Simulations are always helpful to guide the design of a new device, but at some point a prototype needs to be built and tried. Almost invariably, there are a number of surprises that one doesn't anticipate in a simulation. Simply living with a prototype and keeping an eye out for strange behavior is an essential part of the process of designing an improved production model. This short paper reports on our observations of a rudimentary adaptive filter RFI canceler being considered for radio astronomy applications.
After our measurements of the noise characteristics of a 9-tap adaptive RFI canceler reported at the 1999 URSI General Assembly in Toronto, we made a number of hardware improvements to reduce A/D jitter and spurious baseband noise. New measurements are reported here with an emphasis on understanding how an adaptive filter canceler will perform on noise-limited signals found in radio astronomy receivers.
Figure 1 shows the hardware configuration of the adaptive canceler system. The input frequency band is from 40.5 to 39.7 MHz, which translates to a baseband frequency range of 0 to 0.8 MHz after bandpass sampling and lowpass filtering of the output. The spectrometer used for these tests is an FFT device with a bandwidth of 1.25 MHz and a channel spacing of 1.22 kHz. Spectrometer integration times were typically 10 seconds.
First, we remeasured the amount of attenuation achieved by the adaptive canceler as a function of interference-to-noise ratio in the reference channel. The results are shown in Figure 2. The curve in this figure shows the attenuation predicted in the paper by Barnbaum and Bradley (1998, Astron. J., vol. 116, p2598, see their Equation 17 and Figure 4 (top))
Unlike the similar measurements made in 1999 (Figure 3) we see a deviation from the expected attenuation at the high end of the curve. Two possibilities come to mind, either a quantization error in the filter coefficients or random noise in the main channel causing a random error in the coefficients that shows up as a residual interference in long spectrum integrations. Unfortunately, we did not record all of the parameters of the 1999 measurements so we can only speculate that coefficient operating points or the interference-to-noise ratio in the main channel were different in the earlier measurements. Intuitively, one expects the noise in the main channel to have some effect on the cancellation performance since, even with infinite INR in the reference channel, there will be some error in the adaptive filter coefficients. However, in the absence of a quantitative estimate of the coefficient errors, this must remain only a conjecture.
The action of the adaptive canceler and its dependence on reference channel INR may be understood by considering the output spectrum shown in Figure 4. With a noise-free sample of the narrowband RFI in the reference channel the adaptive filter will be adjusted to produce a 180-degree phase reversal in this signal, and its amplitude will be adjusted to be exactly equal to its counterpart in the main channel. This will produce the minimum output power condition from the summing junction sought by the feedback algorithm.
However, if there is uncorrelated noise in the reference channel, the adaptive filter will still seek a 180-degree phase flip in the RFI signal, but in the process of increasing the filter gain to cancel the RFI it will add noise to the summing junction output. The minimum output condition will occur at a point where further reduction in the RFI signal is overcome by the added noise power from the reference channel. In Figure 4 you can see this added noise as an offset from the main channel baseline intensity of 1.0. Since the adaptive filter gains some advantage by suppressing noise at frequencies away from the RFI signal, the added noise power will be greatest near this signal. The effective bandwidth for computing the reference channel INR is the frequency resolution of the adaptive filter as set by the number of delay taps.
A related reference noise problem was discovered in the adaptive canceler due to a small DC offset in the A/D converters. This offset acts like a signal at zero frequency in the baseband spectrum which the adaptive filter attempts to cancel out by creating a finite gain at low frequencies even in the absence of RFI. The resulting spectrum is shown in Figure 5, which is the normalized difference of the output spectrum with the adaptive filter idling minus the spectrum with the filter coefficients set to zero. You can see the noise added at low frequencies.
Another test we tried was injecting two simulated RFI signals into the main and reference channels of the adaptive canceler. Two configurations were used as shown in Figure 6. In the top configuration one of the two RFI signals is given an extra delay in its path to the reference channel to force the canceler to treat the signals independently since it cannot cancel both with the same filter phase shift. The extra delay used was roughly a half wavelength at the oscillator frequencies near 40 MHz. This presents the worst case situation to the adaptive filter. The bottom configuration shown in Figure 6 emulates the case where both signals arrive through the same delay paths, e.g., a broadband signal from the same transmitter.
Figure 7 shows the test results from the first configuration with an extra delay in one of the oscillators' reference signal paths. There are two measurement sets shown in this figure. The first places one oscillator at a fixed frequency of 30.9 MHz (0.6 MHz at baseband), and the second oscillator's frequency is varied from 39.8 (0.7) to 40.0 (0.5) MHz. On the right hand side of Figure 7 the attenuations on each of the two signals achieved by the canceler are shown with different symbols as a function of the baseband frequency of the variable frequency oscillator. Since both signals were attenuated nearly equally, the two symbols overlap. With a separation of about 0.1 MHz the adaptive filter was able to modify each signal independently and achieve about the same cancellation as on a single signal alone. When the two signals are very close in frequency, the filter cannot cancel either signal. At intermediate separations the canceler appeared to be at a rather unstable situation where from one second to the next it would cancel one signal much more than the other, then switch to attenuating the other signal, sometimes not doing a good job on either.
On the left hand side of Figure 7 the measurements with the fixed oscillator set at 40.2 (0.3) MHz are plotted. When the variable oscillator is on the high frequency side at baseband the cancellation was about the same as was measure around 0.6 MHz. However, on the low frequency side the attenuation was very poor because of the distortion of the filter's response by the A/D offset mentioned in connection with Figure 5. In effect, the filter was wrestling with three signals, the two oscillators and the DC offset. There were too few free parameters in this frequency range to allow a viable solution. Again, the canceler was quite unstable in the range where it could find only a partial solution to canceling more than one signal.
The second set of two-signal measurements used the configuration at the bottom of Figure 6 where the two signals traveled identical paths to both canceler channels. As expected, the canceler did a good job on both signals even when they were at the same frequency as can be seen on the high frequency side of the fixed-frequency signal in Figure 8. On the low frequency side the canceler ran into the same three-signal dilemma due to the presence of the A/D offset.
Our final measurement was to use only one oscillator to simulate RFI, but this oscillator was frequency modulated with a 710 Hz sine wave using various frequency deviations. Figure 9 shows the spectrum of this test signal with a deviation of +/-50 kHz. The center frequency of the 0.45 MHz at baseband was intentionally kept away from the low frequency part of the baseband spectrum where the DC offset caused a problem.
Figure 10 shows the amount of cancellation on the FM signal as a function of frequency deviation. The attenuation at zero deviation is what was expected from the reference channel INR. One might expect the attenuation to decrease gradually with deviation as the signal spreads beyond the frequency resolution of the tapped delay filter and, hence, be contending with a wider noise passband and lower average INR. However, the cancellation was considerably worse with a deviation of only 10 kHz so some other confounding effect must be taking place. Both sides of the FM signal spectrum were not always suppressed equally as is shown in the example of Figure 11.
We are pleased with the good agreement between theory and experiment on the cancellation as a function of reference channel INR. Some study remains to be done to understand the deviation at high INR observed in these latest measurements.
A number of technical improvements can be added to the current prototype. Removing the A/D offset is straightforward, although this is important enough to warrant a routine calibration procedure. A larger number of delay taps is required for better frequency resolution. When two independent signals cannot be resolved in the frequency domain, more reference channels may be added to provide independent phase and amplitude conditioning of the canceling signals. In some cases one will want separate reference antennas to spatially isolate signals within a filter frequency resolution element so that they may be independently processed. The stability of the adaptive process to multiple signals is of some concern and requires further investigation.
Perhaps the biggest challenge for radio astronomy applications is what to do about the noise added from the reference channel(s). One solution may be to implement a reference noise spectrum calibration scheme. This information could then be used in the adaptive filter weighting algorithm to correct for the noise offset in the minimization algorithm. The reference noise spectrum along with the logged filter weights employed during an observation could also be used to remove the integrated effects of the variable reference noise baseline. The higher effective system temperature caused by added reference noise needs to be minimized with adequate reference antenna gain.
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