1043  UWB Ranging Techniques

1043.1 Learning Objectives

By the end of this chapter, you will be able to:

  • Understand Two-Way Ranging (TWR) protocol and calculate distance from time measurements
  • Compare TWR with Time Difference of Arrival (TDoA) and understand their trade-offs
  • Explain Angle of Arrival (AoA) and how it complements ranging techniques
  • Select the appropriate ranging technique based on scale, power, and infrastructure requirements

1043.2 Introduction

UWB’s primary advantage is precise distance measurement through time-of-flight calculations. Several ranging techniques exist, each with different trade-offs for accuracy, scalability, power consumption, and infrastructure complexity.

This chapter covers the three main UWB ranging approaches: Two-Way Ranging (TWR), Time Difference of Arrival (TDoA), and Angle of Arrival (AoA).

NoteKey Takeaway

TWR is simpler (no sync required) but scales poorly. TDoA scales to thousands of tags but requires synchronized anchors. Choose based on deployment size: TWR for <50 tags, TDoA for larger deployments.

1043.3 Two-Way Ranging (TWR)

Two-Way Ranging is the most common UWB ranging technique, measuring round-trip time to eliminate clock synchronization requirements.

TWR Process:

  1. Poll Message: Device A (initiator) sends a poll message at time T1
  2. Response Delay: Device B (responder) receives at T2, processes, then responds at T3
  3. Response Reception: Device A receives response at T4
  4. Calculate Distance:
    • Round trip time: RTT = (T4 - T1) - (T3 - T2)
    • Distance = (RTT × speed of light) / 2

Key Advantages: - No clock synchronization needed between devices - Works with just two devices - Simple implementation - High accuracy (10-30 cm typical)

Limitations: - Requires active exchange (power consumption) - Scales poorly with many devices (each pair needs exchange) - Double the radio time compared to one-way

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sequenceDiagram
    participant A as Device A<br/>(Initiator)
    participant Air as Air Interface
    participant B as Device B<br/>(Responder)

    Note over A: T1: Send Poll
    A->>Air: Poll Message
    Air->>B: Poll Received
    Note over B: T2: Receive Poll<br/>Processing Time<br/>T3: Send Response
    B->>Air: Response Message
    Air->>A: Response Received
    Note over A: T4: Receive Response

    Note over A: Calculate:<br/>RTT = (T4-T1) - (T3-T2)<br/>Distance = RTT × c / 2

    rect rgb(22, 160, 133, 0.1)
        Note over A,B: Time of Flight = RTT / 2<br/>Accuracy: 10-30 cm
    end

Figure 1043.1: UWB Two-Way Ranging (TWR) Message Exchange and Distance Calculation

This variant shows UWB ranging through a technology comparison lens - useful for understanding why UWB achieves centimeter-level precision compared to other indoor positioning technologies.

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xychart-beta
    title "Indoor Positioning Accuracy by Technology"
    x-axis ["Wi-Fi RSSI", "BLE RSSI", "Wi-Fi RTT", "BLE AoA", "UWB TWR", "UWB DS-TWR"]
    y-axis "Accuracy (meters)" 0 --> 5
    bar [3.0, 2.5, 1.5, 0.5, 0.15, 0.05]

Figure 1043.2: Bar chart comparing indoor positioning accuracy: Wi-Fi RSSI (3m), BLE RSSI (2.5m), Wi-Fi RTT (1.5m), BLE AoA (0.5m), UWB TWR (15cm), UWB DS-TWR (5cm)

{fig-alt=“Bar chart comparing indoor positioning accuracy across technologies. Wi-Fi RSSI achieves 3 meter accuracy, BLE RSSI 2.5 meters, Wi-Fi Round-Trip Time 1.5 meters, BLE Angle of Arrival 0.5 meters, UWB Two-Way Ranging 15 centimeters, and UWB Double-Sided TWR 5 centimeters. UWB provides 10-60x better accuracy than RSSI-based methods due to nanosecond timing precision enabled by wide bandwidth impulse signals.”}

This variant helps you determine when UWB is the right positioning technology:

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flowchart TD
    START["Indoor Positioning<br/>Requirement"] --> Q1{"Accuracy<br/>needed?"}

    Q1 -->|"Room-level (3-5m)"| Wi-Fi["Wi-Fi RSSI<br/>Low cost, existing infra"]
    Q1 -->|"Zone-level (1-2m)"| BLE["BLE Beacons<br/>Low power, cheaper"]
    Q1 -->|"Sub-meter (<50cm)"| Q2{"Security<br/>critical?"}

    Q2 -->|"Yes - Access control"| UWB_SEC["UWB Secure Ranging<br/>802.15.4z HRP<br/>Relay attack protection"]
    Q2 -->|"No"| Q3{"Update rate?"}

    Q3 -->|"< 1 Hz"| BLE_AOA["BLE 5.1 AoA<br/>Lower cost anchors"]
    Q3 -->|"> 10 Hz (real-time)"| UWB["UWB TDoA/TWR<br/>High-rate tracking"]

    Q3 -->|"1-10 Hz"| Q4{"Budget?"}
    Q4 -->|"High"| UWB2["UWB<br/>Best accuracy"]
    Q4 -->|"Medium"| BLE_AOA2["BLE AoA<br/>Good compromise"]

    style START fill:#2C3E50,stroke:#16A085,color:#fff
    style UWB fill:#16A085,stroke:#2C3E50,color:#fff
    style UWB2 fill:#16A085,stroke:#2C3E50,color:#fff
    style UWB_SEC fill:#16A085,stroke:#2C3E50,color:#fff
    style BLE fill:#E67E22,stroke:#2C3E50,color:#fff
    style BLE_AOA fill:#E67E22,stroke:#2C3E50,color:#fff
    style BLE_AOA2 fill:#E67E22,stroke:#2C3E50,color:#fff
    style Wi-Fi fill:#7F8C8D,stroke:#2C3E50,color:#fff

UWB excels at cm-level precision, secure ranging (access control), and high update rates (10-100 Hz). For room-level accuracy or lower budgets, consider Wi-Fi RSSI or BLE alternatives.

This variant shows where UWB is being deployed across industries:

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graph TB
    UWB["UWB Applications"] --> AUTO["Automotive"]
    UWB --> CONSUMER["Consumer"]
    UWB --> INDUSTRIAL["Industrial"]
    UWB --> HEALTHCARE["Healthcare"]

    AUTO --> A1["Digital car keys<br/>BMW, Audi, VW"]
    AUTO --> A2["Keyless entry<br/>Which door?"]
    AUTO --> A3["Theft prevention<br/>Relay attack proof"]

    CONSUMER --> C1["AirTags, SmartTags<br/>Find my items"]
    CONSUMER --> C2["Smart home<br/>Room presence"]
    CONSUMER --> C3["Gaming/AR<br/>Controller tracking"]

    INDUSTRIAL --> I1["Forklift tracking<br/>Collision avoidance"]
    INDUSTRIAL --> I2["Tool tracking<br/>Manufacturing"]
    INDUSTRIAL --> I3["Geofencing<br/>Safety zones"]

    HEALTHCARE --> H1["Asset tracking<br/>Equipment, wheelchairs"]
    HEALTHCARE --> H2["Staff location<br/>Response time"]
    HEALTHCARE --> H3["Patient monitoring<br/>Fall detection"]

    style UWB fill:#2C3E50,stroke:#16A085,color:#fff
    style AUTO fill:#E67E22,stroke:#2C3E50,color:#fff
    style CONSUMER fill:#16A085,stroke:#2C3E50,color:#fff
    style INDUSTRIAL fill:#7F8C8D,stroke:#2C3E50,color:#fff
    style HEALTHCARE fill:#c0392b,stroke:#2C3E50,color:#fff

UWB has found major adoption in automotive (secure keyless entry), consumer (item finding), industrial (asset tracking, safety), and healthcare (equipment/staff location). The common thread: applications requiring centimeter-level precision or secure ranging.

1043.3.1 Double-Sided Two-Way Ranging (DS-TWR)

An enhanced version performs TWR in both directions and averages results, compensating for clock drift:

  • Device A → B → A (first exchange)
  • Device B → A → B (second exchange)
  • Average both measurements
  • Accuracy improves to ~5-10 cm

1043.4 Time Difference of Arrival (TDoA)

TDoA is preferred for systems with many tags because it’s more scalable.

TDoA Architecture: - Multiple anchors with synchronized clocks (typically 4+ anchors) - Tag transmits a single blink message - All anchors record precise arrival time - Central positioning engine compares time differences - Hyperbolic trilateration determines position

Mathematical Basis:

If a signal arrives at Anchor 1 at time t1 and Anchor 2 at time t2:

\[ d_2 - d_1 = c \cdot (t_2 - t_1) \]

This defines a hyperbola. With 4 anchors, you get 3 independent hyperbolas that intersect at the tag’s position.

Advantages: - Tag only transmits once (low power) - Scales to thousands of tags - Tag can be very simple (no ranging computation)

Disadvantages: - Requires infrastructure (synchronized anchors) - More complex backend processing - Anchor synchronization critical

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graph TB
    Tag[UWB Tag<br/>Transmits Once]

    A1[Anchor 1<br/>Receives at t1]
    A2[Anchor 2<br/>Receives at t2]
    A3[Anchor 3<br/>Receives at t3]
    A4[Anchor 4<br/>Receives at t4]

    Tag -.->|Signal| A1
    Tag -.->|Signal| A2
    Tag -.->|Signal| A3
    Tag -.->|Signal| A4

    A1 --> Sync[Synchronized<br/>Time Base]
    A2 --> Sync
    A3 --> Sync
    A4 --> Sync

    Sync --> Engine[Positioning Engine]
    Engine --> Calc[Time Difference<br/>Calculations]
    Calc --> Tri[Hyperbolic<br/>Trilateration]
    Tri --> Pos[Tag Position<br/>X, Y, Z]

    style Tag fill:#E67E22,stroke:#2C3E50,stroke-width:2px,color:#fff
    style Sync fill:#16A085,stroke:#2C3E50,stroke-width:2px,color:#fff
    style Pos fill:#16A085,stroke:#2C3E50,stroke-width:3px,color:#fff

Figure 1043.3: Time Difference of Arrival (TDoA) Architecture with Synchronized Anchors

1043.5 Angle of Arrival (AoA)

While less common in UWB, Angle of Arrival uses antenna arrays to determine the direction of incoming signals.

AoA Principle: - Multiple antennas with known spacing - Phase difference indicates arrival angle - Combined with ranging for 3D position - Reduces number of anchors needed (2-3 vs 4+)

Trade-offs: - Requires more complex antenna arrays - More expensive hardware - Good complement to ranging (angle + distance = position)

1043.6 Technique Comparison

Factor TWR TDoA AoA
Clock Sync Required No Yes (critical) No
Tag Complexity Active (ranging) Passive (blink only) Active
Tag Power Higher Lower Medium
Scalability ~50-100 tags 1000s of tags Medium
Infrastructure Simple Complex (sync) Complex (arrays)
Best For Small deployments Large deployments Reduced anchors

1043.7 Worked Example: UWB Two-Way Ranging Distance Calculation

Scenario: A UWB digital car key system performs Two-Way Ranging (TWR) to verify the smartphone is within 2 meters of the driver’s door before unlocking.

Given:

  • UWB channel 9 (7.9872 GHz center frequency)
  • Bandwidth: 500 MHz
  • Tag (smartphone) initiates ranging to Anchor (car door)
  • Measured timestamps:
    • T1 (Tag sends Poll): 0.000000000 seconds
    • T2 (Anchor receives Poll): 0.000000008 seconds (anchor clock)
    • T3 (Anchor sends Response): 0.000000108 seconds (100ns processing delay)
    • T4 (Tag receives Response): 0.000000116 seconds
  • Speed of light: 299,792,458 m/s

Steps:

  1. Calculate round-trip time (RTT):
    • Total elapsed at Tag: T4 - T1 = 0.000000116 - 0 = 116 ns
    • Processing delay at Anchor: T3 - T2 = 108 - 8 = 100 ns
    • RTT = (T4 - T1) - (T3 - T2) = 116 - 100 = 16 ns
  2. Calculate one-way time of flight (ToF):
    • ToF = RTT / 2 = 16 ns / 2 = 8 ns
  3. Convert time to distance:
    • Distance = ToF x c = 8 x 10^-9 s x 299,792,458 m/s
    • Distance = 2.398 meters
  4. Apply error bounds:
    • UWB timing precision: +/-65 picoseconds (from 500 MHz bandwidth)
    • Distance precision: +/-65ps x c = +/-0.019 meters (+/-1.9 cm)
    • Measured distance: 2.398 +/- 0.019 meters
  5. Security check for relay attack:
    • Maximum legitimate distance for unlock: 2.0 meters
    • Measured: 2.398 meters > 2.0 meters
    • Decision: DENY unlock (phone too far from door)

Result: The measured distance of 2.40 meters exceeds the 2.0 meter threshold, so the car door remains locked. This prevents accidental unlock when passing by and relay attacks where attackers amplify signals.

Key Insight: UWB’s nanosecond timing precision translates directly to centimeter distance accuracy. A relay attack that adds even 10 nanoseconds of delay (from signal amplification electronics) would add 3 meters to the calculated distance, making it trivially detectable. This physics-based security is why UWB is replacing traditional keyless entry systems vulnerable to relay attacks.

1043.8 Summary

UWB ranging techniques provide the foundation for precise indoor positioning. The choice between TWR and TDoA depends primarily on deployment scale and infrastructure constraints.

Key Takeaways:

  1. TWR (Two-Way Ranging): Simple, two-device, no synchronization required - ideal for small deployments (<50 tags) and peer-to-peer applications

  2. TDoA (Time Difference of Arrival): Scalable to thousands of tags with low tag power, but requires synchronized anchor infrastructure

  3. DS-TWR: Enhanced TWR with bidirectional ranging improves accuracy to 5-10 cm by compensating for clock drift

  4. AoA: Useful complement to ranging when anchor count must be minimized

  5. Selection Criteria: Consider tag count, power budget, infrastructure complexity, and update rate requirements

1043.9 What’s Next?

Now that you understand UWB ranging techniques, continue to: