Radio Frequency Interference Excision Using Spectral‐Domain Statistics

Abstract

A radio frequency interference (RFI) excision algorithm based on spectral kurtosis, a spectral variant of time-domain kurtosis, is proposed and implemented in software. The algorithm works by providing a robust estimator for Gaussian noise that, when violated, indicates the presence of non-Gaussian RFI. A theoretical formalism is used that unifies the well-known time-domain kurtosis estimator with past work related to spectral kurtosis, and leads naturally to a single expression encompassing both. The algorithm accumulates the first two powers of M power spectral density (PSD) estimates, obtained via Fourier transform, to form a spectral kurtosis (SK) estimator whose expected statistical variance is used to define an RFI detection threshold. The performance of the algorithm is theoretically evaluated for different time-domain RFI characteristics and signal-to-noise ratios h. The theoretical performance of the algorithm for intermittent RFI (RFI present in R out of M PSD estimates) is evaluated and shown to depend greatly on the duty cycle, . The algorithm is most effective for d p R/M , but cannot distinguish RFI from Gaussian noise at any h when . The expected efficiency d p 1/(4 ϩ h) d p 0.5 and robustness of the algorithm are tested using data from the newly designed FASR Subsystem Testbed radio interferometer operating at the Owens Valley Solar Array. The ability of the algorithm to discriminate RFI against the temporally and spectrally complex radio emission produced during solar radio bursts is demonstrated.1 Throughout this paper, we use a "hat" notation to indicate an estimator of a quantity to distinguish it from the quantity itself.

Hardware Implementation of an SK Spectrometer

“…No single approach will work in all cases, and it is necessary to employ layered RFI avoidance [12] and excision algorithms. The work of Nita et al [8] and Nita & Gary [6,7] has placed the SK algorithm on a firm theoretical footing, while Gary et al [5], briefly summarized here, shows the practical application of the algorithm in hardware. Although the algorithm does not work optimally for all cases, notably for digitally encoded transmissions, it is especially powerful for one problematic type of RFI, highly intermittent RFI in frequency and time.…”

“…Although the algorithm does not work optimally for all cases, notably for digitally encoded transmissions, it is especially powerful for one problematic type of RFI, highly intermittent RFI in frequency and time. This includes both fixed and mobile transmitters, especially aircraft DME (distance measuring equipment), as shown but not discussed by Nita et al [8] (their figures 9 and 10). Its ability to identify and flag such RFI in real time makes it an important first line of defense after avoidance and front-end filters.…”

“…the digitizer during an accumulation can alter the statistics of RFI-free data (see [8] for further discussion). Each of the four SK spectrometer boards digitizes a 500 MHz bandwidth at 8-bits using a 1 GHz clock, and uses an FFT-based filterbank to divide the signal into 2048 frequency channels.…”

“…RFI), Nita et al [8] compared the theoretical response of SK to a continuous-wave (CW) signal of constant amplitude, which can be used to simulate transient RFI by considering its presence or absence with some duty cycle d. Consider M contiguous PSD estimates of which R are contaminated by RFI at signal to noise ratio (S/N), η k , where k is the spectral channel index. The duty cycle is therefore defined as d = R/M.…”

“…The Korean Solar Radio Burst Locator (KSRBL) [1] is the first spectrometer to employ the technique of spectral kurtosis (SK), which has been described in detail by Nita et al [8] and Nita & Gary [6]. Gary et al [5] have demonstrated the effectiveness of the SK algorithm for identifying and removing certain kinds of radio frequency interference (RFI) from radio astronomical data.…”