Sebastian Torres
NEXRAD Range-Velocity Ambiguity Mitigation
Staggered PRT andPhase Coding
Algorithms
Part One
Staggered PRTCurrent Status
RRDA CapabilitiesStaggered PRT
• Expanded VCP definitions▪ Staggered PRT modes are specified using patterns
T1 T1 T2 T2 T2 T3 T1 T1 T2 T2 T2 T3 T1 T1 T2 T2 T2 T3 …
• Expanded set of PRTs▪ Exact PRT ratios▪ Resolution given by 9.6 MHz clock
• Real-time staggered PRT algorithm▪ Hardware and software modifications
• Level I and II recorder▪ Uninterrupted data collection for up to 8 hours
Block 1 Block 2 Block 3
Pattern Pattern Pattern
The Staggered PRT Technique
• Transmitter alternates two PRTs▪ T1 < T2
▪ PRT ratio: K = T1/T2 = m/n (m,n integers)▪ ra1 = cT1/2, ra2 = cT2/2▪ va1 = /4T1, va2 = /4T2
• Maximum unambiguous range▪ ra = ra2 (one-overlay resolution)
• Maximum unambiguous velocity▪ va = m va1 = n va2 (velocity dealiasing)
T1 T2
time
T1 T2…
The Staggered PRT Technique
va = 25.36 m s-1 va = 45.17 m s-1
148 km184 km
KTLXVCP 11 – Batch Mode
KOUNStaggered 184/276EL = 2.5 deg
04/06/03 4:42 GMT
The Staggered PRT Algorithm
• Computation of autocovariances▪ P1, R1 for short range sweeps▪ P2, R2 for long range sweeps
▪ P1, R1, and R2 computed up to ra1
▪ P2 computed up to ra2
T1 T2 T1
o oo oP1 P1
R1 R1
P2 P2
R2 R2
The Staggered PRT Algorithm
• Ground clutter filtering▪ Magnitude squared of DC component is
removed from autocovariances▪ Bypass map is used▪ Filter is simple but suppression is limited to
about 10 dB▪ Future work: Test other filtering schemes
• Sachidananda’s GCF (Rep. 3 & 4)– Frequency domain filter
• Regressive filters• Others
Clutter Filter Performance
KOUNStaggered PRT
KOUNUniform PRTEL = 0.5 deg
03/17/03 23:06 GMT
The Staggered PRT Algorithm
• Velocity dealiasing algorithm▪ v1 and v2 are computed from R1 and R2
vv2va2
v1
va1
v1 – v2^ ^
v1 - v2
closest level
True velocity
add 2va1 to v1^
^ ^
Velocity Dealiasing Algorithm Performance
va = 45.1 m s-1 va = 34.6 m s-1
KOUNStaggered 184/276
KOUNStaggered 240/360EL = 2.5 deg
04/06/03 4:50 GMT
184 km
240 km
Velocity Dealiasing Algorithm Performance
• What happens if SD(v1) and SD(v2) are large?
v1 – v2^ ^
v1 - v2
v
v1
va1
closest level
True velocity
closest level
Wrong velocity
Catastrophic error!!
Velocity Dealiasing Algorithm PerformanceVelocity
Staggered 240/360Spectrum WidthStaggered 240/360EL = 2.5 deg
04/06/03 4:48 GMT
Can be used for censoring
The Staggered PRT Algorithm
• Reflectivity computation▪ Use clean powers
▪ Computed to ra2
▪ Future work: Extend Z to 2ra1
• Censoring▪ Overlaid echoes do not bias v, but act as noise▪ Future work: Test Sachidananda’s one-overlaid resolution scheme
(Rpt. 4)T1 T2
I II I II III
Censoring
ReflectivityStaggered 184/276
VelocityStaggered 184/276EL = 1.5 deg
03/18/03 3:28 GMT
276 km
184 km
Summary
• Range coverage▪ Z to ra2 and v to ra1, where ra1/ra2 = m/n = K▪ Natural “match” for NEXRAD requirements
• Extension of maximum unambiguous velocity▪ va = m va1 = n va2
• Range-velocity ambiguities▪ Uniform PRT
• rava = c/8 → Inadequate for = 10 cm
▪ Staggered PRT • ra1va = m(c/8)• ra1 vs. va trade-off controlled by PRTs
PRT Trade-Off
Long PRTsStaggered 336/466
va = 26.7 m s-1Medium PRTs
Staggered 240/360va = 34.6 m s-1
Short PRTsStaggered 184/276
va = 45.1 m s-1
336 km
240 km
184 km
K = 2/3
K = 2/3
Conclusions
• Algorithm works with any PRT ratio▪ No need to add new PRTs to the system
(initially)▪ Only need exact ratios for Sachidananda’s
ground clutter filter and one-overlaid recovery
• Need good velocity estimates to avoid catastrophic errors▪ Future work: Determine maximum allowable
errors for a given set of PRTs
Conclusions
• Recommended for intermediate elevations to replace legacy Batch Mode▪ Need better ground clutter filters to be useful
at lower elevations▪ Future work: Derive optimum choice of PRTs
to match current performance
• Achieves “clean” separation of echoes
• Results in very simple algorithm
Part Two
Phase CodingSZ-2 AlgorithmCurrent Status
RRDA CapabilitiesPhase Coding
• Expanded VCP definitions▪ Can specify phase coding sequence number for each scan
• Standard (or predefined)• Downloadable
– Proposed new RPG-RDA Message
• Real-time 1st-trip decoding of phase-coded signals▪ Hardware and software modifications▪ Use WSR-88D phase shifter (7 bits)
• Level I and II recorder▪ Uninterrupted data collection for up to 8 hours
SZ-2 Algorithm
• Transmitted pulses are phase-modulated with SZ(8/64) switching code
• Phase-coded scan is preceded by long-PRT surveillance scan▪ Surveillance scan is not phase coded▪ Powers from the surveillance scan are used to
determine overlaid trips in the phase-coded scan▪ Spectrum widths from the surveillance scan can
be used for censoring• Future work: Study limitations of spectrum width
estimates obtained from long PRTs
SZ-2 Algorithm
• Censoring and overlaid trip determination
▪ Significant return? ▪ Above noise plus sum of out-of-trip powers?▪ Within recovery region?
• Based on plots of SD(vw) on the Ps/Pw vs. ww plane
range1st trip 2nd trip 3rd trip 4th trip
PL
Pth
P1
P2
P3 P4
SZ-2 Algorithm
• 1st trip cohering▪ Use measured switching code
• Ground clutter filtering▪ Use bypass map▪ Frequency domain filter▪ Future work: Study other filtering schemes
2nd trip modulated1st trip cohered
Ground clutter
3rd trip modulated4th trip modulated
v
SZ-2 Algorithm
• Lag-one autocorrelation computation▪ From cohered data for two strongest trips
• Final strong/weak trip determination▪ Use |R(Ts)| for the two strongest trips
• Strong-trip cohering
• Strong-trip velocity computation (vs)
v
Strong trip cohered
Weak trip modulated
Weak trip cohered
Strong trip modulated
vs
SZ-2 Algorithm
• Processing notch filter (PNF)▪ Location determined by vs and presence of
clutter
▪ Notch Width determined by strong and weak trip numbers
• 8 replicas → NW = 3M/4• 4 replicas → NW = M/2
1st trip cohered
2nd trip modulatedPNFPNF
vvsvs/2
SZ-2 Algorithm
• Weak-trip cohering
• Weak-trip velocity computation (vw)
▪ From lag-one autocorrelation of notched and cohered weak signal
v
Weak trip cohered
Sidebands
Strong trip residue
vw
SZ-2 Censoring
• Power adjustments▪ Windowing▪ PNF▪ Weak-trip
• Assignment of correct range▪ Trip numbers are used to assign correct range
location to strong- and weak-trip moments
• Censoring and thresholding▪ Tag trips with significant powers that are
unrecoverable
SZ-2 Algorithm Performance
ReflectivityLong PRT
VelocitySZ-2 with short PRTEL = 0.5 deg
04/06/03 4:26 GMT
117 km
234 km
SZ-2 Algorithm Performance
VelocityNon PC “Split cut”
VelocitySZ-2 with medium PRTEL = 0.5 deg
04/06/03 4:28 GMT
175 km175 km
va = 23.7 m s-1
SZ-2 vs. Staggered PRT
VelocityStaggered 240/360
VelocitySZ-2 with medium PRTEL = 0.5 deg
04/06/03 4:30 GMT
240 km 175 km
va = 34.6 m s-1 va = 23.7 m s-1
Conclusions
• SZ-2 uses a non-phase-coded, long-PRT, surveillance scan to determine overlaid trips▪ Substitute for “split cuts” in the legacy WSR-88D
• SZ-2 handles up to 2 trips out of 4 possible▪ Two strongest trips are selected▪ Future work: Fine-tune thresholds
• Can use overlapping radials if M ≠ 64▪ Future work: Test this technique with real data
Conclusions
• Phase coding may require ground clutter filters with zero phase response▪ Future work: Study alternatives to recursive filters▪ Future work: Study ways to compensate for phase
distortions
• Censoring in SZ-2 is simpler than in the stand-alone version (SZ-1)▪ Use P and v from surveillance or both scans
▪ Future work: Fine-tune/add(?) parameters
Conclusions
• SZ-2 is very sensitive to clutter residue▪ From the long-PRT surveillance scan
• Recovery region test does not pass• Ring of censored data at the beginning of 2nd, 3rd,
and 4th trips
▪ From the phase-coded scan• Noisy data at the beginning of 2nd, 3rd, and 4th trips• Could add CSR as a censoring parameter
• SZ-2 is very sensitive to out-of-trip leakage▪ Fixed by fine-tuned censoring parameters
SZ-1 vs. SZ-2
VelocitySZ-1
No cens., No GCF, 1st and 2nd trips only
VelocitySZ-2EL = 0.5 deg
04/06/03 4:30 GMT
