A Simplified Calculation of the Kurtosis for RFI Detection

The kurtosis statistic is an excellent detector of pulsed sinu-soidal RFI in a digital microwave radiometer. The kurtosis is the ratio of the 4th central moment to the 2nd central moment, squared. However, to create the kurtosis, accumulations of every power of the digitized voltage up to 4th order must be calculated in the digital back-end of the radiometer, and these accumulations are offloaded for postprocessing. This paper investigates the possibility of eliminating the accumulation of the 3rd power of the digitized voltage. The elimination of this operation liberates some resources in the back-end digital electronics, and reduces the burden of data offloading from the radiometer for each integration period. Without the 3rd power of digitized voltage, the kurtosis can still be calculated under the assumption of zero skew in the IF signal. The kurtosis so calculated has the same mean value as that calculated with all the powers of the voltage, and the covariance of the kurtosis with the variance remains zero, indicating that this simplified kurtosis remains an unbiased detector of RFI. However, the lack of the 3rd accumulation in the calculation of the kurtosis results in an increase in the variance of the kurtosis statistic which is proportional to the DC offset between the back-end digitizer and the analog ground, which can result in reduced sensitivity of the kurtosis statistic to RFI.