1. Final Project: Phase Coding to Mitigate Range/Velocity Ambiguities
Group #2
Svetlana Bachmann, Aditya Turlapati
May 2, 2005

2. Outline Problem and its importance SZ(8/64) coding technique
Simulation
Algorithm
Data
Results
Comparison
Conclusions

3. Problem and its importance
Measuring of ra and va  is limited due to rava = c/8.
Tradeoff  measure long ra or large va
va , ra
va , ra
long Ts
short Ts
r-v ambiguities  errors in the weather observation
There are no solutions that can eradicate completely the r-v ambiguities of weather echoes.
Phase coding is one of the techniques that can help to mitigate the ambiguities.

4. SZ(8/64) coding illustartion
ak(m – 1)
ak(m)
V(m) = V1(m) + V2(m)
ak = exp(– jk)
V(m) = V1(m) ak(m) + V2(m) ak(m – 1) Ts
Cohering for the 2nd trip
( ) ak*(m – 1)
S(f)
-va va v
V1(m) ak(m) ak*(m – 1) + V2(m)
Tx pulses are shifted by ak  Rx samples are multiplied by ak*
The 1st trip signal coherent and the 2nd trip signal is phase modulated by a code ck = ak-1 ak*.
Or, the 2nd trip signal is coherent and the 1st trip is modulated by code ck*.
The overlaid power needs to be less then the coherent signal power.
To recover the weaker signal velocity:
the stronger signal is cohered and the weaker one is phase modulated;
the stronger signal is notched (deleting ¾ M sc centered on the vmean)
the weaker signal cohered and its velocity computed from autocovariance.
S1(f) S(f) + S2(f)

5. SZ(8/64) coding illustartion
ak(m – 1)
ak(m)
V(m) = V1(m) + V2(m)
ak = exp(– jk)
V(m) = V1(m) ak(m) + V2(m) ak(m – 1) Ts
Cohering for the 1st trip
( ) ak*(m)
S(f)
-va va v
V1(m) + V2(m) ak(m – 1) ak*(m)
Tx pulses are shifted by ak  Rx samples are multiplied by ak*
The 1st trip signal coherent and the 2nd trip signal is phase modulated by a code ck = ak-1 ak*.
Or, the 2nd trip signal is coherent and the 1st trip is modulated by code ck*.
The overlaid power needs to be less then the coherent signal power.
To recover the weaker signal velocity:
the stronger signal is cohered and the weaker one is phase modulated;
the stronger signal is notched (deleting ¾ M sc centered on the vmean)
the weaker signal cohered and its velocity computed from autocovariance.
S1(f) + S2(f) S(f)

6. SZ(8/64) coding illustartion
ak(m – 1)
ak(m)
V(m) = V1(m) + V2(m)
ak = exp(– jk)
V(m) = V1(m) ak(m) + V2(m) ak(m – 1) Ts
Cohering for the 1st trip
( ) ak*(m)
S(f)
-va va v
V1(m) + V2(m) ak(m – 1) ak*(m)
Tx pulses are shifted by ak  Rx samples are multiplied by ak*
The 1st trip signal coherent and the 2nd trip signal is phase modulated by a code ck = ak-1 ak*.
Or, the 2nd trip signal is coherent and the 1st trip is modulated by code ck*.
The overlaid power needs to be less then the coherent signal power.
To recover the weaker signal velocity:
the stronger signal is cohered and the weaker one is phase modulated;
the stronger signal is notched (deleting ¾ M sc centered on the vmean)
the weaker signal cohered and its velocity computed from autocovariance.
S1(f) + S2(f) S(f)
Recovering weaker trip
Notch ¾ sc
( )ak*(m – 1) ak(m)
Cohering for the weaker trip
V2(m)
S2(f)
S(f)
-va va v

7. Simulation Results: an example
[V] = weatherlike(S, v, v, M, va, SNR)
[V1] = weatherlike(10, 15, 1, 64, va, 40);
(1) Generate 1st trip echo voltage V1.
(2) Generate 2nd trip echo V2.
(3) Generate SZ code ak
(4) Encode both with proper phases
(5) Sum encoded voltages to create overlaid return
[V2] = weatherlike(5, -15, 2, 64, va, 40);

8. Simulation Results: an example
[V] = weatherlike(S, v, v, M, va, SNR)
[V1] = weatherlike(10, 15, 1, 64, va, 40);
(1) Generate 1st trip echo voltage V1.
(2) Generate 2nd trip echo V2.
(3) Generate SZ code ak
(4) Encode both with proper phases
(5) Sum encoded voltages to create overlaid return
[V2] = weatherlike(5, -15, 2, 64, va, 40);

9. Simulation Results: SD(v2)
Ts = ms
f = 2705 MHz
ra = ~ 175 km
va = ~ 23.8 m/s
v1, v2 are random (-va va)
-va va
P1 >> P2
w1 

10. Simplified and Simplified Algorithm
Block diagram
Torres, S., D. Zrnic, and Y. Dubel, 2003:
Signal Design and Processing Techniques for WSR-88D Ambiguity Resolution
NOAA/NSSL Report, Part 7, 103 pp.

11. Simplified and Simplified Algorithm
Order weather
Obtain time series data
Estimate echoes location
Cohere 1st trip signal
Filter the ground clutter
Cohere 2nd trip signal
Estimate S, v, w to determine Stronger signal.
Notch ¾ sc centered on the v of the Strong trip signal.
Make the Weak trip signal coherent.
Determine R and estimate v.
Assign to a proper range
Censor
2nd trip
long PRT
long PRT
1st trip
1st trip


12. Data 10/08/2002 at 15:11:03 UTC, elevation 0.5°, f = 2705 MHz
ra = cTs / 2
va =  / 4Ts
Ts = 3106 s
ra = 466 km
va = 8.9 m s–1
Ts = 1166 s
ra = 175 km
va = 23.8 m s–1
466 km
175 km
350 km
Surveillance Scan
Doppler
SZ(8/64) Phase Coding

13. Surveillance Scan Large region of stratiform precipitation -400 -200
Z, dB
Large
region of
stratiform
precipitation
-400
-200
400 Range, km
200

14. Surveillance Scan Th, r = 350 km
Z, dB Th
-300
-150
300 Range, km
150

15. Doppler Velocity, r = 175 km
v, m s–1
-300
-150
300 Range, km
150

16. Doppler Velocity, r = 175 km, Th
v, m s–1 Th
-300
-150
300 Range, km
150

17. SZ Doppler Velocity, r = 350 km, Th
v, m s–1 Th
-300
-150
300 Range, km
150

18. Ground Clutter example radial @ azimuth 297o
va va
va va

19. Comparing SZ coding with no coding
v, m s–1
Z, dB

20. Conclusions Phase coding allows to mitigate the r, v ambiguities
significantly decrease the obscured area due to the overlaid echoes
Phase coding fails
in the regions where the strong GC overlays the second trip echo.