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

I. FOUNDATIONS OF WIRELESS COMMUNICATION

Wireless Services Classification:

• Mobile services: Cellular voice/data (e.g., 4G/5G), paging.

• Fixed services: Wireless local loop (WLL), point-to-point backhaul.

• Broadcast services: TV/radio broadcasting, satellite.

• Personal services: Bluetooth, WPANs.

Key Performance Metrics:

• Data rate: Peak and average throughput (Mbps/Gbps).

• Latency: End-to-end delay (ms), critical for URLLC.

• Reliability: Packet success rate, outage probability.

• Coverage: Area/cell size, penetration loss.

[!TIP]

Exam Focus: 5G vision eMBB (enhanced Mobile Broadband), URLLC (Ultra-Reliable Low-Latency Comm), mMTC (massive Machine-Type Comm). Often asked to compare with 4G.

Spectrum Challenges:

• Scarcity: Limited licensed bands; crowded sub-6 GHz.

• Regulatory: Fragmented global allocations, licensing costs.

• Impact on design: Necessitates carrier aggregation (combine fragmented bands) and high spectral efficiency modulations (e.g., 256-QAM).

Core Technical Challenges:

1. Multipath propagation: Causes intersymbol interference (ISI) → requires equalization/OFDM.

2. User mobility: Induces Doppler shift → channel time-variation → needs fast tracking.

3. Power efficiency: Battery life limits → low-power circuit design, discontinuous reception (DRX).

II. WIRELESS CHANNEL PROPAGATION CHARACTERISTICS

A. Large-Scale Propagation

• Path loss: Signal power decay with distance.

  • Free-space: $$\displaystyle PL(d) = \left( \frac{4\pi d}{\lambda} \right)^2 $$ (inverse square law).

  • Log-distance: $$\displaystyle PL(d) = PL(d_0) + 10n \log_{10}\left(\frac{d}{d_0}\right) + X_\sigma $$, where $n$ = path loss exponent, $$\displaystyle X_\sigma $$ = log-normal shadowing (std dev $\sigma$ dB).

• Shadowing: Slow variations due to obstacles; modeled as log-normal distribution in dB domain.

B. Small-Scale Fading

• Causes: Multipath delay spread, Doppler spread.

• Flat fading: Channel bandwidth $$\displaystyle B_c \ll B_{channel} $$; all frequencies fade equally.

• Frequency-selective fading: $$\displaystyle B_c \ll B_{channel} $$; different frequencies fade independently → ISI.

• Time-selective fading: Channel varies within symbol duration due to mobility.

C. Delay Spread and Coherence Bandwidth

• Delay spread ($$\displaystyle \tau_{rms} $$): RMS from power delay profile (PDP):

$$\tau_{rms} = \sqrt{\frac{\sum_p (\tau_p - \bar{\tau})^2 P_p}{\sum_p P_p}}, \quad \bar{\tau} = \frac{\sum_p \tau_p P_p}{\sum_p P_p}$$

• Coherence bandwidth ($$\displaystyle B_c $$): Frequency separation over which channel is highly correlated.

  • Approx: $$\displaystyle B_c \approx \frac{1}{5\tau_{rms}} $$ (50% correlation).

  • $$\displaystyle \boxed{B_c \propto \frac{1}{\tau_{rms}}} $$

[!TIP]

Common Pitfall: Confusing coherence bandwidth (frequency domain) with coherence time (time domain). $$\displaystyle B_c $$ relates to delay spread; $$\displaystyle T_c $$ relates to Doppler spread.

D. Doppler Shift and Doppler Spread

• Doppler shift for single path: $$\displaystyle f_d = \frac{v}{\lambda} \cos\theta = \frac{v f_c}{c} \cos\theta $$, where $v$ = velocity, $\theta$ = angle relative to motion.

• Maximum Doppler spread: $$\displaystyle f_{d,\max} = \frac{v f_c}{c} $$ (when $$\displaystyle \cos\theta = \pm 1 $$).

• Coherence time ($$\displaystyle T_c $$): Time duration over which channel is correlated. Approx: $$\displaystyle T_c \approx \frac{1}{f_{d,\max}} $$ (for high correlation).

  • $$\displaystyle \boxed{T_c \propto \frac{1}{v}} $$

E. Reflection, Transmission, and Scattering

• Fresnel equations: Determine reflection/transmission coefficients for perpendicular ($$\displaystyle R_\perp $$, $$\displaystyle T_\perp $$) and parallel ($$\displaystyle R_\parallel $$, $$\displaystyle T_\parallel $$) polarizations at dielectric interfaces.

• Scattering:

  • Smooth surfaces: Specular reflection (Kirchhoff theory, Rayleigh criterion).

  • Rough surfaces: Diffuse scattering (perturbation theory, Rayleigh roughness criterion).

F. Time-Variant Channel Models

• Two-path model: $$\displaystyle h(t) = a_1 e^{j\phi_1(t)} + a_2 e^{j\phi_2(t)} $$, where $$\displaystyle \phi_i(t) = 2\pi f_c \tau_i(t) $$.

• General LTV system: Channel impulse response $h(t, \tau)$ depends on both absolute time $t$ and delay $\tau$.

III. CHANNEL MODELING APPROACHES

A. Deterministic Models

• Ray tracing: Shoot rays from Tx, track reflections/diffractions, sum contributions.

  • Accuracy: High if environment database precise.

  • Efficiency: Computationally intensive for complex urban scenarios.

B. Stochastic Channel Models

1. Narrowband, Wideband, and Directional Models

2. WSSUS Model

• Assumptions:

  • Wide-sense stationary (WSS): Statistics invariant with time shift.

  • Uncorrelated scattering (US): Scattering components at different delays uncorrelated.

• Condensed parameters: Delay spread $$\displaystyle \tau_{rms} $$, Doppler spread $$\displaystyle f_{d,\max} $$.

• Scattering function: $$\displaystyle S(\tau, f_D) = R_h(\tau, \Delta f) $$, delay-Doppler spectrum.

  • $$\displaystyle \boxed{S(\tau, f_D) \text{ is the Fourier transform of } R_h(\tau, \Delta t)} $$

3. Fading Distributions

• Rayleigh fading (no LOS):

  • Amplitude PDF: $$\displaystyle f(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)} $$

  • Phase: Uniform $[0, 2\pi)$.

• Rician fading (with LOS):

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

  • $A$ = LOS amplitude, $$\displaystyle K = A^2/(2\sigma^2) $$ = Rician K-factor.

  • $$\displaystyle \boxed{\text{Rayleigh is special case of Rician with } K=0} $$

C. Doppler Spectra

• Jakes spectrum: For isotropic scattering, $$\displaystyle S(f) \propto \frac{1}{\sqrt{f_{d,\max}^2 - f^2}} $$.

• Gaussian spectrum: $$\displaystyle S(f) \propto e^{-f^2/(2\sigma_f^2)} $$ for limited scattering.

• Flat spectrum: Uniform within $$\displaystyle [-f_{d,\max}, f_{d,\max}] $$.

D. Baseline Channel Models

• AWGN channel: $$\displaystyle y = x + n $$, $$\displaystyle n \sim \mathcal{CN}(0, N_0) $$.

• Error probability (BPSK in AWGN): $$\displaystyle P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) $$.

IV. CHANNEL MEASUREMENT AND SOUNDING

A. Channel Sounding Fundamentals

• Purpose: Extract channel parameters (delay spread, Doppler, fading stats) for model validation.

• Direct sounding: Transmit impulse, measure impulse response directly.

• Indirect sounding: Measure frequency response, IFFT to get impulse response.

B. Measurement Methods

• Time-domain: Transmit pseudo-noise (PN) sequences; cross-correlation at receiver yields CIR.

  • Advantage: Good dynamic range.

  • Resolution: $$\displaystyle \Delta \tau \approx T_{PN} $$ (PN sequence length).

• Frequency-domain: Swept-sine or multi-tone; measure transfer function $H(f)$ over band.

  • Resolution: $$\displaystyle \Delta f = 1/T_{sweep} $$.

C. Characterization and Data Processing

1. Compute power delay profile from CIR → $$\displaystyle \tau_{rms} $$.

2. Track CIR over time → Doppler spectrum, $$\displaystyle f_{d,\max} $$.

3. Fit amplitude/phase histograms → Rayleigh/Rician distribution.

4. Validate models via Kolmogorov-Smirnov test or moment matching.

V. TRANSCEIVER ARCHITECTURE AND MODULATION

A. Wireless Transceiver Block Diagram

[RF Front-end] → [Down-conversion] → [Filtering/Amplification] → [ADC] → [Baseband Processing: Equalization, Demodulation] → [Decoder]

↑
[Encoder] → [Modulation] → [DAC] → [Up-conversion] → [RF Amplification] → [Antenna]

• Baseband processing mitigates channel impairments (ISI, fading).

B. Modulation Techniques

[!TIP]

Exam Derivation: Compare spectral efficiency: QPSK = $$\displaystyle \log_2(4)=2 $$ bits/symbol; MSK = $$\displaystyle \log_2(2)=1 $$ bit/symbol. But MSK has constant envelope → robust to non-linearities.

C. Demodulation and Detection

• Coherent detection: Requires phase reference (pilot/training); optimal performance.

• Non-coherent detection: No phase tracking (e.g., DPSK); simpler but ~3 dB worse.

D. Error Probability Analysis

• AWGN channel: For M-QAM, $$\displaystyle P_s \approx 4Q\left(\sqrt{\frac{3E_b}{N_0(M-1)}}\right) $$.

• Fading channels: Average error probability $$\displaystyle P_b = \int_0^\infty P_b(\gamma) f_\gamma(\gamma) d\gamma $$.

  • Rayleigh BPSK: $$\displaystyle \boxed{P_b = \frac{1}{2}\left(1 - \sqrt{\frac{E_b/N_0}{1+E_b/N_0}}\right)} $$

• Frequency-dispersive fading: Causes error floor even at high SNR due to residual ISI.

VI. EQUALIZATION FOR FREQUENCY-SELECTIVE FADING

A. Need for Equalization

• Mitigate ISI caused by multipath delay spread exceeding symbol period.

B. Equalizer Classifications

1. Linear vs. Nonlinear

• Zero-forcing (ZF): Inverts channel → $$\displaystyle W_{ZF} = H^{-1} $$. Enhances noise at deep fades.

• MMSE: Minimizes MSE → $$\displaystyle W_{MMSE} = (H^H H + N_0 I)^{-1} H^H $$. Better noise trade-off.

• Decision Feedback Equalizer (DFE): Nonlinear; uses past decisions to cancel post-cursor ISI. No noise enhancement but error propagation.

2. Blind vs. Decision-Directed

• Blind equalization: Uses higher-order statistics (e.g., Constant Modulus Algorithm). No training overhead → efficient for non-stationary channels.

• Decision-directed: Uses detected symbols after initial training. Simpler but may diverge if errors accumulate.

  • $$\displaystyle \boxed{\text{Blind preferred when training overhead high or channel rapidly changing}} $$

3. Fractional Spaced Equalizer (FSE)

• Structure: Samples at $L/T$ ($$\displaystyle L>1 $$), e.g., 2 samples/symbol.

• Advantages:

  • Avoids timing sensitivity of symbol-spaced equalizers.

  • Can correct for carrier phase offset.

  • Better performance in multipath channels.

C. Equalizer Structures

• FIR: Always stable, flexible, but higher order.

• IIR: Lower order, but stability issues; rarely used in wireless.

D. Sequence Detection

• MLSE: Maximizes $P(\mathbf{r}|\mathbf{s})$ over sequence $\mathbf{s}$.

• Viterbi algorithm: Trellis-based implementation; complexity $$\displaystyle O(2^L) $$ for $L$-tap channel.

  • States: $$\displaystyle 2^{L-1} $$ for binary modulation.

VII. DIVERSITY TECHNIQUES

A. Diversity Principle

• Goal: Reduce fading depth by combining multiple independent fading paths.

• Improvement: Average SNR increases, error probability decreases.

• Types: Time, frequency, space, polarization, code.

B. Microdiversity

• Scale: Within a cell (meters).

• Implementation: Multiple antennas at mobile or base station.

• Antenna spacing: $$\displaystyle < \lambda/2 $$ (correlated fading).

• Combining: Max-ratio, selection, equal-gain.

• Purpose: Combat small-scale fading (fast fading).

C. Macrodiversity

• Scale: Between cells/base stations (kilometers).

• Implementation: Multiple base stations serve same user (soft handoff in CDMA), cooperative relays.

• Channel correlation: Low (independent shadowing).

• Purpose: Combat large-scale shadowing, improve coverage.

D. Microdiversity vs. Macrodiversity

[!TIP]

Exam Question: "Explain microdiversity and macrodiversity. How does diversity improve signal reception?" → Emphasize independent fading paths and combining gain.

VIII. ANTENNA SYSTEMS FOR MOBILE STATIONS

A. Design Constraints

• Size: Must fit handheld device ($\ll \lambda$).

• Cost: Low-cost materials (e.g., PCB, foam).

• Efficiency: Low due to small size, ground plane losses.

• Radiation pattern: Often omnidirectional for mobility.

• Common types:

  • Monopole: Quarter-wave, simple.

  • Patch: Low-profile, directional.

  • PIFA (Planar Inverted-F): Compact, used in phones.

B. Performance Parameters

• Gain ($G$): Directional amplification (dBi).

• Directivity: Focus of radiation pattern.

• Polarization: Linear (vertical/horizontal) or circular.

• Bandwidth: VSWR $$\displaystyle < 2 $$ bandwidth.

• Rayleigh distance ($$\displaystyle d_R $$): Boundary between near-field and far-field.

  • Derivation: For antenna of largest dimension $D$, far-field when phase variation across aperture $$\displaystyle < \pi/4 $$ rad.

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

• Square antenna example:

  • Side length $a$, area $$\displaystyle A = a^2 $$.

  • Gain (aperture efficiency $\eta \approx 1$): $$\displaystyle G = \frac{4\pi A}{\lambda^2} = \frac{4\pi a^2}{\lambda^2} $$.

  • Thus $$\displaystyle a^2 = \frac{G \lambda^2}{4\pi} $$.

  • Rayleigh distance: $$\displaystyle d_R = \frac{2a^2}{\lambda} = \frac{2}{\lambda} \cdot \frac{G \lambda^2}{4\pi} = \frac{G \lambda}{2\pi} $$.

  • For $$\displaystyle G = 20 $$ dB $$\displaystyle = 100 $$:

$$\boxed{d_R = \frac{100 \lambda}{2\pi} \approx 15.9 \lambda}$$

C. Role in Modern Systems

• Diversity/MIMO: Multiple antennas for spatial streams.

• 5G mmWave challenges: Small wavelengths → tiny antennas, but high path loss requires antenna arrays for beamforming. Mobile terminal antennas must be compact and integrated.

IX. MULTIPLE ACCESS AND DATA SERVICES

A. Multiple Access Techniques

[!TIP]

Comparison: TDMA → synchronous, fixed allocation. CDMA → asynchronous, interference-limited, requires precise power control.

B. Data Services in Cellular Communication

• Circuit-switched: Dedicated channel, constant rate (e.g., voice). Inefficient for bursty data.

• Packet-switched: Shared resources, on-demand (e.g., internet). Enables QoS differentiation:

  • eMBB: High throughput, moderate latency.

  • URLLC: Ultra-low latency ($$\displaystyle <1 $$ ms), high reliability.

  • mMTC: Massive connections, low data rate, long battery life.

• Evolution to all-IP: 4G/5G core networks are packet-switched (EPC/5GC), enabling network slicing.

X. ADVANCED TOPICS AND SYSTEM INTEGRATION

A. Performance Trade-offs

• Spectral efficiency vs. power efficiency: High-order modulation (e.g., 256-QAM) increases rate but requires high SNR → higher transmit power.

• Complexity vs. performance: MLSE optimal but high complexity; DFE suboptimal but lower complexity.

• Link budget: Must account for path loss, shadowing margin, fading margin, implementation losses.

B. 5G-Ready Techniques

• OFDM: Robust to frequency-selective fading (parallel narrowband subcarriers).

• Massive MIMO: Exploits spatial degrees of freedom; requires accurate channel estimation.

• Network slicing: Virtual networks on shared infrastructure → relies on SDN/NFV.

• Context: These build on fundamentals: channel modeling (for MIMO channels), equalization (for OFDM), diversity (for MIMO).

C. Emerging Challenges

• mmWave channels: High path loss, sensitive to blockage, sparse multipath (directional models critical).

• Ultra-dense networks: Small cells → severe interference → need advanced ICIC/CoMP.

• Mobility at high frequencies: Rapid beam misalignment → fast beam tracking.

Final Exam Strategy:

1. Derivations: Practice coherence bandwidth, Doppler shift, Rayleigh distance, fading PDFs.

2. Comparisons: Micro vs macro diversity, TDMA vs CDMA, linear vs nonlinear equalizers.

3. Diagrams: Sketch transceiver block, WSSUS model, diversity combining schemes.

4. Formulas: Box key results (e.g., Rayleigh distance, Rician PDF, BER in fading).