3 - Propagation of Radar Signals: Interaction with the Atmosphere

Propagation of Radar Signals: Coping with the Atmosphere

This article is based on the third part (Lecture 3 - Propagation Effects) of the MIT Lincoln Laboratory "Introduction to Radar Systems" lecture series. As radar signals travel from the antenna to the target and back, they pass through the atmosphere. Understanding what happens in this "soup" is critically important for accurately predicting radar performance.

1. Propagation Effects: Overview

The radar signal passes through the atmosphere as it leaves the antenna, reaches the target, and returns. This medium, referred to as the "soup," affects the signal in four different ways:

Attenuation: The atmosphere absorbs or scatters part of the signal.

Reflection: The signal reflects off the ground surface and mixes with the direct signal.

Diffraction: The signal "bends" behind obstacles.

Refraction: The changing density of the atmosphere bends the signal.

2. Atmospheric Parameters

The properties of the atmosphere change dramatically with altitude:

• Temperature: 20°C at sea level, but can be -50°C at 10 km altitude.

• Pressure: Decreases with altitude (on the summit of Everest, about ~1/3 of sea level).

• Water vapor: Decreases with altitude.

• Refractive index: Depends on all these factors and determines how the signal bends.

3. Atmospheric Attenuation

Electromagnetic waves lose energy as they pass through the atmosphere. This loss is strongly dependent on frequency.

3.1 Water Vapor and Oxygen Absorption

Water vapor and oxygen molecules in the atmosphere exhibit strong absorption at certain frequencies:

Water vapor resonance: Strong absorption around ~22 GHz

Oxygen resonance: Very strong absorption around ~60 GHz

Practical result: Building radar near these frequencies is avoided.

3.2 Attenuation by Frequency

Critical observation: For a range of 50 km, 0.1 dB/km attenuation = 10 dB two-way loss. This means the received power drops to 1/10!

3.3 Effect of Rain and Fog

If there is precipitation, attenuation increases dramatically:

• Raindrops scatter and absorb the signal.

• The effect increases strongly with frequency.

• At X-band and higher frequencies, even moderate rain causes significant losses.

• Low frequencies (L, S-band) are more resistant to rain.

Design consequence: High-frequency radars are generally short-range or operate above the atmosphere (aircraft, space). Long-range surveillance radars operate at low frequencies.

4. Multipath and Interference

A critical effect for radars operating near the ground: the signal reaches the target via two paths.

4.1 Direct and Reflected Path

Direct path: Radar → Target → Radar (straight line)

Reflected path (Multipath): Radar → Ground → Target → Ground → Radar

These two signals reach the target with different phases and interfere with each other.

4.2 Consequences of Interference

Depending on the phase difference:

Constructive interference: Voltage doubles → Power quadruples → 16-fold increase in both directions!

Destructive interference: Voltage 0 → Power 0 → Complete blind spot!

Result: With constructive interference, range can double; with destructive interference, it can drop to zero.

4.3 Lobe Structure

Interference varies with elevation angle. This creates a structure called "lobing":

• Maximum detection at certain elevation angles (constructive interference)

• Minimum detection or blind spots in between (destructive interference)

• Number of lobes increases with frequency (higher frequency = more lobes)

• Lower frequency = fewer but wider lobes

4.4 Surface Reflectivity

The reflection coefficient (Γ) depends on the surface:

5. Diffraction

Electromagnetic waves "bend" behind obstacles. This is a behavior not predicted by geometric optics.

5.1 Everyday Examples

• Tsunami waves wrapping around a peninsula

• Hearing a speaker from behind a door in a conference hall

• Formation of sea waves behind a breakwater

5.2 Implications for Radar

Diffraction region: The area below the tangent line drawn from the radar to the horizon point. There is signal in this region, but severe attenuation occurs.

Frequency effect:

• Low frequencies diffract better (over-the-horizon detection is easier).

• High frequencies behave almost like geometric optics.

• Example: 60 dB loss at 60 km in L-band, 80 dB loss in X-band.

5.3 Multipath vs Diffraction Trade-off

6. Atmospheric Refraction

Just as a spoon appears "broken" in a glass of water, a radar signal also bends in the atmosphere.

6.1 Refractive Index

Refractive index (n): The ratio of the speed of light in vacuum to its speed in the medium.

At sea level, n ≈ 1.000350 (only 350 ppm different from vacuum). However, this small difference causes significant bending over long distances.

The refractive index depends on:

• Temperature

• Pressure

• Partial pressure of water vapor

6.2 Refractivity and Types of Atmosphere

Refractivity (N): Defined as (n - 1) × 10⁶. Decreases with altitude.

6.3 4/3 Earth Model

To simplify calculations, the curvature of the radar beam in a normal atmosphere is represented by a "flattened" model in which the Earth's radius is multiplied by 4/3.

Equivalent Earth radius = k × a,  k = 4/3 (normal atmosphere)

6.4 Ducting

Under extreme super-refraction conditions, the radar signal follows the curvature of the Earth and propagates within a "duct".

• Low altitude detection is dramatically extended.

• However, unexpected "holes" (blind spots) may occur.

• Ground clutter may appear at distances that would not normally be visible.

Real example: A radar near Boston detected ground clutter from Cape Cod (over 100 km away, only 30 m above sea level) under ducting conditions — normally impossible.

What Did We Learn in This Section?

✓ Frequency dependence of atmospheric attenuation

✓ Water vapor and oxygen absorption bands

✓ Effect of rain and fog on radar performance

✓ Multipath reflection and lobing mechanism

✓ Effect of constructive/destructive interference on range

✓ Diffraction and beyond-the-horizon detection

✓ Refractive index and atmospheric types

✓ 4/3 Earth model

✓ Ducting phenomenon

Design rule: Low frequency for long range and all-weather conditions; high frequency for high resolution and compact size. Propagation effects determine this trade-off.

Source: MIT Lincoln Laboratory, "Introduction to Radar Systems Online" - Lecture 3: Propagation Effects, 2018.