  With the ongoing growth in radio communications, there is an increased
contamination of radio astronomical source data, which hinders the study of
celestial radio sources. In many cases, fast mitigation of strong radio
frequency interference (RFI) is valuable for studying short lived radio
transients so that the astronomers can perform detailed observations of
celestial radio sources. The standard method to manually excise contaminated
blocks in time and frequency makes the removed data useless for radio astronomy
analyses. This motivates the need for better radio frequency interference (RFI)
mitigation techniques for array of size M antennas. Although many solutions for
mitigating strong RFI improves the quality of the final celestial source
signal, many standard approaches require all the eigenvalues of the spatial
covariance matrix ($\textbf{R} \in \mathbb{C}^{M \times M}$) of the received
signal, which has $O(M^3)$ computation complexity for removing RFI of size $d$
where $\textit{d} \ll M$. In this work, we investigate two approaches for RFI
mitigation, 1) the computationally efficient Lanczos method based on the
Quadratic Mean to Arithmetic Mean (QMAM) approach using information from
previously-collected data under similar radio-sky-conditions, and 2) an
approach using a celestial source as a reference for RFI mitigation. QMAM uses
the Lanczos method for finding the Rayleigh-Ritz values of the covariance
matrix $\textbf{R}$, thus, reducing the computational complexity of the overall
approach to $O(\textit{d}M^2)$. Our numerical results, using data from the
radio observatory Long Wavelength Array (LWA-1), demonstrate the effectiveness
of both proposed approaches to remove strong RFI, with the QMAM-based approach
still being computationally efficient.
