Algorithms for FFT Beamforming Radio Interferometers

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from $\mathcal{O}(n^2)$ in the number of antennas to $\mathcal{O}(n\log n)$. We develop a formalism for describing this process and apply this formalism to derive a number of algorithms with a range of observational applications. These include algorithms for forming arbitrarily pointed tied-array beams from the regularly spaced Fourier-transform formed beams, sculpting the beams to suppress sidelobes while only losing percent-level sensitivity, and optimally estimating the position of a detected source from its observed brightness in the set of beams. We also discuss the effect that correlations in the visibility-space noise, due to cross-talk and sky contributions, have on the optimality of Fourier transform beamforming, showing that it does not strictly preserve the sky information of the $n^2$ correlation, even for an idealized array. Our results have applications to a number of upcoming interferometers, in particular the Canadian Hydrogen Intensity Mapping Experiment--Fast Radio Burst (CHIME/FRB) project.Comment: 17 pages, 4 figures, accepted to Ap

A GPU Spatial Processing System for CHIME

We present an overview of the Graphics Processing Unit (GPU) based spatial processing system created for the Canadian Hydrogen Intensity Mapping Experiment (CHIME). The design employs AMD S9300x2 GPUs and readily-available commercial hardware in its processing nodes to provide a cost- and power-efficient processing substrate. These nodes are supported by a liquid-cooling system which allows continuous operation with modest power consumption and in all but the most adverse conditions. Capable of continuously correlating 2048 receiver-polarizations across 400\,MHz of bandwidth, the CHIME X-engine constitutes the most powerful radio correlator currently in existence. It receives $6.6$\,Tb/s of channelized data from CHIME's FPGA-based F-engine, and the primary correlation task requires $8.39\times10^{14}$ complex multiply-and-accumulate operations per second. The same system also provides formed-beam data products to commensal FRB and Pulsar experiments; it constitutes a general spatial-processing system of unprecedented scale and capability, with correspondingly great challenges in computation, data transport, heat dissipation, and interference shielding

RXTE All-Sky Monitor Detection of the Orbital Period of Scorpius X-1

The orbital period of Scorpius X-1 has been accepted as 0.787313 d since its discovery in archival optical photometric data by Gottlieb, Wright, & Liller (1975). This period has been confirmed in both photometric and spectroscopic optical observations, though to date only marginal evidence has been reported for modulation of the X-ray intensity at that period. We have used data taken with the RXTE All Sky Monitor to search for such a modulation. A major difficulty in detecting the orbit in X-ray data is presented by the flaring behavior of Sco X-1, which contributes white noise to Fourier transforms of the intensity time series, and tends to obscure weak modulations. We present a new technique for substantially reducing the effects of the flaring behavior while retaining much of any periodic orbital modulation, provided only that the two temporal behaviors exhibit different spectral signatures. Through such a search, we have found evidence for orbital modulation at about the 1% level with a period of 0.78893 d, equal within our accuracy to a period which differs by 1 cycle per year from the accepted value. If we compare our results with the period of the 1 year sideband cited by Gottlieb et al. we conclude that the actual period may be 0.78901 d.Comment: AASTeX, 20 pages, 5 Postscript figure

A GPU-based Correlator X-engine Implemented on the CHIME Pathfinder

We present the design and implementation of a custom GPU-based compute cluster that provides the correlation X-engine of the CHIME Pathfinder radio telescope. It is among the largest such systems in operation, correlating 32,896 baselines (256 inputs) over 400MHz of radio bandwidth. Making heavy use of consumer-grade parts and a custom software stack, the system was developed at a small fraction of the cost of comparable installations. Unlike existing GPU backends, this system is built around OpenCL kernels running on consumer-level AMD GPUs, taking advantage of low-cost hardware and leveraging packed integer operations to double algorithmic efficiency. The system achieves the required 105TOPS in a 10kW power envelope, making it among the most power-efficient X-engines in use today.Comment: 6 pages, 5 figures. Accepted by IEEE ASAP 201