77  Path Loss and Link Budgets

77.1 Learning Objectives

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

  • Calculate free-space path loss (FSPL) for different frequencies and distances
  • Apply real-world path loss models for indoor and outdoor environments
  • Construct a complete link budget for an IoT wireless system
  • Interpret signal strength measurements (dBm, RSSI) and their practical meaning
  • Determine whether a wireless link will work before deployment

77.2 Prerequisites

Before diving into this chapter, you should be comfortable with:

TipMVU: IoT Deployment Link Budget

Core Concept: A link budget is a simple equation that predicts whether your wireless IoT system will work: Received Power = Transmit Power + Antenna Gains - Path Loss - Fading Margin. If received power exceeds receiver sensitivity, communication succeeds.

Why It Matters: Link budgets prevent expensive field failures. Industry data shows that 40% of IoT pilot failures are due to connectivity issues that could have been predicted with a 5-minute link budget calculation. The FCC and ETSI define regulatory transmit power limits (14 dBm EU, 30 dBm US for ISM bands), so you cannot simply “turn up the power” when deployments fail.

Key Takeaway: Always include a 20 dB fading margin for outdoor deployments and 15 dB for indoor. The difference between a “working” lab demo and a reliable production system is margin. Sub-GHz frequencies (LoRa at 868/915 MHz) provide approximately 9 dB better path loss than 2.4 GHz at the same distance - equivalent to 3x the range with identical hardware.

77.3 Path Loss: Signal Attenuation Over Distance

TipMinimum Viable Understanding: Path Loss Fundamentals

Core Concept: Path loss is the reduction in radio signal strength as it travels through space, following the inverse-square law where signal power decreases proportionally to the square of the distance - doubling distance reduces power by 6 dB (a factor of 4).

Why It Matters: Path loss determines whether your IoT devices can communicate at all. Every wireless link budget calculation starts with path loss, and underestimating it is the most common cause of IoT deployment failures. A sensor that works perfectly at 100m in the lab may fail completely at 200m in the field because path loss increased by 6 dB - and that is free-space loss only, before accounting for walls, terrain, or interference.

Key Takeaway: Use the “6-20 rule” for quick mental calculations: every doubling of distance adds 6 dB loss, and every doubling of frequency adds another 6 dB. For real-world deployments, multiply free-space loss by the path loss exponent (n=2 for free space, n=3-4 for indoor, n=4-5 for obstructed urban). Always add 15-25 dB fading margin to your calculations - if your link budget is exactly zero, your system will fail half the time.

77.3.1 Free Space Path Loss (FSPL)

In perfect conditions (no obstacles, no reflections), signal strength decreases with distance following the inverse square law:

\[FSPL_{dB} = 20\log_{10}(d) + 20\log_{10}(f) + 20\log_{10}\left(\frac{4\pi}{c}\right)\]

Simplified for common units:

\[FSPL_{dB} = 20\log_{10}(d_{km}) + 20\log_{10}(f_{MHz}) + 32.45\]

Example calculations:

Distance 868 MHz (LoRa) 2.4 GHz (Wi-Fi) 5 GHz (Wi-Fi)
1 m 31 dB 40 dB 47 dB
10 m 51 dB 60 dB 67 dB
100 m 71 dB 80 dB 87 dB
1 km 91 dB 100 dB 107 dB
10 km 111 dB 120 dB 127 dB
ImportantKey Insight

At 2.4 GHz, you lose an additional 9 dB compared to 868 MHz at the same distance. That’s why LoRa and Sigfox (sub-GHz) achieve much longer ranges than Wi-Fi and Bluetooth.

77.3.2 Real-World Path Loss Models

Free space is ideal; real environments add extra loss. The log-distance path loss model accounts for this:

\[PL(d) = PL(d_0) + 10n\log_{10}\left(\frac{d}{d_0}\right) + X_\sigma\]

Where: - \(PL(d_0)\) = path loss at reference distance (usually 1m) - \(n\) = path loss exponent (environment-dependent) - \(X_\sigma\) = random variable for shadowing (obstacles)

Environment Path Loss Exponent (n) Notes
Free space 2.0 Ideal, no obstacles
Urban cellular 2.7-3.5 Buildings cause reflection
Urban (obstructed) 4-5 Non-line-of-sight
Indoor (open office) 2.5-3.0 Few walls
Indoor (partitioned) 3.5-4.5 Cubicles, walls
Indoor (through walls) 4-6 Multiple walls
Factory/Industrial 3.0-4.0 Metal, machinery 

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xychart-beta
    title "Path Loss vs Distance (Different Environments)"
    x-axis "Distance (m)" [1, 10, 50, 100, 200, 500]
    y-axis "Path Loss (dB)" 40 --> 140
    line "Free Space (n=2)" [40, 60, 74, 80, 86, 94]
    line "Indoor Open (n=3)" [40, 70, 91, 100, 109, 121]
    line "Indoor Walls (n=4)" [40, 80, 108, 120, 132, 148]

Figure 77.1: Path Loss vs Distance Chart for Different Indoor and Outdoor Environments

77.5 Understanding Signal Strength Measurements

77.5.1 dBm: Absolute Power

dBm measures absolute power in milliwatts on a logarithmic scale: \[P_{dBm} = 10\log_{10}(P_{mW})\]

dBm mW Typical Source
+30 1000 Maximum Wi-Fi (US, with antenna)
+20 100 High-power Wi-Fi router
+14 25 LoRaWAN EU limit
+4 2.5 Bluetooth Class 2
0 1 Reference level
-10 0.1
-30 0.001
-70 10^-10 Typical Wi-Fi signal at 20m
-90 10^-12 Weak but usable Wi-Fi
-120 10^-15 Near noise floor
-137 10^-16.7 LoRa SF12 sensitivity

77.5.2 RSSI: Received Signal Strength Indicator

RSSI is a vendor-specific measurement of signal strength. It’s often (but not always) related to dBm:

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flowchart TD
    subgraph RSSI["RSSI Quality Levels"]
        E["Excellent<br/>RSSI > -50 dBm<br/>Very close to AP"]
        G["Good<br/>-50 to -60 dBm<br/>Reliable connection"]
        F["Fair<br/>-60 to -70 dBm<br/>Usually works"]
        W["Weak<br/>-70 to -80 dBm<br/>Occasional issues"]
        P["Poor<br/>-80 to -90 dBm<br/>Unreliable"]
        N["No Connection<br/>< -90 dBm<br/>Link failure"]
    end

    E --> G --> F --> W --> P --> N

    style E fill:#16A085,stroke:#0D6655
    style G fill:#27AE60,stroke:#1E8449
    style F fill:#F39C12,stroke:#D68910
    style W fill:#E67E22,stroke:#AF5F1A
    style P fill:#E74C3C,stroke:#B03A2E
    style N fill:#7F8C8D,stroke:#5D6D7E

Figure 77.4: RSSI Signal Quality Levels from Excellent to No Connection 

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graph LR
    subgraph EXCELLENT["-40 to -50 dBm"]
        E1["Video streaming"]
        E2["VoIP calls"]
        E3["Real-time gaming"]
    end

    subgraph GOOD["-50 to -67 dBm"]
        G1["Web browsing"]
        G2["Email/messaging"]
        G3["IoT sensors"]
    end

    subgraph FAIR["-67 to -80 dBm"]
        F1["Basic web pages"]
        F2["Sensor data"]
        F3["Low-rate LPWAN"]
    end

    subgraph POOR["-80 to -90 dBm"]
        P1["Packet loss likely"]
        P2["Retransmissions"]
        P3["LoRa still works!"]
    end

    EXCELLENT -->|"Degrading"| GOOD -->|"Degrading"| FAIR -->|"Degrading"| POOR

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    style G1 fill:#27AE60,stroke:#2C3E50,stroke-width:1px,color:#fff
    style G2 fill:#27AE60,stroke:#2C3E50,stroke-width:1px,color:#fff
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    style F3 fill:#E67E22,stroke:#2C3E50,stroke-width:1px,color:#fff
    style P1 fill:#E74C3C,stroke:#2C3E50,stroke-width:1px,color:#fff
    style P2 fill:#E74C3C,stroke:#2C3E50,stroke-width:1px,color:#fff
    style P3 fill:#2C3E50,stroke:#16A085,stroke-width:2px,color:#fff

Figure 77.5: Alternative view: RSSI Levels with Application Requirements - Instead of abstract quality labels, this diagram shows what applications work at each signal strength level. Excellent signal (-40 to -50 dBm) supports demanding apps like video streaming and VoIP. Good signal (-50 to -67 dBm) handles normal browsing and most IoT sensors. Fair signal (-67 to -80 dBm) still works for basic web and sensor data. Even poor signal (-80 to -90 dBm) works for LoRa, which is designed for weak signals. Key insight: IoT protocols like LoRa work at signal levels where Wi-Fi fails. {fig-alt=“Four-column diagram showing application requirements at different RSSI levels. Excellent -40 to -50 dBm (teal): Video streaming, VoIP calls, Real-time gaming. Good -50 to -67 dBm (green): Web browsing, Email and messaging, IoT sensors. Fair -67 to -80 dBm (orange): Basic web pages, Sensor data, Low-rate LPWAN. Poor -80 to -90 dBm (red except LoRa): Packet loss likely, Retransmissions, but LoRa still works (navy highlight). Arrows show signal degrading from excellent to poor across columns.”}
WarningRSSI vs SNR

RSSI only tells you signal strength, not quality. A strong signal can still be useless if there’s strong interference.

SNR (Signal-to-Noise Ratio) tells you how much your signal stands out from the noise: \[SNR_{dB} = P_{signal,dBm} - P_{noise,dBm}\]

For reliable communication, you typically need SNR > 10-20 dB, depending on the modulation scheme.

77.6 Understanding Check

Scenario: You’re designing a smart agriculture system. Soil moisture sensors are deployed across a 500-acre (2 km squared) field. A gateway is placed at the farm building in the center.

Given: - Sensors transmit at +14 dBm with 2 dBi antenna - Gateway has sensitivity of -137 dBm with 6 dBi antenna - Environment is rural/open (path loss exponent n approximately 2.5) - Frequency: 915 MHz

Questions:

  1. What is the maximum theoretical range in free space?
  2. What is the practical range with the real environment?
  3. Will sensors at the field edges (1 km away) work reliably?
  4. What fading margin would you recommend?

1. Maximum theoretical range (free space):

Link budget: +14 + 2 - 1 (cable) + 6 - 1 (cable) - (-137) = 157 dB

Free space path loss: 157 = 32.45 + 20log(915) + 20log(d_km) 157 = 32.45 + 59.2 + 20log(d) 65.35 = 20log(d) d = 10^(65.35/20) = 1850 km (theoretical!)

Note: This is a mathematical upper bound in an idealized free-space model. In practice, line-of-sight/horizon limits, Fresnel clearance, interference, and regulations dominate long before this distance.

2. Practical range (n=2.5):

Using log-distance model with n=2.5: 157 = 91.65 + 25log(d_km) 65.35 = 25log(d) d = 10^(65.35/25) = 46 km (without fading margin)

3. Sensors at 1 km:

Path loss at 1 km: 91.65 + 25log(1) = 91.65 dB Received power: +14 + 2 + 6 - 91.65 = -69.65 dBm Link margin: -69.65 - (-137) = 67.35 dB

Yes! Sensors at 1 km will work very reliably.

4. Recommended fading margin:

For outdoor agriculture: 15 dB is typically sufficient With 67 dB margin, you have excellent reliability even in adverse conditions.

77.8 Summary

Concept Key Points
Path Loss Signal weakens with distance; lower frequencies lose less
FSPL Formula \(FSPL = 20\log(d) + 20\log(f) + 32.45\)
Path Loss Exponent n=2 (free space), n=3-4 (indoor), n=4-5 (obstructed)
Link Budget Balance transmit power, gains, losses, and sensitivity
dBm Absolute power measure (0 dBm = 1 mW)
RSSI Received signal strength; > -70 dBm is typically good
Link Margin > 20 dB for reliable links

77.9 What’s Next

With path loss and link budgets understood, continue to:

NoteRelated Chapters