Sensitivity of the Kurtosis Statistic as a Detector of Pulsed Sinusoidal RFI

Abstract

A new type of microwave radiometer detector that is capable of identifying low-level pulsed radio frequency interference (RFI) has been developed. The Agile Digital Detector can discriminate between RFI and natural thermal emission signals by directly measuring other moments of the signal than the variance that is traditionally measured. The kurtosis is the ratio of the fourth central moment of the predetected voltage to the square of the second central moment. It can be an excellent indicator of the presence of RFI. A number of issues that are related to the proper calculation of the kurtosis are addressed. The mean and standard deviation of the kurtosis, in both the absence and the presence of pulsed sinusoidal RFI, are derived. The kurtosis is much more sensitive to short-pulsed RFI-such as from radars-than to continuous-wave RFI. The minimum detectable power for pulsed sinusoidal RFI is found to be proportional to ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/4</sup> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of independent samples and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the number of frequency subbands in the receiver.