Transcript Radiometer systems

Radiometer systems
Chris Allen ([email protected])
Course website URL
people.eecs.ku.edu/~callen/823/EECS823.htm
1
Outline
Equivalent noise temperature
– Characterization of noise
– Noise of a cascaded system
– Noise characterization of an attenuator
– Equivalent-system noise power at the antenna terminals
– Equivalent noise temperature of a superheterodyne receiver
Radiometer operation
– Effects of gain variations
– Dicke radiometer
Examples of developed radiometers
Synthetic-aperture radiometers
2
Radiometer systems
A radiometer is a very sensitive microwave receiver that
outputs a voltage, Vout, that is related to the antenna
temperature, TA.
Based on the output voltage, the radiometer estimates TA
with finite uncertainty, T, which is referred to as the
radiometer’s sensitivity or radiometric resolution.
Radiometric resolution is a key parameter that
characterizes the radiometer’s performance.
An understanding of the factors affecting radiometer’s
performance characteristics requires an understanding of
noise, radiometer design, and calibration techniques.
3
Equivalent noise temperature
In any conductor with a temperature above absolute zero,
the electrons move randomly with their kinetic energy
proportional to the temperature T.
The randomly moving electrons produce a fluctuating
voltage Vn called thermal noise, Johnson noise, or Nyquist
noise.
Other kinds of noise include quantum noise (related to the discrete
nature of electron energy), shot noise (fluctuations due to discrete
nature of current flow in electronic devices), and flicker noise (also
known as pink noise or 1/f noise) that arises from surface
irregularities in cathodes and semiconductors.
Thermal noise is characterized with a zero mean, Vn = 0,
and is has equal power content at all frequencies, hence it
is often called white noise.
4
Equivalent noise temperature
For a conductor with resistance R connected to an ideal
filter with bandwidth B, the output noise power Pn is
Pn  k T B
where k is Boltzmann’s constant (1.38  10-23 J K-1), T is the
absolute temperature (K).
The thermal noise power delivered by a noisy resistor at
temperature T is found by replacing the noisy resistor with
a noise-free resistor and a voltage generator Vrms.
The reactance X represents the
resistor’s inductive and capacitive
aspects.
2
Vrms
 Vn2 t   4 R k T B
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Why V2rms = 4 R k T B ?
Experimental studies in 1928 by J.B. Johnson and theoretical
studies by H. Nyquist of Bell Laboratories showed that the
mean-squared voltage from a metallic resistor is
Vn2 t   4 R k T B
Therefore when attached to a matched load, RL = R,
the voltage developed across the load is cut in half
(voltage divider) and therefore the mean-squared
voltage is reduced by a factor of 4
Open
circuit
voltage
VL2 t   R L k T B
The power transferred to the matched load is
Pn 
VL2 t 
RL
k T B
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Is it really white noise
Quantum theory shows that the mean square spectral density of
thermal noise is
G v f  
2R h f
e
h f kT
1
V 2 Hz
At “low” frequencies this expression reduces to

hf 


G v f   2 R k T  1 

2
k
T


for
kT
f 
h
For most applications where To  290 K (63 ºF)
[which conveniently simplifies the numerical work as kTo = 4 x 10-21 J]
If the resistance is at To then Gv(f) is essentially constant for
f  0.1k To h  1012 Hz or 1 THz
This conclusion holds even for cryogenic temperatures (T  0.001 To)
7
Equivalent noise temperature
Now replace the noisy resistor with an antenna with
radiometric antenna temperature TA′.
TA′ is the antenna weighted apparent temperature that includes the
self-emission of the lossy antenna.
If the same average power is delivered into the matched
load, then we can relate TA′ to the thermodynamic
temperature T of the resistor.
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Characterization of noise
Now consider the added noise of a linear two-port device
(e.g., amplifier, filter, attenuator, cable).
Input to this device is a signal, Psi, and noise, Pni.
Output from this device is a signal, Pso, and noise, Pno.
The signal-to-noise ratio, SNR, can be determined at the
input as well as the output.
SNR in  Psi Pni
SNR out  Pso Pno
For an ideal component (e.g., ideal amplifier), the input
signal and noise would both be amplified by the same gain
resulting in an SNRout = SNRin.
However noise sources within the component will cause
SNRout < SNRin.
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Characterization of noise
The ratio of SNRin to SNRout is called the noise figure, F.
P P
F  SNR in SNR out  si ni
Pso Pno
Psi Pno 1 G k T0 B  Pno
F

Pso Pni G
k T0 B
Pno
G k T0 B
where T0 is defined to be 290 K.
F  1
Therefore F  1 and is may be expressed in decibels
FdB  10 log 10 F
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Characterization of noise
The noise added by the two-port component, Pno, is
Pno  (F  1) G k T0 B
and the total output noise power, Pno, is
Pno  G k T0 B  (F  1) G k T0 B
Pno  F G k T0 B  F G Pni
The two-port device may be treated as an ideal (noise-free)
device with an external noise source added to the device’s
input.
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Characterization of noise
Alternatively the noise added by the two-port component,
Pno, can be expressed in terms of an equivalent input
noise temperature, TE, such that
Pno  (F  1) G k T0 B  G k TE B
TE  (F  1) T0
Therefore if the noise power input to the device is
characterized in terms of its noise temperature, TI, then the
output noise temperature is TI + TE such that
Pno  G k TI  TE  B
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Characterization of noise
13
Characterization of noise
Example cases
The NEXRAD (WSR-88D) weather radar has an effective
receiver temperature of 450 K.
Therefore its receiver noise figure is F=1+TE/T0
so F = 2.55 or 4 dB.
The SKYLAB RADSCAT radiometer had a 7.1-dB receiver
noise figure.
Therefore its effective receiver temperature was TE  (F  1) T0
where F = 5.1 so that TE = 1200 K.
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Noise of a cascaded system
Now consider a system composed of two components
(systems) in cascade (i.e., connected in series).
Assuming B1 = B2, it can be shown that
F2  1
F  F1 
G1
TE 2
TE  TE1 
G1
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Noise of a cascaded system
So the gain of the first component reduces the impact of
the second component’s noise characteristics on the
overall system’s noise performance.
For a system with N components or subsystems cascaded
FN  1
F2  1 F3  1
F  F1 


G1
G1 G 2
G1 G 2  G N 1
TE  TE1 
T
TEN
TE 2
 E3   
G1 G1 G 2
G1 G 2  G N 1
Clearly if components with “large” gain values are placed
nearest the input, their noise characteristics will determine
the system’s noise characteristics.
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Noise characterization of an attenuator
Next consider an attenuator with a physical temperature Tp
and a loss factor L.
L  1 G  Pin Pout
For L > 1, Pout < Pin.
Examples include a lossy cable, a filter with insertion loss,
or an RF switch.
For L = 1 dB, L =1.26; if L = 1.5 dB, then Pout = 70.8% of Pin
The noise figure, F, of an attenuator is
F  1  (L  1) TP T0
where T0 = 290 K. If TP = T0, then F = L.
Similarly the equivalent temperature is
TE  (L  1) T0
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Noise of a cascaded system
Example
Preamp
Limiter
Amplifier
Given:
Assume B = B = B
T (atten) = T
F1 = 2
G
G = 1/L
G
F
F =L
F
L = 3 dB, F2 = 2
G3 = 30 dB, F3 = 5
Find Fsys for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB
1
P
1
1
2
2
3
0
3
2
3
F2  1 F3  1
Fsys  F1 

G1
G1 L
(a) G1 = 5 dB or 3,
(b) G1 = 10 dB or 10,
(c) G1 = 30 dB or 1000,
Fsys = 2 + (2-1)3 + (5-1)(3/2) = 5
Fsys = 2 + (2-1)10 + (5-1)5 = 2.9
Fsys = 2 + (2-1)1000 + (5-1)500 = 2.01
Therefore, if G1 » L  Fsys  F1
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Noise of a cascaded system
Example
Given:
G
G = 1/L
F
F =L
F1 = 2, TE1 = 290 K
T
T
L = 3 dB, F2 = 2, TE2 = 290 K
G3 = 30 dB, F3 = 5, TE3 = 1160 K
Find TE for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB
1
1
E1
2
2
E2
G3
F3
TE3
Assume B1 = B2 = B3
TP (atten) = T0
TE 3
TE 2
TE  TE1 

G1 G1 L
(a) G1 = 5 dB or 3,
TE = 290 + 2903 + 1160(3/2) = 1160 K
(b) G1 = 10 dB or 10,
TE = 290 + 29010 + 11605 = 551 K
(c) G1 = 30 dB or 1000, TE = 290 + 2901000 + 1160500 = 293 K
Therefore, if G1 » L  TE  TE1
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Equivalent-system noise power
at the antenna terminals
Losses in the antenna (radiation efficiency, l < 1) add
noise to the antenna’s output
TA  l TA  1  l  TP
And transmission-line losses raise the receiver’s equivalent
input noise temperature
  L  1TP  L TREC
TREC
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Equivalent-system noise power
at the antenna terminals
The overall system input noise temperature, TSYS, is
TSYS  l TA  1  l TP  L  1TP  L TREC
Assuming the antenna and transmission line are at the same temperature, TP.
Recall that TA, the desired parameter, must be estimated from
PSYS
PSYS  k TSYS B
Estimation of TA from PSYS requires accuracy and precision
Accuracy: conformity of a measured value to its actual value without bias
Bias: a systematic deviation of a value from a reference value
Precision: ability to produce the same value on repeated independent
observations
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Equivalent-system noise power
at the antenna terminals
Calibration provides a means to achieve the desired accuracy.
A linear transfer function relates Vout to TA′
TA  a Vout  b
Find a and b using two different calibration temperatures, TCAL
thus removing any systematic biases.
Why is Vout  TA′? Isn’t TA′  P instead of V?
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Equivalent-system noise power
at the antenna terminals
Vout is the output of a square-law detector
( )2
Vin
Vout
Vout  Vin2
Vout  Pin
TA  Pin
so
Vout  TA
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Equivalent-system noise power
at the antenna terminals
Precision relates to T, the radiometric resolution which is
the smallest detectable change in TA′.
Determination of T requires an understanding of the
signal’s statistical properties.
Consider the total-power radiometer
Total-power radiometer
block diagram
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Equivalent-system noise power
at the antenna terminals
The total system input noise power is PSYS where
  k TSYS B
PSYS  PA  PREC
and

TSYS  TA  TREC
The average power at the IF amplifier output, PIF, is
PIF  G k TSYS B
PIF
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Equivalent-system noise power
at the antenna terminals
26
Equivalent-system noise power
at the antenna terminals
The instantaneous IF voltage, VIF(t), has the characteristics
of thermal noise, i.e., Gaussian probability distribution and a
zero mean and  standard deviation, while the envelope of
VIF(t) has a Rayleigh distribution
 Ve  Ve2
 2 e

pVe   
0 ,


2 2
, for Ve  0
for Ve  0
For a Rayleigh distribution,
the mean value of Ve2 is
Ve2  2  2
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Equivalent-system noise power
at the antenna terminals
After the square-law detector we have Vd = Cd Ve2 where Cd
is the power-sensitivity constant of the square-law detector
(V W-1) and Vd is the output voltage.
Vd  Cd PIF  Cd G k B TSYS
Vd will have an exponential distribution
1  Vd Vd
pVd  
e
Vd
with the property that the variance of Vd is d, which leads
to d / Vd = 1.
This is significant since the variance is the uncertainty, so
the measured uncertainty = the mean value.
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Equivalent-system noise power
at the antenna terminals
So without additional signal processing, a measured value of
250 K would have an uncertainty of ±250 K! (unacceptable)
To reduce the measurement uncertainty, multiple
independent samples of the signal are averaged.
The low-pass filter which acts as an integrator, performs this
averaging.
Assuming the signal is constant over the averaging interval,
the mean value should remain unchanged while the
variance is reduced.
2
out
d2 1
 2
2
Vout
Vd B 
out

Vout
1
B
Here B is the RF bandwidth and  is the integration time (s)
constant which is related to the low-pass filter’s bandwidth
by BLPF  1/(2 ), Hz.
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Equivalent-system noise power
at the antenna terminals
So the ratio of the measurement uncertainty to the
measured value is
TSYS
1

TSYS
B
and since TSYS = TA′ + TREC′
TSYS 

TA  TREC
B
So the measurement uncertainty due to noise processes,
TN, is
TSYS
TN 
B
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Equivalent-system noise power
at the antenna terminals
Besides uncertainties due to noise processes, variations in
the receiver gain will also introduce measurement
uncertainty, TG.
Since Vd = CdG k B TSYS, variations in G will cause
variations in the detected signal, Vd.
The uncertainty resulting from gain variations is
TG  TSYS G S GS 
where GS is the average system power gain and GS is the
RMS variation of the power gain.
The magnitude of GS can be reduced (though not to 0) by
periodically calibrating the radiometer output voltage when
inputting a known noise source.
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Equivalent-system noise power
at the antenna terminals
The combination of these two uncertainty terms, TN and
TG , produce an total uncertainty, T through a root-sumsquare (RSS) process
T 
TN 2  TG 2
or
T  TSYS
1  G S 

 
B   GS 
2
32
Equivalent-system noise power
at the antenna terminals
Example
Radiometer center frequency, f = 1.4 GHz
Bandwidth, B = 100 MHz
Receiver noise temperature, TREC′ = 600 K (F = 3 or 4.9 dB)
Antenna temperature, TA′ = 300 K
Low-pass filter bandwidth, BLPF = 50 Hz ( = 10 ms)
System gain, GS = 50 dB ± 0.044 dB over 10 ms interval
Find T and determine which factor (noise or gain variation)
dominates.
33
Equivalent-system noise power
at the antenna terminals
Example (cont.)
Find TN: TSYS = TREC′ + TA ′ = 600 + 300 = 900 K
TN = TSYS (B )- ½ = 900 (108 ·10-2)- ½ = 0.9 K
Find TG: GS = 50 dB or 100,000
GS + GS = 50.044 dB or 101,018
GS  GS = 49.956 dB or 98,992
so |GS|  1013
GS / GS = 1013/100,000 = 1%
TG = TSYS (GS / GS) = 9 K
T = [TN2 + TG2] ½ = [(0.9)2 + (9)2]½ = 9.05 K
34
Equivalent-system noise power
at the antenna terminals
Example (cont.)
T = 9.05 K and is dominated by TG (9K)
To reduce the affect of TG so that it is comparable to TN
requires that GS/GS = 0.001 or G = 100
so that GS = 100,000 ± 100
or GS = 50 dB ± 0.004 dB over a 10 ms interval
A study of GS properties shows the following:
GS varies as 1/f
for f  1 kHz, GS  0
worst for f < 1 Hz
Therefore we want  < 1 ms to make TG small.
However to make TN small we want  > 1 ms.
35
Dicke radiometer
The Dicke radiometer solves the dilemma concerning .
Synchronous switching and detection permits
fs > 1 kHz with  » 1 ms
36
Dicke radiometer
The Dicke radiometer alternates between two
configurations, one where it samples the TA′ and the other
where it samples a reference load, TREF.
When the switch connects the antenna to the receiver
 ,
Vd ANT  C d G k B TA  TREC
for 0  t  S 2
When the switch connects the reference load to the receiver
 ,
Vd REF  C d G k B TREF  TREC
for S 2  t  S
These are combined in the synchronous detector to form
1
The ½ term is due to the dwell
Vd SYN 
Vd ANT  Vd REF
time in each switch position
2

Vd SYN 

1
Cd G k B TA  TREF 
2
Notice that TREC′ cancels out
37
Dicke radiometer
VSYN is integrated in the low-pass filter to yield VOUT
VOUT
1
 G S TA  TREF 
2
where GS is a constant representing the radiometer’s
transfer characteristics.
The low-pass filter not only integrates the signal but also
rejects the components at fs and its harmonics that are
introduced by the square-wave modulation.
This requires that fs  2 BLPF.
Under these conditions VOUT  (TA′ – TREF) and is
independent of TREC′.
38
Dicke radiometer
To evaluate the Dicke radiometer’s sensitivity T begin with
VOUT
1
   TREF  TREC
 
 G S TA  TREC
2
Three components contribute to T
Gain variations
TG  TA  TREF  GS GS
Noise uncertainty in TA′
 
2 TA  TREC
TN ANT 
B
Noise uncertainty in TREF
So that
T 
TN REF
 
2 TREF  TREC

B
TG  2  TN ANT 2  TN REF 2
39
Dicke radiometer
Now it might appear that we’re no better off than we were
with the total-power radiometer (and maybe worse off with
3 terms comprising T now)
T 
TG  2  TN ANT 2  TN REF 2
However notice the difference in TG
total power
  GS GS
TG  TA  TREC
Dicke
TG  TA  TREF  GS GS
In the Dicke radiometer this term (which dominated T in
the total-power radiometer) is significantly smaller.
40
Dicke radiometer
Example
Bandwidth, B = 100 MHz
Low-pass filter bandwidth, BLPF = 0.5 Hz ( = 1 s)
Receiver noise temperature, TREC′ = 700 K (F = 3.4 or 5.3 dB)
Reference temperature, TREF = 300 K
System gain variations, GS/ GS = 1%
When viewing a 0-K target (TA′ ~ 0 K)
T (total-power) = 7.0 K
T (Dicke) = 3.0 K
[TG = 7.0 K, TN ANT = 0.07 K]
[TG = 3.0 K, TN ANT = 0.1 K, TN REF = 0.14 K]
When viewing a 300-K target (TA′ ~ 300 K)
T (total-power) = 10.0 K
T (Dicke) = 0.2 K
[TG = 10.0 K, TN ANT = 0.1 K]
[TG = 0.0 K, TN ANT = 0.14 K, TN REF = 0.14 K]
(Note that TREF – TA′ = 0, a balanced condition)
41
Balanced Dicke radiometer
Operating in a balanced mode requires adjusting TREF.
Using a “cold” noise source and a variable attenuator (TP = 290 K)
permits balanced mode operation for a wide range of targets.
42
Radiometer calibration
As mentioned earlier calibration is needed for accurate
measurements.
For ground-based systems warm calibration targets are
abundant so the cold target calibration poses a challenge.
Shown here is a cryoload
that is useful for periodic
calibration of modestsized antennas.
When filled with liquid
nitrogen this cold target has
a radiometric temperature of
around 77 K.
43
Radiometer calibration
Another approach that may accommodate modest-sized as
well as medium sized antennas is the bucket method that
uses the naturally cold sky as a cold target.
As seen previously, TSKY is dependent on the operating
frequency and on the weather conditions.
For clear-sky conditions the zenith
sky temperature will range
between about 5 and 120 K.
Using this calibration
technique the antenna
efficiency, l, can be
estimated.
44
Radiometer calibration
Calibration of spaceborne radiometer systems requires
features that enable periodic calibration during flight.
45
Scanning Multichannel Microwave Radiometer (SMMR)
Flew on two platforms
SEASAT (28 June 1978 to 10 October 1978)
NIMBUS-7 (26 October 1978 to 20 August 1987)
Intended to obtain ocean circulation parameters
such as sea surface temperatures, low altitude
winds, water vapor and cloud liquid water content
on an all-weather basis.
Ten channels: five frequencies, dual polarized
Mechanically scanned antenna
46
Scanning Multichannel Microwave Radiometer (SMMR)
47
Scanning Multichannel Microwave Radiometer (SMMR)
Antenna system
• Shared 79-cm diameter offset parabolic reflector used by all channels
• Mechanical scanning, 42 off-nadir look angle, ±25 azimuth angle range,
scan period 4.096 s
• Provided constant 50.3 incidence angle across 780-km swath
Offset-fed parabolic reflector geometry
48
Scanning Multichannel Microwave Radiometer (SMMR)
Antenna scan characteristics
49
Radiometer antennas
Antennas pose a challenge in some radiometer applications.
Spatial resolution (x, y) is set by the antenna beamwidth.
Consider an antenna with L  20  or  = 3.
A spot diameter at nadir of 520 m
results at aircraft altitudes (10 km).
At spacecraft altitudes (700 km)
a spot diameter at nadir of 37 km
is produced.
To achieve a finer resolution
requires a smaller beamwidth,
i.e., a larger antenna.
In addition, mechanical beamsteering limits the scan rate and
reliability.
50
Synthetic-aperture radiometers
From antenna array theory we know that arraying separate
apertures produces a radiation pattern that is the product of
the pattern of the individual element and the array pattern.
However grating lobes result from large element spacings.
Tapers (weighting functions) are used for sidelobe
suppression.
51
Synthetic-aperture radiometers
The underlying idea of the synthetic-aperture radiometer is
that with an array of receiving elements, multiple beams
can be formed simultaneously to image a swath.
This is accomplished by cross-correlated signals from a
pair of antennas with overlapping fields of view.
From Ruf CS; Swift CT; Tanner AB; LeVine DM; “Interferometric aperture synthesis,”
IEEE Trans. Geoscience and Remote Sensing, 26(5), pp 597-611, 1988.
The approximate null-to-null beamwidth () is
  2 D , radians
Where D is the maximum antenna spacing.
52
Synthetic-aperture radiometers
The Electronically Steered
Thinned Array Radiometer
(ESTAR) is a hybrid which
uses real aperture for alongtrack resolution and
aperture synthesis for crosstrack resolution.
From Elachi C; van Zyl J; Introduction to the physics and techniques of remote sensing, Wiley, 2006.
53
Synthetic-aperture radiometers
HYDROSTAR concept
For mapping soil moisture and sea salinity
54
Synthetic-aperture radiometers
SMOS concept (Soil Moisture and Ocean Salinity)
Aperture synthesis in two dimensions
55
SMOS satellite
SMOS satellite
– 1,451-pound, $464M
– launched on 1 Nov 2009
– altitude of 465 miles to 476 miles
– inclination of 98.4°
SMOS carries as the L-band MIRAS radiometer
that uses a Y-shaped antenna resembling the
rotors of a helicopter, is a first-of-a-kind payload
comprising 69 individual antennas strung together
in an inferometer-like array to maximize the
sensor's sensitivity.
A Rockot launch vehicle blasts
off on Nov. 1, 2009 with the
Europe's Proba 2 and Soil
Moisture Observation Satellite
(SMOS) from the Plesetsk
Cosmodrome in northern
Russia.
56
MIRAS radiometer
3-year mission is to investigate Earth's water cycle
– measures soil moisture, 4% accuracy, 30-mile resolution
– measures ocean salt concentration, 120-mile resolution
Soil moisture is a key factor in determining humidity in the atmosphere
and the formation of precipitation. These data will also aid researchers
studying plant growth and vegetation distributions.
Ocean salinity maps reveal
how the atmosphere and
oceans interact by providing
new insights on ocean
circulation, a major driver of
world climate.
An artist's concept of the Soil and
Moisture Observation Satellite
(SMOS) satellite with deployed solar
arrays and instrument
57
MIRAS radiometer
The MIRAS radiometer operates in the L-band of the electromagnetic
spectrum in a band (1400-1427 MHz) reserved (by the International
Telecommunications Union) for space research, radio astronomy and a
radio communication service between Earth stations and space, known
as the Earth Exploration Satellite Service.
Since its 2009 launch and system check out, project scientists noticed
that over certain areas the MIRAS radiometer data were badly
contaminated by radio-frequency interference (RFI).
The unwanted signals have mainly come from TV transmitters, radio links
and networks such as security systems. Terrestrial radars appear to also
cause some problems.
SMOS data revealed that there were many instances of other signals
within this protected band, particularly in southern Europe, Asia, the
Middle East and some coastal zones.
58
MIRAS radiometer data
Google Earth image
March 2010 SMOS image from, over Spain showing
contamination by unwanted transmissions from
various radio systems.
59
MIRAS radiometer data
Google Earth image
July 2010 image following cooperation between ESA
and the National Spectrum Authority, SMOS data
over Spain showing far less RFI contamination.
60
RFI mitigation in radiometers
In their paper [1] “RFI detection and mitigation for microwave radiometry
with an agile digital detector,” the authors state that:
– A new type of radiometer has been developed that incorporates an “agile
digital detector” (ADD)
– This radiometer is capable of identifying high and low levels of radio
frequency interference (RFI)
– The effects of this RFI on measured brightness temperature can be reduced
or eliminated
High-level RFI has a high SNR and a narrow bandwidth
• communication source
Low-level RFI has a low SNR and a broad bandwidth or is persistent
• radar
The agile digital detector exploits
– Difference of signal probability density function (pdf)
• noise  Gaussian pdf, sinusoid  non-Gaussian pdf
– Spectrally localized RFI
[1[ Ruf CS; Gross SM; Misra S; “RFI detection and mitigation for microwave radiometry with an agile digital detector,” IEEE Transactions on
Geoscience and Remote Sensing, 44 (3), pp. 694-706, 2006.
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RFI mitigation in radiometers
Signal pdf analysis
– Conventional radiometers use analog square-law detector  2nd moment
– With a digitized waveform the 2nd moment can be computed thus replicating
conventional signal processing;
but it can also compute the higher-order moments, e.g., 4th moment
– The ratio between the 4th moment and the 2nd moment is stable for Gaussian
signals and “quite responsive to low-level RFI
– Subbands filtering allows isolation of subband containing RFI
– Channel crosscorrellation is possible permitting cross-polarization analysis
62
RFI mitigation in radiometers
Functional block diagram of ADD signal processor
63
RFI mitigation in radiometers
ADD filter bank characteristics
Predicted transfer function of ADD filter banks using a
Kaiser  = 3.2 window with 47 taps and nine-bit signed
coefficients.
64
RFI mitigation in radiometers
Sample ADD
measurement of the pdf
of the signal entering the
radiometer while viewing
a continuous sine wave
at 1412 MHz (centered on
subband #4) added to
background radiometric
emission with the
antenna pointed toward
cold sky. The pdf is
shown for four of the
eight frequency
subbands.
ADD measurements
over 1 min of the
continuous sine wave
plus background cold
sky scene as above.
Brightness temperature
is shown versus time for
four of the eight
frequency subbands.
The RFI is centered in
subband #4, which
exhibits a brightness
temperature of ~2000 K.
Subband #3 has 50–60K levels of RFI due to
the out-of-band rejection
limitations of their
filters. Subbands #1–2
are essentially RFI free.
65
RFI mitigation in radiometers
ADD measurements as before. The normalized ratio between the fourth moment and the square of the second moment of the signal
is shown for four of the eight frequency subbands.
A normalized ratio of unity indicates that the signal has a Gaussian distributed amplitude consistent with natural thermal emission.
The ratio for subband #4 is approximately 0.6 due to the strong sine wave present.
Subband #3 also has small nonunity ratios as a result of the RFI. The other subbands are RFI free.
Note the scale change for subbands #3–4.
66