Wireless Channel: Path Loss, Fading, Multipath, Noise & Capacity

TAKEAWAYS:

• Path loss follows the Friis free-space equation and log-distance model, and is worse in urban areas due to buildings and foliage.
• Multipath fading (Rayleigh/Rician) occurs when signals take multiple paths, causing destructive interference and deep signal drops.
• Noise (thermal, interference, man-made) is quantified by SNR and SINR, directly limiting channel capacity via the Shannon-Hartley theorem.
• Channel capacity depends on bandwidth, SNR, and modulation efficiency—higher SNR or wider bandwidth yields more bits per second.
• Doppler shift explains how moving receivers (e.g., cars, drones) experience frequency shifts, affecting symbol timing and synchronization.
• Practical tools like path loss exponents (n) and fading margins help engineers design reliable wireless links (e.g., for Ncell towers or eSewa hotspots).

---

1. Wireless Channel Basics: What Degrades Signals?

Wireless signals weaken and distort as they travel through air, buildings, and obstacles. The wireless channel is the medium (air, atmosphere) that carries radio waves from transmitter to receiver. Unlike wired cables, it is uncontrolled—subject to:

• Path loss (signal attenuation over distance)
• Multipath fading (signal reflections causing interference)
• Noise (random disturbances)
• Doppler effect (frequency shifts due to motion)

1.1 Path Loss: Why Signals Weaken Over Distance

Path loss is the reduction in signal power as it travels from transmitter to receiver. It depends on:

• Distance (farther = weaker)
• Frequency (higher frequencies attenuate faster)
• Environment (urban, suburban, rural)

Key Models for Path Loss

Worked Example: Ncell Base Station Coverage A Ncell 4G base station transmits at 40 dBm with 18 dBi antenna gain. At 1 km, the received power in free space is: $$P_r=40+18+18-20{\log }_{10}(1000)-20{\log }_{10}(2.4\times 10^9)-32.45=-65.5\text{ dBm}$$ In Kathmandu’s urban area (n = 3.5), the log-distance model gives: $$P_r(1\text{ km})=P_r(100\text{ m})-10\times 3.5{\log }_{10}(10)=-70\text{ dBm}-15=-85\text{ dBm}$$ Why? Buildings and traffic increase path loss beyond free-space predictions.

---

---

2. Multipath Fading: Why Signals Disappear and Reappear

When radio waves reflect off buildings, vehicles, or the ground, they arrive at the receiver via multiple paths. These paths can:

• Constructively interfere (stronger signal)
• Destructively interfere (signal cancellation, "fading")

Types of Multipath Fading

Rayleigh vs. Rician Fading

• Rayleigh fading: No direct (LOS) path → signal amplitude follows Rayleigh distribution. $$p(r)=\frac{r}{{\sigma }^2}{e}^{-r^2/(2{\sigma }^2)}$$
• Rician fading: Strong LOS component → signal follows Rician distribution (less severe drops). $$p(r)=\frac{r}{{\sigma }^2}{e}^{-(r^2+K{\sigma }^2)/(2{\sigma }^2)}{I}_0\left(\frac{r\sqrt{K}}{\sigma }\right)$$ (K = Rician K-factor: higher K = less fading)

Real-World Example: Daraz Delivery Drone A drone delivering packages in Pokhara flies at 100 m/s over hilly terrain. The Doppler shift causes frequency shifts: $$f_d=\frac{v}{\lambda }=\frac{100}{0.125}=800\text{ Hz}(\text{for }2.4\text{ GHz Wi-Fi})$$ This shift can desynchronize symbols, requiring equalization (covered in Unit 4).

---

Caption: Multipath propagation: how reflections create fading.

---

3. Noise in Wireless Channels

Noise is unwanted random signals that corrupt the desired signal. Types:

1. Thermal noise (from resistor motion, white Gaussian noise) $$N=kTB(\text{Watts})$$ (k = Boltzmann’s constant, T = temperature in Kelvin, B = bandwidth)
2. Interference (from other transmitters, e.g., Wi-Fi, Bluetooth)
3. Man-made noise (motors, power lines)

Signal-to-Noise Ratio (SNR) and Capacity

The Shannon-Hartley theorem defines the maximum channel capacity (C) in bits per second: $$C=B{\log }_2(1+\text{SNR})$$ Worked Example: eSewa Hotspot Capacity An eSewa hotspot operates at:

• Bandwidth (B) = 20 MHz
• SNR = 10 dB (20:1 linear) $$C=20\times 10^6{\log }_2(1+20)=20\times 10^6\times 4.32=86.4\text{ Mbps}$$ If SNR drops to 0 dB (1:1), capacity falls to 20 Mbps—why? Noise limits data rates!

---

---

4. Doppler Effect: How Motion Affects Signals

When the receiver or transmitter moves, the frequency shifts due to the Doppler effect: $$f_d=\frac{v}{\lambda }\cos (\theta )$$

• v = relative velocity
• λ = wavelength
• θ = angle between motion and signal path

Example: NTC’s 5G Trial in Kathmandu A 5G user in a car moving at 60 km/h (16.67 m/s) on a 28 GHz signal: $$f_d=\frac{16.67}{0.0107}\cos (0)=1558\text{ Hz}$$ This shift can disrupt OFDM symbols (used in 5G), requiring Doppler-resistant modulation.

---

Caption: Doppler effect: frequency shift due to relative motion.

---

5. Channel Capacity and Bandwidth Trade-offs

Real-World Trade-off: Pathao’s Bike Delivery

• Problem: Bikes move fast → Doppler fading.
• Solution: Use lower-order modulation (QPSK) instead of 64-QAM to tolerate fading.
• Trade-off: Lower data rate but more reliable connections.

---

Caption: Factors affecting wireless channel capacity.

---

In the Real World

1. Ncell 4G/LTE Networks

   • Path loss modeling: Ncell uses log-distance path loss (n = 3.2–3.8) to place towers in Kathmandu’s dense urban areas.
   • Multipath mitigation: Uses MIMO (Multiple Input Multiple Output) to exploit multiple paths constructively.
   • Doppler handling: Accounts for vehicle speeds (up to 120 km/h) in Doppler-resistant OFDM design.

2. eSewa and Khalti Mobile Payments

   • SNR requirements: Transactions require >15 dB SNR for secure data transfer. Poor SNR in rural areas leads to failed payments.
   • Bandwidth vs. latency: Khalti uses narrowband IoT (NB-IoT) for low-power transactions, sacrificing speed for reliability.

3. Daraz and Pathao Logistics

   • Multipath in warehouses: Daraz’s automated sorting uses UHF RFID (900 MHz), which suffers from Rayleigh fading in metal shelves.
   • Doppler in delivery drones: Pathao’s drones must compensate for frequency shifts when hovering near buildings.

---

Exam Tip

1. Memorize key formulas:

   • Friis free-space equation
   • Log-distance path loss
   • Shannon capacity (C = B log₂(1 + SNR))
   • Doppler shift (f_d = v/λ)

2. Compare scenarios:

   • Urban vs. rural path loss (higher n in cities)
   • Rayleigh vs. Rician fading (LOS vs. no LOS)
   • Thermal noise vs. interference (which dominates in exams?)

3. Worked examples are critical:

   • Always show steps for path loss calculations.
   • For capacity, convert dB to linear before plugging into Shannon’s formula.
   • Doppler effect: Remember f_d = v/λ—examiners love testing this!

4. Diagrams save marks:

   • Draw multipath fading (direct + reflected paths).
   • Sketch SNR vs. capacity curve.
   • Label Doppler shift in a sequence diagram.

5. Real-world applications:

   • Link path loss to base station placement (Ncell).
   • Relate fading to retransmissions (WhatsApp messages failing in valleys).
   • Connect Doppler to high-speed trains (Nepal’s upcoming metro).

---

Final Checklist Before Exam: ✅ Can you derive path loss for both free-space and log-distance models? ✅ Do you know when to use Rayleigh vs. Rician fading? ✅ Can you calculate channel capacity given SNR and bandwidth? ✅ Can you explain Doppler effect in a moving vehicle scenario? ✅ Do you recognize multipath fading in real networks (e.g., Wi-Fi drops in offices)?