UNIT 5: Wireless Communication Systems

1. Introduction to Wireless Communication Systems

Wireless Services & Requirements:

• Voice-centric (1G-2G): Circuit-switched, low data rate (< 10 kbps), high reliability.

• Data-centric (3G-4G): Packet-switched, higher data rates (Mbps), support for internet, multimedia.

• Ultra-reliable & Low Latency (5G): Mission-critical IoT, autonomous systems, < 1 ms latency, > 10 Gbps peak rate.

• Massive IoT: Extremely low power, massive device connectivity.

Evolution (1G to 5G):

Economic & Social Impact:

• Economic: Trillion-dollar industry, job creation, driver for digital economy, new business models (app economy, sharing economy).

• Social: Ubiquitous connectivity, social networking, access to information/education/healthcare, changed lifestyle and work patterns.

Key Technical Challenges:

1. Multipath Propagation: Causes frequency-selective fading and delay spread.

2. User Mobility: Induces Doppler shift/spread, requiring fast signal tracking and handoffs.

3. Spectrum Limitations: Scarcity of licensed spectrum, need for efficient utilization (e.g., cognitive radio, mmWave bands).

[!TIP] Exam Focus: Be prepared to contrast 1G-5G and link technical challenges (multipath, mobility) to specific system impairments (fading, Doppler).

2. Wireless Propagation and Channel Characteristics

Propagation Mechanisms:

• Reflection & Transmission: Occur at boundaries between media with different dielectric constants. Governed by Fresnel equations. Reflection coefficient $$\displaystyle \Gamma = \frac{\eta_2 - \eta_1}{\eta_2 + \eta_1} $$.

• Scattering: From rough surfaces or small objects. Described by:

  • Kirchhoff Theory: For surfaces with large radius of curvature compared to wavelength.

  • Perturbation Theory: For slightly rough surfaces (Rayleigh criterion: height variance $$\displaystyle \sigma_h^2 << \lambda^2 $$).

Large-Scale Fading (Path Loss & Shadowing):

• Path Loss: $$\displaystyle PL(d) = PL(d_0) + 10n \log_{10}(d/d_0) + X_\sigma $$ (dB)

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

  • $$\displaystyle X_\sigma $$: Log-normal shadowing (zero-mean Gaussian in dB).

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

Small-Scale Fading:

• Caused by multipath propagation with delay spread $$\displaystyle < T_s $$ (symbol period).

• Doppler Shift: $$\displaystyle f_d = \frac{v f_c}{c} $$ (Hz), where $v$ is relative velocity, $$\displaystyle f_c $$ carrier freq, $c$ light speed.

• Doppler Spread: $$\displaystyle B_d = f_{d,\max} = \frac{v_{max} f_c}{c} $$ (range of Doppler shifts).

Channel Parameters & Relationships:

1. Delay Spread ($$\displaystyle \tau_{rms} $$): RMS delay spread. $$\displaystyle \tau_{rms} = \sqrt{\overline{\tau^2} - (\overline{\tau})^2} $$

2. Coherence Bandwidth ($$\displaystyle B_c $$): Approximate bandwidth over which channel response is flat.

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

   • Definition 2: $$\displaystyle B_c \approx \frac{1}{\tau_{rms}} $$ (for 90% correlation).

   • Relationship: $$\displaystyle \boxed{B_c \propto \frac{1}{\tau_{rms}}} $$ (Inverse relationship).

3. Coherence Time ($$\displaystyle T_c $$): Time duration over which channel is stationary.

   • $$\displaystyle T_c \approx \frac{1}{B_d} = \frac{c}{v_{max} f_c} $$ (for 50% correlation).

   • Relationship: $$\displaystyle \boxed{T_c \propto \frac{1}{v_{max}}} $$ (Inversely proportional to max velocity).

4. Rayleigh Distance ($$\displaystyle d_R $$): Distance beyond which angular beamwidth is constant.

   • $$\displaystyle \boxed{d_R = \frac{2D^2}{\lambda}} $$ where $D$ is antenna aperture diameter, $\lambda$ wavelength.

[!TIP] Common Pitfall: Confusing coherence bandwidth (frequency domain) with coherence time (time domain). Remember: Delay Spread → Coherence Bandwidth, Doppler Spread → Coherence Time.

3. Wireless Channel Modeling

Statistical Fading Models:

• Rayleigh Fading: No dominant line-of-sight (LOS) component. Amplitude: Rayleigh PDF $$\displaystyle f(r) = \frac{r}{\sigma^2}e^{-r^2/(2\sigma^2)} $$. Phase: Uniform $[0, 2\pi]$.

• Rician Fading: One dominant LOS component + scattered multipath.

  • Amplitude: Rician PDF with parameter $$\displaystyle K = \frac{\text{LOS power}}{\text{scattered power}} $$.

  • Phase: Non-uniform.

  • Derivation: $$\displaystyle Z = X + jY $$, where $$\displaystyle X \sim \mathcal{N}(\mu_x, \sigma^2) $$, $$\displaystyle Y \sim \mathcal{N}(\mu_y, \sigma^2) $$. Amplitude $$\displaystyle R = \sqrt{X^2+Y^2} $$ follows Rician distribution.

• Nakagami-m Model: General model encompassing Rayleigh ($$\displaystyle m=1 $$) and one-sided Gaussian ($$\displaystyle m=0.5 $$). PDF: $$\displaystyle f(r) = \frac{2m^m}{\Gamma(m)\Omega^m} r^{2m-1} e^{-m r^2/\Omega} $$.

Channel Model Classifications:

WSSUS (Wide-Sense Stationary Uncorrelated Scattering) Model:

• Assumptions: Channel is WSS in time, and scattering components are uncorrelated in delay.

• Condensed Parameters:

  • Delay Spread ($$\displaystyle \tau_{rms} $$): Characterizes multipath in delay domain.

  • Doppler Spread ($$\displaystyle B_d $$): Characterizes time variation.

• Channel Impulse Response: $$\displaystyle h(t, \tau) = \sum_{i} \alpha_i(t) \delta(\tau - \tau_i) $$.

• Scattering Function: $$\displaystyle S(\tau, f_d) = \phi_h(\tau, f_d) $$ (delay-Doppler power spectrum).

Deterministic Modeling:

• Ray Tracing: Computationally intensive. Simulates electromagnetic waves along paths (direct, reflected, diffracted). Efficiency: Requires accurate 3D database of environment (buildings, terrain). Used for site-specific planning.

Time-Variant Two-Path Model:

• Simplest model: $$\displaystyle h(t) = a_1 e^{j(2\pi f_{d1} t + \phi_1)} + a_2 e^{j(2\pi f_{d2} t + \phi_2)} $$.

• Captures interference between two rays with different delays and Doppler shifts.

Doppler Spectra:

• Classical (Uniform AoA): $$\displaystyle S(f_d) \propto \frac{1}{\sqrt{f_{d,\max}^2 - f_d^2}} $$ (for 2D scattering).

• Flat (for isotropic scattering): $$\displaystyle S(f_d) = \frac{1}{2f_{d,\max}} $$ for $$\displaystyle |f_d| \le f_{d,\max} $$.

[!TIP] Exam Focus: Be able to derive Rician amplitude distribution and explain WSSUS assumptions. Know when to use deterministic (ray tracing) vs. statistical models.

4. Channel Measurement and Sounding

Channel Sounding Process: Transmit a known probing signal, measure channel response, estimate CIR/CFF. Measurement Methods:

• Time-Domain: Transmit wideband pulse/impulse. Measure received signal in time. Directly yields CIR $h(t, \tau)$. Requires high-speed sampling.

• Frequency-Domain: Transmit signal with known frequency content (e.g., multi-tone, chirp). Measure transfer function $H(f, t)$. Inverse FFT gives CIR. More common with vector network analyzers.

Characterization: Extract parameters like delay spread, Doppler spread, path loss exponent, shadowing statistics, fading distribution from measured data.

5. Wireless Transceiver and Modulation

Block Diagram (Simplified):

Source → Encoder → Interleaver → Modulator → Upconverter → TX Antenna → Channel → RX Antenna → Downconverter → Demodulator → Deinterleaver → Decoder → Destination

Modulation Techniques:

• BPSK: 1 bit/symbol. $$\displaystyle s(t) = \sqrt{2E_b/T_b} \cos(2\pi f_c t + \pi(1-b)) $$. Robust, spectral efficiency = 1 bps/Hz.

• QPSK: 2 bits/symbol. Four phases (0°, 90°, 180°, 270°). Same $$\displaystyle E_b $$ as BPSK, same BER, spectral efficiency = 2 bps/Hz.

• MSK (Minimum Shift Keying): Type of continuous-phase FSK with modulation index $$\displaystyle h=0.5 $$. Frequency separation = $$\displaystyle 1/(2T_b) $$. Key Property: Phase continuity, constant envelope. Better spectral containment than QPSK.

Spectral Efficiency Comparison (MSK vs QPSK):

• QPSK: Rectangular pulse shaping → higher sidelobes.

• MSK: Continuous phase → main lobe 1.5x wider than QPSK, but sidelobes decay faster ($$\displaystyle f^{-4} $$ vs $$\displaystyle f^{-2} $$). MSK has better spectral efficiency in crowded bands due to lower out-of-band radiation.

Multiple Access Techniques:

• TDMA: Users share frequency in time slots. Requires precise synchronization. (e.g., GSM).

• CDMA: Users share frequency/time using unique spreading codes. Resistant to interference, soft capacity. (e.g., IS-95, 3G).

Impact on Performance: Modulation choice affects BER vs. $$\displaystyle E_b/N_0 $$, spectral efficiency, power efficiency, and resistance to channel impairments (e.g., constant envelope of MSK robust to nonlinear amplifiers).

[!TIP] Key Point: MSK's main advantage is spectral containment (lower out-of-band emissions), not higher data rate. QPSK has higher spectral efficiency but worse spectral shape.

6. Impact of Wireless Channel on Signal Reception

Delay Dispersion & Frequency-Selective Fading:

• Delay Dispersion ($$\displaystyle \tau_{rms} $$): Causes intersymbol interference (ISI) when $$\displaystyle \tau_{rms} > T_s $$.

• Frequency-Selective Fading: Channel transfer function $H(f)$ varies significantly over signal bandwidth $$\displaystyle B_s $$. Deep fades at specific frequencies.

Error Probability in Fading Channels:

• AWGN Channel: $$\displaystyle P_b = Q\left(\sqrt{2E_b/N_0}\right) $$ for BPSK.

• Flat Fading (Rayleigh): $$\displaystyle P_b = \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right) $$, where $$\displaystyle \bar{\gamma} = E_b/N_0 $$ average SNR. Much worse than AWGN at low SNR.

• Frequency-Selective Fading: Requires equalization; error rate depends on equalizer performance.

7. Equalization Techniques

Need: To mitigate ISI caused by delay dispersion.

Classification:

1. Linear Equalizers:

   • Zero-Forcing (ZF): Inverts channel exactly. $$\displaystyle W_{ZF} = H^{-1} $$. Amplifies noise at frequencies with deep fades.

   • MMSE (Minimum Mean Square Error): Compromise between inversion and noise amplification. $$\displaystyle W_{MMSE} = (H^H H + \sigma_n^2 I)^{-1} H^H $$.

2. Decision-Directed Equalization: Uses detected symbols (after slicer) to update weights. Requires initial training.

3. Blind Equalization: Updates weights without training sequence (e.g., Constant Modulus Algorithm - CMA). Preferred when: Training overhead is high, or channel varies rapidly during data transmission.

4. Fractional Spaced Equalizer (FSE): Sampling rate > symbol rate (e.g., 2 samples/symbol). Avoids need for precise timing recovery, better performance.

Viterbi Detector (MLSE): Maximum Likelihood Sequence Estimation. Finds most probable transmitted sequence through channel trellis. Optimal but complexity grows exponentially with channel memory.

Comparison:

[!TIP] Exam Focus: Contrast ZF (noise amplification) vs MMSE (trade-off). Know when blind equalization is used (non-stationary channels, training overhead).

8. Diversity Techniques

Concept: Provide multiple independent (or partially correlated) signal replicas to receiver to combat fading. Improves SNR/reliability, not data rate.

Microdiversity: Combats small-scale fading at a single location (local area).

• Antenna Diversity: Spatially separated antennas (e.g., MIMO). Requires antenna spacing > $\lambda/2$ for independence.

• Time Diversity: Same channel at different times (requires channel coherence time $$\displaystyle T_c $$). Achieved via interleaving and channel coding.

• Frequency Diversity: Same channel at different frequencies. Requires coherence bandwidth $$\displaystyle B_c $$. Achieved via spread spectrum or OFDM with interleaving.

Macrodiversity: Combats large-scale fading (shadowing). Antennas separated by many wavelengths (e.g., different base stations in cellular network). Used in soft handoff.

Micro vs. Macro Diversity:

Diversity Combining Methods:

1. Selection Combining (SC): Choose branch with highest instantaneous SNR. Simple, 1 RF chain.

2. Equal Gain Combining (EGC): Co-phased branches, equal weights. $$\displaystyle \hat{y} = \sum_{i=1}^L r_i e^{-j\theta_i} $$.

3. Maximal Ratio Combining (MRC): Weigh each branch by its SNR. Optimal. $$\displaystyle \hat{y} = \sum_{i=1}^L \alpha_i r_i e^{-j\theta_i} $$, where $$\displaystyle \alpha_i \propto \text{SNR}_i $$.

Performance (for L i.i.d. Rayleigh branches):

• SC: $$\displaystyle P_{out} = (1 - e^{-\gamma_{th}/\bar{\gamma}})^L $$

• MRC: $$\displaystyle P_{out} = e^{-\gamma_{th}/\bar{\gamma}} \sum_{k=0}^{L-1} \frac{(\gamma_{th}/\bar{\gamma})^k}{k!} $$

[!TIP] Key: MRC provides the best performance (3 dB gain per branch over SC). Diversity order increases with number of branches $L$.

9. Antennas and Data Services

Antennas for Mobile Stations:

• Constraints: Size, cost, radiation pattern (omnidirectional for mobility), efficiency.

• Types:

  • Monopole/Quarter-wave whip: Common in handsets, vertical polarization.

  • PIFA (Planar Inverted-F Antenna): Compact, used in modern smartphones, covers multiple bands.

  • Patch Antennas: Low profile, used in laptops, vehicles.

  • Diversity Antennas: Two antennas spaced apart (e.g., at top/bottom of phone).

Data Services in Cellular Communication:

• Circuit-Switched Data (2G): GSM CSD (9.6 kbps).

• Packet-Switched Data (3G): UMTS HSPA (Mbps).

• Broadband (4G): LTE (100+ Mbps), VoLTE.

• Ultra-Broadband (5G): eMBB (Gbps), URLLC (<1ms), mMTC.

• Services: Web browsing, video streaming, VoIP, IoT, AR/VR.

10. Advanced Topics in Wireless Channel Modeling

Scattering on Rough Surfaces:

• Kirchhoff Theory (Physical Optics): Assumes locally plane waves on surface with large radius of curvature. Scattered field derived from surface integral using tangential field approximations. Valid for $$\displaystyle \sigma_h^2 \ll \lambda^2 $$ and large correlation length.

• Perturbation Theory (Small Perturbation Method): For $$\displaystyle \sigma_h \ll \lambda $$. Treats surface as slightly perturbed plane. Scattered field expressed as series in $$\displaystyle \sigma_h/\lambda $$. First-order gives Bragg scattering.

Rayleigh Distance Derivation:

• From Fresnel diffraction for a circular aperture.

• Rayleigh distance $$\displaystyle d_R $$ is distance where far-field (Fraunhofer) pattern begins. Path difference between center and edge = $\lambda/8$.

• $$\displaystyle \frac{D^2}{2d_R} - \frac{D^2}{2(d_R + \Delta d)} \approx \frac{D^2 \Delta d}{2 d_R^2} = \frac{\lambda}{8} $$.

• For $$\displaystyle \Delta d \approx d_R $$, solving gives $$\displaystyle \boxed{d_R = \frac{2D^2}{\lambda}} $$.

Delay Dispersion in Directional Channels & Remedial Measures:

• Cause: Multipath components arriving from different angles have different path lengths → different delays.

• Remedial Measures:

  1. Directional Antennas (at BS/MS): Reduce multipath by spatial filtering.

  2. Beamforming: Form beams towards dominant directions, suppress others.

  3. MIMO Processing: Use spatial multiplexing or diversity to handle directional multipath.

  4. Equalization: Still required for residual delay spread within a beam.

[!TIP] Remember: Rayleigh distance defines far-field for antennas. In directional channels, delay spread is linked to angular spread $$\displaystyle \sigma_\theta $$ and array size: $$\displaystyle \tau_{rms} \approx \frac{D \sin(\sigma_\theta)}{c} $$.