International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
SNR Performance of a Multi-channel Microwave
Radiometer with Digital Integration
Nisha Jain1, Archana Sharma3
Department of Electronics and Communications
Radharaman Institute of Technology and Science
Bhopal, India
Abstract— Conventional analog microwave receivers consist of
amplifiers, filters and down-converters (IQ demodulators) to
convert the analog signals to base-band frequencies. This
processing philosophy works well for a single or dual channel
system where the number of analog channels or receivers is
limited. In a multi-channel radiometer it is highly impractical to
implement an analog receiver consisting of IQ demodulator for
each channel owing to unmanageable mass, power and volume
associated with these demodulators. The most viable option is the
digital receiver. The digital integration and control module of the
digital receiver carries out the functions of analog processing of
the received video signals, digitization of the video signals and
integrating the digitized video signals using digital domain
approach. In this paper, an analytical and simulation model of
digital integrators has been developed to compare their
frequency response and to arrive at optimum averaging factors
for the digital integration of different channels of a multi-channel
radiometer. Simulation results showed that performance of
digital integrator is much better than analog integrator over
wide frequency band. This paper discusses the developed models
for signal integration and signal-to-noise ratio (SNR)
performance of a multi-channel microwave radiometer due to
digital integration of optimized averaging factors.
Keywords— microwave radiometer, digital integrator, signal-tonoise ratio, IQ demodulator.
I. INTRODUCTION
A microwave radiometer, onboard a spacecraft, measures
the energy of atmospheric and terrestrial radiations at submillimeter to centimeter wavelengths. By understanding the
physical processes associated with energy emission at these
wavelengths, scientists can calculate a variety of surface and
atmospheric parameters from these measurements, including
air temperature, sea surface temperature, salinity, soil
moisture, sea ice, precipitation, the total amount of water
vapor and the total amount of liquid water in the atmospheric
column directly above or below the instrument. Development
of ultra-high resolution microwave radiometers involves
challenges like implementation of high bandwidth receiver
section. Conventionally an analog microwave receiver,
consisting of amplifiers, filters and down-converters (IQ
demodulators), is used to convert the analog signals to baseband frequencies. Conversion of these analog signals to digital
samples is done at base-band by analog-to-digital (A/D)
converters and further digital processing is done at lower
ISSN: 2231-5381
frequency. However, it is highly impractical to implement
such an analog receiver consisting of IQ demodulators for
each channel for a multi-channel radiometer owing to
unmanageable mass, power and volume. The most viable
option for a multi-channel radiometer is the digital receiver.
Digital implementation of receiver offers advantages like
programmability, high accuracy, better stability, repeatability
etc. Most efficient utilization of on-board resources and better
SNR requirements puts constraints on digital receiver
integration factors. Robust digital integrator design requires
optimization of averaging factors. The signal integration and
dump process required in a total power microwave radiometer
can be implemented using analog or digital means. Digital
processing offers advantages like programmability, accuracy,
better stability, repeatability etc ([1], [2]).
The digital implementation of integrate and dump filter
requires the input signal to be sampled. To eliminate aliasing,
the input signal is filtered using an anti-aliasing low pass prefilter prior to sampling. This band limiting of input signal
causes inter symbol interference which degrades the
performance of the receiver. In this paper, performance of an
analog integrator is compared with a digital integrator with
different bandwidths for a multi-channel microwave
radiometer. Models are developed to optimize averaging
factors for best signal-to-noise ratio of the designed digital
integrate and dump filter.
II. ANALOG AND DIGITAL INTEGRATOR DESIGN
Integrate and dump filter of a microwave radiometer can be
designed using both analog and digital means. For a scanning
radiometer, the dwell times (integration times) for the various
channels are computed by taking into account the nominal
values for the orbital height, scan rate, foot print size etc. The
proposed integrator is designed for a three channel microwave
radiometer having following integration times:
Channel - 1
Channel - 2
Channel - 3
:
:
:
8 ms
2 ms
1 ms
A. Analog integrator
An analog integrator can be designed using an operational
amplifier. Basic integrator circuit using an operational
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
amplifier is shown in Fig.1 below and the corresponding
equation of the circuit is given in (1).
Magnitude: -20dB/decade
Phase: 90° phase shift for all frequencies
This filter is easy to implement in a digital signal processor.
III. DIGITAL FILTER PERFORMANCE ANALYSIS
Fig. 1 An Analog Integrator using Op-Amp.
V
(t) = −
∫ V (t)dt
(1)
Simulations in MATLAB are carried out to determine the
frequency response of above analog filter for different
channels of radiometer with 8ms, 2ms and 1ms integration
times. Simulation results are tabulated in Table 1 below.
TABLE I
ANALOG FILTERS FREQUENCY RESPONSE
Channel
1
2
3
Integration Time / RC
Filter Time Constant (ms)
8
2
1
-3dB
Frequency (Hz)
20
80
160
Even though the integrator circuit may be realized using
above op-amp circuit, it has some inherent disadvantages like
high offset error, inherent leakage currents and temperature
drift which causes variations in op-amp output over long
period of operation.
A. Sum and Dump Algorithm
The digital filter is designed primarily to provide the
necessary dynamic loop behaviour for optimum control of the
noise injection process. The concept used to reduce the
variance of the data in the post loop processor is well known
sample mean algorithm. This process will hereafter be
denoted as a “sum- and- dump” algorithm due to its close
similarity to the integrated and dump circuit used in analog
matched filter and estimation system. Indeed mathematically
the behaviour of the sum and dump algorithm on a discrete
time basis is virtually identical to the behaviour of the
integrated and dump filter on a continuous time basis [3].
The steady state frequency response of a discrete time sum
and dump filter, denoted as HN(f), is given in (3):
(
H (f) = / )
(
/ )
e
(
)
/
(3)
The equivalent one-sided noise bandwidth BN can be
expressed as
B = ∫
. [H (f)] df
(4)
where, fos = 1 / To
Due to these disadvantages an analog integrator is not
preferable. Further an analog integrator is impractical for a
multi-channel radiometer due to high power, mass and volume.
A digital “equivalent”
implementation
offers
some
advantages over analog circuitry including the ability to be
dumped in an extremely short time with no overshoot
freedom from drift, and the use of digital ICs or a computer
for processing.
B. Digital integrator
Integration in time domain is equivalent to a filter in
frequency domain. The time domain equation of an analog
integrator and its equivalent in frequency domain are shown
(2):
V
(t) = −
∫ V (t)dt
Time Domain
V
=−
(2)
Frequency Domain
The frequency domain equation represents a filter with
following specifications:
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Substituting HN(f) from (3), the value of this integral is
B =
[
=
]
(5)
(6)
Let  = NTo = total time interval for averaging.
Substituting these values of  in (6), the one sided equivalent
noise bandwidth is:
B = (7)
This result is exactly the same as for the continuous time
integrate and dump filter with  as the integration time. Thus,
the sum and dump algorithm for a discrete time signal
functions exactly the same as the integrate and dump filter for
a continuous time signal provided that the summation interval
in the discrete time case is equal to the integration interval in
the continuous time case. This would imply optimum
sampling at the Nyquist rate for the discrete time system [4].
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
B. Implementation of sum and dump algorithm
The digital implementation inherently requires that the
input waveform be sampled and “folding” of the noise
spectrum will greatly reduce the filter effectiveness unless
a low-pass pre-filter is used to limit the input bandwidth
[5].
The front-end receiver output in radiometer has a low pass
filter with the following characteristics: 5 KHz cut off (-3 dB)
and 20 dB / decade roll off. Block schematic of digital
implementation of integrate and dump filter is shown in Fig.2.
Low Pass
Filter
Sampler &
Quantiser
Fc = 5KHz
Decimator
N
FIR Filter
Length N
Min. Fs = 10KHz
N = 128/64/16/8
Fig. 2 Digital implementation of Integrate and Dump Filter
The output of the low pass filter is first sampled, digitized
and then integrated with a FIR digital filter. The output of this
filter is appropriately down sampled (decimated) after the
filtering operation depending on the integration time
requirement of that particular channel.
C. Digital filter frequency response
This chain was simulated using MATLAB to arrive at
optimum averaging factors for different channels of the
radiometer. The transfer function used for simulating digital
integrator is given in (8).
( ) = ∑
( )
(8)
where, N = number of samples integrated,
Simulation results are tabulated in Table 2 below.
TABLE III
DIGITAL FILTERS FREQUENCY RESPONSE
Channel
1
Integration
Time (ms)
No. of Samples
Integrated (N)
8
2
2
3
1
128
64
32
16
128
64
32
16
128
64
32
16
Sampling
Rate
(KHz)
16
8
4
2
64
32
16
8
128
64
32
16
-3dB
Freq
(Hz)
55
110
219
429
221
440
876
1716
441
880
1752
3432
Overall comparison of frequency response of simulated
analog and digital filters for all the channels of radiometer is
shown in Table 3 below.
TABLE IIIII
ANALOG AND D IGITAL FILTERS FREQUENCY COMPARISON
Analog
Digital Filter
Filter
Bandwidth
Channel -3dB
Improvement
No. of
Freq
-3dB Freq
(B/A)
Samples
(Hz)
(Hz) (B)
Integrated
(A)
128
55
2.75
64
110
5.50
1
20
32
219
10.95
16
429
21.45
128
221
2.75
64
440
5.50
2
80
32
876
10.95
16
1716
21.45
128
441
2.75
64
880
5.50
3
160
32
1752
10.95
16
3432
21.45
From Table 3 it is observed that the -3dB cut-off frequency
for each digital filter is much higher than the corresponding
analog filter for the respective channels. Signal bandwidth due
to digital integration for all the channels improves by 2.75
times to 21.45 times over the analog filter bandwidth for
different integration factors. Hence, the performance of digital
filters is better than analog filter.
Also among the digital filters with in a channel, it is
observed that the bandwidth reduces with increase in number
of samples for integration. Bandwidth of digital filter with 16
samples is 7.8 times better than bandwidth of digital filter
with 128 samples. Hence, a digital filter with 16 samples for
integration is better than a digital filter with higher samples
for integration.
IV. DETERMINATION OF OPTIMUM AVERAGING FACTORS FOR
DIGITAL INTEGRATION AND SNR IMPROVEMENT
As already explained in section – III B, the front-end
receiver output radiometer has a low pass filter with 5 KHz
cut-off frequency to limit the input bandwidth. According to
Nyquist criterion i.e. (fs ≥ 2 BW), the minimum sampling rate
can be 10 KHz. Considering the sampling rates available for
different integration factors for different channels following
conclusions are made:
• 2 KHz, 4 KHz and 8 KHz sampling rates cannot be used
for channel-1.
• 8 KHz sampling rate cannot be used for channel-2.
D. Comparison of analog and digital filters response
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013
Channel-3 has all sampling rates above the Nyquist
sampling rate of 10 KHz and hence all sampling rates can
be used.
Hence, the minimum sampling rate for all the channels is
16 KHz and the optimum averaging factors corresponding to
16 KHz sampling rate for different channels are given in
Table 4 below.
TABLE IVV
OPTIMUM AVERAGING FACTORS FOR DIGITAL INTEGRATION
Acceptable
sampling
Channel
rates
(fs > 10 KHz)
(KHz)
1
16
2
16, 32, 64
3
16, 32, 64, 128
Minimum
acceptable
sampling rate
for all
channels
Optimum
Averaging
Factors
(corresponding
to 16 KHz)
16 KHz
Digital Receiver SNR (Proposed Work)
300
250
200
150
100
50
0
18.7 GHz
V. CONCLUSIONS
The digital integration and control module of a microwave
radiometer carries out the functions of analog processing of
the received video signals, digitization of the video signals
and integrating the digitized video signals using digital
domain approach. An analytical and simulation model of
analog and digital integrators has been developed to compare
their frequency response and to arrive at optimum averaging
factors for the digital integration of different channels of a
multi-channel radiometer. Simulation results showed that
performance of digital integrator is much better than analog
integrator over wide frequency band. Signal bandwidth
improvement due to digital integration of samples. Signal-tonoise ratio of digital integrator is much better than its analog
counterpart.
Analog Receiver SNR
141
107
141
ACKNOWLEDGMENT
Authors would like to acknowledge the help rendered by all
scientists / engineers of Space Applications Centre, ISRO,
Ahmedabad and Director, RITS, Bhopal for his
encouragement and guidance during various phases of the
project.
REFERENCES
SNR of digital receiver for three low frequency channels of
MADRAS radiometer with optimized averaging factors is
calculated using (9) and the results are shown in Table 6
below.
[2]
[3]
TABLE VI
DIGITAL RECEIVER SNR
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[4]
Bandwidth
Improvement
2.75
2.75
2.75
36.5 GHz
16
[1]
Analog Bandwidth (Hz)
Receiver Analog Digital
SNR
Filter
Filter
18.7GHz
141
20
55
23.8GHz
107
20
55
36.5GHz
141
20
55
23.8 GHz
Fig. 3 Analog and digital receiver SNR comparison
TABLE V
ANALOG RECEIVER SNR
Channel
Analog Receiver SNR (Previous Work)
350
32
(9)
An analog receiver is already designed by French Space
Agency (CNES) for three low frequency channels (18.7 GHz,
23.8 GHz and 36.5 GHz) of MADRAS microwave radiometer
and SNR performance of these three channels for analog
receiver as reported in literature is given in Table 5 below [6].
18.7 GHz
23.8 GHz
36.5 GHz
400
Channel
Digital receiver SNR = Analog receiver SNR X Improvement factor
Integration Time
(ms)
8
8
8
SNR Comparison
450
128
Signal bandwidth improvement due to digital integration of
samples is already established in section – III D and the
improvement factors for different channels with different
integration factors is give in Table 3. Signal-to-noise ratio
(SNR) for digital receiver due to digital integration of
optimized averaging factors can be calculated using (9).
Channel
SNR comparison of analog and digital receivers of a three
channel microwave radiometer is shown in Fig.3 below.
Signal to Noise Ratio
•
Digital
Receiver
SNR
388
294
388
[5]
[6]
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Astronautical Congress), Daejeon, Korea, Oct. 12-16, 2009.
F. D. Natali, “ Comparison of Analog and Digital Integrate-and-Dump
Filters,” Proc. IEEE, Vol. 57, pp. 1766 – 1768, October 1969
William D. Stanley, “Preliminary Development of Digital Signal
Processing in Microwave Radiometer,” NASA CR-3327, September
1980.
N. Papamarkos and C. Chamzas, “A new approach for the design of
digital integrators,” IEEE Trans. Circuits Syst. I, Fundam. Theory
Appl., vol. 43, no. 9, pp. 785–791, Sep. 1996.
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Microwave radiometer,” IEEE MicroRad 2006, pp. 60-65
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