Modeling the effects of power efficient approximate multipliers in radio astronomy correlators

Large scale Radio Telescopes for Radio Astronomy highly depend on the availability of large (digital) processing capacities for imaging. Estimates concerning power efficiency for future Radio Telescopes lead to anticipated power consumption numbers beyond feasibility. To reduce the power budget, the use of approximate multipliers within the correlator is explored. A baseband equivalent executable model of a radio synthesis telescope is constructed to assess the effects of approximate multipliers. Besides ideal multipliers with floating point accuracy, the use of accurate 8-bit multipliers and 4 different types of approximate multipliers is explored. For each of these multipliers, the energy efficiency of an individual multiplier is known and used to determine the energy efficiency improvement of a correlator when using approximate multipliers. The effects of approximation are quantified by 3 metrics (Signal-to-Noise-Ratio (SNR), Spurious-Free-Dynamic-Range (SFDR) and Root-Mean-Square (RMS) level) derived from maps constructed by the executable model based on an empty sky with only a single point source. This is considered to be the worst case scenario. For illustration purposes, a more realistic input is processed by the model as well. The metrics have been determined based on different SNR levels at the input of each antenna element. For input SNR levels up to 10 dB, all types of approximate multipliers used in this paper can be exploited to improve energy efficiency of correlators, leading to a maximum energy reduction of 19 %. For input SNR values up to 30 dB an energy improvement up to 12 % can be achieved. These percentages are based on implementations in a 40nm low power IC technology at 1 GHz.