32 How UWB Measures Distance

rfid-nfc-uwb

32.1 Start With the Story

UWB is useful when distance evidence matters. A tag near a door, tool, forklift, phone, or robot is not just “near”; the system needs timing, channel quality, geometry, confidence, and security boundaries to make that claim meaningful.

Read this chapter by following one ranging exchange. Wide bandwidth helps measure time precisely, but the deployment still has to prove line of sight, calibration, interference, policy, and relay resistance for the decision it wants to make.

Phoebe’s Field Notes: Why Wide Bandwidth Buys Timing, Not Power

Phoebe the physics guide

Phoebe’s Why

UWB is impulse-radio, time-domain physics, and it would be dishonest to force it through a narrowband channel-gain story – but it is still a radio wave, and every radio wave obeys the same spherical spreading law no matter how its energy is sliced across time or frequency. Spreading a signal across hundreds of megahertz is what buys the fine timing resolution this chapter measures in nanoseconds; it says nothing about how much power reaches the receiver. Regulators cap UWB by power spectral density – power per megahertz – not by total power, so widening the signal to win timing precision does not add power; it only gives the receiver’s matched filter more spectrum to pull each timing feature out of an unusually thin power budget. That is the honest physical reason a first path can be too weak to trust even when the same message eventually decodes on a stronger reflection.

The Derivation

FCC/ETSI cap UWB transmit power as a spectral-density limit over the occupied bandwidth \(B\) (MHz), not as a single total-power number:

\[\mathrm{EIRP}_{\mathrm{total}}(\mathrm{dBm}) = \mathrm{EIRP}_{\mathrm{PSD}}(\mathrm{dBm/MHz}) + 10\log_{10}(B)\]

That total, once fixed, still spreads over a sphere exactly like any other radio wave – the same Friis physics used for a narrowband link:

\[\mathrm{FSPL} = \left(\frac{4\pi d}{\lambda}\right)^2, \qquad P_r(\mathrm{dBm}) = \mathrm{EIRP}_{\mathrm{total}} - \mathrm{FSPL}(\mathrm{dB})\]

Worked Numbers: Channel 5’s Power Budget

IEEE 802.15.4z channel 5 (6489.6 MHz center, 499.2 MHz bandwidth, a common DW1000/DW3000-class channel), under the FCC’s \(-41.3\) dBm/MHz average EIRP spectral-density limit for indoor UWB:

Total permitted EIRP: \(-41.3+10\log_{10}(499.2)=-41.3+27.0=-14.3\) dBm \(\approx 0.037\) mW – roughly 2700 times less total power than a 20 dBm (100 mW) narrowband ISM radio is allowed
Wavelength: \(\lambda=c/f=3.00\times10^{8}/6.4896\times10^{9}=0.0462\) m
Free-space Rx at 10 m: \(\mathrm{FSPL}=20\log_{10}(4\pi\times10/0.0462)=68.7\) dB, so \(P_r=-14.3-68.7=-83.0\) dBm – only about 2.0 dB above a catalog-typical \(-85\) dBm UWB receiver sensitivity, in clear line of sight
Add one interior wall (catalog-typical 6 dB): \(P_r=-89.0\) dBm, already 4.0 dB under sensitivity

That is why this chapter’s channel-quality boundaries – first-path detectability, NLOS rejection, stale-data recheck – matter more for UWB than for most radios. The PSD ceiling leaves almost no spare power budget, so a single ordinary wall between a tag and an anchor can be the difference between a trustworthy first path and no usable range estimate at all. No antenna-gain trick recovers that margin, because the same PSD cap also limits how much EIRP a compliant UWB antenna is allowed to add.

32.2 Overview: UWB Is Timing Evidence, Not Magic Location

Ultra-Wideband, or UWB, spreads radio energy across a very wide signal bandwidth. That wide signal can expose short timing features, which makes time-of-flight ranging useful for indoor proximity and positioning systems. The radio does not directly prove "where an object is." It first creates timestamp, range, and channel-quality evidence.

A useful UWB review keeps the evidence chain visible. Wide bandwidth supports timing evidence. Timing evidence supports a range or arrival-time claim. Range evidence becomes position only after geometry, calibration, filtering, confidence checks, and policy decide how the application should act.

UWB fundamentals should keep the evidence chain visible from timing features through range, geometry, confidence, and policy.

The arithmetic is small enough to audit by hand. Radio waves travel at roughly 300,000,000 m/s, so 1 ns of one-way timing error is about 0.30 m. In a two-way ranging exchange, the range estimate divides the round-trip timing by two, so a 2 ns round-trip timing error becomes about 300,000,000 x 2 ns / 2 = 0.30 m of range error. That is why antenna delay calibration, timestamp quality, first-path selection, and clock behavior matter. A display that says "42 cm" may look precise, but the review still has to ask whether the timing evidence, channel quality, and installed geometry justify consuming that number.

Use this mental model for every UWB claim. A phone-to-lock proximity check may only need "inside 1.2 m with fresh confidence." A warehouse map may need several anchors, known positions, tag mounting rules, and stale-data filtering. A safety workflow may need independent guarding and a deny state even when UWB looks good. UWB fundamentals are strongest when the team can state what the measured timing proves, what it does not prove, and which change forces a retest.

If you only need the intuition, this layer is enough: approve UWB only for the bounded range, position, proximity, or access decision that has observed timing, channel, geometry, confidence, owner, and retest evidence.

Core Evidence Boundaries

Wideband signal

The physical layer can expose fine timing features, but placement, antenna delay, obstruction, and receiver behavior still affect the evidence.

Range evidence

Two-way ranging, arrival-time methods, and channel review create distance or timing observations with confidence, not unconditional truth.

Position evidence

Anchors, geometry, calibration, synchronization, filtering, and quality rules turn several observations into a position estimate.

Application policy

Access, safety, asset tracking, navigation, and privacy workflows decide what to do when confidence is high, weak, stale, or missing.

Beginner Examples

A single distance estimate can support a narrow proximity claim, but it does not prove a full indoor positioning system.
A coordinate estimate is strongest when the anchor geometry and channel quality were reviewed where the tag actually moves.
Secure-ranging language matters only when key handling, freshness, relay resistance, policy, logs, and fallback behavior are part of the design.
A weak or obstructed channel should lead to recheck, lower confidence, or fallback instead of automatic action.

Overview Knowledge Check

32.3 Practitioner: Build the UWB Review Record

A practical UWB review record starts with the decision being made. The decision might be distance between two devices, a room-level zone, a tracked asset position, a nearby-device unlock, or a safety stop. Each decision needs a different evidence boundary, so the record should avoid approving a broad "UWB location" claim when only a narrow range behavior was tested.

The record should name the ranging method, anchor or peer roles, device mounting, clock or synchronization assumptions, channel evidence, geometry, confidence handling, security boundary, privacy boundary, and retest trigger. That makes it clear whether later failures belong to radio placement, calibration, geometry, filtering, policy, or operations.

Evidence Area

Review Question

Evidence To Record

Failure If Missing

Decision claim

Does the workflow need range, position, proximity, access, safety, or tracking?

Decision type, object population, required confidence, latency need, user action, fallback, and unsupported cases.

A range demo is treated as proof for every map, zone, and security workflow.

Ranging method

Which timing evidence is in scope?

Two-way ranging, arrival-time method, anchor synchronization, message exchange, timestamp source, antenna-delay calibration, and logs.

The team cannot explain whether a bad result came from timing, synchronization, firmware, or calibration.

Geometry and placement

Can the installed layout support the reviewed decision?

Anchor positions, tag mounting, line-of-sight assumptions, body blockage, metal or rack layout, orientation, and movement zones.

One bench result is transferred to an installed site with different paths, angles, and obstructions.

Channel quality

Is the range evidence strong enough to consume?

First-path quality, multipath indicators, confidence score, stale data handling, outlier rejection, and recheck rule.

The strongest reflected path or a stale estimate is used as if it were high-confidence distance evidence.

Security and policy

What happens when UWB evidence drives an action?

Secure-ranging context, freshness, relay-risk handling, authorization, privacy, audit, denied action, manual fallback, and owner.

A precise-looking number is accepted even when confidence, freshness, or authorization is outside the reviewed boundary.

Worked Review: Tool Positioning in a Workshop

A workshop wants UWB tags on mobile tools and anchors near work cells. The review should approve only the installed positioning behavior that was observed: anchor locations, tag orientation, body and metal blockage, channel quality, confidence thresholds, stale-position handling, and the application rule that decides whether a tool is present, missing, or in transit.

The safe approval statement is narrow. It can say that under the reviewed geometry and movement paths, the system produces position evidence strong enough for inventory awareness. It should not say the same evidence is ready for safety interlocks, access control, or every future anchor layout.

Worked Review: Secure Proximity Unlock

A lock workflow may need UWB because it wants physical proximity evidence, not just radio reachability. The review should record the ranging exchange, freshness requirement, secure session context, confidence threshold, relay-risk handling, denied-state behavior, logs, fallback, and what happens when the path is obstructed or confidence is weak.

Practitioner Knowledge Check

32.4 Under the Hood: Timing, Multipath, Confidence, and Drift

Under the hood, UWB measurements are useful because timing evidence can be very fine, not because every received waveform is clean. A receiver may see a weak first path and a stronger reflection. A tag may be blocked by a body. An anchor may be moved without updating the geometry record. A confidence score may become stale while the application still displays the last position.

The review should preserve handoff evidence between the radio layer and the application layer. Timestamp quality, channel impulse response, first-path selection, calibration, anchor geometry, filtering, and policy all need owners. Without that handoff evidence, later troubleshooting turns into guessing.

Channel impulse response evidence helps reviewers distinguish first-path timing from stronger reflections before consuming a range or position estimate.

Boundary

What It Proves

What It Does Not Prove

Retest Trigger

Signal to timestamp

The receiver extracted timing evidence under the tested antenna, channel, firmware, and noise conditions.

Correct distance, position, security decision, or behavior under blocked or reflected paths.

Antenna, enclosure, firmware, channel, mounting orientation, nearby material, or RF environment change.

Timestamp to range

The ranging exchange, delay handling, clock behavior, and calibration support the reviewed distance estimate.

Anchor geometry, map position, application confidence, or secure decision validity.

Calibration, ranging method, peer role, clock behavior, message exchange, or firmware change.

Range to position

Several range or timing observations can produce a position estimate within the reviewed geometry and quality boundary.

That every room, anchor layout, height, orientation, or obstruction condition inherits the same confidence.

Anchor move, tag mount change, floorplan change, line-of-sight change, filter change, or zone-policy change.

Position to policy

The application can act on fresh, bounded confidence with known fallback, audit, privacy, and owner rules.

That stale, weak, spoofed, relayed, or privacy-sensitive evidence is safe to consume automatically.

Access rule, safety rule, privacy policy, confidence threshold, log retention, owner, or fallback workflow change.

Diagnosis Pattern

Name the failing claim. Separate bad range, bad position, stale coordinate, weak confidence, relay risk, privacy issue, and application policy error.
Check channel evidence before policy guesses. If values drift near a rack, inspect first-path quality, reflections, mounting, and obstruction before changing the workflow rule.
Retest the changed boundary. A moved anchor, new tag enclosure, changed firmware, new floorplan, or revised confidence threshold invalidates different evidence.
Write the unsupported claim. If validation covered inventory awareness, do not silently reuse it for access control or safety interlocks.

Under-the-Hood Knowledge Check

32.5 Summary

UWB fundamentals review starts with the claim being made: range, position, proximity, access, safety, tracking, or privacy-sensitive decision.
Wide bandwidth supports fine timing evidence, but channel quality, antenna delay, mounting, obstruction, and firmware still shape the result.
Range evidence becomes position only through geometry, calibration, synchronization or peer exchange, filtering, confidence handling, and retest discipline.
Security-sensitive UWB decisions need secure-ranging context, freshness, confidence thresholds, fallback, logs, and ownership.
A useful review record names the evidence boundary and the changes that reopen the decision.

32.6 Key Takeaway

Approve UWB only when timing, range, channel quality, geometry, confidence, policy, owner, and retest evidence support the exact IoT decision being released.