistical distributions of the real and imaginary components of the sampled signal. The distributions involved include the normal (Gaussian), the chi-square, the half normal, the truncated normal, and the Rayleigh distributions. We first review some of the properties of these distributions before and after (1) the absolute values of the real and imaginary components are summed, (2) when the absolute value of the sum of these components is taken, (3) when the squares of these components are summed, and (4) the square root of the sums of the squares is determined. These four distinct sums result in four different distributions. We compare of the respective means and variances of these distributions.
Simulations of sinusoidal signals added to noise with a standard normal distribution at five different sinusoidal amplitudes were evaluated for distribution type. The comparison shows that the distribution of the square root of the sums of the squares of the real and imaginary components has the smallest variance over those of the absolute value of the sums or the sum of the absolute values, though the statistical significance of the differences must be determined per sample size. When the difference is is not significant, the most convenient additive combination may be used.

A project to characterize the beam profile of the primary lobe of a 2.3-meter, parabolic dish, using a quarter-wave dipole connected to a receiver system centered at 1.42 GHz embedded within a feed horn at the dish focus, was conducted at the Front Range Community College, Boulder County, Colorado. Antenna theory provides sufficient information to design an experiment to provide the beam profile, using the Sun as a source, in two orthogonal dimensions. A central composite experimental design is used to generate a second order, rotatable, response surface of antenna temperature versus the two spatial dimensions. The date and time of day are treated as a covariate variable as the azimuth and elevation dish mount permits an orthogonal dish beam projection onto the celestial sphere only when the Sun’s center is the coordinate system origin at the local meridian. The primary lobe profile is elliptical in which the maximum (stationary point) is shifted from the solar-based coordinate origin by (1.23°,-0.15°). The Half-Power Beam Width is 14° in azimuth and 12° in elevation. This two-dimensional temperature response surface, central composite experimental design is a method not currently used for determining beam profiles, and, as the number of sample points is optimized for a preselected power of test, gives the minimum samples needed.