1. Bearing is a direction
AoA says "the tag is 32 deg to the right of the anchor's front direction." It does not by itself say how far away the tag is.
UWB Angle of Arrival Workbench
UWB Angle of Arrival Workbench
Explore how an antenna array turns UWB phase and timing evidence into a bearing estimate
animation
uwb
positioning
protocols
short-range
Learner-ready UWB Angle of Arrival workbench with antenna-array geometry, phase-difference calculation, ambiguity guardrails, multipath and calibration scenarios, TWR comparison, diagnosis cards, quick reference, guided practice, and primary source links.
UWB
AoA / PDoA
Positioning
UWB angle of arrival: from antenna timing to bearing
An AoA-capable UWB anchor does not learn a tag's position from signal strength. It compares what multiple antennas receive, estimates a bearing, and then combines that bearing with range or extra anchors. This workbench shows the geometry, the phase formula, and the practical cases where the estimate becomes weak.
Teaching channel
6.5 GHz, lambda 4.62 cm
Spacing guardrail
d = 0.50 lambda avoids phase wrap
AoA output
Bearing, not distance
UWB advantage
Wideband pulses help separate direct path
TryUse Half-wave LOS at 6.5 GHz, Antenna spacing 0.50 lambda, and True tag bearing 28 deg.
ObservePhase offset reads about 84 deg and bearing tracks the tag; One-wave aliases introduces multiple plausible angles. Step confirms this readout.
ExplainAn array converts inter-element path difference into phase, but spacing above half wavelength permits identical wrapped phases. Step exposes this mechanism.
Technical boundariesThe model omits element patterns, mutual coupling, channel calibration drift, CIR estimation, polarization, 3D geometry, and stochastic multipath.
Colour keyrfid nfc uwb identitycurrent / primaryreference / datasuccesscautionerror / failure
Beginner ramp
Read this before moving the controls
Use the first preset, then change one control at a time. The page treats phase difference as a center-frequency teaching model because real UWB receivers also need calibration, channel impulse response processing, and direct-path selection.
2. Phase comes from path difference
If a wavefront reaches antenna A before antenna B, the receiver sees a phase offset. The sign tells left versus right; the size helps estimate angle.
3. Practical systems need confidence
Spacing, edge angles, multipath, NLOS, and board calibration can make the same phase evidence fit more than one angle.
Interactive workbench
Move the tag and inspect the bearing estimate
Play steps through the receive pipeline. Scenario buttons set up useful comparisons; manual controls let you stress the formula and diagnosis cards.
Teaching default: clean line of sight
The tag sits inside the anchor's useful field of view, antenna spacing is at lambda/2, and calibration error is small.
High confidence
1
Tag bearing 28 deg rightThe tag is inside the anchor front sector.
2
Phase offset 84 degThe sign gives left or right. The size maps to angle only if spacing and calibration are known.
3
Spacing is safed/lambda <= 0.5 keeps this two-antenna teaching model unambiguous.
4
High confidenceUse this bearing with TWR range or a second anchor for a position fix.
Receive the UWB burst
Multiple antennas capture the same short pulse at slightly different phases and times.
Find the direct path
The receiver tries to use the first path, not a later reflection from walls or metal.
Measure PDoA
Phase difference of arrival is compared against array spacing and center wavelength.
Solve bearing
The model inverts sin(theta), then applies calibration and confidence checks.
Fuse with range
TWR range plus AoA bearing forms a polar position estimate relative to the anchor.
Scenarios
Wavelength
4.62 cm
Spacing
2.31 cm
Path difference
1.08 cm
Estimated bearing
28 deg
Useful bearing estimate
The phase evidence maps cleanly to one side of the anchor.
Spacing guardrail satisfied
d/lambda is at or below 0.5, so adjacent antennas avoid simple phase ambiguity.
AoA still needs range
Pair this bearing with TWR distance or another anchor before claiming a position.
Formula and evidence
What the receiver is estimating
The formula below is intentionally simple. It assumes a far-field plane wave, adjacent antennas, known spacing, and a center wavelength. Production UWB devices add calibration, channel impulse response processing, and quality gates.
| Evidence | Teaching model | What can break it | Current result |
|---|---|---|---|
| Phase difference | delta_phi = 2*pi*d*sin(theta)/lambda | Antenna/cable phase offsets or phase wrapping. | 84 deg phase offset |
| Antenna spacing | d <= lambda/2 is the common ambiguity guardrail. | Wider spacing can make different angles share similar wrapped phase. | 0.50 lambda, safe |
| Direct path | UWB's wide bandwidth helps separate early and late paths. | NLOS or strong reflections can hide the true direct path. | Low multipath stress |
| AoA plus TWR | Bearing + range gives a polar fix from one anchor. | A single bad bearing still needs cross-checks for safety-critical systems. | Good for guided finding |
Quick reference
Keep these distinctions clear
AoA / PDoA
- AoA is the bearing estimate.
- PDoA is one way to estimate bearing from phase differences.
- The sign of phase separates left from right when the array orientation is known.
TWR / ToF
- TWR estimates distance from radio time of flight.
- It does not know direction without AoA, TDoA geometry, or more anchors.
- UWB secure ranging features help resist simple relay distance fraud.
Design guardrails
- Keep adjacent spacing near or below lambda/2 unless using a calibrated array design.
- Calibrate antenna delays and phase offsets in the final enclosure.
- Use multiple anchors or confidence filters in NLOS-heavy spaces.
Guided practice
Three tasks to confirm understanding
Task 1: Find the spacing limit
Start with clean LOS. Increase spacing above 0.50 lambda and watch the ambiguity warning. Explain why a bigger array is not automatically better when phase wraps.
Task 2: Compare AoA and range
Use the edge angle preset. Decide whether a single anchor should act on this bearing alone or request a second anchor/TWR confirmation.
Task 3: Diagnose multipath
Use the multipath preset. Note that UWB bandwidth helps identify the direct path, but NLOS can still turn a confident-looking phase into a wrong bearing.
Deeper note: why UWB is not just "phase radio"
UWB location systems commonly combine time-domain evidence from short pulses with antenna-array evidence. The simple phase equation is useful for intuition, but real receivers use channel impulse response quality, antenna calibration, packet timestamps, and sometimes multiple measurements over time.
Exact spacing-and-reflector mode
Separate spatial aliases from one-path multipath bias
Use one two-element, narrowband calculation to keep the LOS candidate set and the observed two-path bearing visible at the same time.
Load Half-wave LOS, then change only Reflected-path amplitude from 0 to 0.750.
The LOS candidate stays +30.0 deg and spacing stays ambiguity-free, but the two-path diagnosis flips to -74.0 deg.
At 0.50 lambda, spacing removes ideal full-field LOS aliases but cannot identify which coherent arrival is direct.
Half-wave LOS
One ideal direct arrival produces one +30.0 deg candidate and the same principal diagnosis.
module identity: UWB tag
reference: LOS paths
current diagnosis
caution: reflected path
Convert centre frequency to lambda.
Project spacing onto the arrival direction.
Keep unwrapped and [-pi, pi) phase.
Enumerate every valid integer k.
Add one coherent reflected arrival.
Compare LOS candidates with principal AoA.
Wavelength46.1 mmd/lambda = 0.500
LOS path difference11.5 mmdelta L = d sin(theta)
LOS phase1.57 rad wrapped1.57 rad unwrapped
Direct-path candidates[+30.0 deg]Full-field ambiguity-free: yes
Two-path principal estimate+30.0 degerror 0.00 deg
Combined magnitudes|z1| 1.00 / |z2| 1.00No cancellation warning
One exact field ledger
lambda=c/f; deltaL_LOS=d sin(theta); phi_LOS=2 pi deltaL/lambda; candidates=asin(lambda(phi_wrapped+2 pi k)/(2 pi d)); z1=1+rho exp(-j2 pi excess/lambda); z2=exp(-j2 pi d sin(theta)/lambda)+rho exp(-j2 pi(excess+d sin(theta_reflection))/lambda); phi_observed=wrap(arg(z1)-arg(z2)); theta_principal=asin(clamp(lambda phi_observed/(2 pi d),-1,1)).
Half-wavelength LOS is correct in the ideal model.
The direct candidate set and the two-path principal estimate both report +30.0 deg.
Fixture assertions at relative tolerance 1e-6
Technical boundaries. This is a two-element, narrowband, far-field plane-wave phase model at one centre frequency with perfect element positions and exactly one coherent reflected path. It is not a UWB channel-impulse-response processor or a general RF ray tracer. It does not model antenna patterns, mutual coupling, polarization, calibration drift, finite bandwidth, array aperture, near-field curvature, diffuse multipath, NLOS classification, clock error, phase noise, quantization, multiple anchors, beamforming weights, or position solving. Half-wavelength spacing removes full-field spatial aliases in the ideal LOS model; it does not certify the direct path or deployment accuracy.
Primary sources
Standards and implementation references
Use these to check the standard, interoperability context, channel/regulatory background, and practical antenna-array notes.
IEEE
IEEE 802.15.4z-2020
Enhanced UWB PHYs and associated ranging techniques.
FiRa How UWB worksIndustry explanation of UWB ranging, bandwidth, security, and channels.
Qorvo UWB application notesImplementation notes including RTLS, antenna, NLOS, and AoA fundamentals.
ETSI Ultra Wide Band standardsEuropean UWB radio standards and regulatory context.
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