  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.
