Digital signal processing methods for large-N, low-frequency radio telescopes - Hickish, J (2014)
Current attempts to make precision measurements of the HI power spectrum at high redshifts have led to the construction of several low-frequency, large-N, interferometric arrays. The computational demands of digital correlators required by these arrays present a significant challenge. These demands stem from the treatment of radio telescopes as collections of two-element interferometers, which results in the need to multiply O(N2) pairs of antenna signals in an N-element array. Given the unparalleled flexibility offered by modern digital processing systems, it is apt to consider whether a different way of treating the signals from antennas in an array might be fruitful in current and future radio telescopes. Such methods potentially avoid the unfavourable N2 scaling of computation rate with array size. In this thesis I examine the prospect of using direct-imaging methods to map the sky without first generating correlation matrices. These methods potentially provide great computational savings by creating images using efficient, FFT-based algorithms. This thesis details the design and deployment of such a system for the Basic Element of SKA Training II (BEST-2) array in Medicina, Italy. Here the 32-antenna BEST-2 array is used as a test bed for comparison of FX correlation and direct-imaging systems, and to provide a frontend for a real-time transient event detection pipeline. Even in the case of traditional O(N2) correlation methods, signal processing algorithms can be significantly optimized to deliver large performance gains. In this thesis I present a new mechanism for optimizing the cross-correlation operation on Field Programmable Gate Array (FPGA) hardware. This implementation is shown to achieve a 75% reduction in multiplier usage, and has a variety of benefits over existing optimization strategies. Finally, this thesis turns its focus towards The Square Kilometre Array (SKA). When constructed, the SKA will be the world's largest radio telescope and will comprise a variety of arrays targeting different observing frequencies and science goals. The low-frequency component of the SKA (SKA-low) will feature ~250,000 individual antennas, sub-divided into a number of stations. This thesis explores the impact of the station size on the computational requirements of SKA-low, investigating the optimal array configuration and signal processing realizations.