UNIT 3: WIRELESS CHANNEL CHARACTERISTICS & MITIGATION TECHNIQUES

1.0 INTRODUCTION & WIRELESS SYSTEM OVERVIEW

Wireless Evolution (1G to 5G):

Types of Wireless Services & Requirements:

• Voice: Low latency (< 100 ms), moderate reliability.

• Data/Internet (eMBB): High throughput (Gbps), moderate latency.

• Mission-Critical (URLLC): Ultra-low latency (< 1 ms), high reliability (> 99.999%).

• Massive IoT (mMTC): Massive connectivity (1M devices/km²), low power, low data rate.

[!TIP] Exam Focus: Be prepared to contrast eMBB, URLLC, and mMTC in terms of their Key Performance Indicators (KPIs).

Key Technical Challenges:

1. Limited Spectrum: Scarcity drives need for efficiency (e.g., massive MIMO, mmWave).

2. Multipath Propagation: Causes fading and Inter-Symbol Interference (ISI).

3. User Mobility: Causes Doppler shift/spread, leading to time-varying channels.

4. Noise & Interference: From other users, cells, and electronics (thermal noise).

5. Power Constraints: Battery life limits for mobile devices.

2.0 WIRELESS CHANNEL IMPAIRMENTS & FUNDAMENTAL PARAMETERS

2.1 Large-Scale Fading

• Path Loss: Average signal power decay with distance.

  • Free-space Path Loss (FSPL):

$$PL(d) = \left( \frac{4\pi d}{\lambda} \right)^2 = \left( \frac{4\pi d f_c}{c} \right)^2$$

*   **Log-distance Path Loss:** 

$$PL(d) = PL(d_0) + 10n \log_{10}\left(\frac{d}{d_0}\right) + X_\sigma$$

where n = path loss exponent, X_σ = log-normal shadowing.

• Shadowing: Slow variations due to large obstacles (buildings, hills). Modeled as log-normal distribution.

2.2 Small-Scale Fading (Multipath)

Core Concept: Rapid signal fluctuations over short distances (λ/2) due to constructive/destructive interference of multipath components.

A. Doppler Shift & Spread

• Doppler Shift (Single Path):

$$f_d = \frac{v}{\lambda} \cos \theta = f_c \frac{v}{c} \cos \theta$$

*   `v` = mobile speed, `θ` = angle between mobile direction and incoming wave, `f_c` = carrier frequency.

• Maximum Doppler Spread:

$$f_{d,\max} = \frac{v}{\lambda} = f_c \frac{v}{c}$$

• Impact: Higher v or f_c → larger f_d → faster channel variation.

B. Delay Spread & Coherence Bandwidth

• RMS Delay Spread:

$$\tau_{rms} = \sqrt{\overline{\tau^2} - (\overline{\tau})^2}$$

where \overline{\tau} and \overline{\tau^2} are first and second moments of the Power Delay Profile (PDP).

• Coherence Bandwidth (B_c): Approximate bandwidth over which channel response is highly correlated.

  • Rule of thumb:

$$B_c \approx \frac{1}{5\tau_{rms}}$$

(for frequency-selective fading when symbol duration T_s > B_c).

• Impact: Large τ_rms → small B_c → frequency-selective fading → causes ISI.

C. Coherence Time & Time-Selectivity

• Coherence Time (T_c): Time duration over which channel impulse response is invariant.

  • Approximation:

$$T_c \approx \frac{1}{f_d}$$

• Impact: Fast fading if symbol duration T_s > T_c. Channel must be tracked frequently.

[!TIP] Common Pitfall: Do NOT confuse Coherence Bandwidth (frequency domain, related to delay spread) with Coherence Time (time domain, related to Doppler spread).

2.3 Fading Channel Models (Amplitude Statistics)

$$f(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)}, \; r \ge 0$$

|

| Rician | Yes (dominant) | Rician |

$$f(r) = \frac{r}{\sigma^2} e^{-(r^2 + A^2)/(2\sigma^2)} I_0\left(\frac{rA}{\sigma^2}\right)$$

A = LOS amplitude, I_0 = modified Bessel function. |

| Nakagami-m | General | Nakagami |

$$f(r) = \frac{2m^m}{\Gamma(m)\Omega^m} r^{2m-1} e^{-m r^2/\Omega}$$

m = fading figure (m=1 → Rayleigh). |

Rician Fading Derivation (Key Idea): Resultant of N independent Rayleigh scatterers + 1 deterministic LOS component. LOS component shifts the PDF from origin.

3.0 WIRELESS CHANNEL MODELING

3.1 Classification

• Narrowband (Flat Fading): B_signal << B_c. Channel gain is constant over signal bandwidth. Example: Slow fading with low data rates.

• Wideband (Frequency-Selective): B_signal > B_c. Channel has frequency-dependent amplitude/phase. Example: Modern OFDM systems.

• Directional (Angular) Models: Characterize channel in angle-of-arrival (AoA) and angle-of-departure (AoD). Essential for MIMO.

3.2 Stochastic Models: WSSUS

• WSSUS (Wide-Sense Stationary Uncorrelated Scattering): Fundamental assumption for many models.

  • Wide-Sense Stationary (WSS): Statistics do not change with absolute time.

  • Uncorrelated Scattering (US): Scattering components with different delays are uncorrelated. → Power Delay Profile (PDP) fully describes delay characteristics.

• Channel Impulse Response (CIR):

$$h(\tau, t) = \sum_{i=1}^{L} \alpha_i(t) \delta(\tau - \tau_i(t))$$

*   `α_i(t)` = complex gain, `τ_i` = delay of i-th path.

• Condensed Parameters: τ_rms, f_d,max, path loss, shadowing standard deviation.

3.3 Deterministic Models: Ray Tracing

• Principle: Solve Maxwell's equations (or use approximations) for a specific, mapped environment (buildings, streets).

• Steps: 1) Build 3D database, 2) Launch rays from TX, 3) Trace reflections, diffractions, scattering, 4) Sum contributions at RX.

• Efficiency: Computationally intensive. Uses shooting-and-bouncing rays (SBR) and wall/edge diffraction models (e.g., UTD).

• Kirchhoff & Perturbation Theory: Used for rough surface scattering (e.g., sea, terrain). Kirchhoff for large-scale smooth surfaces; perturbation for small-scale roughness.

3.4 Physical & Empirical Models

• Saleh-Valenzuela (S-V) Model: For indoor channels. Characterized by cluster of rays arriving at similar times, with exponential decay of ray amplitudes within and between clusters.

• COST-207/259/273: Empirical outdoor models for macrocellular environments (e.g., urban, hilly, rural). Define delay spread profiles (e.g., τ_rms values) for different scenarios.

4.0 CHANNEL SOUNDING & MEASUREMENT

• Purpose: To obtain real-world PDP and Doppler spectrum → validate/calibrate models.

• Time-Domain Methods:

  • Direct Pulse Sounding: Transmit very short pulse, measure received waveform. Limited by pulse width and peak power.

  • Spread Spectrum Sliding Correlator: Transmit PN sequence. At receiver, correlate with delayed version. Advantage: High resolution, good noise rejection.

• Frequency-Domain Methods:

  • Network Analyzer: Sweep frequency across band, measure S21 parameter. Advantage: High accuracy, but slow (not for time-varying channels).

• Parameter Extraction: From measured PDP → τ_rms, path powers. From time-varying measurements → Doppler spectrum, f_d.

5.0 TRANSCEIVER ARCHITECTURE & PERFORMANCE

Generic Block Diagram:

Source → Channel Encoder → Interleaver → Mapper → Pulse Shaping → Upconverter → TX Antenna → [Wireless Channel] → RX Antenna → Downconverter → Matched Filter → Equalizer → Demapper → Deinterleaver → Channel Decoder → Destination

Impact of Channel on Reception:

1. Delay Spread (ISI): Smears symbols → increases error probability. Requires equalization or cyclic prefix (OFDM).

2. Frequency-Selective Fading (Deep Fades): Causes spectral nulls → severe signal attenuation at specific frequencies → high error probability in those bands.

3. AWGN Baseline: Performance in Additive White Gaussian Noise (AWGN) channel is the ideal reference. Fading degrades performance (requires higher SNR for same BER).

Modulation in Fading:

• MSK (Minimum Shift Keying): Constant envelope, robust to nonlinearities. Lower spectral efficiency (1 bps/Hz).

• QPSK (Quadrature PSK): Higher spectral efficiency (2 bps/Hz), but sensitive to nonlinear distortion and amplitude fading.

Comparison: In flat fading, both have similar BER vs. SNR performance. QPSK is spectrally more efficient but requires more linear PA.

6.0 EQUALIZATION TECHNIQUES

Need: To mitigate ISI caused by delay spread.

6.1 Classification

6.2 Structures & Algorithms

• Transversal (FIR) Structure: Standard tapped-delay line. Used in LMS/RLS algorithms.

• Lattice Structure: Numerically stable, modular. Used in adaptive prediction.

• Viterbi Detector (MLSE): Maximum Likelihood Sequence Estimation. Finds most likely transmitted sequence through channel trellis. Optimal for severe ISI, but complexity grows exponentially with channel memory.

[!TIP] Key Comparison: DFE vs Viterbi:

• DFE: Lower complexity, but sub-optimal, error propagation.

• Viterbi: Optimal, high complexity (O(M^L) for L-tap, M-ary).

7.0 DIVERSITY TECHNIQUES

Concept: Provide multiple independent (or partially correlated) signal replicas to combat deep fades.

7.1 Classification

7.2 Diversity Combining

How Diversity Helps: Converts Rayleigh fading (deep fades) into a distribution with higher average SNR and lower outage probability. For N-branch MRC with i.i.d. Rayleigh paths, average SNR increases by factor N.

8.0 SPECIALIZED TOPICS & SHORT NOTE POTENTIALS

8.1 Antennas for Mobile Stations

• Constraints: Small size, low cost, low profile, efficiency, radiation pattern.

• Types:

  • Monopole/PIFA (Planar Inverted-F): Common in handsets, compact.

  • Patch (Microstrip): Low profile, used in vehicles/modules.

  • Diversity Antennas: Two antennas spaced > λ/2 (or using polarization) for space diversity.

8.2 Data Services in Cellular Communication

• Evolution: Circuit-switched (2G voice) → Packet-switched (GPRS/EDGE → HSPA → LTE-Advanced → 5G NR).

• Requirements: Throughput (Mbps/Gbps), Latency (ms), Mobility support, QoS classes.

• 5G Focus: eMBB (enhanced Mobile Broadband), URLLC (Ultra-Reliable Low-Latency), mMTC (massive Machine-Type Comm).

8.3 Multiple Access: TDMA vs. CDMA

8.4 Other Recurring Topics

• Rayleigh Distance (Far-field criterion):

$$D_R = \frac{2D^2}{\lambda}$$

where D = largest antenna dimension. For square antenna with gain G:

$$D = \sqrt{\frac{G \lambda^2}{4\pi}} \Rightarrow D_R = \frac{G \lambda}{2\pi}$$

*   **Application:** Minimum distance for valid far-field antenna measurements.

• Two-Path Time-Variant Channel Model:

  • CIR:

$$h(t, \tau) = \alpha_1(t) \delta(\tau) + \alpha_2(t) \delta(\tau - \tau_d)$$

*   **Doppler:** Each path has its own Doppler shift `f_d1`, `f_d2`.

*   **Frequency Response:** Periodically nulls at `f = n / τ_d` (if `f_d` small).

• Computational Efficiency in Sampling Rate Converters: Use polyphase filter structures to reduce computation rate by factor L (interpolation) or M (decimation). CIC filters are efficient for large rate changes.

[!TIP] Final Exam Strategy: For 7-mark questions, provide a clear definition, key formula (if any), and 2-3 concise bullet points on impact/applications. For derivations (Doppler, Rician PDF), show key steps and box the final result. Always link theory to 5G context (e.g., "This Doppler spread limits mobility in mmWave 5G").