In radio astronomy, reference signals from auxiliary antennas that receive only the radio frequency interference (RFI) can be modified to model the RFI environment at the astronomy receivers. The RFI can then be canceled from the astronomy signal paths. However, astronomers typically only require signal statistics. If the RFI statistics are changing slowly, the cancellation can be applied to the signal correlations at a much lower rate than is required for standard adaptive filters. In this paper we describe five canceler setups; precorrelation and postcorrelation cancelers that use one or two reference signals in different ways. The theoretical residual RFI and added noise levels are examined and are demonstrated using microwave television RFI at the Australia Telescope Compact Array. The RFI is attenuated to below the system noise, a reduction of at least 20 dB. While dual-reference cancelers add more reference noise than single-reference cancelers, this noise is zero-mean and only adds to the system noise, decreasing the sensitivity. The residual RFI that remains in the output of single-reference cancelers (but not dual-reference cancelers) sets a nonzero noise floor that does not act like random system noise and may limit the achievable sensitivity. Thus, dual-reference cancelers often result in superior cancellation. Dual-reference precorrelation cancelers require a double-canceler setup to be useful and to give equivalent results to dual-reference postcorrelation cancelers.
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