Module 04 of 11 · Academy overview

Multipath Effects & Signal­Propagation

Wave propagation, ground reflection, Fresnel zones, ghost targets and an interactive ray-tracing visualization.

Academy Module

Published by: Ozense
Last reviewed: 13 August 2026

FUNDAMENTALS

Fundamentals of Wave­Propagation

Before we can understand multipath effects, we need to know the fundamental mechanisms of electromagnetic wave propagation. In a real scenario, the radar signal does not reach the target only via the direct path – it is reflected, refracted and absorbed.

Free-Space Path Loss (FSPL):

Pr / Pt = (λ / (4πR))²

The received power Pr decreases quadratically with distance R. This free-space attenuation factor describes the ideal case with no obstacles, reflections or atmospheric losses. For a radar with a two-way path, an R4 dependency even applies (see the radar equation).

Atmospheric Attenuation

In addition to the geometric loss, gas molecules (O2, H2O) absorb electromagnetic energy. The attenuation is strongly frequency-dependent:

Frequency Atmos. Attenuation Rain Attenuation (25 mm/h) Application
24 GHz ~0.1–0.2 dB/km ~3.7 dB/km ISM band, smart-home sensors
60 GHz ~15 dB/km (O2 absorption) ~10.1 dB/km Short range, in-cabin monitoring
77 GHz ~0.4 dB/km ~11.4 dB/km Automotive, drone detection

Rain attenuation per ITU-R P.838-3 (γ = k·Rα, horizontal polarization, R = 25 mm/h). Gas attenuation per ITU-R P.676 for a standard atmosphere. For radar, the double value applies because the path is traversed twice – at 77 GHz and a 500 m target range that amounts to roughly 11 dB of two-way loss.

Humidity & Fog

Water vapor increases attenuation particularly around 22 GHz (the H2O resonance line). Fog (droplets < 0.1 mm) has only a minor effect at millimeter waves (< 1 dB/km), because the droplets sit in the Rayleigh regime.

Atmospheric Refraction

The refractive index of the atmosphere decreases with altitude (temperature and pressure gradient). This causes radar beams to curve slightly toward the earth. The effective earth radius is corrected with the factor k ≈ 4/3: Reff = k · REarth.

GROUND REFLECTION

Two-Ray Ground Reflection Model

The two-ray model is the simplest and most important multipath model. Besides the direct path, it accounts for a path reflected off the ground. The superposition of both signals produces a characteristic interference pattern.

Path-Length Difference:

ΔR = 2 · ht · hr / R

Valid for ht, hr << R (shallow incidence angle). Here ht is the transmitter height, hr the receiver/target height and R the horizontal distance. The phase difference follows as Δφ = 2πΔR / λ.

Propagation Factor F

The propagation factor describes the deviation of the field strength from the free-space value. For a perfectly conducting, flat ground surface (reflection coefficient Γ ≈ -1), it works out to:

Propagation Factor:

F = 2 · sin(2π · ht · hr / (λ · R))

The received power is multiplied by |F|². Under constructive interference (|F| = 2), the power is 6 dB higher than in free space. Under destructive interference (|F| = 0), nulls occur – the target disappears entirely.

Lobing Pattern – Maxima

Constructive interference occurs at:

Rmax,n = 4 · ht · hr / ((2n-1) · λ)

At these distances, the direct and reflected paths add in phase. The signal is up to 6 dB stronger than in free space.

Lobing Pattern – Nulls

Destructive interference occurs at:

Rnull,n = 2 · ht · hr / (n · λ)

At these distances, the two paths cancel destructively. The target is not detectable despite sufficient RCS – a so-called „blind spot“.

FRESNEL ZONES

Fresnel Zones & Line-of-Sight­Analysis

Fresnel zones describe ellipsoidal regions around the direct line of sight (LOS) between transmitter and receiver. Obstacles that intrude into this zone weaken the signal – even when the geometric line of sight is clear.

Radius of the First Fresnel Zone:

r1 = √(λ · d1 · d2 / (d1 + d2))

Here d1 is the distance from the transmitter to the cross-section point and d2 the distance from that point to the receiver. The maximum radius occurs at the midpoint of the path (d1 = d2 = d/2): r1,max = √(λ · d / 4).

Practical Clearance Rule

For near-lossless transmission, at least 60% of the first Fresnel zone should be free of obstacles. If an obstacle just grazes the line of sight, the diffraction loss is around 6 dB; with full blockage of the first Fresnel zone it lies well above that.

Frequency λ r1,max at d = 100 m r1,max at d = 500 m 60% Clearance
24 GHz 12.5 mm 0.56 m 1.25 m 0.75 m
60 GHz 5.0 mm 0.35 m 0.79 m 0.47 m
77 GHz 3.9 mm 0.31 m 0.70 m 0.42 m

Effect on the Link Budget:

When planning a radar deployment, the Fresnel zone must be taken into account. A sensor at 1 m height intended to detect out to 200 m has a Fresnel zone of ~0.44 m at its midpoint (at 77 GHz). Terrain irregularities, fences or low shrubs in this region can significantly reduce detection performance.

GHOST TARGETS

Ghost-Target Formation via Multipath

Multipath reflections generate apparent targets (ghost targets) that appear as additional peaks in the range profile. The radar cannot distinguish whether an echo originates from the direct path or a reflected one – it interprets the additional travel time as a greater distance.

Single-Bounce Ghost

The signal takes a detour via a reflecting surface (ground, wall). The ghost appears at the sum of the partial lengths:

Rghost = (RTx→wall + Rwall→target + Rtarget→Rx) / 2

Because the detour is longer than the direct path, the ghost target always appears behind the true target in the range profile.

Double-Bounce Ghost

The signal reflects twice: first off a wall, then off the target, then off the wall again. Especially problematic in corners and corridors:

Rghost = Rdirect + ΔRdetour

Double-bounce ghosts can have an RCS similar to the true target, because the reflection coefficient of metal surfaces is close to 1.

Multi-Bounce in Indoor Environments

In enclosed spaces (offices, corridors, warehouses), multiple reflections between walls, ceiling and floor can occur. Every reflection path creates a potential ghost target in the range profile: 

# Range profile with multipath ghosts (simulation)
import numpy as np

R_true = 5.0          # True target at 5 m
R_wall = 3.0          # Wall distance 3 m

# Image-source method: wall as plane y = R_wall.
# Radar at (0,0), target at (R_true,0), mirror radar at (0, 2*R_wall).
d_direct  = R_true
d_via_wall = np.sqrt(R_true**2 + (2 * R_wall)**2)

# Measured range = half the total path length (out + back)
# Single-bounce: out via the wall, back direct
R_ghost1 = (d_via_wall + d_direct) / 2
# = 6.41 m → ghost 1.41 m behind the target

# Double-bounce: out and back via the wall
R_ghost2 = d_via_wall
# = 7.81 m

# Amplitude decreases with every bounce (Γ^n)
print(f"True target: {R_true} m")
print(f"Ghost 1 (single-bounce): {R_ghost1:.1f} m")
print(f"Ghost 2 (double-bounce): {R_ghost2:.1f} m")

Recognition Feature of Ghost Targets:

Ghosts typically have a lower amplitude than the true target, because energy is lost at every reflection (|Γ| < 1 for imperfect conductors). Ghosts also move inconsistently – their apparent velocity depends on the geometry of the reflection path, not on the true target kinematics.

MITIGATION

Mitigation­Strategies

Suppressing multipath artifacts is critical for reliable radar systems. There are approaches at several levels: antenna design, signal processing, tracking and machine learning.

Antenna Design

A narrow beamwidth reduces illumination of reflecting surfaces. Low sidelobes (sidelobe level < -20 dB) reduce energy pickup from multipath directions. Beamforming enables spatial filtering.

Detection Threshold (CFAR)

Ghost targets often have a lower SNR than the true target and then fall below the threshold. That is, however, a side effect, not a mechanism: CFAR keeps the false-alarm rate constant against fluctuating interference level and does not distinguish between a real target and a ghost. A ghost with sufficient SNR is detected like any other target – the actual suppression is done by the clutter map, track plausibility checking and geometry knowledge.

Track-Level Filtering

In the Kalman tracker, ghost targets show inconsistent kinematics: unrealistic accelerations, sudden jumps or unphysical velocities. The normalized innovation (NIS), i.e. the Mahalanobis distance νTS-1ν, serves as the measure – the deviation measured against the expected uncertainty S, not S itself, which merely describes the modelled uncertainty.

Clutter Map Subtraction

For stationary radar systems, an „empty“ reference measurement of the environment can be recorded. Stationary multipath echoes (walls, ground) are removed by subtraction. Only moving targets remain. Advantage: simple and effective. Drawback: works only for stationary reflectors.

Machine Learning

CNNs and CRNNs can be trained on range-Doppler maps to recognize ghost patterns. The network learns the typical signatures: ghosts appear at predictable offsets relative to the true target and have correlated Doppler shifts. Transfer learning from simulated to real data is promising.

Multipath Exploitation (NLOS Radar):

A current research trend is exploiting multipath instead of suppressing it. By analyzing the reflection paths, a radar can detect targets „around the corner“ (non-line-of-sight, NLOS). This uses known room geometry to reconstruct reflection paths and map ghost positions back to true positions.

ENVIRONMENT COMPARISON

Indoor vs. Outdoor Multipath

Multipath characteristics differ fundamentally between indoor and outdoor areas. This has direct consequences for system design and signal processing.

Indoor Environment

Walls, ceiling, floor and furniture create numerous reflection paths. The signal energy stays „trapped“ in the room – similar to reverberation in acoustics.

Reverberation time τrev = typically 50–200 ns

• Many reflection paths (10–50+ echoes)
• Short path differences (0.1–10 m)
• High reflection coefficients (concrete: |Γ| ≈ 0.4 at normal incidence, notably higher at grazing incidence; metal: |Γ| ≈ 0.95)
• Application: smart home, vital-signs monitoring, room presence

Outdoor Environment

Outdoors, ground reflection dominates. Buildings and terrain features can cause further reflections, but with substantially longer paths.

Dominant reflection: ground (two-ray model)

• Few dominant reflection paths (1–5)
• Ground reflection often dominant (|Γ| depends on ground properties)
• Large path differences possible (10–1000 m)
• Application: drone detection, perimeter protection, traffic monitoring

Property Indoor Outdoor
Number of reflection paths High (10–50+) Low (1–5)
Dominant mechanism Wall reflections, multiple reflections Ground reflection (two-ray)
Ghost-target severity High Medium
Mitigation Clutter map, ML-based Antenna height, beamforming
Reverberation time 50–200 ns < 10 ns

Practical Example – Smart Home (60 GHz):

A 60 GHz presence sensor in a 4×5 m room receives, besides the direct echo of a person (≈ 3 m), reflections from the back wall (6 m), the side wall (4.5 m), the ceiling (4.2 m) and a metal cabinet (5.8 m). Without a clutter map, these stationary wall and ceiling echoes appear as additional targets – strictly speaking, real clutter rather than ghost targets in the sense of multipath propagation. With background subtraction and CFAR, only the moving real targets remain.

INTERACTIVE

Ray-Tracing Visualization

Explore the two-ray model interactively: change antenna height, target height and frequency to visualize ground reflection, ghost-target positions and the propagation factor.

Computed Values:

Path difference: 0.478 m

Ghost range: 50.5 m

|F|²: 1.4 dB

Computed for a fixed reference distance of 50 m: a simulation parameter – not a demonstrated Ozense range.

Propagation factor |F|² vs. distance:

Scope and Limits

This module explains a method that is actually used in the Ozense processing chain. It describes the method and its limits – not the measured performance of the system. The visualizations shown are simulated in the browser and are not field performance evidence.

How the methods work together at Ozense: Technology. What is actually measured today: Validation and Development Status.

Ozense · last reviewed on 13 August 2026

All Academy Modules