633  Fresnel Zones and Practical Deployment

633.1 Learning Objectives

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

  • Understand Fresnel zone requirements for reliable outdoor deployments
  • Calculate first Fresnel zone radius for different frequencies and distances
  • Apply the 60% clearance rule for reliable wireless links
  • Design antenna heights for long-range deployments
  • Troubleshoot ground-mounted sensor range issues
  • Plan practical IoT deployments considering terrain and buildings

633.2 Introduction

While path loss calculations assume a direct line-of-sight path between transmitter and receiver, wireless signals actually occupy a three-dimensional ellipsoid volume around this path called the Fresnel Zone. Understanding Fresnel zones is critical for outdoor IoT deployments, especially long-range links like LoRaWAN, Sigfox, and point-to-point Wi-Fi.

Time: ~25 min | Difficulty: Intermediate | P07.C15.U05d

633.3 What Are Fresnel Zones?

Fresnel zones are concentric ellipsoid regions around the direct line-of-sight path. Radio waves traveling through these zones can constructively or destructively interfere at the receiver depending on their path length.

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graph TD
    subgraph Fresnel["Fresnel Zone Ellipsoid (Side View)"]
        TX["Transmitter<br/>(Height h1)"]
        RX["Receiver<br/>(Height h2)"]

        LOS["Direct path<br/>(Line of Sight)"]
        F1["First Fresnel Zone<br/>(60% must be clear)"]
        F2["Second Fresnel Zone"]

        Ground["Ground / Obstacles"]

        TX -->|Direct LOS| LOS
        LOS --> RX

        TX -.->|Radius r at midpoint| F1
        F1 -.-> RX

        TX -.->|Larger radius| F2
        F2 -.-> RX

        Ground -->|Reflection/Blockage| F1
    end

    subgraph Clearance["Clearance Rule of Thumb"]
        Rule1["60% of First Fresnel Zone Clear<br/>= Reliable Link"]
        Rule2["40% of First Fresnel Zone Clear<br/>= Marginal Link (fading)"]
        Rule3["Less than 20% of First Fresnel Zone Clear<br/>= Link Failure Likely"]
    end

    style TX fill:#16A085,stroke:#2C3E50,color:#fff
    style RX fill:#16A085,stroke:#2C3E50,color:#fff
    style LOS fill:#2C3E50,stroke:#16A085,color:#fff
    style F1 fill:#E67E22,stroke:#2C3E50,color:#fff
    style F2 fill:#E8F6F3,stroke:#16A085,color:#2C3E50
    style Ground fill:#7F8C8D,stroke:#2C3E50,color:#fff
    style Rule1 fill:#2ECC71,stroke:#27AE60,color:#fff
    style Rule2 fill:#F39C12,stroke:#E67E22,color:#fff
    style Rule3 fill:#E74C3C,stroke:#C0392B,color:#fff

Figure 633.1: Fresnel zone ellipsoid showing clearance requirements for reliable wireless links

{fig-alt=“Diagram showing Fresnel zone ellipsoid between transmitter and receiver with concentric zones, illustrating the first Fresnel zone (must be 60% clear), second Fresnel zone, direct line-of-sight path, and ground obstacles, along with clearance rules for reliable, marginal, and failed links”}

633.4 First Fresnel Zone Radius Formula

The radius of the first Fresnel zone at the midpoint between transmitter and receiver is:

\[r_1 = 17.3 \sqrt{\frac{d}{4f}}\]

Where: - r_1 = First Fresnel zone radius (meters) - d = Total distance between TX and RX (kilometers) - f = Frequency (GHz)

Alternative Formula (for any point along the path):

\[r_1 = \sqrt{\frac{\lambda d_1 d_2}{d_1 + d_2}}\]

Where: - lambda = Wavelength (meters) = c/f - d_1 = Distance from TX to obstacle (meters) - d_2 = Distance from obstacle to RX (meters)

60% Clearance Rule:

For reliable wireless links, at least 60% of the first Fresnel zone radius must be clear of obstacles. This accounts for ground reflections, diffraction, and multipath interference.

\[r_{clearance} = 0.6 \times r_1\]

633.5 Worked Example: Wi-Fi 2.4 GHz Fresnel Zone

Scenario: Point-to-point Wi-Fi link between two buildings 100 meters apart at 2.4 GHz. What antenna height is required?

Given: - Distance: d = 100 m = 0.1 km - Frequency: f = 2.4 GHz - 60% clearance required

Step 1: Calculate first Fresnel zone radius at midpoint

\[r_1 = 17.3 \sqrt{\frac{0.1}{4 \times 2.4}}\] \[r_1 = 17.3 \sqrt{\frac{0.1}{9.6}}\] \[r_1 = 17.3 \sqrt{0.01042}\] \[r_1 = 17.3 \times 0.102\] \[r_1 = 1.76 \text{ meters}\]

Step 2: Calculate required clearance (60% rule)

\[r_{clearance} = 0.6 \times 1.76 = 1.06 \text{ meters}\]

Step 3: Determine minimum antenna height

If antennas are mounted at same height h, the midpoint sag due to Earth’s curvature (negligible at 100m) and required clearance:

\[h_{min} = r_{clearance} + h_{obstacle}\]

For ground-level obstacles (h_obstacle = 0):

\[h_{min} = 1.06 \text{ meters}\]

Practical antenna height: 2-3 meters (provides 60% Fresnel clearance plus margin for ground reflections).

What if antennas are ground-mounted (h = 0.5m)?

At 100m distance with 0.5m antenna height, the Fresnel zone would be partially blocked by ground, causing: - 6-10 dB additional loss from ground reflection/diffraction - Reduced effective range from 100m to ~40-60m - This explains why ground-mounted sensors have poor range!

633.6 Worked Example: LoRa 915 MHz Long-Range Link

Scenario: LoRaWAN gateway to sensor link across 5 km farmland at 915 MHz. How high should the gateway antenna be?

Given: - Distance: d = 5 km - Frequency: f = 915 MHz = 0.915 GHz - Flat farmland with crops up to 2 meters tall

Step 1: Calculate first Fresnel zone radius at midpoint (2.5 km from each end)

\[r_1 = 17.3 \sqrt{\frac{5}{4 \times 0.915}}\] \[r_1 = 17.3 \sqrt{\frac{5}{3.66}}\] \[r_1 = 17.3 \sqrt{1.366}\] \[r_1 = 17.3 \times 1.169\] \[r_1 = 20.22 \text{ meters}\]

Step 2: Calculate required clearance (60% rule)

\[r_{clearance} = 0.6 \times 20.22 = 12.13 \text{ meters}\]

Step 3: Account for crop height + clearance

\[h_{min} = h_{crop} + r_{clearance} = 2 + 12.13 = 14.13 \text{ meters}\]

Practical deployment: - Gateway antenna height: 15 meters (pole-mounted on rooftop) - Sensor antenna height: 3 meters (above crop level) - Result: Clear first Fresnel zone, reliable 5 km link

What if gateway is only 3m high (same as sensor)?

Fresnel zone radius at midpoint: 20.22 m
Gateway height: 3 m
Crop height: 2 m
Clearance above crops: 3 - 2 = 1 m

Percentage of Fresnel zone clear: 1 / 20.22 = 4.9% (X)

Expected loss: 15-20 dB additional diffraction loss
Link budget impact: May exceed -137 dBm sensitivity, causing link failure!

This is why LoRa gateways are mounted on towers/rooftops, not ground level!

633.7 Fresnel Zone Clearance by Protocol

Different IoT protocols operating at different frequencies have vastly different Fresnel zone requirements:

633.7.1 Fresnel Zone Radius at 1 km Distance

Protocol Frequency Fresnel Radius (r_1) 60% Clearance Height Requirement
Sigfox 868 MHz 9.6 m 5.8 m 6-8 m minimum
LoRa US 915 MHz 9.4 m 5.6 m 6-8 m minimum
Wi-Fi 2.4 GHz 2.4 GHz 5.8 m 3.5 m 4-5 m minimum
Wi-Fi 5 GHz 5 GHz 4.0 m 2.4 m 3-4 m minimum
BLE 2.4 GHz 5.8 m 3.5 m 4-5 m minimum

633.7.2 Fresnel Zone Radius at 5 km Distance

Protocol Frequency Fresnel Radius (r_1) 60% Clearance Height Requirement
Sigfox 868 MHz 21.5 m 12.9 m 13-15 m minimum
LoRa US 915 MHz 20.9 m 12.5 m 13-15 m minimum
LoRa EU 868 MHz 21.5 m 12.9 m 13-15 m minimum
Wi-Fi 2.4 GHz 2.4 GHz 12.9 m 7.7 m 8-10 m minimum
NB-IoT 900 MHz 21.1 m 12.7 m 13-15 m minimum

Key Observations:

  1. Lower frequency = larger Fresnel zone: LoRa/Sigfox at 900 MHz have 2x larger Fresnel zones than Wi-Fi at 2.4 GHz
  2. Longer distance = larger Fresnel zone: At 5 km, Fresnel zones are 2.2x larger than at 1 km (sqrt(5) scaling)
  3. Height requirements scale with distance: 1 km link needs 6m height, 5 km link needs 15m height for same protocol

633.8 Building Penetration and Fresnel Zones

Fresnel zone analysis also explains why lower frequencies penetrate buildings better than higher frequencies:

Building Penetration Loss at 60% Fresnel Blockage:

Material 900 MHz LoRa 2.4 GHz Wi-Fi 5 GHz Wi-Fi Explanation
Drywall 2 dB 3-5 dB 5-8 dB Higher freq = more diffraction loss
Brick wall 4-6 dB 6-10 dB 10-15 dB Wavelength vs brick size
Concrete 6-8 dB 10-15 dB 15-25 dB Absorption scales with frequency
Metal mesh 15-20 dB 20-30 dB 30-50 dB Aperture size vs wavelength

Why LoRa Penetrates Better Than Wi-Fi:

At 915 MHz LoRa: - Wavelength: lambda = c/f = 3x10^8 / 915x10^6 = 0.328 m = 32.8 cm - Typical wall thickness: 10-20 cm ~ 0.3-0.6 lambda - Diffraction around obstacles is effective when obstacle size ~ wavelength

At 2.4 GHz Wi-Fi: - Wavelength: lambda = 3x10^8 / 2.4x10^9 = 0.125 m = 12.5 cm - Typical wall thickness: 10-20 cm ~ 0.8-1.6 lambda - Less effective diffraction when obstacle size > wavelength

Result: LoRa experiences ~40% less building penetration loss than Wi-Fi due to longer wavelength allowing better diffraction around obstacles.

633.9 Ground-Mounted Sensors: Why Range is Poor

Real-World Problem: Smart agriculture soil moisture sensors placed at ground level (10-20 cm height) consistently fail to reach gateways at 1-2 km distance, despite theoretical range calculations showing 5-10 km capability.

Root Cause: Fresnel Zone Blockage

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graph TD
    subgraph Bad["Ground-Mounted Sensor (h=0.2m)"]
        GW1["Gateway<br/>h=15m<br/>(1 km away)"]
        GS1["Sensor<br/>h=0.2m"]
        FZ1["Fresnel Zone<br/>r=9.4m at midpoint"]
        GND1["Ground + Vegetation<br/>(Blocks 95% of Fresnel zone)"]

        GW1 -.->|Fresnel zone| FZ1
        FZ1 -.-> GS1
        GND1 -->|Blocks signal| FZ1
    end

    subgraph Good["Elevated Sensor (h=3m)"]
        GW2["Gateway<br/>h=15m<br/>(1 km away)"]
        GS2["Sensor<br/>h=3m<br/>(on pole)"]
        FZ2["Fresnel Zone<br/>r=9.4m at midpoint"]
        GND2["Ground + Vegetation<br/>(Below Fresnel zone)"]

        GW2 -.->|Clear Fresnel zone| FZ2
        FZ2 -.-> GS2
        FZ2 -->|Above ground| GND2
    end

    subgraph Impact["Signal Impact"]
        Loss1["Ground-mounted:<br/>15-25 dB extra loss<br/>Range: 200-500m"]
        Loss2["Elevated (3m):<br/>0-3 dB extra loss<br/>Range: 5-10 km"]
    end

    style GW1 fill:#E67E22,stroke:#2C3E50,color:#fff
    style GW2 fill:#16A085,stroke:#2C3E50,color:#fff
    style GS1 fill:#E74C3C,stroke:#C0392B,color:#fff
    style GS2 fill:#2ECC71,stroke:#27AE60,color:#fff
    style FZ1 fill:#E8F6F3,stroke:#E67E22,color:#2C3E50
    style FZ2 fill:#E8F6F3,stroke:#16A085,color:#2C3E50
    style GND1 fill:#7F8C8D,stroke:#2C3E50,color:#fff
    style GND2 fill:#7F8C8D,stroke:#2C3E50,color:#fff
    style Loss1 fill:#E74C3C,stroke:#C0392B,color:#fff
    style Loss2 fill:#2ECC71,stroke:#27AE60,color:#fff

Figure 633.2: Ground-mounted vs elevated sensor showing Fresnel zone blockage impact on range

{fig-alt=“Comparison diagram showing ground-mounted sensor at 0.2m height with 95% Fresnel zone blockage causing 15-25 dB loss and 200-500m range, versus elevated sensor at 3m height with clear Fresnel zone achieving 0-3 dB loss and 5-10 km range, demonstrating critical importance of sensor height for long-range wireless links”}

Numerical Analysis (LoRa 915 MHz, 1 km link):

Ground-mounted sensor (h = 0.2m):

Fresnel zone radius at midpoint: r_1 = 9.4 m
Sensor height: 0.2 m
Ground clearance: 0.2 / 9.4 = 2.1% (FAR below 60% requirement!)

Diffraction loss from Fresnel blockage: ~18 dB
Ground reflection loss: ~5 dB
Total extra loss: 23 dB

Link budget impact:
Original margin: +25 dB
After ground loss: 25 - 23 = +2 dB (marginal link, unreliable)

Elevated sensor (h = 3m):

Fresnel zone radius at midpoint: r_1 = 9.4 m
Sensor height: 3 m
Ground clearance: 3 / 9.4 = 31.9% (still below 60%, but much better)

Diffraction loss: ~6 dB
Ground reflection loss: ~2 dB
Total extra loss: 8 dB

Link budget impact:
Original margin: +25 dB
After losses: 25 - 8 = +17 dB (excellent, reliable link)

Design Guideline: For long-range LoRa/Sigfox sensors, mount antennas at minimum 2-3 meters height, even for ground-level sensing applications (use cables to connect sensors at ground to antenna on pole).

633.10 Practical Deployment Examples

633.10.1 Example 1: Smart Agriculture (5 km LoRaWAN)

Problem: Soil sensors at ground level can’t reach gateway 5 km away.

Solution: - Move sensors to 3m poles with antenna at top - Use waterproof cables to connect ground-level soil probes to elevated transceivers - Result: Achieve 60% Fresnel clearance, maintain 5 km range

Cost Impact: - 3m pole per sensor: $50 - Labor for pole installation: $100 - Total per sensor: $150 - ROI: Reliable connectivity vs sensor failures requiring gateway densification ($5,000+ per gateway)

633.10.2 Example 2: Point-to-Point Wi-Fi Bridge (500m between buildings)

Problem: Direct line-of-sight between buildings, but connection is unstable.

Root cause analysis:

Distance: 500 m
Frequency: 5 GHz
Fresnel radius at midpoint: r_1 = 17.3 sqrt(0.5 / (4 x 5)) = 4.3 m
60% clearance: 2.6 m

Building A antenna: 3m above roof (20m total height)
Building B antenna: 3m above roof (22m total height)
Midpoint height: (20 + 22) / 2 = 21 m

Trees in path: 18m tall
Clearance: 21 - 18 = 3m (only 3/4.3 = 69% Fresnel clearance -> marginal!)

Solution: - Raise Building A antenna to 5m above roof (22m total) - Midpoint height: (22 + 22) / 2 = 22 m - Clearance: 22 - 18 = 4m (4/4.3 = 93% Fresnel clearance -> excellent!) - Result: Stable 500 Mbps link

633.10.3 Example 3: Urban NB-IoT Deployment

Problem: NB-IoT smart parking sensors (ground-level) have poor coverage.

Analysis:

NB-IoT frequency: 900 MHz (LTE Band 8)
Distance to cell tower: 2 km
Fresnel radius: r_1 = 17.3 sqrt(2 / (4 x 0.9)) = 12.1 m

Sensor height: 0.1 m (embedded in pavement)
Ground clearance: 0.1 / 12.1 = 0.8% (X)

Buildings, cars, and urban clutter block Fresnel zone
Additional loss: 20-30 dB

Why NB-IoT still works despite blockage:

  1. High transmit power: 23 dBm (200 mW) vs LoRa 14 dBm (25 mW) = +9 dB advantage
  2. Excellent receiver sensitivity: -140 dBm vs LoRa -137 dBm = +3 dB advantage
  3. Total extra margin: 12 dB compensates for some (but not all) Fresnel blockage
  4. Multipath propagation: Urban reflections provide alternative signal paths (not available in rural areas)

Result: NB-IoT works for ground-level urban sensors, but LoRa would fail in same conditions without elevation.

633.11 Advanced Worked Examples

NoteWorked Example: Multi-Floor Building Wi-Fi Coverage Planning

Scenario: A 5-story office building (each floor 40m x 30m) needs Wi-Fi coverage for 200 IoT devices per floor. Building has concrete floors (15 dB attenuation) and drywall partitions (4 dB each). Determine access point placement.

Given: - Floor dimensions: 40m x 30m = 1,200 sq m per floor - Concrete floor attenuation: 15 dB per floor - Drywall partition attenuation: 4 dB - Wi-Fi 2.4 GHz AP specifications: - TX power: 20 dBm - Receiver sensitivity: -90 dBm - Antenna gain: 3 dBi (omnidirectional) - Minimum required signal: -75 dBm for reliable IoT operation

Steps:

  1. Calculate available link budget:
    • TX EIRP: 20 + 3 = 23 dBm
    • Required received: -75 dBm
    • Maximum allowable path loss: 23 - (-75) = 98 dB
  2. Calculate single-floor horizontal coverage:
    • Path loss at 20m (indoor office, n=3.0):
    • FSPL at 20m, 2.4 GHz: 20 log(20) + 20 log(2400) + 32.45 = 66 dB
    • Environmental excess (n=3 vs n=2): 10(1.0) log(20) = 13 dB
    • Total at 20m: 66 + 13 = 79 dB
    • Add 2 partitions: 79 + 8 = 87 dB
    • Margin at 20m: 98 - 87 = 11 dB (acceptable)
  3. Test vertical coverage (floor-to-floor):
    • Horizontal distance: 10m (directly above/below)
    • Path loss at 10m: 60 + 10 = 70 dB
    • Add concrete floor: 70 + 15 = 85 dB
    • Received power: 23 - 85 = -62 dBm (above -75 dBm, works!)
    • One AP can serve devices directly above/below
  4. Calculate APs needed per floor:
    • Effective coverage radius: ~20m (with margin)
    • Coverage area per AP: pi x 20 squared = 1,257 sq m
    • Floor area: 1,200 sq m
    • Minimum APs per floor: 1,200 / 1,257 = 1 (theoretically)
    • Add 30% overlap: 1.3 APs per floor
    • Recommend: 2 APs per floor for redundancy and load balancing

Result: Deploy 2 APs per floor (10 total) in a staggered pattern. Each AP covers 600 sq m per floor plus partial coverage to adjacent floors. Total received signal ranges from -62 dBm (near AP) to -75 dBm (floor corners), with 13+ dB margin.

Key Insight: Concrete floors attenuate more than horizontal distance in most cases. An AP 10m away through concrete (85 dB loss) has similar path loss to an AP 25m away horizontally (86 dB loss). Plan coverage in 3D, not just 2D floor plans.

NoteWorked Example: Outdoor LoRaWAN Network Coverage with Terrain

Scenario: A utility company deploys LoRaWAN water meters across a 15 km x 10 km service area with varied terrain: urban core (2 km radius), suburban ring (5 km radius), and rural edge. A 50m hill blocks line-of-sight to 30% of the rural area. Determine gateway placement strategy.

Given: - LoRa 915 MHz specifications: - TX power: 14 dBm (sensor), 27 dBm (gateway) - Receiver sensitivity: -137 dBm (SF12) - Antenna gain: 2 dBi (sensor), 8 dBi (gateway) - Environment path loss exponents: - Urban (n=4.0), Suburban (n=3.0), Rural (n=2.3) - Hill height: 50m above surrounding terrain - Required link margin: 15 dB for 99.9% reliability

Steps:

  1. Calculate uplink budget (sensor to gateway):

    • TX EIRP (sensor): 14 + 2 = 16 dBm
    • RX (gateway): -137 + 8 = -129 dBm effective sensitivity
    • Max path loss: 16 - (-129) - 15 = 130 dB
  2. Determine range by environment:

    Urban (n=4.0):

    • Path loss = 58 + 40 log(d) = 130 dB
    • 40 log(d) = 72, log(d) = 1.8, d = 63m… too short!
    • Problem: n=4.0 assumes heavy obstruction
    • With gateway at 30m height (above buildings): n reduces to ~3.2
    • 58 + 32 log(d) = 130 dB, d = 1.26 km
    • Urban coverage radius: ~1.2 km

    Suburban (n=3.0):

    • 58 + 30 log(d) = 130 dB
    • 30 log(d) = 72, log(d) = 2.4, d = 251m… still seems short
    • Gateway height advantage: reduces n to 2.6
    • 58 + 26 log(d) = 130, d = 2.77 km
    • Suburban coverage radius: ~2.8 km

    Rural (n=2.3):

    • 58 + 23 log(d) = 130 dB
    • 23 log(d) = 72, log(d) = 3.13, d = 8.5 km
    • Rural coverage radius: ~8.5 km
  3. Address hill obstruction using knife-edge diffraction:

    • Hill creates 50m obstruction
    • Fresnel zone radius at 5 km (midpoint): 17.3 sqrt(10 / (4 x 0.915)) = 28.6m
    • Hill exceeds first Fresnel zone by 50 - 28.6 = 21.4m
    • Diffraction loss: approximately 6 + 20 log(v) where v = sqrt(2) x 21.4 / 28.6 = 1.06
    • Additional loss: 6 + 20 log(1.06) = 6.5 dB
    • Link still works (we have 15 dB margin, losing 6.5 dB leaves 8.5 dB)
  4. Gateway placement plan:

    • Primary gateway: Urban center, 30m rooftop, covers urban + inner suburban
    • Secondary gateway: Opposite side of hill, 15m tower, covers blocked rural area
    • Tertiary gateway: Far edge of service area for redundancy

Result: 3 gateways provide full coverage with redundancy. Primary gateway at urban center reaches 2.8 km (covers urban + most suburban). Secondary gateway behind the hill eliminates the obstruction shadow zone. Gateway costs: $1,500 each ($4,500 total) versus 15,000 meters served = $0.30/meter for infrastructure.

Key Insight: A single high-elevation gateway in urban areas outperforms multiple low-elevation gateways. The urban n=4.0 path loss exponent assumes ground-level propagation; elevating gateways 30m+ reduces effective path loss exponent by 0.5-1.0, dramatically increasing range. For terrain obstructions, calculate knife-edge diffraction loss rather than assuming complete blockage.

633.12 Summary

  • Fresnel zones require 60% clearance for reliable wireless links - obstacles in the ellipsoid cause diffraction loss
  • Lower frequency = larger Fresnel zone: LoRa at 915 MHz needs more clearance than Wi-Fi at 2.4 GHz
  • Antenna height scales with distance: 1 km needs 6m height, 5 km needs 15m height for same frequency
  • Ground-mounted sensors have 80-90% range reduction due to Fresnel blockage - elevate antennas to 2-3m minimum
  • Lower frequencies penetrate buildings better because wavelength enables diffraction around obstacles
  • Practical deployments must account for terrain, vegetation, and seasonal changes
TipDesign Checklist: Wireless IoT Deployment

Before deploying wireless IoT devices:

  1. Calculate link budget for worst-case distance and obstacles
  2. Measure actual RSSI at planned deployment locations (don’t trust theoretical models!)
  3. Add 10-20 dB fade margin for seasonal changes (foliage growth, rain, snow)
  4. Account for material attenuation: Concrete = 10-15 dB, metal = 20-30 dB per obstacle
  5. Consider frequency tradeoffs: Lower frequency = better penetration but larger antennas and less bandwidth
  6. Test in actual environment before large-scale deployment
  7. Plan for 20-30% coverage overlap to ensure handoff between access points/gateways

Common Mistake: Assuming line-of-sight range applies to indoor/urban deployments. Real range is typically 30-60% of theoretical maximum!

633.13 What’s Next

Continue to the Knowledge Checks chapter to test your understanding of radio propagation, link budgets, and Fresnel zones.