Abstract
This study provides a general framework to analyze the effects on correlation radiometers of a generic quantization scheme and sampling process. It reviews, unifies and expands several previous works that focused on these effects separately. In addition, it provides a general theoretical background that allows analyzing any digitization scheme including any number of quantization levels, irregular quantization steps, gain compression, clipping, jitter and skew effects of the sampling period.
Highlights
Microwave radiometry is today a mature technology that was first used in radio-astronomy in the 1930s [1]
In the late 1950s, Price published a work focusing on the relationship between the ideal correlation between two random signals with Gaussian probability density function, and the correlation measured after a non-linear manipulation of these random signals [9]
Despite the quantization can significantly affect the value of the ideal cross-correlation
Summary
Microwave radiometry is today a mature technology that was first used in radio-astronomy in the 1930s [1]. It is not possible to apply the well-known Gaussian statistical relationships to the quantified signal This effect has a large impact when limited quantization levels are considered, and it can be mitigated by increasing the number of quantization levels. In the late 1950s, Price published a work focusing on the relationship between the ideal correlation between two random signals with Gaussian probability density function (pdf), and the correlation measured after a non-linear manipulation of these random signals [9] This relationship is used to study the effects of arbitrary quantization schemes on the correlation of two signals. This work provides a general context to analyze the digitization effects on the cross-correlation of two Gaussian random signals in the most general case including any number of quantization levels, irregular quantization steps, gain compression, clipping, bandwidth, sampling frequency, and the skew and jitter inaccuracies of the sampling periods.
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