ITIT-11

Estimation of Self-Clutter for HF Ionospheric Radars
that Employ the Multi-Pulse Technique
A. S. Reimer and G. C. Hussey
Institute for Space and Atmospheric Studies, University of Saskatchewan
Generalized Estimation of Self-Clutter
The Multiple-Pulse Technique
Some ionospheric radars, such as the Super Dual Auroral Radar Network (SuperDARN) radars, take
advantage of long-distance multi-hop propagation that is possible in the high-frequency (HF) band
(Greenwald et al., 1995). The multi-pulse technique is used to overcome range–Doppler ambiguities
characteristic of overspread ionospheric targets (long range: > 1000 km; high velocity: ∼ 1 km/s) at the
expense of introducing self-clutter. Farley (1972) first discussed estimating this self-clutter for incoherent
scatter radars assuming uniform scattering. The present study discusses a generalized algorithm
for more accurately estimating self-clutter by utilizing measurements of echo power,
allowing for an improved estimate of the mean square error in the radar observations.
Generally, ionospheric radars measure echo power as a function of range. The self-clutter can be estimated using the voltage samples from the echo power measurements. Sometimes, the voltage
samples are not kept (large amount of storage required) so only the power profile is available when retroactively processing raw data. In this case, an upper-bound of self-clutter may still be estimated (see the following
equations). Following the discussion in the preceding section “Illustrating the ACF”, the generalized estimate for self-clutter was derived by using the sum of terms in the sample correlations
that include interfering ranges. In general when two samples are correlated, there will be N interfering ranges in one of the samples and M interfering ranges in the other sample.
Using voltage samples, the multiple-pulse self-clutter can be estimated as
p
C=
PR
p
p p
p
N
M
N
M
Σi=1 Pi ρR,i + Σj=1 Pj ρR,j + Σi=1Σj=1 Pi Pj ρi,j ,
(2)
where P is the echo power (square of the magnitude of voltages) with subscripts indicating origin of the power. Subscript R indicates the range of interest (red diamonds, Figure 1). Subscripts i and j indicate
interfering ranges (black diamonds, Figure 1) with Pi being the ith interfering power from N interfering ranges and with Pj being the jth interfering power from M interfering ranges. ρ is the normalized correlation
between echo powers.
Pulse Table: [0, 14, 22, 24, 27, 31, 42, 43], Gate: 75
2000
15000
Knowing only the power at each range (only magnitude of voltage is known, no phase information), one cannot calculate ρ. To be conservative, we set ρ = 1 to obtain the upper estimate of the self-clutter,
p
p p
p p N
M
N
M
C = PR Σi=1 Pi + Σj=1 Pj + Σi=1Σj=1 Pi Pj .
5000
4
5
0
0
6
10
20
Lag, τ
30
40
Using the estimate for self-clutter from Equation 3, the average signal-to-clutter ratio was calculated for 1 hour of raw data from the Saskatoon SuperDARN radar. The self-clutter tends to decrease for increasing τ .
50
Figure 1: Left: An example of a multiple-pulse sequence using 3 pulses. The grey filled rectangles indicate transmission pulses and the rectangles
with blue borders indicate received samples. The red diamonds indicate signal backscattered from a repeated range of interest, in contrast to the
black diamonds indicating signal backscattered from non-repeated unwanted ranges. Right: The 8 pulse “katscan” multiple-pulse sequence typically
in use on SuperDARN radars with τ = 1.8 ms, tp = 300 µs, Np = 8, and ptab = [0,14,22,24,27,31,42,43] (see text for definitions).
pwr0
(dB)
Lag Number
A multiple-pulse sequence can be identified by 4 characteristics: the pulse length (tp ), the pulse repetition
time or lag time (PRT or τ ), the number of pulses transmitted (Np ), and the pulse table (ptab). Pulse
spacings in multiple-pulse sequences are non-redundant and integer multiples of τ . The multiple-pulse
sequence in Figure 1 (Left) was made using τ = 2.4 ms, tp = 300 µs, Np = 3, and ptab = [0,1,3]. The
three possible pairs of pulses give three samples of the autocorrelation function (ACF) obtained using
correlations between the received signals from pulse pairs. It is clear from Figure 1 that each sample
contains signals from both the range of interest (red diamonds) and unwanted ranges (black diamonds).
The signal from unwanted ranges is referred to as self-clutter. Self-clutter is pulse
sequence–dependent as seen by comparing the left and right plots in Figure 1.
Previously Farley (1972) discussed estimating the self-clutter introduced by the multiple-pulse technique for
incoherent scatter radars. He assumed uniform scattering and that all pulses are transmitted before any
signal is received. The estimate was given as
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14
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12
11
10
9
8
7
6
5
4
3
2
1
30
20
10
0
Average SCR τ = 1.8 ms 01 Dec, 2013 Saskatoon
20
16
12
8
4
0
−4
−8
−12
−16
−20
10
20
30
40
Range Gate
50
60
70
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
30
20
10
0
Average SCR τ = 2.4 ms 01 Dec, 2013 Saskatoon
20
16
12
8
4
0
−4
−8
−12
−16
−20
10
20
30
40
Range Gate
50
60
70
24
23
22
21
20
19
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17
16
15
14
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11
10
9
8
7
6
5
4
3
2
1
30
20
10
0
Average SCR τ = 3.0 ms 01 Dec, 2013 Saskatoon
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16
12
8
4
0
−4
SCR (dB)
3
Lag, τ
Lag Number
2
pwr0
(dB)
1
SCR (dB)
0
0
(3)
Self-Clutter Estimation from Data
Lag Number
500
pwr0
(dB)
1000
10000
SCR (dB)
Range (km)
Range (km)
1500
−8
−12
−16
−20
10
20
30
40
Range Gate
50
60
70
Figure 3: Plots of the signal-to-clutter ratio (SCR) calculated using the “katscan” multiple-pulse sequence with τ = Left: 1.8 ms, Middle: 2.4 ms, Right: 3.0 ms. Red indicates a large SCR (better) and blue indicates a small SCR (poor).
(1)
pwr0
(dB)
The generalized estimate is blind to ranges not covered by echo power measurements. If echo power is not
measured to sufficiently large ranges, the generalized estimate will fail to include potentially large
contributions of self-clutter from long-range echoes.
Illustrating the ACF: SuperDARN
Ionospheric radars measure the autocorrelation function (ACF) of a plasma target and
extract plasma parameters from it. Received signals are binned in range bins referred to as range
gates. The ACF at time t is the correlation between two signal samples separated by time t. For Figure 1
(Left), the ACF at time t = 2τ is the correlation between 4τ and 6τ , the sum of 9 correlations: 1 between
the signals from the range of interest, 4 between the interfering ranges and the range of interest, and 4
between the interfering ranges.
Figure 2 shows a typical ACF measured by a SuperDARN radar using an 8 pulse multiple-pulse sequence.
Each complex value of the ACF is calculated from a pair of pulses and plotted as a function of the
separation between the pulses (multiples of the pulse repetition time, τ ).
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
20
30
40
Range Gate
50
60
70
05 Jan, 2014 13:30:00 UT
ACF
0.0
0.3
0.2
0.1
0.0
10
20
30
10
5
−0.5
−1.0
5
10
15
Lag Number
20
−4000−2000 0 2000 4000
Velocity (m/s)
40
Range Gate
50
60
70
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
20
30
40
Range Gate
50
60
70
3
2
1
0
−1
−2
−3
1.2
1.0
0.8
0.6
0.4
0.2
0
5
10
15
Lag Number
20
0
5
10
15
Lag Number
Future Work
I
I
I
I
Checking self-clutter estimates against radar data simulator
Implementing weighted least-squares fitting using errorbars to extract plasma parameters
Running experiments to test the voltage-based estimate given by Equation 2
Prototyping voltage-based estimate in day-to-day radar operation
0
Phase
0.0
Lag Power
ACF
0.5
Acknowledgements
The author is grateful to these institutes and granting agencies: Institute for Space and Atmospheric Studies at the University of Saskatchewan, Natural Sciences and
Engineering Research Council of Canada (NSERC CGS-D3), Canadian Space Agency, and the Canada Foundation for Innovation. The author is grateful to Matthew
Wessel for his constructive editing advice.
20
Figure 5: Plots of the ACF, power spectrum, ACF power, and ACF phase. The error bars for the ACF were calculated using Equation 4 and
propagated to ACF power and ACF phase.
I
I
I
Institute of Space and Atmospheric Studies, University of Saskatchewan
0.4
15
0
For example, the real and imaginary values of the ACF measured at t = 10τ (lag number 10) were
obtained by correlating samples of received signal separated by a time of t = 10τ . In Figure 1 (Right), the
ACF at t = 10τ for range gate 75 is obtained from the second and fourth samples (blue markers).
0.5
20
−1.0
Figure 2: An ACF measured by the Clyde River SuperDARN radar using the 8 pulse “katscan” pulse sequence. The real and imaginary parts of the
ACF function are indicated by blue and green curves, respectively. The period of oscillation is proportional to the Doppler shift imposed by a moving
plasma target.
0.6
Clyde River Beam: 15 Gate: 1825
0.5
1.0
20
0.7
There are now error estimates for measured data from SuperDARN radars.
−0.5
10
15
Lag Number
0.8
1.0
Results and Conclusions
05 Jan, 2014 13:30:00 UTClyde River Beam: 15 Gate: 18
5
0.9
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8
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1
30
20
10
0
Average Error τ = 3.0 ms 01 Dec, 2013 Saskatoon
Figure 4: Plots of average measurement error calculated using the plots of SCR in Figure 3 and the “katscan” multiple-pulse sequence with τ = Left: 1.8 ms, Middle: 2.4 ms, Right: 3.0 ms. Red indicates a large measurement error and blue indicates a small measurement error.
1.0
0
1.0
dS/S
0.9
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10
0
Average Error τ = 2.4 ms 01 Dec, 2013 Saskatoon
Lag Number
1.0
pwr0
(dB)
Lag Number
The assumptions for Farley (1972)’s self-clutter estimate break down for HF
ionospheric radars. For example, SuperDARN radars start receiving signal before all the pulses from a
multiple-pulse sequence are sent and scatter is typically received at quasi-periodic ranges as HF radio waves
travel between the ionosphere and the ground. Therefore, the signal-to-clutter ratio (SCR) is expected to
be anything but constant for long-range HF radars.
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0
Average Error τ = 1.8 ms 01 Dec, 2013 Saskatoon
dS/S
Farley (1972) Estimate:
I Uniform scattering (equal echo power)
I All pulses transmitted before receiving
begins
I Ranges are completely correlated
Spectral Power (arb)
Assumptions
Generalized Estimate:
I Non-uniform scattering
I Transmission of pulses is not complete
before receiving signal
I Correlations between ranges are estimated
It is now possible to estimate the measurement error in the radar data using the estimate for self-clutter. Radar measurements are subject to random fluctuations. The mean-square error in the estimate of the ACF, in
the presence of noise and clutter, to leading order, is given by Farley (1972) as
2
1 S +N +C
2
h(dS/S) i =
,
(4)
K
S
where S, N, and C are the signal, noise, and clutter powers, respectively. K is the number of samples. Using Equation 4 and the average signal-to-clutter ratio as depicted in Figure 3, the average mean-square error
was calculated for 1 hour of raw data from the Saskatoon SuperDARN radar.
Lag Number
Comparing Assumptions
Mean-Square Error
pwr0
(dB)
meaning that the signal-to-clutter ratio (S/C ) is a function of the number of transmitted pulses and is
constant for all ranges. For a 7 pulse sequence, Equation 1 gives S/C ≈ −7.8 dB and for an 8 pulse
sequence, S/C ≈ −8.5 dB.
dS/S
C ≈ (Np − 1)S,
I
I
The signal-to-clutter ratio is not uniform for HF radars
For HF radars, self-clutter decreases as pulse repetition time increases
Can retroactively estimate mean-square error for existing raw data
Can actively estimate mean-square error for new raw data
Clutter estimates could be used to actively change radar parameters to mitigate the effects of
self-clutter
References
Farley, D. T. (1969). Incoherent scatter correlation function measurements. Radio Science, 4(10):935–953.
Farley, D. T. (1972). Multiple-pulse incoherent-scatter correlation function measurements. Radio Science, 7(6):661–666.
Greenwald, R. A., Baker, K. B., Dudeney, J. R., Pinnock, M., Jones, T. B., Thomas, E. C., Villain, J. P., Cerisier, J. C., Senior, C., and Hanuise, C. (1995).
DARN/SuperDARN: a global view of the dynamics of high-latitude convection. Space Science Reviews, 71(1-4).
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