A Measure of Well-Spread Points in Noise Wave-Based Source Matrix for Wideband Noise Parameter Measurement: The SKA-Low Example

Abstract

The existence of a figure of merit for measuring the degree of well-spread source points in noise parameter extraction has long been conjectured. This article proposes a measure based on noise waves that is physically motivated and is directly connected to linear algebra through the matrix condition number and/or determinant. The key to this figure of merit is the selection of the noise temperature equation and the removal of singularity due to the 1/(1-|\Gamma _{s}|^{2}) factor. The result is a well-scaled source matrix with entries bounded within a unit circle. We demonstrate the effectiveness of this measure by extracting the noise parameters of an amplifier in the low-frequency Square Kilometre Array (SKA-Low) band of 50-350 MHz using seven tuner positions. The noise parameters in the 50-100-MHz band are successfully measured despite being below the 100-MHz tuner rating. This outcome is very well predicted by the condition number and the determinant of the source matrix in question.