Wireless Communication (EC-802 (B)) - Unit 2 Short Notes

UNIT 2: WIRELESS COMMUNICATION CHANNEL & MITIGATION TECHNIQUES

Based on RGPV Past Paper Analysis (2022-2025)

1.0 Wireless Services, Evolution & System Challenges

1.1 Wireless Services & Requirements

Types of Wireless Services:

• Voice: Circuit-switched, low data rate, high reliability (e.g., 2G GSM).

• Data: Packet-switched, variable rate (e.g., email, web browsing – GPRS/EDGE/LTE).

• Multimedia: High data rate, QoS-sensitive (video streaming, video calls – 4G/5G).

• IoT/M2M: Low power, low data rate, massive connectivity (NB-IoT, LTE-M).

Key Requirements:

Economic & Social Impact:

[!TIP] Exam Focus: Link requirements to real-world impact.

• Economic: GDP contribution, job creation, new business models (app economy).

• Social: Connectivity in remote areas, emergency services, education/healthcare access, digital divide.

1.2 Evolution of Wireless Generations (1G to 5G/6G)

Major Shifts: Analog→Digital, Circuit→Packet, Single-antenna→MIMO, Human-centric→Machine-centric.

1.3 Fundamental Technical Challenges

• Spectrum Scarcity: Limited licensed bands → need for sharing (CBRS), mmWave, massive MIMO for spatial reuse.

• Multipath Propagation: Causes ISI (delay spread) and fading (constructive/destructive interference).

• User Mobility: Causes Doppler shift (f_d = v/λ * cosθ), limits coherence time.

• Interference & Noise: Co-channel interference (CCI), adjacent channel interference (ACI), thermal noise (AWGN).

• Power Constraints: Battery life → need for low-power circuits, sleep modes, energy harvesting.

2.0 Wireless Channel Propagation & Large-Scale Fading

2.1 Propagation Mechanisms

Free-Space Path Loss (FSPL):

$$ \boxed{PL_{FS}(d) [dB] = 20\log_{10}(d) + 20\log_{10}(f_c) + 20\log_{10}\left(\frac{4\pi}{c}\right)} $$

where d = distance, f_c = carrier frequency, c = light speed.

Large-Scale Path Loss Models:

1. Log-Distance Model: PL(d) [dB] = PL(d_0) + 10n \log_{10}(d/d_0) + X_σ

   • n = path loss exponent (free-space=2, urban=3-5).

   • X_σ = log-normal shadowing (zero-mean Gaussian, std dev σ).

2. Shadowing (Log-Normal Distribution):

$$ p(x) = \frac{1}{\sqrt{2\pi}\sigma} \exp\left(-\frac{x^2}{2\sigma^2}\right) $$

where x = shadowing in dB.

2.2 Delay Dispersion & Coherence Bandwidth

Delay Spread Definitions:

• Maximum Excess Delay (τ_max): Delay between first and last significant multipath component.

• RMS Delay Spread (σ_τ):

$$ \sigma_\tau = \sqrt{\frac{\sum_{i} P_i \tau_i^2}{\sum_{i} P_i} - \left(\frac{\sum_{i} P_i \tau_i}{\sum_{i} P_i}\right)^2} $$

where P_i, τ_i = power and delay of i-th path.

Coherence Bandwidth (B_c):

Correlation bandwidth ≈ inverse of delay spread.

• Statistical definition: Frequency separation where channel correlation drops below 0.5.

• Approximation:

$$ \boxed{B_c \approx \frac{1}{5\sigma_\tau}} \quad \text{(for 50% correlation)} $$

$$ \boxed{B_c \approx \frac{1}{\sigma_\tau}} \quad \text{(for 90% correlation)} $$

Impact on System:

• If signal bandwidth B_sig > B_c → frequency-selective fading → ISI.

• Requires equalization or OFDM.

• If B_sig < B_c → flat fading (all frequencies fade equally).

2.3 Antenna Considerations

Key Parameters:

• Gain (G): Directional amplification, G = (4πA_e)/λ².

• Directivity: Ratio of max radiation intensity to average.

• Radiation Pattern: 3D plot of field/power vs. angle.

Rayleigh Distance (R_R):

Distance beyond which angular field distribution is essentially independent of distance.

For antenna aperture D (max dimension):

$$ \boxed{R_R = \frac{2D^2}{\lambda}} $$

[!TIP] Derivation Critical: From Fraunhofer distance condition (phase variation < π/8 across aperture).

Mobile Station Antennas:

• Constraints: Small size, low cost, omnidirectional pattern, efficiency vs. size trade-off.

• Common Types: Monopole (quarter-wave), PIFA (Planar Inverted-F Antenna), Patch antenna.

3.0 Small-Scale Fading & Multipath Channel Characteristics

3.1 Small-Scale Fading Fundamentals

• Cause: Rapid fluctuations due to multipath + mobile motion (Doppler).

• Channel Model: Time-variant linear system:

$$ r(t) = \int_{-\infty}^{\infty} h(\tau, t) x(t-\tau) d\tau + n(t) $$

where h(τ,t) = time-variant impulse response.

• Classification:

  • Flat Fading: B_sig < B_c → constant gain/phase across bandwidth.

  • Frequency-Selective Fading: B_sig > B_c → frequency-dependent fading → ISI.

3.2 Statistical Models for Small-Scale Fading

Rayleigh Fading (No LOS):

• Model: Sum of many scattered waves (CLT → Gaussian I/Q).

• Amplitude R: Rayleigh distribution:

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

• Power R²: Exponential distribution: p_{R²}(x) = (1/2σ²) e^{-x/(2σ²)}.

• Phase θ: Uniform on [0, 2π).

• Mean power: E[R²] = 2σ².

Rician Fading (With Dominant LOS):

• Model: LOS component A + scattered Z (Gaussian).

• Complex envelope: h = A e^{jθ_0} + Z (Z ~ CN(0, 2σ²)).

• Amplitude R: Rician distribution:

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

where I_0 = modified Bessel function.

• K-factor: K = A²/(2σ²) (LOS power / scattered power). K=0 → Rayleigh; K→∞ → AWGN.

Nakagami-m Distribution (Generalized):

• Amplitude PDF:

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

• m = fading figure (m=1 → Rayleigh; m→∞ → AWGN).

• Ω = E[R²].

• Use: Fits experimental data better than Rayleigh/Rician for some environments.

3.3 Doppler Shift & Frequency Dispersion

Doppler Shift (f_d):

Relative motion between MS and BS.

$$ \boxed{f_d = \frac{v}{\lambda} \cos\theta} $$

where v = velocity, λ = wavelength, θ = angle between velocity vector and wave direction.

Doppler Spread (B_D):

• Max/min Doppler: ±f_{d,max} = ±v/λ (θ=0°/180°).

• Doppler spread ≈ 2f_{d,max}` (bandwidth of Doppler spectrum).

Doppler Power Spectrum:

• Classical (Jakes'): For uniform scattering in 2D plane:

$$ S(f) = \frac{1}{\pi f_{d,max} \sqrt{1 - (f/f_{d,max})^2}}, \quad |f| \le f_{d,max} $$

Zero elsewhere.

• Clipped: For non-uniform scattering (e.g., 3D with limited elevation angles).

Coherence Time (T_c):

Time duration over which channel is approximately constant.

• Approximation:

$$ \boxed{T_c \approx \frac{1}{f_{d,max}}} $$

• If symbol period T_sym > T_c → time-selective fading → time-varying channel → need channel tracking.

3.4 Coherence Parameters Summary

Relationship: B_c * T_c ≈ 1 (for wideband channels).

4.0 Wireless Channel Modeling

4.1 Modeling Classifications

4.2 Stochastic (Statistical) Models

WSSUS Model (Wide-Sense Stationary Uncorrelated Scattering):

• Assumptions:

  1. WSS: Statistics independent of absolute time t.

  2. US: Scattering components with different delays are uncorrelated: R_h(τ₁,τ₂; Δt) = P(τ) δ(τ₁-τ₂).

• Condensed Parameters:

  • Delay Power Spectrum (P(τ)): Power vs. excess delay.

  • Doppler Power Spectrum (S(f)): Power vs. Doppler shift.

  • Delay Spread (σ_τ) and Doppler Spread (B_D) fully characterize WSSUS channel.

• Significance: Simplifies analysis; valid for many outdoor channels.

Two-Path Model (Time-Variant):

• Impulse response: h(t,τ) = α₁ δ(τ) + α₂ δ(τ - τ_d).

• α₁, α₂ = complex gains (time-varying due to Doppler).

• Simple model to illustrate ISI and Doppler effects.

4.3 Deterministic Models

Ray Tracing:

• Method: Geometric optics + uniform theory of diffraction (UTD).

• Process: Define 3D environment (buildings, terrain), transmitter/receiver positions → compute all rays (reflection, diffraction, scattering) → sum contributions.

• Efficiency Considerations: Computationally intensive; requires accurate 3D database; suitable for site-specific planning.

• Limitations: Not scalable for large areas; accuracy depends on model fidelity (material properties, edge sharpness).

4.4 Channel Measurement & Sounding

Purpose: Obtain h(τ,t) or H(f,t) for model validation, system design.

Measurement Methods:

Channel Impulse Response Estimation:

• Direct: ĥ(τ) = r(τ) * x^*(-τ) (if x(t) known).

• Sounding Signal Design: Low PAPR, good correlation properties (e.g., Zadoff-Chu sequences).

5.0 Wireless Transceiver & Modulation Impact

5.1 Wireless Communication Link Block Diagram

[Source] → [Channel Encoder] → [Modulator] → [Upconverter] → [PA] → [Antenna]

                                                                  ↓ Channel (fading, noise)

[Antenna] ← [LNA] ← [Downconverter] ← [Equalizer] ← [Demodulator] ← [Channel Decoder] ← [Sink]

Key Impairments per Stage:

• Transmitter: Nonlinear PA (spectral regrowth), IQ imbalance.

• Channel: Fading (flat/frequency-selective), Doppler, AWGN.

• Receiver: Noise figure, phase noise, frequency offset.

5.2 Modulation & Demodulation Techniques

MSK vs QPSK Spectral Efficiency:

• MSK: B/R_b = 1.5 (main lobe width).

• QPSK: B/R_b = 2 (raised cosine with roll-off α=0).

MSK has narrower main lobe (15% more bandwidth efficient) but same BER in AWGN as QPSK.

5.3 Performance in Fading Channels

• Flat Fading: r = h * s + n, h = complex fading coefficient.

  • BER increases due to random |h|² (deep fades).

  • Average BER: P_b ≈ (1/2) P_b(AWGN) for BPSK in Rayleigh (no diversity).

• Frequency-Selective Fading: ISI from delayed taps → error floor even at high SNR.

  • Requires equalization to suppress ISI.

  • Without equalization, BER degrades severely.

6.0 Mitigation Techniques: Equalization & Diversity

6.1 Equalization

Need: Compensate for ISI in frequency-selective channels.

Classification:

Equalizer Structures:

• Transversal Filter (FIR): y[n] = Σ_{k=0}^{N-1} w_k^* x[n-k].

• Decision Feedback (DFE): Feedforward (FF) + Feedback (FB) filter. FB cancels past ISI using detected symbols.

• Viterbi Detector (MLSE): Maximum Likelihood Sequence Estimation. Optimal but complexity O(M^L) (M=constellation, L=channel memory). Used when ISI severe.

Adaptation Algorithms:

• Training-based: Transmit known sequence → adjust taps to minimize error e = d - y.

• Decision-Directed: Use detected symbols after convergence.

• Blind Equalization: No training sequence (e.g., Constant Modulus Algorithm - CMA). Used when training overhead undesirable (e.g., broadcasting).

[!TIP] Blind vs Decision-Directed: Blind uses statistical property (e.g., constant modulus), decision-directed uses hard decisions. Blind preferred when training overhead high or channel varies rapidly during training.

6.2 Diversity Techniques

Concept: Provide multiple independent (or partially correlated) signal copies to combat fading.

Types of Diversity:

Diversity Combining Methods:

1. Selection Combining (SC): Choose antenna with highest instantaneous SNR.

   • SNR_out = max(SNR_i).

   • Simple, but loses diversity gain if all deep fades.

2. Maximal Ratio Combining (MRC): Weighted sum with SNR weights.

   • y = Σ_i w_i r_i, w_i ∝ h_i^*.

   • Optimal – maximizes output SNR.

   • SNR_out = Σ_i SNR_i.

3. Equal Gain Combining (EGC): Phase-aligned sum (equal weights).

   • y = Σ_i r_i e^{-j∠h_i}.

   • Near-MRC performance, simpler than MRC.

4. Switch & Stay Combining (SSC): Switch to new antenna only if current SNR < threshold.

How Diversity Improves SNR:

• For N i.i.d. Rayleigh branches, MRC output SNR distribution is Gamma with shape N.

• Fading depth reduction: Probability of deep fade P(SNR < γ_th) decreases exponentially with N.

• Average SNR improvement: E[SNR_out] = N * E[SNR_branch] (MRC).

7.0 Additional High-Frequency Topics (Short Notes)

7.1 Multiple Access Techniques

• TDMA vs CDMA:

  • TDMA: Fixed number of users per cell, tight synchronization.

  • CDMA: Flexible capacity, requires power control, resistant to narrowband interference.

7.2 Data Services in Cellular Communication

• Evolution: Circuit-switched (2G voice/data) → Packet-switched (GPRS/EDGE – 2.5G) → All-IP (LTE/5G).

• QoS Classes (LTE/5G):

  • Conversational: Voice/video (low latency).

  • Streaming: Video/audio (steady rate).

  • Interactive: Web browsing (low delay).

  • Background: Email, FTP (high delay tolerant).

7.3 Antennas for Mobile Stations

• Design Constraints:

  • Size: << λ (e.g., λ/4 monopole at 900 MHz ≈ 8 cm).

  • Efficiency: Low due to small size, body loss.

  • Multipath: Need omnidirectional pattern.

• Common Types:

  • Monopole: Simple, quarter-wave, external.

  • PIFA: Planar, used in phones (size reduction via shorting pin).

  • Patch: Low profile, directional (often used in arrays for MIMO).

7.4 Specific Models & Concepts

• AWGN Channel: Additive White Gaussian Noise. r = s + n, n ~ CN(0, N_0).

  • Error Probability (BPSK): P_b = Q(√(2E_b/N_0)).

• Fractional-Spaced Equalizer (FSE): Tap spacing T_s/2 (instead of T_s). Advantages:

  • Avoids timing sensitivity (no need for perfect symbol timing).

  • Can correct for non-ideal pulse shapes.

  • Better noise enhancement than symbol-spaced ZF.

• Doppler Spectra: Jakes' model assumes 2D isotropic scattering. Real-world: clipped (limited elevation angles), flatter for high BS.

8.0 Key Derivations & Theoretical Foundations

8.1 Doppler Shift Derivation

Geometry: MS moving with velocity v, angle θ between velocity vector and direction of arrival (DoA) of wave.

• Relative velocity along wave direction: v_r = v cosθ.

• Doppler shift: f_d = f_c * (v_r / c) = (v/λ) cosθ.

8.2 Delay Spread & Coherence Bandwidth Derivation

From power delay profile P(τ):

1. Mean excess delay: τ_mean = (∫ τ P(τ) dτ) / (∫ P(τ) dτ).

2. RMS delay spread:

$$ \sigma_\tau = \sqrt{\frac{\int (\tau - \tau_{mean})^2 P(\tau) d\tau}{\int P(\tau) d\tau}} $$

3. Coherence bandwidth: Correlation function R_H(Δf) ≈ ∫ P(τ) e^{-j2πΔfτ} dτ.

   • For small Δf, R_H(0) - R_H(Δf) ≈ (2πΔf)^2 σ_τ^2.

   • Set correlation coefficient = 0.5 → (2πB_c σ_τ)^2 ≈ 0.5 → B_c ≈ 1/(5σ_τ).

8.3 Rayleigh Distance Derivation

For aperture D (max dimension), wavelength λ:

• Path difference across aperture at angle θ: Δ = D sinθ.

• Phase difference: Δφ = (2π/λ) D sinθ.

• Far-field (Fraunhofer) condition: Max phase difference across aperture ≤ π/8 (for < 1 dB gain error).

• So (2π/λ) D sinθ_max ≤ π/8 → sinθ_max ≈ λ/(16D).

• Rayleigh distance: R_R = D / (2 sinθ_max) ≈ 2D^2/λ.

8.4 Rician Fading Distribution Derivation

Complex envelope: h = A e^{jθ_0} + Z, Z ~ CN(0, 2σ²).

• PDF of h (complex Gaussian with mean A e^{jθ_0}):

$$ p_h(u) = \frac{1}{\pi 2\sigma^2} \exp\left(-\frac{|u - A e^{jθ_0}|^2}{2\sigma^2}\right) $$

• Transform to polar (u = R e^{jθ}):

$$ p_{R,θ}(r,θ) = p_h(r e^{jθ}) \cdot r = \frac{r}{2\pi\sigma^2} \exp\left(-\frac{r^2 + A^2 - 2rA\cos(θ-θ_0)}{2\sigma^2}\right) $$

• Marginal for R (integrate over θ):

$$ p_R(r) = \frac{r}{\sigma^2} \exp\left(-\frac{r^2+A^2}{2\sigma^2}\right) \frac{1}{2\pi} \int_0^{2\pi} \exp\left(\frac{rA\cos\phi}{\sigma^2}\right) d\phi $$

where φ = θ - θ_0.

• Integral = 2π I_0(rA/σ²) → Rician PDF as given.

8.5 WSSUS Model Justification & Condensed Parameters

• Justification: For rich scattering with no dominant components and mobile motion, channel is WSS over local area (few seconds) and scattering at different delays uncorrelated (independent paths).

• Condensed Parameters:

  • Delay power spectrum P(τ): E[|h(τ,t)|²] (delay profile).

  • Doppler power spectrum S(f): Fourier transform of R_h(0,τ;Δt) w.r.t. Δt.

  • From these, compute σ_τ (RMS delay spread) and B_D (Doppler spread) → fully characterize channel for many purposes (e.g., BER with diversity).

Final Exam Strategy:

1. Prioritize derivations: Doppler shift, coherence bandwidth, Rayleigh distance, Rician distribution (appears every 2-3 years).

2. Compare/contrast: Narrowband vs wideband, Rayleigh vs Rician, TDMA vs CDMA, diversity combining methods.

3. Link concepts: How delay spread → coherence bandwidth → ISI → need for equalization.

4. Use diagrams: Sketch two-path model, WSSUS block diagram, diversity combining setups.

5. Numerical examples: Compute Rayleigh distance (2024 Q), coherence bandwidth from given delay spread.

All topics above are sourced from RGPV past papers (2022-2025). Focus on marked "Very High Frequency" sections for 70%+ coverage.