5G Technology (EC-802 (C)) - Unit 4 Short Notes

UNIT 4: WIRELESS CHANNEL CHARACTERISTICS, MODELING, AND MITIGATION TECHNIQUES

I. FOUNDATIONS OF WIRELESS COMMUNICATION

Evolution of Wireless Systems (1G to 5G)

• 1G (1980s): Analog, circuit-switched, voice-only (e.g., AMPS). Key limitation: poor security, no data.

• 2G (1990s): Digital (GSM, CDMA), introduced SMS, circuit-switched data (CSD). Improved security and capacity.

• 3G (2000s): Packet-switched core (UMTS, CDMA2000), mobile broadband (video calling, mobile internet). Peak rates ~2 Mbps.

• 4G/LTE (2010s): All-IP, high-speed packet access (HSPA, LTE), VoLTE, mobile TV. Peak rates ~1 Gbps, low latency (~50 ms).

• 5G (2020s): Three service pillars: eMBB (enhanced Mobile Broadband), URLLC (Ultra-Reliable Low-Latency Comm), mMTC (massive Machine-Type Comm). Uses mmWave, massive MIMO, network slicing. Peak rates ~20 Gbps, latency <1 ms.

[!TIP] Exam Focus: Be ready to contrast circuit-switched (2G/3G) vs packet-switched (4G/5G) core networks and list three 5G service categories with their primary KPIs (e.g., URLLC: latency <1ms, reliability >99.999%).

Wireless Services and Requirements

Economic & Social Impact:

• Economic: Drives GDP growth, creates new industries (app economy, IoT services), enables digital transformation of sectors (healthcare, agriculture).

• Social: Connects remote areas, enables remote education/health, changes social interaction (social media), raises privacy/security concerns.

Key Technical Challenges

1. Spectrum Scarcity: Limited licensed spectrum; requires dynamic spectrum sharing (e.g., CBRS), mmWave bands, and spectral efficiency techniques (MIMO, advanced modulation).

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

3. User Mobility & Doppler: Causes time-varying channel and Doppler spread. Requires fast channel estimation and robust modulation.

4. Interference Management: Co-channel interference (CCI) in cellular networks; requires frequency reuse planning, ICIC (Inter-Cell Interference Coordination), and advanced receivers.

II. WIRELESS CHANNEL PROPAGATION AND FADING

Propagation Mechanisms

• Reflection & Transmission: Occurs at dielectric boundaries (e.g., wall, ground). Governed by Snell's Law and Fresnel Equations (determine reflection/transmission coefficients based on angle of incidence, permittivity, permeability).

• Scattering from Rough Surfaces:

  • Kirchhoff Theory (Physical Optics): Assumes surface irregularities are small compared to wavelength. Treats surface as collection of point scatterers with phase determined by local surface height.

  • Perturbation Theory: For surfaces with small RMS height (σ << λ). Scattering coefficient derived as a series expansion in σ/λ.

Large-Scale Fading (Path Loss & Shadowing)

• Free-Space Path Loss (FSPL): Power decay in line-of-sight (LOS) environment.

$$ \text{FSPL}(d) = \left( \frac{4\pi d}{\lambda} \right)^2 = \left( \frac{4\pi d f}{c} \right)^2 $$

In dB: 

$$ \text{FSPL(dB)} = 20\log_{10}(d) + 20\log_{10}(f) + 20\log_{10}\left(\frac{4\pi}{c}\right) $$

• Log-Distance Path Loss Model:

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

where `n` = path loss exponent (2=free space, 4=urban), `X_σ` = zero-mean lognormal **shadowing** (std dev σ in dB).

• Shadowing Statistics: X_σ follows a Lognormal Distribution. If X is normal (mean 0, std σ), then 10^(X/10) is lognormal.

Small-Scale Fading

Time-Variant Channel Impulse Response: $h(t, \tau)$. Characterized by Delay Spread (frequency selectivity) and Doppler Spread (time selectivity).

Delay Spread and Coherence Bandwidth

• Power Delay Profile (PDP): $$\displaystyle P(\tau) = |h(t,\tau)|^2 $$ (average power vs. delay).

• Mean Excess Delay: $$\displaystyle \bar{\tau} = \frac{\sum_k P(\tau_k)\tau_k}{\sum_k P(\tau_k)} $$

• RMS Delay Spread:

$$\sigma_\tau = \sqrt{\bar{\tau^2} - (\bar{\tau})^2} = \sqrt{\frac{\sum_k P(\tau_k)(\tau_k - \bar{\tau})^2}{\sum_k P(\tau_k)}} \boxed{}$$

• Coherence Bandwidth ($$\displaystyle B_c $$): Frequency range over which channel impulse response is highly correlated. Approximate relations:

$$ B_c \approx \frac{1}{5\sigma_\tau} \quad \text{(for strong correlation)} \quad \text{or} \quad B_c \approx \frac{1}{\sigma_\tau} $$

*   If signal bandwidth $$\displaystyle B_s \gg B_c $$ → **Frequency-Selective Fading** → causes **ISI**.

*   If $$\displaystyle B_s \ll B_c $$ → **Flat Fading** → all frequencies fade similarly.

Doppler Shift and Coherence Time

• Doppler Shift ($$\displaystyle f_d $$): For mobile moving with velocity v relative to source, maximum Doppler frequency:

$$ f_m = \frac{v f_c}{c} = \frac{v}{\lambda} \boxed{} $$

where $$\displaystyle f_c $$ = carrier frequency, $c$ = speed of light, $\lambda$ = wavelength.

• Doppler Spread ($$\displaystyle B_D $$): Range of frequencies over which received power is non-zero. $$\displaystyle B_D \approx 2f_m $$ for isotropic scattering.

• Coherence Time ($$\displaystyle T_c $$): Time duration over which channel impulse response is highly correlated.

$$ T_c \approx \frac{1}{B_D} \quad \text{(or)} \quad T_c \approx \frac{9}{2\pi f_m} \quad \text{(for Jakes' model)} $$

*   If symbol period $$\displaystyle T_s \gg T_c $$ → **Fast Fading** (channel changes within symbol).

*   If $$\displaystyle T_s \ll T_c $$ → **Slow Fading**.

Amplitude & Phase Distributions

• Rayleigh Fading: No LOS component. Complex envelope $$\displaystyle z = x + jy $$ (Gaussian IID). Amplitude $$\displaystyle R = |z| $$ follows Rayleigh PDF: $$\displaystyle f_R(r) = \frac{r}{\sigma^2}e^{-r^2/(2\sigma^2)} $$, $r \ge 0$. Phase $$\displaystyle \theta = \angle z $$ uniform on $[0,2\pi)$.

• Rician Fading: Dominant LOS component plus scattered. Complex envelope $$\displaystyle z = z_0 + x + jy $$, where $$\displaystyle z_0 $$ is deterministic. Amplitude follows Rician PDF:

$$ f_R(r) = \frac{r}{\sigma^2}e^{-(r^2+z_0^2)/(2\sigma^2)} I_0\left(\frac{rz_0}{\sigma^2}\right), \quad r \ge 0 $$

where $$\displaystyle I_0 $$ is modified Bessel function. **K-factor** $$\displaystyle K = z_0^2/(2\sigma^2) $$ measures LOS strength ($$\displaystyle K=0 $$ → Rayleigh, $K \to \infty$ → AWGN).

[!TIP] Common Pitfall: Do not confuse RMS Delay Spread (time domain, causes frequency selectivity) with Doppler Spread (frequency domain, causes time selectivity). Their reciprocals give Coherence Bandwidth and Coherence Time, respectively.

III. WIRELESS CHANNEL MODELING

Deterministic Channel Models

• Ray Tracing: Computes propagation paths (rays) from Tx to Rx via reflection, diffraction, scattering using geometric optics & uniform theory of diffraction (UTD). Steps: 1) Build 3D environment database, 2) Launch rays from Tx, 3) Test intersections with objects, 4) Apply reflection/diffraction coefficients, 5) Sum contributions at Rx.

• Efficiency: High accuracy for specific sites but computationally intensive (ray explosion problem). Accuracy depends on geometric detail and electromagnetic material properties.

Stochastic Channel Models

Narrowband, Wideband, and Directional Models

WSSUS Model (Wide-Sense Stationary Uncorrelated Scattering)

• Assumptions: 1) WSS in time (statistics invariant to time shift), 2) US (scattering components with different delays are uncorrelated).

• Block Diagram: Input → [Time-Variant Linear Filter with impulse response $h(t,\tau)$] → Output. Scattering function $$\displaystyle S(\tau, f_D) $$ (power density in delay-Doppler) fully characterizes WSSUS channel.

• Condensed Parameters:

  • Delay Spread: $$\displaystyle \sigma_\tau $$ (from $S(\tau)$ marginal).

  • Doppler Spread: $$\displaystyle B_D $$ or $$\displaystyle \sigma_f $$ (from $$\displaystyle S(f_D) $$ marginal).

  • Coherence Bandwidth/Time: $$\displaystyle B_c \approx 1/(5\sigma_\tau) $$, $$\displaystyle T_c \approx 1/(2B_D) $$.

Time-Variant Two-Path Model

Simple model for Doppler: $$\displaystyle h(t) = a_1 e^{j2\pi f_{d1}t} + a_2 e^{j2\pi f_{d2}t} $$. Illustrates how motion causes phase rotation and constructive/destructive interference.

Delay Dispersion in Directional Channels & Remedial Measures

• Cause: Multipath components arrive from different angles with different delays → angular spread also causes frequency selectivity.

• Remedies: 1) Beamforming (spatial filtering to reduce angular spread), 2) OFDM (turns frequency-selective channel into parallel flat-fading subcarriers), 3) RAKE receiver (for CDMA).

Channel Sounding and Measurement

• Purpose: Measure $h(t,\tau)$ or $$\displaystyle S(\tau,f_D) $$ to validate models and estimate channel parameters.

• Time-Domain Methods:

  • Pulse Sounding: Transmit short pulse, measure received pulse shape. Simple but low SNR.

  • Spread Spectrum Sliding Correlator: Transmit PN sequence, correlate at Rx with delayed version. Good resolution, high processing gain.

• Frequency-Domain Methods:

  • Network Analyzer: Sweeps frequency, measures $$\displaystyle S_{21} $$ over bandwidth. High accuracy, lab use.

  • OFDM-Based Sounding: Use OFDM symbols; channel frequency response $H(f)$ estimated from known pilots. Matches modern systems (LTE/5G).

IV. TRANSCEIVER DESIGN AND MODULATION

Wireless Transceiver Architecture (Block Diagram)

[Source] → [Channel Encoder] → [Interleaver] → [Modulator] → [Upconverter] → [Power Amp] → [Antenna] → [Wireless Channel] → [Rx Antenna] → [LNA] → [Downconverter] → [Equalizer] → [Demodulator] → [Deinterleaver] → [Channel Decoder] → [Sink]

Key Functions: Encoding adds redundancy for error correction; Interleaving combats burst errors; Modulation maps bits to RF; Up/Downconversion shifts to carrier; LNA/Power Amp amplify; Equalizer mitigates ISI.

Modulation and Demodulation Techniques

• Impact on Performance:

  • Bandwidth Efficiency (η): Bits/s/Hz. Higher for higher-order modulation (e.g., 16-QAM > QPSK > BPSK).

  • Power Efficiency: BER at given $$\displaystyle E_b/N_0 $$. Lower for simpler constellations (BPSK best).

  • Spectral Efficiency Trade-off: Higher η requires higher $$\displaystyle E_b/N_0 $$ for same BER.

• Spectral Efficiency Comparison: MSK vs. QPSK

  • MSK (Minimum Shift Keying): Continuous-phase FSK, modulation index 0.5. $$\displaystyle \eta = 1 $$ bit/s/Hz. Better spectral containment (lower out-of-band emissions), constant envelope (power efficient PA).

  • QPSK (Quadrature PSK): $$\displaystyle \eta = 2 $$ bits/s/Hz. Higher spectral efficiency but higher out-of-band emissions, non-constant envelope.

  Result: QPSK has higher spectral efficiency but MSK has better spectral containment.

• Coherent vs. Non-Coherent Detection:

  • Coherent: Requires phase reference (pilot/training). Better BER performance (e.g., BPSK coherent vs. DPSK non-coherent: ~3 dB gap).

  • Non-Coherent: No phase reference needed (e.g., DPSK, FSK). Simpler Rx, robust to phase noise, but worse BER.

Detection Techniques

• Viterbi Detector (MLSE): Used for maximum-likelihood sequence estimation in channels with memory (ISI). Implements Viterbi algorithm on trellis representing channel states. Complexity grows exponentially with channel memory length (e.g., for L-tap channel, $$\displaystyle 2^L $$ states). Optimal in ML sense but complex.

V. EQUALIZATION TECHNIQUES

Need for Equalization

In frequency-selective fading (delay spread > symbol period), channel acts as a filter causing ISI. Equalizer at Rx inverts or mitigates channel effect to recover transmitted symbols.

Classification of Equalizers

[!TIP] Key Advantage of FSE: By sampling faster than symbol rate, it avoids the Nyquist criterion ambiguity and can better separate signals from different paths, especially when channel has excess bandwidth.

Adaptive Equalization Algorithms

• Decision-Directed (DD): Uses detected symbols (after equalizer) as training data during tracking mode. Training Mode: Use known training sequence to initialize coefficients. Tracking Mode: Switch to DD. Sensitive to initial convergence and error propagation.

• Blind Equalization: Adapts without training sequence using higher-order statistics (e.g., Godard's algorithm, Bussgang methods). Preferred when: Training overhead is high (e.g., burst transmission, asymmetric links), or channel varies rapidly during training.

Comparison of Equalizer Structures

VI. DIVERSITY TECHNIQUES

Concept of Diversity

Transmit same information over multiple independently faded copies to reduce probability of deep fades. Diversity Gain: Improvement in average SNR or reduction in BER. Diversity Order: Slope of BER vs. SNR curve on log-log scale.

Types of Diversity

Diversity Implementation Methods

• Space Diversity: Multiple antennas (spacing ≥ λ/2). Can be at Tx, Rx, or both (MIMO).

• Time Diversity: Same information sent at different times (via channel coding + interleaving). Requires channel coherence time $$\displaystyle T_c $$ > interleaving depth.

• Frequency Diversity: Same information sent on different frequencies (e.g., spread spectrum (CDMA), OFDM with frequency hopping). Requires coherence bandwidth $$\displaystyle B_c $$ < separation of frequencies.

• Polarization Diversity: Two orthogonal polarizations (e.g., vertical/horizontal) on same antenna location. Reduces space needed, but correlation higher than space diversity.

[!TIP] Combining Techniques: 1) Selection Combining (SC): Pick best branch. Simple, suboptimal. 2) Maximal Ratio Combining (MRC): Weighted sum (SNR proportional to sum of branch SNRs). Optimal but needs channel knowledge. 3) Equal Gain Combining (EGC): Same as MRC but unit weights. Good approximation when SNRs equal.

VII. ANTENNAS AND RF ASPECTS

Antennas for Mobile Stations

• Design Constraints: Size (must fit device, λ/4 or smaller), Efficiency (low due to small size, proximity to body/hand), Omnidirectional Pattern (for mobile orientation).

• Common Types:

  • Monopole (Quarter-wave): Simple, omnidirectional, needs ground plane.

  • PIFA (Planar Inverted-F Antenna): Compact, used in phones (fits PCB), good efficiency for size.

  • Loop Antenna: Small, can be flexible, low efficiency, high reactance.

Antenna Parameters

• Rayleigh Distance ($$\displaystyle d_R $$): Distance beyond which angular beamwidth is constant, and far-field approximations hold.

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

where $D$ = largest antenna dimension (aperture size), $\lambda$ = wavelength.

• Antenna Gain ($G$): Ratio of radiation intensity in direction of max radiation to that of isotropic radiator. Related to Effective Aperture ($$\displaystyle A_e $$):

$$ G = \frac{4\pi A_e}{\lambda^2} \quad \text{or} \quad A_e = \frac{G \lambda^2}{4\pi} \boxed{} $$

> **Example (from May 2024):** Square antenna with gain $$\displaystyle G = 20 $$ dB = 100 (linear). For $\lambda$, $$\displaystyle A_e = \frac{100 \lambda^2}{4\pi} \approx 7.96 \lambda^2 $$. If side length $L$, then $$\displaystyle A_e \approx L^2 $$ (for square), so $L \approx \sqrt{7.96}\lambda \approx 2.82\lambda$. Then Rayleigh distance $$\displaystyle d_R = \frac{2L^2}{\lambda} = \frac{2 \times (7.96\lambda^2)}{\lambda} \approx 15.92\lambda $$.

VIII. MULTIPLE ACCESS AND DATA SERVICES

Multiple Access Techniques

[!TIP] Capacity Comparison: CDMA (theoretical) has softer capacity (graceful degradation) vs. TDMA's hard capacity (fixed slots). In practice, CDMA limited by interference (MAI) and near-far effect.

Data Services in Cellular Communication

• Evolution: Circuit-Switched (CS) for voice (2G/3G) → Packet-Switched (PS) for data (GPRS/EDGE → LTE/5G). Core network becomes all-IP.

• Key Services & Requirements:

  • SMS: Very low data rate, store-and-forward, high latency tolerance.

  • Mobile Broadband (eMBB): High throughput (100 Mbps-1 Gbps), moderate latency.

  • IoT (mMTC): Low power, low data rate, massive connections, long battery life.

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

IX. PERFORMANCE ANALYSIS

Error Probability in AWGN and Fading Channels

• In AWGN: For coherent BPSK, $$\displaystyle P_b = Q\left(\sqrt{2E_b/N_0}\right) $$. For QPSK, same as BPSK but $$\displaystyle E_b $$ per bit.

• In Fading (Rayleigh): Average BER is integral of conditional BER over fading distribution. For BPSK in Rayleigh:

$$ P_b = \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right) \approx \frac{1}{2\bar{\gamma}} \quad (\bar{\gamma} \ll 1) $$

where $$\displaystyle \bar{\gamma} = E_b/N_0 $$ average SNR. **Fading causes an "error floor"** even at high SNR.

• In Rician Fading: BER performance between Rayleigh ($$\displaystyle K=0 $$) and AWGN ($K \to \infty$). Improves with K-factor.

System-Level Performance Metrics

• Spectral Efficiency (η): $$\displaystyle \eta = \frac{\text{Net Data Rate (bps)}}{\text{Bandwidth (Hz)}} $$ (bits/s/Hz). In fading, achievable η is lower than in AWGN for same modulation due to need for redundancy (coding) and diversity.

• Capacity in Fading Channels: Shannon capacity for fading channel with CSIT (channel state info at Tx) is $$\displaystyle C = \mathbb{E}\left[\log_2(1 + \text{SNR} \cdot |h|^2)\right] $$. Without CSIT, capacity is same but no power/rate adaptation.

• Trade-offs:

  • Diversity Gain vs. Complexity: Higher order diversity (more antennas) improves reliability but increases Rx/Tx complexity and cost.

  • Spectral Efficiency vs. Power Efficiency: Higher-order modulation (e.g., 64-QAM) increases η but requires much higher $$\displaystyle E_b/N_0 $$ for same BER.

  • Latency vs. Reliability: URLLC requires short packets and redundancy (e.g., short codes), which reduces spectral efficiency.