5G Technology (EC-802 (C)) - Unit 2 Short Notes

UNIT 2: WIRELESS CHANNEL CHARACTERISTICS & TRANSCEIVER DESIGN

1.0 INTRODUCTION TO WIRELESS COMMUNICATION SYSTEMS

1.1 Wireless Services & Their Requirements

• Voice: Low data rate (≤ 12 kbps), low delay (< 150 ms), high reliability.

• Data: Variable rate (kbps to Gbps), bursty, error-tolerant.

• Multimedia: High data rate (≥ 2 Mbps), low delay (< 100 ms), QoS guarantees.

• IoT/M2M: Low power, low data rate, massive connectivity, long battery life.

1.2 Economic and Social Impact

• Economic: Trillions in GDP contribution, job creation, new business models (apps, services).

• Social: Connectivity everywhere, digital divide reduction, emergency services, social networking.

1.3 Key Technical Challenges

• Limited Spectrum: Scarcity, need for efficient reuse and sharing.

• Multipath Propagation: Causes fading, ISI, Doppler spread.

• User Mobility: Induces Doppler shift, time-varying channel.

• Interference: Co-channel, adjacent-channel, intra-system.

• Power Constraints: Battery life for mobile devices.

• Security & Privacy: Eavesdropping, data theft.

1.4 Spectrum Limitations & Impact on System Design

• Limited Bands: Regulatory allocation (ITU, national bodies), fragmented bands.

• Impact: Necessitates:

  • High spectral efficiency (bits/s/Hz).

  • Advanced multiplexing (OFDM, CDMA).

  • Dynamic spectrum access (cognitive radio).

  • Small cells (femtocells, picocells) for reuse.

1.5 Evolution: 1G → 5G

[!TIP] Exam Focus: Be ready to compare generations in a table. Highlight shift from circuit-switched (2G/3G) to all-IP (4G/5G) and new services (URLLC, mMTC in 5G).

2.0 WIRELESS CHANNEL FUNDAMENTALS & PROPAGATION EFFECTS

2.1 Large-Scale Path Loss & Shadowing

• Free-Space Propagation Model:

$$PL(d) = PL(d_0) + 20\log_{10}\left(\frac{d}{d_0}\right) + 20\log_{10}\left(\frac{4\pi d_0}{\lambda}\right)$$

where $$\displaystyle d_0 $$ is reference distance (usually 1 m or 1 km), $\lambda$ wavelength.

• Log-Distance Path Loss Model:

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

$n$ = path loss exponent (free-space $$\displaystyle n=2 $$, urban $$\displaystyle n=3–6 $$), $$\displaystyle X_\sigma $$ = shadowing (log-normal).

• Shadowing (Log-Normal Distribution):

  $$\displaystyle X_\sigma \sim \mathcal{N}(0, \sigma^2) $$ dB. Caused by large obstacles (buildings, hills). Modeled as zero-mean Gaussian in dB.

2.2 Small-Scale Fading (Multipath Propagation)

Causes of Multipath:

• Reflection: From large objects (walls, buildings).

• Diffraction: Around edges/obstacles (knife-edge model).

• Scattering: From rough surfaces, small objects (Rayleigh roughness criterion).

Time Dispersion & Delay Spread:

• Power Delay Profile (PDP): $$\displaystyle P(\tau) = \sum_{i=1}^{L} p_i \delta(\tau - \tau_i) $$, where $$\displaystyle p_i $$ is power of $i$-th path, $$\displaystyle \tau_i $$ delay.

• Mean Excess Delay:

$$\overline{\tau} = \frac{\sum_{i=1}^{L} p_i \tau_i}{\sum_{i=1}^{L} p_i}$$

• RMS Delay Spread:

$$\sigma_\tau = \sqrt{\overline{\tau^2} - (\overline{\tau})^2}, \quad \overline{\tau^2} = \frac{\sum_{i=1}^{L} p_i \tau_i^2}{\sum_{i=1}^{L} p_i}$$

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

  • Approx: $$\displaystyle B_c \approx \frac{1}{5\sigma_\tau} $$ (50% correlation) or $$\displaystyle B_c \approx \frac{1}{\sigma_\tau} $$ (90% correlation).

  • Relation: $$\displaystyle B_c \propto \frac{1}{\sigma_\tau} $$. Larger $$\displaystyle \sigma_\tau $$ → smaller $$\displaystyle B_c $$ → more frequency-selective.

Frequency Dispersion & Doppler Shift:

• Doppler Shift for mobile moving at velocity $v$ with angle $\theta$ relative to direction of arrival:

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

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

• Derivation: Relative velocity along LOS = $v \cos \theta$, so frequency shift $$\displaystyle f_d = f_c \cdot \frac{v \cos \theta}{c} $$.

• Maximum Doppler Spread:

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

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

  • Approx: $$\displaystyle T_c \approx \frac{1}{2f_{d,\max}} $$ (50% correlation) or $$\displaystyle T_c \approx \frac{9}{16\pi f_{d,\max}} $$ (90% correlation).

  • Relation: $$\displaystyle T_c \propto \frac{1}{f_d} $$. Higher velocity → larger $$\displaystyle f_d $$ → smaller $$\displaystyle T_c $$ → faster channel variation.

Fading Types:

• Flat Fading: Signal bandwidth $$\displaystyle B \ll B_c $$. All frequencies fade similarly.

• Frequency-Selective Fading: $$\displaystyle B \gg B_c $$. Different frequencies experience different fades → ISI.

Fading Statistic Models:

• Rayleigh Fading: No LOS component. Complex envelope $$\displaystyle Z = X + jY $$, $$\displaystyle X,Y \sim \mathcal{N}(0,\sigma^2) $$. Amplitude $$\displaystyle R = |Z| $$ has PDF:

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

Phase $\phi$ uniform on $[0,2\pi)$.

• Rician Fading: Dominant LOS component with amplitude $A$. Complex envelope $$\displaystyle Z = A e^{j\theta_0} + N $$, $$\displaystyle N \sim \mathcal{CN}(0,\sigma^2) $$. Amplitude PDF:

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

where $$\displaystyle I_0(\cdot) $$ is modified Bessel function of first kind, order zero. K-factor: $$\displaystyle K = \frac{A^2}{2\sigma^2} $$ (LOS power / scatter power).

• Nakagami-m Fading: More general, PDF:

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

$m$ = fading figure ($$\displaystyle m=1 $$ → Rayleigh, $m \to \infty$ → no fading), $$\displaystyle \Omega = \mathbb{E}[R^2] $$.

[!TIP] Exam Focus: Derive RMS delay spread from PDP. Derive Doppler shift expression. Distinguish flat vs frequency-selective fading using $B$ vs $$\displaystyle B_c $$. Know Rician PDF and K-factor.

2.3 Impact of Channel Impairments

• Delay Spread → ISI:

  • If symbol duration $$\displaystyle T_s < \sigma_\tau $$, symbols overlap → ISI.

  • Increases error probability, especially for high-order modulation.

  • Requires equalization or OFDM.

• Doppler Spread → Time-Variation:

  • Channel changes within symbol duration if $$\displaystyle T_s > T_c $$.

  • Causes inter-carrier interference (ICI) in OFDM.

  • Requires rapid channel tracking (pilot symbols, adaptive equalization).

3.0 WIRELESS CHANNEL MODELING & CHARACTERIZATION

3.1 Channel Modeling Approaches

• Deterministic: Ray tracing (shoot rays from Tx, trace reflections/diffractions). Accurate but computationally heavy, needs detailed environment map.

• Stochastic: Statistical models (e.g., Rayleigh, Rician, tapped-delay line with random gains). Computationally efficient, generic.

• Hybrid: Combines deterministic (large-scale) with stochastic (small-scale). E.g., ray tracing for mean path loss + stochastic fading.

3.2 Narrowband, Wideband, and Directional Channel Models

3.3 WSSUS Model

• Wide-Sense Stationary Uncorrelated Scattering:

  • WSS: Statistics invariant to time shift (for duration << stationarity time).

  • US: Scattering components with different delays are uncorrelated.

• Delay-Doppler Spread Function $S(\tau, \nu)$: Fourier transform of time-variant impulse response $h(t,\tau)$ w.r.t. $t$.

$$S(\tau, \nu) = \int_{-\infty}^{\infty} h(t,\tau) e^{-j2\pi \nu t} dt$$

Power density: $$\displaystyle \mathbb{E}[|S(\tau,\nu)|^2] = P(\tau) \cdot D(\nu) $$, where $P(\tau)$ is PDP, $D(\nu)$ is Doppler spectrum.

• Condensed Parameters:

  • Delay Spread $$\displaystyle \sigma_\tau $$ (from $P(\tau)$).

  • Doppler Spread $$\displaystyle f_d $$ (from $D(\nu)$).

  • Coherence Time $$\displaystyle T_c \approx 1/(2f_d) $$.

  • Coherence Bandwidth $$\displaystyle B_c \approx 1/(5\sigma_\tau) $$.

[!TIP] Exam Focus: Draw and explain WSSUS model. List condensed parameters. Know that PDP and Doppler spectrum are separable in WSSUS.

3.4 Channel Sounding & Measurement Techniques

• Purpose: Estimate CIR $h(t,\tau)$ or transfer function $H(t,f)$.

• Time-Domain Methods:

  • Pulse Sounding: Transmit short pulse, measure received echo. Simple but low SNR, limited dynamic range.

  • Spread Spectrum Sliding Correlator: Use PN sequence, correlate at receiver. High processing gain, good for wideband.

• Frequency-Domain Methods:

  • Swept Frequency: Transmit tone at discrete frequencies, measure amplitude/phase. Accurate but slow (not for time-varying channels).

  • Multitone: Transmit parallel tones (like OFDM). Fast, good for wideband.

3.5 Two-Path & Multi-Path Channel Models

• Time-Variant Two-Path Model:

$$h(t,\tau) = \alpha_1(t) \delta(\tau) + \alpha_2(t) \delta(\tau - \tau_0)$$

$$\displaystyle \alpha_i(t) $$: complex time-variant gains (fading). $$\displaystyle \tau_0 $$: relative delay.

• Tapped-Delay Line Model (discrete multipath):

$$h(t,\tau) = \sum_{i=0}^{L-1} \alpha_i(t) \delta(\tau - \tau_i)$$

$$\displaystyle \tau_i $$: discrete delays (taps), $L$ = number of taps. $$\displaystyle \alpha_i(t) $$ often modeled as complex Gaussian processes (Rayleigh/Rician) with Doppler spectrum (e.g., Jakes’ model).

4.0 TRANSCEIVER DESIGN FOR FADING CHANNELS

4.1 Wireless Transceiver Block Diagram & Key Components

Transmitter: Source → Channel Encoder → Interleaver → Modulator → Upconverter → Power Amp → Antenna

Receiver: Antenna → LNA → Downconverter → Equalizer → Demodulator → Deinterleaver → Channel Decoder → Sink

• Key Components: Power amplifier (nonlinear → distortion), LNA (noise figure), frequency converters (I/Q imbalance), antennas (pattern, polarization).

4.2 Modulation & Demodulation in Fading Channels

• Impact of Fading: Random amplitude/phase variation → deep fades → high BER.

• Coherent Detection: Requires accurate channel estimation (pilots). Better performance (e.g., BPSK, QPSK).

• Non-Coherent Detection: No channel estimation (e.g., DPSK, FSK). More robust to phase noise but 3 dB worse in AWGN.

• Example: BPSK in Rayleigh fading: BER $$\displaystyle P_b = \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right) $$, where $\bar{\gamma}$ average SNR.

4.3 Equalization Techniques

• Need: Combat ISI caused by frequency-selective fading.

• Linear Equalizers:

  • Zero-Forcing (ZF): Inverts channel impulse response. Transfer function $$\displaystyle C_{ZF}(f) = 1/H(f) $$. Amplifies noise at deep fades.

  • MMSE (Minimum Mean Square Error): Optimizes $$\displaystyle \mathbb{E}[|s(n) - \hat{s}(n)|^2] $$. Transfer function $$\displaystyle C_{MMSE}(f) = \frac{H^*(f)}{|H(f)|^2 + N_0/E_s} $$. Balances noise enhancement and ISI suppression.

• Decision-Feedback Equalizer (DFE):

  • Feedforward Filter: Compensates for precursor ISI.

  • Feedback Filter: Cancels postcursor ISI using detected symbols. No noise enhancement, but error propagation.

• Fractionally Spaced Equalizer (FSE):

  • Taps spaced $T/2$ (or $T/M$, $$\displaystyle M>1 $$) instead of symbol period $T$.

  • Advantages: Avoids need for precise timing recovery, better performance (can correct for channel and matched filter combined response), less sensitive to sampling phase.

• Blind Equalization vs. Decision-Directed:

  • Blind: Uses only received signal statistics (e.g., constant modulus algorithm, Godard algorithm). No training needed, but slow convergence, possible ambiguity.

  • Decision-Directed: Uses detected symbols as training after initial convergence. Faster, but errors can cause divergence.

  • When Blind Preferred: When training overhead is high (e.g., burst transmission), or channel varies rapidly during training.

• Adaptive Algorithms:

  • LMS (Least Mean Squares): $$\displaystyle \mathbf{w}(n+1) = \mathbf{w}(n) + \mu e^*(n) \mathbf{x}(n) $$. Simple, low complexity, but slow convergence.

  • RLS (Recursive Least Squares): Minimizes weighted least-squares cost. Fast convergence, but high complexity ($$\displaystyle O(N^2) $$).

4.4 Diversity Techniques

• Concept: Provide multiple independent fading paths to reduce probability of deep fades.

• Microdiversity (within cell, short distance):

  • Space Diversity: Multiple antennas at Tx/Rx (separation > coherence distance).

  • Polarization Diversity: Orthogonal polarizations (vertical/horizontal).

  • Pattern Diversity: Antennas with different radiation patterns.

• Macrodiversity (between cell sites, large distance):

  • Cell-Site Diversity: Multiple base stations receive same signal (e.g., soft handoff in CDMA).

  • Cooperative Diversity: Relays assist transmission.

• Diversity Combining Methods:

  | Method | Description | Performance | |-----------------|--------------------------------------------------|-------------------------------------| | Selection | Choose branch with highest SNR. | Simple, 2–3 dB worse than MRC. | | MRC | Max ratio: weight each branch by channel gain. | Optimal (max SNR), requires CSI. | | EGC | Equal gain: phase-align, sum with equal weight. | Near-MRC, no amplitude weighting. | | SSC | Switch to diversity branch when main fades. | Simple, used with selection. |

[!TIP] Exam Focus: Compare ZF vs MMSE (noise enhancement). Explain FSE advantage over symbol-spaced equalizer. List differences between micro and macro diversity (5 points: scale, implementation, purpose, combining, etc.). Know combining methods and their complexity/performance trade-off.

4.5 Sequential Detection & Advanced Receivers

• Viterbi Algorithm for Sequence Detection (MLSE):

  • Principle: Maximum likelihood sequence estimation in ISI channels. Uses trellis diagram to find most likely transmitted sequence.

  • Metrics: Branch metric $$\displaystyle |r(n) - \sum_{k=0}^{L} c_k s(n-k)|^2 $$, path metric cumulative.

  • Advantages: Optimal in ML sense, handles severe ISI.

  • Disadvantages: Complexity exponential with memory $L$ (number of channel taps). Often used with reduced-state sequence estimation (RSSE).

5.0 ANTENNAS & MULTIPLE ACCESS FOR MOBILE SYSTEMS

5.1 Antennas for Mobile Stations (Handsets)

• Design Constraints:

  • Size: Must fit small device (λ/10 or less).

  • Efficiency: Low due to small volume, proximity to user/body.

  • Pattern: Often omnidirectional (user orientation unknown).

  • Bandwidth: Must cover multiple bands (multi-band antennas).

• Types:

  • Monopole: Simple, quarter-wave, narrowband.

  • PIFA (Planar Inverted-F Antenna): Compact, good for PCB integration, multi-band.

  • Patch (Microstrip): Low profile, can be arrayed, narrowband.

  • Loop: Small size, less affected by hand/human body.

5.2 Base Station Antennas & Arrays

• Characteristics: High gain, directional (sectorized, 65°–120° beamwidth), high power handling.

• Arrays: Linear or planar arrays for beamforming (adaptive arrays, MIMO).

• Rayleigh Distance (Far-Field Distance):

  • For antenna with largest dimension $D$:

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

• For square antenna of side $L$: $$\displaystyle d_R = \frac{2L^2}{\lambda} $$.

• Relation to Gain: For aperture antenna, gain $$\displaystyle G = \frac{4\pi A}{\lambda^2} = \frac{4\pi L^2}{\lambda^2} $$, so $$\displaystyle d_R = \frac{G \lambda}{2\pi} $$.

• Significance: Beyond $$\displaystyle d_R $$, radiation pattern stable; within $$\displaystyle d_R $$, near-field effects.

5.3 Multiple Access Techniques

[!TIP] Exam Focus: Compare TDMA vs CDMA in a table (synchronization, capacity, handoff, interference, complexity). Mention CDMA’s soft capacity vs TDMA’s hard capacity.

5.4 Data Services in Cellular Communication

• SMS (Short Message Service): Text messaging, store-and-forward, 160 characters.

• GPRS/EDGE (2.5G): Packet-switched data, theoretical speeds up to 114 kbps (GPRS) / 384 kbps (EDGE).

• HSPA (3.5G): High-Speed Packet Access (HSDPA/HSUPA). Downlink up to 14.4 Mbps (HSDPA), uplink 5.76 Mbps (HSUPA). Uses adaptive modulation, fast scheduling.

• LTE-Advanced (4G): Carrier aggregation (up to 100 MHz), MIMO (up to 8x8), relay nodes, CoMP. Peak rates > 1 Gbps (downlink).

KEY DIAGRAMS (Refer for Visualization)

• WSSUS Model: Delay-Doppler plane with scattered power density.

• Tapped-Delay Line Model: Multiple taps with delays $$\displaystyle \tau_i $$ and gains $$\displaystyle \alpha_i(t) $$.

• Transceiver Block Diagram: Show all components from source to sink.

• Antenna Types: Monopole, PIFA, patch (use

  DiagramCANVAS: Draw simple sketches of each antenna type with dimensions
  ).

• Diversity Combining: Block diagrams for MRC, EGC, selection combining.