论文标题
用$ \ Mathcal {O}（N \ log {n}）$缩放的大型N无线电干涉仪的缩放仪的校准方案（N \ log {n}）$
Calibration Schemes with $\mathcal{O}(N\log{N})$ Scaling for Large-N Radio Interferometers Built on a Regular Grid
论文作者
论文摘要
以$ n \ gg 1000 $的宇宙学信号为目标的未来后代的无线电干涉仪在构建与传统体系结构的相关器时，其计算资源要求将其计算资源的扩展为$ \ nathcal {o}（o}（n^2）$。这种相关器的基本输出是阵列中所有天线对的互相关产物。 FFT-Crolelator架构通过通过空间傅立叶变换来计算互相关产品，将计算资源缩放缩放到$ \ MATHCAL {O}（N \ log {n}）$。但是，仅当输入天线电压是增益和相校准时，FFT相关器的输出才有意义。传统上，干涉量校准使用了标准相关器产生的$ \ MATHCAL {O}（n^2）$互相关。本文提出了两个实时校准方案，它们可以与FFT-Crolelator并行工作，作为一个独立的$ \ Mathcal {O}（N \ log {n}）$相关系统，可以缩放到大N冗余数组。我们比较了这两种校准方案的性能和可扩展性，并发现它们导致天线增益，其方差降低为$ 1/\ log {n} $，随着阵列的大小增加。
Future generations of radio interferometers targeting the 21\,cm signal at cosmological distances with $N\gg 1000$ antennas could face a significant computational challenge in building correlators with the traditional architecture, whose computational resource requirement scales as $\mathcal{O}(N^2)$ with array size. The fundamental output of such correlators is the cross-correlation products of all antenna pairs in the array. The FFT-correlator architecture reduces the computational resources scaling to $\mathcal{O}(N\log{N})$ by computing cross-correlation products through a spatial Fourier transform. However, the output of the FFT-correlator is meaningful only when the input antenna voltages are gain- and phase-calibrated. Traditionally, interferometric calibration has used the $\mathcal{O}(N^2)$ cross-correlations produced by a standard correlator. This paper proposes two real-time calibration schemes that could work in parallel with an FFT-correlator as a self-contained $\mathcal{O}(N\log{N})$ correlator system that can be scaled to large-N redundant arrays. We compare the performance and scalability of these two calibration schemes and find that they result in antenna gains whose variance decreases as $1/\log{N}$ with increase in the size of the array.
