Wireless NetworkingUnit 29 min read

Wireless Channel: Path Loss, Fading, Interference & Capacity

Unit 2 of Wireless Networking explores how radio signals behave in free space and real-world environments, covering path loss models, fading types (multipath, shadowing), interference sources, and channel capacity limits. Students learn to calculate signal strength, analyze propagation effects, and design robust wirele

Padhai · Based on the official syllabus and past papers
Updated 3 Oct 2026

Key Concepts and Models

1. Wireless Channel Basics

The wireless channel is the medium through which radio signals propagate between a transmitter and receiver. Unlike wired channels, it is shared, time-varying, and prone to interference. Key factors affecting signal quality include:

Transmitter power (dBm or dBW)
Antenna gain (dBi)
Distance (free-space loss)
Obstacles (buildings, terrain)
Frequency (carrier wavelength)

Wireless channel path loss comparison: ideal free-space vs. real-world with obstacles

2. Path Loss Models

Path loss describes how signal strength decreases with distance. Two fundamental models:

Free-Space Path Loss

Assumes no obstacles and a clear line-of-sight (LOS) path. The formula is derived from the inverse-square law: $P L_{d B} = 32.44 + 20 lo g_{10} (d_{k m}) + 20 lo g_{10} (f_{M H z})$ Example: Calculate the free-space path loss for a 2.4 GHz signal at 1 km. $P L = 32.44 + 20 lo g_{10} (1) + 20 lo g_{10} (2400) = 32.44 + 0 + 67.6 = 99.94 dB$

Log-Distance Path Loss Model

Accounts for real-world obstacles (buildings, terrain) using an empirical path loss exponent $γ$ : $P L (d) = P L (d_{0}) + 10 γ lo g_{10} (\frac{d}{d _{0}})$

$P L (d_{0})$ : Reference path loss at distance $d_{0}$ (typically 1 m).
$γ$ : Path loss exponent (2 ≤ γ ≤ 6; higher in urban areas).
Example: For $P L (1 m) = 40 dB$ , $γ = 3$ , and $d = 100 m$ : $P L (100) = 40 + 10 \times 3 \times lo g_{10} (100) = 40 + 60 = 100 dB$

Comparison Table:

Model	Assumptions	Formula	Typical γ (Urban)
Free-Space	LOS, no obstacles	$32.44 + 20 lo g_{10} (d) + 20 lo g_{10} (f)$	N/A
Log-Distance	Empirical, obstacles present	$P L (d_{0}) + 10 γ lo g_{10} (d / d_{0})$	2.7–4.0

3. Fading in Wireless Channels

Fading occurs when the received signal amplitude fluctuates due to multipath propagation or shadowing. Two main types:

Multipath Fading

Caused by reflections, diffractions, and scattering of signals. Constructive/destructive interference leads to rapid signal fluctuations (Rayleigh or Rician fading).

Time-domain illustration of multipath fading causing signal fluctuations

Multipath fading: how reflections, diffractions, and scattering combine at the receiver

Example: In Kathmandu’s Thamel district, signals from a Wi-Fi router bounce off buildings, creating deep fades at certain spots. A user moving 1 m may experience a 20 dB signal drop.

Shadowing (Slow Fading)

Long-term variations due to large obstacles (e.g., hills, tall buildings). Modeled as a log-normal distribution: $P L_{d B} = \overline{P L} (d) + X_{σ}$

$\overline{P L} (d)$ : Mean path loss.
$X_{σ}$ : Zero-mean Gaussian random variable (σ = 4–12 dB in urban areas).

Real-World Impact:

eSewa App: Uses shadowing models to predict signal drops in hilly regions like Pokhara, adjusting retransmission rates.
NTC’s 4G Rollout: Accounts for shadowing in Kathmandu’s dense buildings by deploying more small cells.

4. Interference in Wireless Networks

Interference degrades signal quality. Types:

Co-channel Interference (CCI): Signals from nearby cells using the same frequency.
Adjacent Channel Interference (ACI): Leakage from adjacent frequency bands.
Inter-symbol Interference (ISI): Delay spread causes symbols to overlap.

Example: In a Pathao driver’s app, interference from nearby Ncell towers on the same 1800 MHz band can cause call drops. Pathao’s backend uses frequency hopping to mitigate this.

Co-channel interference (CCI) example: two Ncell towers on same frequency band causing ISI

5. Channel Capacity

Shannon’s channel capacity defines the maximum data rate for a noisy channel: $C = B lo g_{2} (1 + \frac{S}{N})$

$C$ : Channel capacity (bits/sec).
$B$ : Bandwidth (Hz).
$S / N$ : Signal-to-noise ratio (linear).

Relative channel capacity reduction due to path loss, fading, and interference (normalized to free-space)

Example: For a 20 MHz Wi-Fi channel with $S / N = 10 dB$ (linear = 10): $C = 20 \times 1 0^{6} lo g_{2} (11) \approx 70 Mbps$ Real-World Tie-In:

YouTube (Google): Uses adaptive bitrate streaming to adjust video quality based on measured channel capacity. If your $S / N$ drops (e.g., in a moving bus), YouTube switches to a lower-resolution stream.

6. Practical Measurements and Tools

Students should understand how path loss and fading are measured:

Received Signal Strength Indicator (RSSI): Measures power in dBm (e.g., -50 dBm = strong, -90 dBm = weak).
Path Loss Measurement: Use a spectrum analyzer or software like Wireshark to log signal strength vs. distance.
Fading Simulation: Tools like MATLAB or NS-3 simulate Rayleigh/Rician fading.

In the Real World

Khalti App (Nepal):
- Idea Used: Path Loss and Shadowing
- How: Khalti’s backend servers adjust transaction timeouts based on real-time signal strength reports from users. In hilly areas like Dhading, transactions may take longer due to higher path loss (γ ≈ 4), so Khalti increases retry limits.
Daraz Logistics:
- Idea Used: Multipath Fading and Interference
- How: Daraz’s warehouse Wi-Fi uses MIMO (Multiple Input Multiple Output) to combat fading. In Kathmandu’s crowded markets, signals reflect off metal shelves, causing deep fades. MIMO’s spatial diversity ensures stable connections for inventory updates.
Ncell 4G Network:
- Idea Used: Log-Distance Path Loss and Small Cells
- How: Ncell deploys small cells in high-density areas (e.g., Lakshmi Path) to compensate for path loss. A user at 50 m from a macro cell might experience 100 dB loss (γ ≈ 3.5), but a small cell at 10 m reduces this to 70 dB, improving call quality.

Worked Example: Signal Strength in a Bus

Scenario: A student on a Kathmandu-Kirtipur bus uses WhatsApp at 2.4 GHz. The bus moves from a clear area (LOS) into a tunnel (NLOS).

LOS Path Loss (free-space model): $P L = 32.44 + 20 lo g_{10} (0.5) + 20 lo g_{10} (2400) = 83.8 dB$
NLOS Path Loss (log-distance, γ = 4, $P L (1 m) = 40 dB$ ): $P L = 40 + 10 \times 4 \times lo g_{10} (500) = 40 + 70 = 110 dB$
Shadowing Effect: Add $X_{σ} = - 8 dB$ (typical for tunnels): $P L_{total} = 110 - 8 = 102 dB$
Received Power: If transmitter power = 20 dBm and antenna gain = 2 dBi: $P_{r} = P_{t} + G_{t} - P L = 20 + 2 - 102 = - 80 dBm$ Result: WhatsApp may drop calls or switch to a lower-quality codec.

Exam Tip

Memorize Formulas:
- Free-space path loss: $32.44 + 20 lo g_{10} (d) + 20 lo g_{10} (f)$ .
- Log-distance path loss: $P L (d_{0}) + 10 γ lo g_{10} (d / d_{0})$ .
- Shannon capacity: $C = B lo g_{2} (1 + S / N)$ .
Unit Conversions:
- Always convert distances to km and frequencies to MHz for path loss calculations.
- Convert dB to linear scale: $linear = 1 0^{(d B /10)}$ .
Graphical Questions:
- Expect plots of path loss vs. distance (logarithmic scale) and fading distributions (Rayleigh/Rician).
- Label axes clearly (e.g., "Path Loss (dB)" vs. "Distance (m)").
Real-World Applications:
- Link theoretical concepts to Nepali examples (e.g., Ncell’s small cells, eSewa’s timeout adjustments).
- For capacity questions, assume typical $S / N$ values (e.g., 10 dB for Wi-Fi, 15 dB for 4G).
Common Pitfalls:
- Forgetting to add antenna gains in received power calculations.
- Using the wrong $γ$ (e.g., γ = 2 for rural, γ = 4 for urban).
- Misapplying Shannon’s formula (log base 2, not natural log).

Based on the TU BSc CSIT syllabus for Wireless Networking, unit 2.

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