A Study of the Shapiro–Wilk Test for the Detection of Pulsed Sinusoidal Radio Frequency Interference

The performance of the Shapiro–Wilk (S-W) test of normality for the detection of pulsed sinusoidal radio frequency interference (RFI) in microwave radiometry is analyzed. The study is motivated by the fact that the S-W test has been shown in the statistical literature to be effective in detecting a wide variety of non-Gaussian signal types. The basic properties of the S-W test statistic are reviewed, and the implementation of the test in digital hardware is discussed. Because the properties of the test statistic are difficult to obtain analytically, Monte Carlo simulations are utilized to compute performance. Results show that the test can provide reasonable performance in detecting pulsed sinusoidal RFI and that quantization of data has only a minimal impact on the sensitivity achieved. Detection performance is also compared with that of the kurtosis test for normality. It is shown that the S-W test produces comparable but degraded sensitivity compared to that of the kurtosis test in most cases while avoiding the “blind spot” associated with the kurtosis test for pulsed interferers having 50% duty cycle. Test performance is also shown to be improved if a priori knowledge of expected RFI pulse lengths is incorporated.