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

Statistical errors

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

The End

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