Evaluating Low-Precision Floating-Point Formats for Next-Generation Radio Telescope Correlators and Beamformers: A Quantitative Analysis of Linearity and Dynamic Range

The global environment for Radio Frequency Interference (RFI) is worsening, compelling the next generation of radio telescopes to incorporate resilient designs and implementations. While advances in telecommunications and consumer electronics have led to widespread deployment of such systems resulting in more RFI, they have also contributed to significant improvements in the receiver and processing capabilities of radio telescopes. This is especially significant for the digital signal processing (DSP) systems in the correlators and beamformers of radio telescopes. In an environment filled with strong and pervasive RFI, internal signal chains must support a high dynamic range while maintaining linearity. The floating-point number format allows for a high dynamic range, though it does so at the expense of precision. Prompted by the AI revolution, leading hardware vendors such as Intel-Altera, AMD-Xilinx, and NVIDIA are providing fast and efficient hardware implementations for low-precision floating-point arithmetic in their latest Field Programmable Gate Arrays (FPGAs) and Graphics Processing Units (GPUs). In this paper, we present an analysis of the linearity and dynamic range achieved by implementing key signal processing modules in the Square Kilometre Array (SKA) Mid-Frequency Correlator and Beamformer (Mid.CBF) using low-precision floating-point formats such as float16 and float32.