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A New Approach to Interference Excision in Radio Astronomy:
Real-Time Adaptive Cancellation




Cecilia Barnbaum
Space Telescope Science Institute1 3700 San Martin Dr, Baltimore, MD 21218
Electronic mail: barnbaum@stsci.edu

and

Richard F. Bradley
National Radio Astronomy Observatory2, 520 Edgemont Rd, Charlottesville, VA
22903
Electronic mail: rbradley@nrao.edu




submitted to The Astronomical Journal 1998 May 20
revised 1998 July 27



1 The Space Telescope Science Institute is a facility of the National
Aeronautics and Space Administration operated under cooperative agreement
by Associated Universities for Research in Astronomy.

2 The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc.
ABSTRACT

Every year, an increasing amount of radio frequency spectrum in the VHF,
UHF, and microwave bands is being utilized to support new commercial and
military ventures, and all have the potential to interfere with radio
astronomy observations. Such services already cause problems for radio
astronomy even in very remote observing sites, and the potential for this
form of light pollution to grow is alarming. Preventive measures to
eliminate interference through FCC legislation and ITU agreements can be
effective, however, many times this approach is inadequate and interference
excision at the receiver is necessary. Conventional techniques such as RF
filters, RF shielding, and post- processing of data have been only somewhat
successful, but none has been sufficient. Adaptive interference
cancellation is a real-time approach to interference excision that has not
been used before in radio astronomy. We describe here, for the first time,
adaptive interference cancellation in the context of radio astronomy
instrumentation, and we present initial results for our prototype receiver.

In the 1960's analog adaptive interference cancelers were developed that
obtain a high degree of cancellation in problems of radio communications
and radar. However, analog systems lack the dynamic range, noised
performance, and versatility required by radio astronomy. The concept of
digital adaptive interference cancellation was introduced in the mid-1960's
as a way to reduce unwanted noise in low frequency (audio) systems which
have a bandwidth of only a few tens of kilohertz. Examples of such systems
include the canceling of maternal ECG in fetal electrocardiography and the
reduction of engine noise in the passenger compartment of automobiles.
These audio frequency applications require bandwidths of only a few tens of
kilohertz. Only recently has high-speed digital filter technology made
high dynamic range adaptive canceling possible in a bandwidth as large as a
few megahertz, finally opening the door to application in radio astronomy.

We have built a prototype adaptive canceler that consists of two receivers:
the primary channel (input from the main beam of the telescope) and a
separate reference channel. The primary channel receives the desired
astronomical signal corrupted by RFI (radio frequency interference ) coming
in the sidelobes of the main beam. A separate reference antenna is designed
to receive only the RFI. The reference channel input is processed using a
digital adaptive filter and then subtracted from the primary channel input,
producing the system output. The weighting coefficients of the digital
filter are adjusted by way of an algorithm that minimizes, in a least-
squares sense, the power output of the system. Through an adaptive-
iterative process, the canceler locks onto the RFI, and the filter adjusts
itself to minimize the effect of the RFI at the system output. We have
designed the adaptive canceler with an intermediate frequency (IF) of 40
MHz. This prototype system will ultimately be functional with a variety of
radio astronomy receivers in the microwave band. We have also built a
prototype receiver centered at 100 MHz (in the FM broadcast band) to test
the adaptive canceler with actual interferers which are well characterized.
The initial laboratory tests of the adaptive canceler are encouraging,
with attenuation of strong frequency-modulated(FM) interference to 72 dB (a
factor of more than ten million), which is at the performance limit of our
measurements. We also consider requirements of the system and the RFI
environment for effective adaptive canceling.


KEYWORDS
instrumentation: detectors, methods: analytical, methods: analytical

1. INTRODUCTION

Just as optical astronomy faces serious problems with light pollution,
radio astronomy is similarly plagued by its own brand of light pollution:
radio frequency interference (RFI). Growing technological resources usurp
more and more radio frequency spectrum in the VHF, UHF, and microwave
bands. Advances in both microprocessor and monolithic microwave integrated
circuits have spurred a plethora of new applications, including improved
point-to-point communications, wireless computer communications, and a
growing number of cellular telephones; all have potential to interfere with
radio astronomy observations. Signals from some existing satellites leak
into protected radio astronomy bands, and the problem will likely increase
as more satellites are put into orbit. Low-earth-orbit satellites (LEOS)
create an RFI problem no matter where on the earth a radio telescope is
located, even in remote locations as Tasmania and the Antarctic. The
increasing congestion of the radio spectrum is making astrophysical
research in the designated radio and microwave bands ever more difficult.
Outside the bands protected for astronomy the situation is quite a bit
worse.
Preventive measures through FCC legislation and ITU agreements can be
effective, such as protected radio astronomy bands and designated radio-
quiet areas like the National Radio Quiet Zone around Green Bank
Observatory in West Virginia (Sizemore 1991). When prevention is not
possible, various methods to reduce or eliminate interference have been
employed; conventional approaches include: 1) blanking techniques to
remove pulse-type signals from the data stream (Gerard 1982; Fisher 1982),
2) filtering techniques such as superconducting notch filters to remove
fixed-frequency interference (e.g., Moffet 1982), 3) radio frequency (RF)
shielding to suppress spurious digital signals and local oscillator signals
from adjacent electronic equipment or communication systems (Morrison
1998), 5) post-processing techniques on array systems such as sidelobe-beam
nulling to remove fixed-frequency signals (Erickson 1982), and 6) adaptive
beam forming techniques (Goris 1997). All these schemes are successful to
some degree, yet each suffers from either insufficient interference
cancellation, inability to adapt to changing statistics of the interference
signal, partial removal of wanted data, or excessively large amounts of
post-processing of the accumulated data. Clearly, we need to investigate
new approaches to interference excision that have potential to improve upon
the shortcomings of conventional techniques.
Even with all the efforts described above, removing RFI in a radiometer
remains a very difficult exercise. Astronomical signals are weak compared
to ground (or satellite) signals, and so large attenuation capability is
necessary. Often, RFI and the astronomical signal occur at the same
frequency, and conventional rejection schemes, such as notch filters,
matched filters, and beam nulling, remove some or all of the desired signal
along with the RFI. A notch filter is a very sharp band-reject filter that
can be quite useful in removing strong interference which can cause
saturation to occur in the amplifier and correlator. However, this type of
filter is not easily adjustable in frequency and removes some of the
desired astronomical signal. A matched filter is a digital filter whose
characteristics "match" that of the interference and remove it from the
radiometer data. However, the spectrum of the interference signal must be
known a priori and in some cases the filter characteristics are not
physically realizable. The matched filter can also cause distortion of the
desired signal. In array systems beam-nulling has been tried through
extensive post-processing of the data; although somewhat successful, this
approach is very time consuming and does not attenuate enough for
astronomy observations at frequencies that are plagued by RFI. An adaptive
beam-former is being designed for the Square Kilometer Array Interferometer
(SKAI) (Goris 1997), but the problem here is that the weighting
coefficients that create the null can also cause small distortions in the
main telescope beam.
At first, one might think that a simple correlation technique could work
well, given reference input from a completely separate radiometer that
monitors the interference but not the astronomical source. With this
approach, the reference input is cross-correlated with the signal in the
main feed and, after correcting for differences in phase-delay and
amplitude of the RFI in the two inputs by way of weighting coefficients,
the reference input is subtracted from that of the main feed. This
approach would work as long as the main and reference inputs continue to
see the same magnitude of change in phase-delay or amplitude; if the
relative difference in the characteristics of the RFI in the reference and
primary inputs does not change, the situation is stationary, and the
weighting coefficients do not change over an integration time. However, in
the real world conditions change as the telescope tracks or as propagation
phenomena, such as reflection and multi-path, affect the RFI at the
reference differently than at the main feed. In these non-stationary
conditions, correcting coefficients must be able to update in real-time as
the statistics change. To cancel RFI well enough to retrieve astronomical
signals, the canceling scheme must be able to adapt to changing statistics.
For the simple case of stationary interference, a linear filter is used to
minimize the least mean square value of the difference between the desired
response and the actual output. The resulting solution is commonly known
as the Wiener solution. For the more realistic case of non-stationary
conditions the Wiener solution is inadequate since it is non-adaptive. To
be effective in a non-stationary environment, the Wiener solution must be
updated as quickly as conditions change. An adaptive canceler initially
finds the Wiener solution and continually updates the solution by using a
recursive algorithm to track the changing statistics, providing that these
variations are sufficiently slow. This is the essential difference between
a stationary filter (such as the Wiener variety) and the non-stationary
adaptive filter we describe here.
Adaptive canceling has not been used before in radio astronomy, but the
concept is not a new one. Since the 1960's analog adaptive canceling has
been used successfully for anti-jamming in radar and interference excision
in communication systems (Ghose 1996). Analog adaptive canceling is based
on hardware techniques that are inherently noisy and lack the dynamic range
needed for radio astronomy applications. Digital techniques solve these
problems but until recently have been limited to audio applications due to
their slow processor speed. In 1965 an adaptive echo canceler for
telephone lines was developed (Sondhi 1967). In the early 1970's Stanford
University students used adaptive filtering to cancel the maternal signal
in fetal electrocardiography, where the electrical signature of the
mother's heart has an amplitude from two to ten times stronger than that of
the fetal heartbeat (Widrow et al. 1975). Since then, digital audio
interference cancellation systems have been developed for many diverse
applications from speech enhancement in noisy environments to the reduction
of harmful noise in factories. Audio applications require bandwidths of
only a few tens of kilohertz, which do not require especially fast digital
hardware. Fast digital technology for adaptive interference cancellation
over the wide bandwidths necessary for astronomy has become available only
relatively recently. Operation up to a few megahertz can now be performed
using modern digital signal processing chips at reasonable cost, such as
the Logic Devices Inc. LMA1009 12Ґ12 bit multiplier-accumulator (Logic
Devices 1995). Interference canceling by an adaptive filter in the context
of radio astronomy requires a low-gain reference antenna that monitors the
RFI. The adaptive filter then tracks the two inputs and removes the RFI,
leaving the desired astronomical signal. The canceling is accomplished in
real-time, and post-processing of data is not required.
Given the serious, ever-growing problems that RFI poses to radio astronomy,
new and sometimes radical approaches for interference cancellation must be
examined. If the adaptive interference canceling scheme is shown to be
viable for use in radio astronomy, the potential would be significant.
Viability will depend on how well it attenuates RFI and how much noise is
added to the system output as a result. The prototype adaptive canceling
system we have designed can be used with any radiometer accepting a 40 MHz
IF. We have characterized the performance of the canceler in the
laboratory and present the results here. The next step will be to field-
test the system using actual interference signals. We chose a portion of
the FM broadcast band near 100 MHz, certainly a worst-case frequency
location for astronomical observations, and have developed appropriate low
noise receivers for these tests. The FM broadcast band spans 88-108 MHz
and contains channels that are spaced 200 kHz apart. The signals are
relatively narrow in bandwidth (<100 kHz at the 3 dB level) with non-
varying central frequencies, fixed power levels, and known transmit antenna
polarizations. Multiple FM signals in the filter bandpass will allow us to
test fully the capability of the adaptive canceler. Even at a remote site
such as at NRAO's Green Bank Observatory in West Virginia, the entire FM
band is occupied (Fig. 1). The spectrum shown in Fig. 1 makes it quite
obvious that it would be impossible to observe in this band without highly
effective interference excision. The initial bench tests with our
prototype system are encouraging, with attenuation of strong frequency-
modulated interference down to at least 70 dB (a factor of ten million), at
the limit of the capabilities of our measurements.
In this paper we describe, for the first time, adaptive interference
canceling in the context of radio astronomy instrumentation (see also,
Bradley et al. 1996, 1997). The basic theory of the adaptive canceling
system is described in §2. The special case of the stationary solution and
expected performance are described in §3, and the non-stationary solution
is discussed in §4. The design of our prototype adaptive canceler and
results of initial trials are presented in §5.



2. Basic Concepts of Adaptive Interference Canceling

An adaptive interference canceling system for use on a radio telescope is
illustrated in Fig. 2. All signals are digitized and have a constant
sampling period with discrete time sequences indexed by n. The telescope
radiometer (or primary channel) receives both the astronomical signal [pic]
entering the main beam and the interference [pic] entering the sidelobes.
The primary input is the sum of these two signals, [pic]. A low-gain
antenna is connected to a second receiver (the reference channel) whose
input is only the interference [pic]. The reference antenna is pointed
towards the interferer (at the satellite or toward the horizon). The
collecting area of the reference antenna is much smaller than the primary
telescope, and therefore the astronomical signal would be essentially
absent in the reference input on the filter's adaptation timescale. The
interference in the reference channel [pic] is correlated in some unknown
way with the interference in the primary channel [pic], and the job of the
adaptive filter is to estimate this correlation as a function of time. The
adaptive algorithm compares the previous solution to current information
and sends updated coefficients to the digital filter. The digital filter
uses these coefficients to alter [pic] , producing [pic] which closely
resembles the interference in the primary channel. [pic] is subtracted
from the primary input to produce the system output [pic]:

[pic] , (1)

and then [pic] is sent to the telescope's spectrometer. No prior
knowledge is required of [pic], [pic], [pic], or of their
interrelationships.
The signal path through the adaptive filter shown in Fig. 2 illustrates the
iterative nature of the system. The adaptive algorithm finds new
coefficients by comparing [pic] with [pic] using a least mean squares
algorithm (LMS) that minimizes the total power. The power is the square
the system output:

[pic] . (2)

Since [pic] is uncorrelated with the interference in the primary and
reference channels, the cross-terms vanish, and so the expectation value
(time averaged) of the system output is:

[pic][pic] . (3)

As the filter adjusts the coefficients to minimize [pic], the power in the
astronomical signal [pic] is unaffected, and so [pic] reaches a power
minimum:

[pic][pic] . (4)

Since the astronomical signal is constant, minimizing the total output
power minimizes the output interference power, and therefore maximizes the
output signal-to-interference ratio.
In a stationary environment, once the filter finds the weighting
coefficients so that [pic] is a best least squares estimate of the
interference in the primary channel, those coefficients are fixed. More
specifically, even though the interference signal will have a non-zero
bandwidth due to modulation, as long as the statistics of the waveform
(i.e., mean variance and autocorrelation) in both the primary and reference
channels remain the same, the coefficients found initially will suffice.
However, in more realistic conditions with a radio telescope, the weighting
coefficients will quickly become obsolete if propagation effects cause a
relative change in what the reference and primary channels see.
Significant relative changes that require updated coefficients can be
caused by reflection, dispersion and telescope slewing; the timescale of
these effects is on the order of hundreds of milliseconds. In an adaptive
scheme, the coefficients used to weight [pic] are updated; in our prototype
receiver, coefficients are updated every 2 microseconds.
Two special cases of interest can arise. First, if the reference input is
perfectly correlated with the interference in the primary channel, the
output signal will be completely free of interference, since [pic]. In the
second case, if the reference channel is completely uncorrelated with the
interference in the primary channel (e.g., if for some reason the RFI does
not appear in the primary channel), [pic] goes to zero then (3) becomes

[pic] , (5)

and the filter turns off (in practical terms, the weighting coefficients
are set to zero).
In summary, in an adaptive interference canceling scheme, the system output
is fed back into the adaptive filter, and then the adaptive filter adjusts
itself to minimize the total system output power, updating the weighting
coefficients as the need arises. The advantage of this system is that it
works well in non-stationary conditions, i.e., when the relative difference
in the characteristics of the RFI in the primary and reference channels
change with time. Refer to Widrow & Stearns. (1985) and Haykin (1996) for
a complete discussion of digital adaptive filter theory and techniques.



3. Characteristics of Adaptive Interference Canceling in the Framework of
the Wiener Solution

In stationary conditions, the adaptive system converges to the optimal
Wiener filter. To minimize the output power, the algorithm needs to find
the minimum of an error surface, defined in the next section. This surface
is a multi-dimensional hyperboloid bowl with a unique minimum. Once the
adaptive filter finds the set of coefficients corresponding to the bottom
of the bowl, those coefficients are fixed and are not updated or changed
(the Wiener solution). However, the adaptive version continuously tracks
changing statistics between the reference and primary channels and adjusts
the coefficients in real-time. In a realistic, non-stationary environment,
the bottom of the hyperboloid bowl is slowly moving around, not by large
amounts but significantly, as the sides of the bowl change shape. The
adaptive system finds the Wiener solution by locking onto the minimum point
and then tracking the minimum as the bowl moves around in multi-dimensional
space. Since the basis of adaptive interference canceling is the Wiener
solution, we will start by examining the framework of the Wiener filter.
In this section, we discuss the characteristics of a Wiener filter in the
presence of random noise and formulate performance expectations. In §4 we
discuss methods of tracking and the design of an adaptive interference
canceling receiver for radio astronomy.


3.1 The Optimal Transfer Function-Finding the Bottom of the Bowl

Since [pic] is not an exact duplicate of [pic], we process [pic] with an
adjustable weight filter with coefficients [pic] to produce [pic], which is
a close replica of [pic]. A schematic of the filter is shown in Fig 3; it
is constructed using a tapped-delay line (or transversal filter) in the
reference channel and a linear combiner. The unit delay [pic] is one
sample time (the unit delay is the generalized discrete Fourier transform ,
or z-transform, of the unit sequence delayed by one sample, see Oppenheim
et al. 1989).
The tapped delay line is a finite impulse response (FIR) filter, used in
nearly all digital interference canceling applications due to its inherent
stability. The taps are scaled by weighting coefficients, and then summed
to form the FIR filter whose output is [pic]. Finally, [pic] is subtracted
from the primary input to form the combiner output, [pic]. As described by
(1), [pic] is the difference between the primary output and the processed
output of the reference channel. Note that no filtering is done in the
primary channel.
In analogy to (1), let [pic] be the vector of delayed versions of [pic],
and [pic] be the vector of tap weights containing the set of weights [pic].
Then (1) becomes

[pic] (6)

where T indicates the transpose. The output power is [pic]. The filter
finds [pic] by minimizing the total output power, so [pic] can also be
considered as an estimation of how well the system is working; in control
system theory, [pic] is called the error signal. [pic] is the error
performance surface which is a multi-dimensional quadratic hyperboloid and
has a unique minimum. In stationary conditions, this minimum is fixed and
is described by the optimum weight vector [pic] forming the Wiener filter
response. The values of [pic] are found by setting the derivative of [pic]
with respect to the weights equal to zero. The expectation value for a
stationary process is equivalent to the auto-correlation function (power
spectrum), and so after matrix operations we arrive at:

[pic] (7)
where [pic] is the auto-correlation of the reference input, and [pic] is
the cross-correlation function of the reference with the primary input (see
Widrow & Stearns 1985 for a derivation). Taking the z-transform (the
generalized Discrete Fourier transform) of (7), we have

[pic] . (8)

This result represents the unconstrained, non-causal Wiener solution (see,
e.g., Oppenheim & Schafer 1989 for details). However, any realizable
physical system must be causal. In order for the performance to approach
the ideal non-causal filter, a delay must be inserted in the primary input.
This forces an equal delay in the response of the filter. The length of
the delay is chosen to cause the peak of the impulse response to be
centered along the tapped-delay line. This causal system can behave in a
non-causal manner for a limited time-frame, since the solution will depend
on samples at [pic], [pic], [pic]. A real filter has a finite number of
taps, but the more taps, the closer the impulse response will be to the
ideal, infinitely long filter. The number of taps for a particular digital
signal processor is a cost-performance tradeoff.


3.2 Random Noise and Propagation Path

In this section we include the effects of random noise and propagation
paths on the system output by rewriting [pic] in terms of the interference
power spectra in each channel. A power spectrum of the interference will
depend upon the noise and transfer function through the system. This
discussion is for a Wiener solution but is equivalent for the adaptive
system. In this paper, "noise" always refers to random noise unless
otherwise specified.
Noise temperatures for the primary and reference receivers are the
uncorrelated noise components [pic] and [pic], respectively. However, the
interference in both channels comes from the same source, so [pic] and
[pic] are correlated with each other but are uncorrelated with either [pic]
or [pic]. Therefore, the reference input to the filter is [pic], and
likewise, the interference in the primary input is [pic]. Propagation
paths through the system also affect the output. The interference signal
that arrives at each channel is the original interference signal convolved
with some impulse response function for each path, [pic] and [pic], for
the reference and primary inputs, respectively. The transform of each,
called the transfer function, describes the characteristics of each
propagation path. Since [pic] and [pic] are correlated, we are only
interested in the ratio of their transfer functions. So we can define[pic]
to be normalized to the transfer function in the primary channel, and write
the interference power spectra of the primary and reference channels in
terms of each other:

[pic] . (9)

The auto-correlation function of the reference input becomes:

[pic] (10)

where [pic] is the power spectrum of the noise in the reference channel,
and [pic] is the power spectrum of the interference in the primary channel.
Since the cross-correlation of the reference and primary inputs depends
only on the correlated components of each, we have

[pic] . (11)

Substituting (10) and (11) into (8), we obtain an expression for the
optimal transfer function that includes noise and propagation paths:

[pic] . (12)

Note that [pic] is independent of both [pic] and the power spectrum of the
astronomical signal of interest.


3.3 Performance Expectations

The goal of any interference excision scheme is to recover the astronomical
signal without distortion by the filter. To this end, the interference at
the output of the canceler must be reduced down to or below the rms noise
over the integration time needed for the science, and the averaged baseline
noise should not be altered by the presence of the canceler. The
canceler's performance depends on a number of factors, including: random
noise in each channel, quantization noise, type of algorithm used to find
the optimal weights, and in the case of the adaptive system, tracking
ability. One of the unique characteristics of adaptive interference
cancellation is that the filtering process occurs in the reference channel,
and so the astronomical signal coming through the primary channel is not
distorted by the canceler. As a result, the filter is linear, and so the
attenuation achieved by the filter will be entirely independent of the
astronomical and interference signals in the primary channel. Linearity is
preserved as long as the system is operated within the dynamic range set by
the RF and IF amplifiers, quantization of the A/D converter, etc. We have
used 12-bit converters in our prototype system, resulting in a dynamic
range (see Ifeachor & Jervis 1993) of 72 dB.
In this section, we will describe the performance of an adaptive filter in
a stationary environment as modeled by a Wiener filter; the tracking of the
adaptive system in the case of non-stationary conditions will be considered
separately in §4.

3.3.1 Attenuation of RFI
The canceler's performance over a given integration time is measured by how
well the RFI signal is attenuated, i. e., whether the attenuation reached
the rms noise, and how long one could integrate before the rms noise level
would fall below the residual RFI. Quantities of interest are 1)
theoretical interference attenuation [pic], 2) measured attenuation [pic],
where t is the integration time, and 3) integration time for the rms noise
to fall below the residual RFI [pic]. For an ideal filter [pic], but the
dynamic range of a real filter is limited by the resolution of its digital
processor, so that [pic] will always be less than or equal to [pic],
assuming that no saturation occurs at any point in the radiometer or
canceler. Conditions at the telescope will not always push the system to
the edge of possible performance; if the RFI is weak to start with, a low
value of [pic] might still result in attenuating RFI below the level of rms
noise and yield a successful observation. It is important to note that an
RFI signal is never completely excised; there is always some residual RFI
even when the attenuated RFI is buried in the rms noise. As the
integration time gets longer, the rms noise gets smaller, and eventually
the residual RFI signal could be recovered. Using [pic] we can calculate
the longest integration time before the residual RFI ruins the astronomical
observation. These quantities, [pic], [pic], and [pic] are formulated
below.
The theoretical attenuation is the ratio of the interference power spectra
in the system output to primary input:

[pic] . (13)

To express [pic] in terms of measurable quantities, it can be written as a
function of the interference-to-noise ratios in the primary and reference
channels, [pic] and [pic], respectively, where

[pic] (14)
and

[pic] . (15)

Substituting (14) and (15) into the optimal transfer function, (8) becomes

[pic] , (16)

and after some manipulation, these expressions combine to give

[pic] . (17)

(Note that all these quantities, [pic], [pic], [pic], [pic], and [pic] in
the discussion that follows are explicit functions of [pic].) A plot of
[pic] versus [pic] is shown in Fig. 4 (top). Both axes are in units of
logarithmic relative power, decibels, defined as [pic], if [pic].
Expression (17) gives the somewhat non-intuitive result that the
theoretical attenuation depends on [pic] and is independent of [pic]. Yet,
as mentioned above, this is consistent with the system's linearity; the
filtering process occurs in the reference channel, and so the attenuation
in the system output is independent of both the astronomical signal and
interference in the primary channel. Also, since [pic] goes as [pic],
moderately good interference-to-noise in the reference channel should
produce significant attenuation of interference in the system output. For
example, our prototype system has a maximum dynamic range in the reference
channel of 72 dB; however, with [pic]of 72 dB, Fig. 4 (top) shows an
achievable attenuation of 144 dB. This is achievable in our prototype
system since calculations within the filter are represented by 27-bits
(giving a limit of 162 dB), yet our output D/A converter places an upper
limit of 72 dB. This means that although the attenuation achieved is much
better than 72 dB, it is only measurable in the system output to that
limit.
A useful way to measure the achieved attenuation in a given observation is:

[pic] (18)

where [pic] and [pic] are the interference peaks in the system output
before and after filtering, respectively. If there is no residual
interference peak, i.e., the RFI is attenuated down to or below the noise,
then we take [pic] to be the peak-to-peak noise [pic] in the baseline.
The residual of the interference can be related to the radiometer equation
by comparing the power spectra of the interference and average noise at the
system output:

[pic] . (19)

[pic] is the interference-to-noise of the output, where B is the bandwidth
resolution in Hz, t is the integration time, [pic] is the system
temperature, and [pic] is the rms noise. We are assuming here that the
canceler itself does not introduce additional noise. We can use this
expression for [pic] to find the maximum integration time before the rms
noise would fall below the residual RFI and ruin the observation. If we
define [pic] to be the integration time required for RFI to appear as a 3s
residual above the noise, then (19) gives

[pic] (20)

which is valid for [pic] up to the digitization limit of 72 dB for our
converters. For example, this expression shows that for moderately good
[pic] and[pic] of 30 and 20 dB, respectively, [pic] is 60 dB and so the
integration time could be as long as 3 weeks before a 3s residual would pop
up above the rms noise.

3.3.2 Random Noise Contribution by the Reference Channel
Although noise in the adaptive canceler will not distort the astronomical
signal while attenuating the interference significantly, the contribution
of noise from the reference channel is an important consideration. Noise
added by the canceler is a result of three factors: 1) quantization noise
caused by digitization , 2) residual noise within the bandwidth of the
interference, and 3) residual noise outside the interference bandpass
caused by the tapped-delay line.
Quantization noise is a result of the digitization of the analog signal and
is assumed to be uniformly distributed over the quantization step size,
leading to a signal-to-quantization noise power ratio of approximately 74
dB for the 12-bit digital processor of our prototype system. The
quantization noise contribution can be extremely small with appropriate
signal adjustments, that is, gains in the reference and primary channels
can be adjusted so that [pic] gives a noise floor significantly larger than
the quantum noise floor.
Noise in the system output introduced by the reference channel is a more
critical issue. Random noise in the reference channel is never zero, and
so incorporating a reference channel necessarily injects noise into the
output spectrum. This noise will have structure in the frequency domain.
A measure of this effect is the residual noise ratio ([pic]), defined as
the ratio of the noise power spectra at the system output ([pic]) to that
in the primary channel input ([pic]):

[pic] . (21)

This expression, after some algebra, can be put in terms of interference-to-
noise in the primary and reference channels which are measurable
quantities, and so (21) becomes

[pic] . (22)

For good performance, we want this residual noise ratio to be as close to 1
as possible; that is, we want the noise spectrum in the system output to be
no greater than the noise spectrum in the primary input channel. [pic] is
unity if there is no reference channel in the system. It is useful to
consider (22) in terms of the relative interference-to-noise in the
reference and primary channels; in general, we expect better performance
when [pic]. We want to know how much noise is introduced into the system
output for different ratios of [pic] to [pic]. If we write [pic] in terms
of [pic], so that [pic], then (22) becomes

[pic] . (23)

Figure 4 (bottom) shows the residual noise as a function of [pic] for
different values of [pic]. If the interference-to-noise in the reference
and primary channels are equal ([pic]), the noise in the system output (at
the frequencies where the interference signal was located) will be almost
twice as high as in the primary input before filtering. This is a result
of a noisy interference signal in the reference channel being subtracted
from the interference signal in the primary; since the noise is
uncorrelated, this operation adds significant noise power to the system
output. Therefore, the higher the interference-to-noise in the reference
channel relative to that in the primary, the lower the residual noise in
the system output. In the case of a radio telescope, the primary channel
receives RFI in the relatively weak sidelobes of the beam. The low-gain
antenna for the reference channel is pointed toward the horizon in the
direction of the RFI, so interference-to-noise in the reference channel
can easily be higher than in the primary channel. The curves of Fig. 4
indicate that over a wide range of [pic] (especially for [pic]) the
injected noise is nearly constant. This implies that even though the
interference signal level might fluctuate in the primary channel due to the
telescope's slewing or to propagation effects, the amount of noise injected
in place of the interference will be constant.
Another noise component introduced by the reference channel occurs outside
the bandwidth of the interference and can result in baseline ripple.
Ideally, the digital filter in the reference channel should have a very
sharp frequency response, such that it adjusts to the bandwidth of the
interference but blocks reference channel noise outside this bandwidth.
However, the sharpness of the digital filter is proportional to the number
of taps. If the filter contains too few taps, then excess noise from
outside the interference bandwidth will enter the primary channel, causing
a ripple in the baseline power. Therefore, as large a number of taps as
possible should be used to minimize this effect. However, to choose the
optimal number of taps, many factors must be considered. For a given
filter passband ripple, stopband attenuation, and transition width between
passband and stopband, an estimate of the number of taps required to meet
the specification can be obtained from optimal FIR filter theory (Mintzer &
Liu 1979).
In summary, the adaptive canceler will not distort the spectrum of the
astronomical signal, yet it will provide a high degree of interference
attenuation. Noise injected by the reference channel can be minimized if
[pic] and a large number of filter taps are used.



4. Adaptive Interference Canceling in a Non-stationary Environment

The results of the previous section for a Wiener filter can be applied to
the adaptive filter system. In addition to the considerations for a
stationary filter, an adaptive process introduces other sources of error
and noise, specifically from the tracking capability and multiple reference
channels.


4.1 The Least Mean Square Algorithm and Tracking Concerns and Constraints
The basic algorithm used to find the minimum of the error surface for the
Wiener solution is also used to find the minimum in the case of an adaptive
system, with the added complication of tracking the minimum as it changes.
The least mean square (LMS) algorithm uses an estimate of the error surface
gradient that is closely tied with the structure of the tapped-delay line,
and requires a minimal amount of computing. There are other algorithms
that offer improvements over LMS that would increase the performance of an
adaptive system; examples include Recursive Least Squares (Haykin 1996)
which uses off-line gradient estimations and Higher-Order Statistics (Shin
& Nikias 1994) which is computationally complex. For our prototype
receiver, we have implemented the LMS algorithm for its computational
simplicity.
As in (6), [pic] is the vector of delayed versions of [pic], and [pic] is
the vector of tap weights containing the coefficients [pic]. For the
Wiener solution and for each iteration in the adaptive system, the gradient
of the error surface can be estimated from:

[pic] (24)

where L is the number of filter tap weights, defining a direction in error
space. By starting with this estimate of the gradient and using the method
of gradients (see Widrow & Stearns 1985):

[pic]. (25)

[pic]is found by tweaking [pic]. The parameter [pic] is the gain constant
and is related to the step size in the search for minimum as the system
tracks. The smaller the step size, the longer it takes to find the bottom
of the error surface bowl. This is especially important in an adaptive
filter, since the tracking time must be able to keep up with the timescale
of the changing statistics, i.e., the ongoing movement of the bottom of the
bowl. Speed and stability of adaptation, as well as noise in the weight
vector solution, are determined by the size of [pic]; the smaller [pic] is,
the smaller the error is in [pic], but the longer it takes for the solution
to converge. A compromise between speed and introduced error is made in
choosing [pic]. The weight vector will converge to an optimal solution
when

[pic] (26)

(see Widrow & Stearns 1985). Note that the optimum value of [pic] is a
function of the interference power in the reference channel. The optimal
value of [pic] is a trade-off between better adaptability and time for
convergence. In our prototype system, the value of [pic] is manually
adjustable. For a future system, we plan to make [pic] self-adjustable,
that is, capable of responding to the interference power in the reference
channel (Wilson 1996, personal communication).


4.2 Adaptive Interference Canceler With Multiple Reference Channel

In theory, any number of reference channels can be used to cancel
interference in the primary channel. Multiple reference channels are
necessary if there is more than one interferer in the passband since a
single reference channel does not have the necessary degrees of freedom to
eliminate more than one. Additional degrees of freedom are required
whenever: 1) there are several uncorrelated interference signals in the
filter bandpass, 2) a single interference signal encounters severe multi-
path propagation and appears as several signals, or 3) the spatial
polarization of a single interference signal differs significantly between
the primary and reference inputs. With two or more uncorrelated sources of
interference, the synthesis of the transfer functions, and hence the set of
optimal weight vectors, becomes more complicated. Not only are there
transfer functions that describe the propagation paths from the sources
through the primary input, but there are other transfer functions that
represent propagation paths through all the reference inputs with allowance
for cross-coupling.
Additional degrees of freedom can be achieved by increasing the number of
reference channels processed by the canceler. In the case of multiple
interference signals in the filter passband (in our case, more than one
radio station), uncompromised performance occurs when the number of
reference channels is equal to or greater than the number of interferers.
This is also relevant under severe multi-path conditions where time delays
cause the same interference source to appear multiple times (similar to
ghost images on a television receiver). Note that a one-to-one
correspondence between an interferer and a given reference channel is not a
requirement; the adaptive filter will synthesize the individual transfer
functions as linear combinations of the reference channel inputs.
Another degree of freedom is needed when the spatial polarization of the
reference antenna differs from that of the sidelobe of the telescope
antenna in the direction of the interference source, as when the telescope
slews across the sky during any given observation. As an example, the RFI
in our bandpass is from broadcast stations in the FM band which transmit
with circular polarization. Yet propagation effects between the
transmitter and the telescope can cause the polarization of the arriving
RFI to change from its initial state or even to fluctuate randomly with
time. If the polarization response in the reference and primary antennas
match that of the RFI, then there is no problem and another degree of
freedom is not needed. However, if there is a spatial polarization
difference between the reference and primary antennas, then one or the
other will see a stronger signal (even a null at the reference antenna
which would result in the adaptive filter turning off) and possibly a phase-
delay. If the difference in antenna orientations causes [pic] to be higher
than [pic], the attenuation of RFI in the output will be less than optimal.
It is unlikely that a single reference antenna will always be oriented to
match the telescope sidelobe polarization, especially as the telescope
slews. The addition of a second reference antenna that responds to the
orthogonal polarization sense with respect to the first reference antenna
should be adequate to achieve optimal attenuation of RFI. The transfer
function is then synthesized as a linear combination of the signals from
the two orthogonal reference inputs.




4.3 Practical Considerations for an Adaptive Canceling System on Radio
Telescopes

Adaptive canceling shows promise as an effective means to attenuate
interference in both single-dish and interferometer radio telescope
systems. However, there are three basic requirements of the system and the
RFI environment for success with adaptive canceling: 1) the receiver must
always operate in the linear regime, 2) the adaptive convergence time must
be finite, on the order of a few seconds, and 3) interference-to-noise in
the reference channel must be greater than that in primary channel.
A linear operating regime assures that the RFI will not overload the
receiver front-end, since distorted interference cannot be removed through
a linear adaptive filter system. A finite adaptive convergence time places
practical limits on the type of RFI that can be canceled effectively by
this method. Signals of the continuous wave variety such as from broadcast
stations or satellite downlinks (regardless of the modulation type) and
moderately long-duration signals (greater than a few seconds) from personal
communication systems can be attenuated effectively since the canceler has
the necessary time required to lock on and adapt. However, short bursts of
interference from systems such as aviation or ship-board radar make
canceling difficult without additional processing to "remember" the filter
parameters from burst to burst yet turn the filter off rapidly between
bursts to eliminate unwanted noise injection. Therefore, quasi-random
frequency hopping signals from certain spread-spectrum systems simply
cannot be canceled using this adaptive design.
Maintaining a greater interference-to-noise in the reference channel than
that in the primary channel places limits on where the interference source
is located with respect to the main beam of the telescope. For example, if
the main beam happens to be pointing directly at a satellite producing RFI,
it will be impossible for the reference channel [pic]to be greater than
that in the primary channel since the gain of the main beam of the
telescope will be greater that the gain of the reference antenna. In
contrast, if it is the sidelobes that pick up the interference, [pic] can
easily be greater than [pic] since the gain of the telescope in the
direction of the interference can be quite low. Note that when the
interference source is moving, e.g., LEO satellites such as the Iridium
series, the reference antenna must track the satellite across the sky to
achieve good [pic]. Finally, in the case of interference arriving at the
telescope from an over-the-horizon source, the adaptive filter performance
is reduced as the telescope elevation is decreased in the direction of the
interference, but the larger the telescope, the greater the tolerable
elevation angle.
Even with these practical restrictions, however, adaptive canceling can
greatly improve observing in many current and future situations where RFI
poses serious problems for radio astronomy.



5. The Adaptive Interference-Canceling Receiver-The Prototype

Ultimately, we hope to build adaptive interference cancelers for bands of
interest in radio astronomy which have serious RFI problems, e.g., L-band.
As a first step toward this goal, we have built a prototype adaptive
canceler with a single reference channel which we will use with a receiver
in the FM band. Our next effort will be to complete the system with four
pairs of reference channels to test on the 140 ft radio telescope at Green
Bank Observatory. Here, we report the results of our single reference
channel prototype tested under controlled laboratory conditions.


5.1 The Design

The primary and reference inputs to this canceler are centered at 40 MHz
and can be used with a variety of microwave receiver front-ends that have a
compatible IF bandpass. All of our laboratory measurements were performed
by injecting controlled signals directly into the IF band. Initial system
tests were performed using a front-end designed for 100 MHz. The canceler
design and measurements are described below.

5.1.1 The Adaptive Canceler
A block diagram of the prototype adaptive canceler is shown in Fig. 5. The
primary and reference inputs, both centered at 40 MHz and assumed band-
limited to 500 kHz, are down-converted to baseband using a common local
oscillator. At baseband, both signals are pre-filtered, amplified, and
then digitized using a 12-bit A/D converter sampling at a 4 MHz rate. To
achieve the Nyquist-sampled 0-1 MHz baseband, the A/D outputs are decimated
by two (i.e., every other sample is used). The primary channel input is
directed to the summing junction. The reference channel input is directed
to a 9-tap FIR adjustable-weight filter whose coefficients are determined
by the microprocessor which implements the LMS algorithm. The filter
output is directed to the summing junction where it is subtracted from the
primary data and forms the system output (which is also the error signal
input to the LMS algorithm). The microprocessor, operating at 22 MHz, is
capable of handling up to eight reference channels for future expansion.

5.1.2 The 100 MHz Front-End
We chose the FM band for our first effort to build an adaptive filter
receiver for radio astronomy mainly because the characteristics of the
broadcast signals are well known: 1) each station occupies a relatively
narrow bandwidth (<100 kHz at the defined level of 3 dB), 2) each station
is well characterized in frequency (spaced at 200 kHz intervals), 3) each
station is in continuous operation at a fixed power level, 4) most stations
have a known transmit polarization, 5) the filter bandpass includes several
FM channels to gauge the effectiveness of multi- reference channel system,
and 6) each FM channel can have multiple interference signals on the same
frequency. Green Bank Observatory is centrally located in the radio quiet
zone, and although broadcast stations are spaced 200 kHz apart, it is
possible to receive multiple stations per channel at this location.
Cautiously, we expect four radio stations broadcasting in our passband near
100 MHz. Although our prototype system currently has only one reference
channel, there will be eight in the final system, one for each polarization
for the four interferers.
A block diagram of the RF section is shown in Fig. 6. The primary channel
input is half of a cross dipole feed located at the prime focus of the
radio telescope. Four pairs of orthogonal Yagi antennas will be the inputs
to the eight reference channels (only two are shown in the Figure). Each
of the five RF inputs have a room temperature, low-noise amplifier (T = 30
K), followed by a bandpass filter and additional amplification. The inputs
are translated to the 40 MHz IF bands using mixers that share a common
local oscillator and are then directed to the adaptive canceler.
5.2 Bench Tests

We have completed a first phase performance characterization of our
prototype receiver in the laboratory. These initial tests were performed
at NRAO Headquarters in Charlottesville, VA, in the Central Development
Laboratory. The goal was to measure the dynamic range of the adaptive
filter and gauge the filter's performance under stationary and non-
stationary conditions.
Figure 7 shows a block diagram of the bench test configuration. We created
an interference signal using a signal generator with the option of single
tone, and/or random frequency modulation. The output of the signal
generator was split and directed to the reference and primary inputs. Both
inputs were pre-filtered using a 500 kHz bandpass filter centered at 40
MHz, with random noise power from two independent noise sources coupled
into each input. In some experiments we injected a test source into the
primary input to evaluate the canceler's ability to recover the test signal
in the system output. The test source was used to simulate an astronomical
signal, that is, a signal that does not vary in strength or frequency over
the course of the observations. To simulate non-stationary conditions, we
used a voltage-controlled amplitude and phase shifter driven by a sine wave
generator that varied the amplitude and phase of the primary input
interference signal relative to that present at the reference input. The
output of the adaptive filter was directed to a Hewlett-Packard spectrum
analyzer for processing. The bandwidth resolution was 1 kHz and
integration time was typically 30 seconds. There was no capability to
measure rms noise, so we quote the peak-to-peak noise in mWatts for each
test.
Initial tests confirmed system linearity. The first experiments described
below characterize the system's dynamic range under stationary conditions,
as well as its ability to recover a weak test signal buried in the
interference. The second set of experiments tests the adaptive tracking
capability in non-stationary conditions. In these experiments the term
"deviation of modulation" refers to the spread of the RFI signal on either
side of the central frequency, and the term "modulation function"
designates the band-limited signal which carries the RFI about the central
frequency. Modulation signals can be random (gaussian), and/or single tone
sine wave.

5.2.1 Performance for Stationary Conditions
To establish performance at or near maximum dynamic range, the first tests
address the ability of the adaptive filter to attenuate very strong
interference in the primary channel for different values of [pic], without
tracking (stationary solution) and without the presence of a simulated
astronomical signal. The results are shown in Table 1. The integration
time for all measurements was 30 sec; once the canceler was activated, it
took less than one second for the canceler to lock up on the signal and
typically <20 sec to extinguish the RFI below the rms noise. The RFI is
successfully attenuated below the noise for all the experiments in Table 1.
The RFI in each of these experiments had a sine wave modulation function
of 500 Hz with a deviation of 5 kHz. The measured interference attenuation
[pic] in all cases goes up to or near the theoretical limit of the 12-bit
digitization (72 dB). Based on the error in our measurements of the power,
we find the error in [pic] is ±2 dB.
Figure 8 shows spectra from Column 2 in Table 1. For all spectra in this
and subsequent figures, the data were recorded in volts. The right axis
shows the linear scale in volts, and the left axis shows the quantity of
interest, power, which is directly proportional to the antenna temperature;
note that the left axis is not linear since power is proportional to the
square of the voltage. The top plot in Fig. 8 is the RFI at the system
output before the canceler is activated (this spectrum shows a 1 second
integration; after 30 seconds the peak of the RFI integrated down to 0.071
mW which is the value we use in the Table). The filtered spectrum appears
below. Note that the RFI in the top plot is a factor of 103 times stronger
than the strongest FM station shown in Fig. 1 (after correcting for the
gain and bandwidth resolution of the systems).
The next set of experiments tested the ability of the filter to recover a
weak test signal buried in relatively strong RFI. The results for four
trials with different values of [pic] are in Table 2. Figure 9 shows
spectra for the first trial in Table 2. The RFI signal was simulated with
a deviation of 5 kHz and a random modulation function band-limited to 20
kHz. The middle panel shows a ~5s test signal before the RFI was turned
on, and the canceler's successful recovery of the test signal is in the
bottom panel. The RFI signal disappears within the noise, and the test
signal is recovered. Figure 9 shows that the random noise in the spectrum
before and after filtering has not changed significantly, so the presence
of the reference channel does not seriously degrade the output. However, a
slight structure to the baseline is introduced by the reference channel.
Notice that a second, very weak RFI signal centered at -13 kHz (coming from
some unidentified RFI source in the room) appears in the middle panel and
is also successfully removed by the canceler.
Figures 10, 11, and 12 show spectra from the experiments of the last three
columns of Table 2. The top panel of each figure displays the RFI alone
coming through the system output. The test source alone in the system
output is shown in the second panel. The canceler is not turned on for
either. The third panel in each figure shows the "OFF position" obtained
by turning off the test source and turning on the RFI and canceler. This
approximates beam switching off-source in astronomical observations. The
OFF position spectra in Fig. 10 and 12 show no measurable sign of residual
RFI, and the bottom panels (with the OFF position subtracted) show a good
recovery of the test signal with no significant increase in rms noise.
Even with a 30 kHz deviation for the RFI in Fig. 12, the canceler performs
well. The experiment shown in Fig. 11, however, was performed with a
random plus single tone modulation function and a 15 kHz deviation. As can
be seen from the OFF position spectrum in the third panel, the canceler was
not able to extinguish the RFI to the level of the rms noise. Notice that
the residual RFI is double-peaked. It is as if the canceler is seeing two
separate RFI signals and cannot eliminate both at once. Yet when the OFF
position is subtracted from the ON source spectrum, the test signal is
recovered (bottom panel). A single tone modulation is atypical in the real
world, but this set up pushes the system to its limit and these results
will be useful when the prototype is being tested at the telescope.

5.2.2 Performance for Non-Stationary Conditions - The Adaptive Solution
Given the success with stationary conditions in the previous trials, we
simulated non-stationary conditions. We injected input that continuously
varied the difference between the reference and primary channels in both
amplitude and phase. Limitations of our equipment determined the magnitude
of variations in amplitude and phase between the reference and primary
inputs. We expect that these values are quite large compared to realistic
conditions at the telescope, so these experiments pushed the filter beyond
the edge of best performance. The four experiments in Table 3 were
performed with sinusoidal amplitude and phase variations of 2 mW and 15?,
respectively, between the reference and primary inputs. The first trial
cycled the amplitude and phase and once every second, and the last three
cycled every 10 seconds.
Spectra for trial 1 are shown in Fig. 13. The test source was recovered
and the RFI disappeared into the noise. This experiment had the same RFI
of Fig. 12 but this time with non-stationary conditions. The top and
bottom panels show the recovered test signal after 30 and 150 seconds,
respectively. The noise values in the Table are for the 30 second
integration. The positive baseline in the bottom panel is most likely due
to the finite nature of our 9-tap system and not to the canceler. Trial 2
used a very strong RFI signal and weak test source, and again, good
attenuation was achieved. Trials 3 and 4 were the only cases where the RFI
was not attenuated down to the level of the noise. However, the canceler
was still able to bring down the RFI by at least a factor of one hundred
thousand ([pic]). In this prototype, we have used a fixed step size,
[pic], and the most simplistic algorithm available (LMS) for finding and
tracking the solution for the weighting coefficients. Since the tracking
success depends on the algorithm and on [pic], future design improvements
will use a more sophisticated algorithm and allow m vary as necessary.


5.3 System Compatibility Tests on the 140 ft Telescope

In 1997 June we had an engineering test of the single reference channel
prototype receiver on the 140 ft telescope at Green Bank Observatory. The
primary feed was a cross dipole mounted at prime focus. For the reference
channel, we used two FM antennas mounted on the top of the receiver box
(see Fig. 14). The input from the main feed was mixed before arriving at
the IF. There were four interferers in the passband. We also found RFI
leaking into our system from the control room and from the spectral
processor, so a design improvement will be to put the adaptive canceler in
a shielded box. During this shake down of the system, we found that the
anti-imaging filters need sharpening to confine the bandwidth, and that a
better interface to the spectral processor is necessary. We also verified
that a separate canceler is needed for each polarization.
Even in the face of multiple interferers in our passband, polarization
effects, and having only one reference channel, the system still attenuated
radio stations to better than 25 dB. In light of the design limitations of
this first prototype, we find these results to be very encouraging. The
next step will be to implement the changes mentioned above and build up the
system to have four reference channels with a canceler for each
polarization. We plan to begin this work during the summer of 1998.






6. Conclusions

Laboratory experiments with a prototype adaptive canceling receiver have
shown that with one interferer in the passband, under stationary or non-
stationary conditions, the system can attenuate RFI to the maximum
performance limited by its digital processor, 72 dB. The canceler locks up
on the interference signal in less than one second and attenuates down to
the rms noise in typically <20 seconds . The noise added by one reference
channel is minimal for the experiments we performed. Since the
interference-to-noise in the reference and primary inputs is a function of
frequency, a slight ripple is introduced into the baseline when using the
adaptive canceling system. Tests that will be performed under more
realistic conditions will allow a good characterization of this problem.
We have verified that a separate adaptive canceling filter is necessary for
each polarization, and we will implement this in the next system we build.
We also expect that a more sophisticated algorithm than LMS and the ability
to vary the step size parameter [pic] will also improve the results. The
attenuation performance is related to a higher interference-to-noise in the
reference than primary channel, and if the RFI signal can be kept in the
sidelobes of the main beam, [pic] can be higher than [pic]. To keep the
RFI signal in the sidelobes, there will be an elevation angle limit of the
telescope (e.g., the main beam should not be pointed at the horizon in the
direction of the RFI source). This is an important consideration if the
interference is coming from a satellite. The limit on the elevation angle
will, of course, depend on the telescope and the nature of the interference
sources.
We conclude that these initial results for the prototype adaptive
interference canceling receiver are promising.


ACKNOWLEDGMENTS

We wish to thank R. Escoffier and R. Fisher for invaluable contributions to
the development and implementation of the digital hardware. We are also
indebted to S. Wilson for directing much of the theoretical design.
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TABLE 1

High Dynamic Range Tests1 - Stationary Conditions

| | | | | | | | | | | | | | | |trial 1 |trial 2 |trial 3 |trial 4 | | | |
| | | | | | | | | | | |[pic] |[dB] |10 |10 |20 |20 | |[pic] |[dB] |62 |62
|52 |48 | |deviation of modulation |[kHz] |5 |5 |5 |5 | |modulation func (1
freq) |[kHz] |5 |5 |4 |5 | |RFI before filtering 2 |[Ґ 10-6 mW] |157 000
|71 000 |9 380 |12 480 | |output peak-to-peak noise |[Ґ 10-6 mW] |0.008
|0.003 |0.008 |0.01 | |[pic]3 |[dB] |72 |72 |61 |61 | | | | | | | | |
1 The errors are: ±2% in [pic] and the RFI peak, ±0.002 in the output
peak-to-peak noise, and ±2 dB in the attenuation [pic].

2 Note that there was no measurable residual RFI after filtering

3 [pic] is the measured attenuation, achieved, to a limit here of 72 dB.
It is defined to be the peak of the RF signal before filtering divided by
the peak-to-peak noise after filtering. It is the measured attenuation


TABLE 2

Recovery of a Test Source Buried in the RFI1 - Stationary Conditions

| | | | | | | | | | | | | | | | | | | | | | | | | | |trial 1 |trial 2
|trial 3 |trial 4 | | | | | | | | | | | | | | | | | | | | | | | | | |[pic]
|[dB] | |10 |20 |15 |15 | |[pic] |[dB] | |62 |20 |11 |16 | |deviation of
modulation |[kHz] | |5 |5 |15 |30 | |modulation func2. (random) |[kHz] | |5
|4 |4 |4 | |peak of test signal |[Ґ 10-6 mW] | |0.22 |0.08 |0.12 |0.08 |
|RFI signal before filtering |[Ґ 10-6 mW] | |58 000 |48.0 |6.48 |20.4 |
|RFI signal after filtering |[Ґ 10-6 mW] | |??? |??? |0.09 |??? | |output
peak-to-peak noise |[Ґ 10-6 mW] | |0.01 |0.001 |0.0013 |0.002 | |[pic]4
|[dB] | |68 |47 |38 (19)5 |40 | | | | | | | | | |
1 The errors are: ±2% in [pic] and the RFI peak, ±0.002 in the output
peak-to-peak noise, and ±2 dB in the attenuation [pic].

2 The frequency function for trial 3 was random plus single tone.

3 This is the peak-to-peak noise measured in the filtered spectrum after
subtracting the OFF position

4 [pic] as in Table 1.

5 The numbers in parentheses are the results in the filtered spectrum
before subtraction by the OFF position. The other values are the results
after subtraction by the OFF position (see Fig. 12).


TABLE 3

High Dynamic Range Tests1 - Non-Stationary Conditions2

| | | | | | | | | | | | | | | | | | | | | | |test source | |no test source
| | | | |trial 1 |trial 2 |trial 3 |trial 4 | | | | | | | | | | | | | | | |
| | | | | | |[pic] |[dB] |15 |10 |10 |10 | |[pic] |[dB] |16 |61 |62 |62 |
|deviation of modulation |[kHz] |30 |10 |10 |10 | |modulation func (random)
|[kHz] |4 |5 |20 |20 | |peak of test signal |[Ґ 10-6 mW] |0.10 |0.56 |???
|??? | |RFI before filtering |[Ґ 10-6 mW] |20.4 |45 000 |95 050 |95 050 |
|residual RFI after filtering |[Ґ 10-6 mW] |??? |??? |0.10 |0.12 | |output
peak-to-peak noise |[Ґ 10-6 mW] |0.003 (0.001)3 |0.008 |0.02 |0.02 |
|[pic] 4 |[dB] |40 |67 |60 |59 | | | | | | | | |
1 The errors are: ±2% in [pic] and the RFI peak, ±0.002 in the output
peak-to-peak noise, and ±2 dB in the attenuation [pic].

2 Non-stationary conditions: for all trials, Damplitude and Dphase is 2
mW and 15?, respectively; for trial 1, statistics cycle once a second. For
trials 2, 3, and 4, the statistics cycle once every 10 seconds.

3 The number in parentheses is the peak-to-peak noise after 150 seconds
integration (see Fig. 13)

4 [pic] as in Table 1.
Figure Captions

Figure 1 - A spectrum of the FM broadcast band near 93 MHz. The data were
taken using the 50-500 MHz receiver and cross-dipole feed on the 140 ft
Telescope at Green Bank Observatory. The receiver gain was 44.5 dB and the
system temperature was 750 K, with a bandwidth resolution of 10 kHz.

Figure 2 - A schematic of the adaptive interference canceler. The
telescope receiver, or primary channel, is located at prime focus and
receives the primary input, which consists of the astronomical signal [pic]
in the main beam and the interference [pic] entering the sidelobes. A low-
gain antenna is connected to a second receiver, the reference channel,
whose input is the interference [pic] which is correlated in some unknown
way with [pic]. The adaptive algorithm sends updated weighting
coefficients to the digital filter which are found by comparing the
previous solution to the current information. The digital filter uses the
weighting coefficients to alter [pic] thus producing [pic] which closely
resembles [pic]. Subtracting [pic] from the primary input produces the
system output [pic] which is then sent to the spectral processor. The
signal path through the adaptive filter illustrates the iterative nature of
this system. Note that no prior knowledge of [pic], [pic], or [pic] is
required.

Figure 3 - An ideal Wiener filter with an infinitely long tapped-delay
line. The filter tap weights, [pic] (or weighting coefficients) are
adjusted to yield optimal filter performance for the case of stationary
conditions (the Wiener solution). [pic] is one sample-time.

Figure 4 - (top) The theoretical interference attenuation [pic] as a
function of the interference-to-noise in the reference channel [pic]. Both
axes are in units of logarithmic relative power, dB, defined to be [pic].
Since [pic] goes as [pic], moderately good interference-to-noise in the
reference channel produces significant attenuation of interference in the
primary channel. The maximum achievable attenuation depends on the
resolution of the digital processor in the reference channel. The dynamic
range for the 12-bit processor is 72 dB.
(bottom) The residual noise ratio [pic] as a function of the relative
interference-to-noise in the primary and reference channels. [pic] is a
measure of the noise introduced into the system output by the reference
channel. Several curves are shown, each for a different ratio of [pic] to
[pic], such that [pic]. [pic] is given in dB, so that if [pic]= 0 dB, the
interference-to-noise is the same in the reference and primary channels.

Figure 5 - A block diagram of the intermediate frequency (IF) downconverter
and adaptive filter for a system with a single reference channel.

Figure 6 - A block diagram of the radio frequency (RF) and intermediate
frequency (IF) downconverter for a system with a two reference channels.
The reference feeds are Yagis. In this diagram, both polarizations of the
primary input are power combined.

Figure 7 - A block diagram of the experimental setup to test the prototype
in the laboratory. The test source, imitating an astronomical signal, and
the interference signal are produced by a separate signal generators. The
IF downconverter and adaptive filter box referred to in this figure are
shown in detail in Fig. 5.

Figure 8 - A high dynamic range test of the adaptive canceling system under
stationary conditions. The data are shown in Column 2 of Table 1. The
spectra in this and subsequent Figures were recorded in volts. The right
axis shows the linear scale in volts, and the left axis is power. Note
that the left axis is not linear since power is proportional to the square
of the voltage. The top panel shows the RFI at the system output before
the adaptive canceler is activated (this spectrum shows a 1 second
integration; with a 30 seconds, the peak of the RFI integrated down to
0.071 mW which is the value we use in Column 2 of Table 1). The bottom
panel shows the spectrum after activating the adaptive canceler and
integrating for 30 seconds.

Figure 9 - A simulated astronomical signal [pic] (or "test signal") buried
in strong RFI with stationary conditions. The top panel shows the RFI
alone in the system output before the filter is activated. In the middle
panel, the test signal alone is shown (RFI and canceler are off). Note
that the test signal is offset by about 5 kHz from the central frequency.
The spectrum in the bottom panel results when the RFI and test signal are
on and the canceler activated. The test signal that was buried in the RFI
is recovered. Note that in this Figure, the baseline has not been
subtracted. Also note that at -15 kHz a very weak RFI signal leaked into
the primary channel (coming from some extraneous source in the laboratory);
the canceler was able to excise this as well as the much stronger RFI
signal. The data are displayed in Column 1 of Table 2. See Fig. 8 for an
explanation of the axes.

Figure 10 - Results of adaptive cancellation with a test signal buried in
strong RFI, random modulation, "OFF source position" subtraction, and with
stationary conditions. The experimental procedure is the same for Fig. 11,
and 12. The first panel shows the RFI alone in the system output before
the canceler has been activated. The second panel shows the test signal
before the canceler is activated. To obtain an "OFF source position", we
turned off the test signal generator but kept the canceler on. This is
equivalent to beam switching during an astronomical observation, and the
resulting spectrum is shown in the third panel. The bottom panel shows the
ultimate result, with test source, RFI, and canceler operating, and
subtracted by OFF position spectrum. See Column 2 of Table 2. See Fig. 8
for an explanation of the axes.

Figure 11 - Results of adaptive cancellation with a test signal buried in a
broad (15 kHz) RFI signal, random and single tone modulation function, "OFF
source position" subtraction, and with stationary conditions. The legend
for Fig. 10 describes the basic experimental setup. See Column 4 of Table
2 for measurements.

Figure 12 - Results of adaptive cancellation with a test signal buried in a
very broad (30 kHz) RFI signal, random modulation function, "OFF source
position" subtraction, and with stationary conditions. The legend for Fig.
10 describes the basic experimental setup. See Column 3 of Table 2 for
measurements.

Figure 13 - The same experiment as in Fig. 12 but with NON-stationary
conditions. A spectrum of the RFI in the system output, and OFF source
position are shown in Fig. 12. The test signal has about the same strength
as in Fig. 12 but is displaced in frequency. Both panels here show the
recovered test source, with RFI and canceler operating and with the OFF
position spectrum subtracted, but differ in integration time. The
integration time is 30 seconds in the top panel and 150 sec in the bottom
panel. See Column 4 of Table 2 for measurements.

Figure 14 - The 140 ft telescope at Green Bank Observatory with the
prototype adaptive interference canceling receiver for 100 MHz mounted at
prime focus. The orthogonal Yagi antennas mounted at the top of the
receiver box are pointed toward the horizon and serve as the reference
feed.