Wireless Communication (EC-802 (B)) - Unit 3 Short Notes

UNIT 3: WIRELESS COMMUNICATION

1.0 INTRODUCTION & SYSTEM OVERVIEW

Wireless Services & Applications

Wireless services are classified by traffic type (voice, data, multimedia, IoT) and quality requirements (data rate, latency, reliability, mobility, coverage).

• Voice: Low data rate (~kbps), strict latency (<150 ms), high reliability.

• Data (IoT): Low power, low data rate, massive connectivity.

• Multimedia (Video/Streaming): High data rate (Mbps-Gbps), moderate latency.

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Economic/Social Impact: Wireless enables ubiquitous connectivity, driving digital economies (e-commerce, remote work) and social networking. Challenges include digital divide and privacy concerns.

Evolution of Wireless Generations

Fundamental Technical Challenges

1. Limited Spectrum: Scarcity requires efficient reuse and dynamic allocation (cognitive radio).

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

3. User Mobility: Induces Doppler shift, limiting coherence time.

4. Power Constraints: Battery life limits device complexity and transmission power.

5. Security & Privacy: Wireless links are inherently open, requiring encryption and authentication.

2.0 WIRELESS CHANNEL PROPAGATION & LARGE-SCALE FADING

Fundamental Propagation Mechanisms

• Reflection: Occurs when wave hits a large obstacle (e.g., building). Phase may invert if conductivity high.

• Diffraction: Bending around sharp edges (e.g., rooftops). Modeled by Fresnel zones.

• Scattering: From rough surfaces or small objects (e.g., foliage, street furniture). Creates multipath.

Path Loss Models

1. Free-space Path Loss:

$$P_r = P_t G_t G_r \left( \frac{\lambda}{4\pi d} \right)^2$$

\boxed{PL_{fs}(d) = \left( \frac{4\pi d}{\lambda} \right)^2 \frac{1}{G_t G_r}}

Valid for far-field ($$\displaystyle d > \frac{2D^2}{\lambda} $$, Rayleigh distance).

2. Log-distance Path Loss:

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

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

3. Shadowing: Large-scale fluctuations due to obstacles. Modeled as lognormal distribution:

$$p(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-(x-\mu)^2/(2\sigma^2)}$$

Link Budget Analysis

\boxed{P_{r,\text{min}} = P_t + G_t + G_r - PL - L_{\text{margin}}}

where $$\displaystyle P_{r,\text{min}} $$ is receiver sensitivity, $$\displaystyle L_{\text{margin}} $$ accounts for fading/interference.

Antenna Fundamentals

• Gain $G$: Directivity × efficiency.

• Radiation Pattern: Directional response (e.g., omnidirectional vs. sectoral).

• Polarization: Linear (vertical/horizontal) or circular. Mismatch causes 3 dB loss.

• Rayleigh Distance (far-field):

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

  where $D$ = largest antenna dimension. For $$\displaystyle D=1 $$ m, $$\displaystyle \lambda=0.03 $$ m (10 GHz), $$\displaystyle d_R \approx 67 $$ m.

Antennas for Mobile Stations (MS) vs. Base Stations (BS)

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Common Pitfall: Confusing Rayleigh distance with path loss distance. Rayleigh distance defines far-field for antenna pattern measurements, not path loss.

3.0 SMALL-SCALE FADING & TIME-VARIANT CHANNEL CHARACTERISTICS

Multipath Propagation & Delay Dispersion

• Tapped-Delay Line Model: Channel impulse response $$\displaystyle h(t, \tau) = \sum_{k=1}^{L} \alpha_k(t) e^{j\phi_k(t)} \delta(\tau - \tau_k) $$, where $L$ = number of paths.

• RMS Delay Spread $$\displaystyle \tau_{rms} $$: Measure of time dispersion.

$$\tau_{rms} = \sqrt{\frac{\sum_{k} (\tau_k - \bar{\tau})^2 P(\tau_k)}{\sum_{k} P(\tau_k)}}$$

where $$\displaystyle \bar{\tau} = \frac{\sum_k \tau_k P(\tau_k)}{\sum_k P(\tau_k)} $$ (mean excess delay).

• Coherence Bandwidth $$\displaystyle B_c $$: Frequency range over which channel is flat (correlated). Approximations:

  \boxed{B_c \approx \frac{1}{5\tau_{rms}}} \quad (50% \text{ correlation})

  \boxed{B_c \approx \frac{1}{50\tau_{rms}}} \quad (90% \text{ correlation})

• Impact: If symbol duration $$\displaystyle T_s < \tau_{rms} $$ → ISI (Frequency-selective fading). Increases BER without equalization.

Doppler Effect & Frequency Dispersion

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

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

  Derivation: Relative velocity along wavefront $$\displaystyle v_r = v \cos \theta $$, frequency shift $$\displaystyle f_d = f_c v_r / c = (v/\lambda) \cos \theta $$.

• Maximum Doppler Spread $$\displaystyle f_{d,\max} = v/\lambda $$ (when $$\displaystyle \theta=0^\circ $$).

• Coherence Time $$\displaystyle T_c $$: Time duration over which channel is stationary.

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

  Rule-of-thumb: $$\displaystyle T_c = \frac{9}{16\pi f_d} $$ for 50% correlation.

• Doppler Power Spectral Density (PSD):

  • Clarke’s Model (isotropic scattering):

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

• Jakes’ Model: Discrete approximation of Clarke’s, used in simulations.

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Key Relationship: Delay spread $$\displaystyle \tau_{rms} $$ → Coherence Bandwidth $$\displaystyle B_c $$; Doppler spread $$\displaystyle f_d $$ → Coherence Time $$\displaystyle T_c $$. If $$\displaystyle T_s \gg T_c $$ → fast fading; if $$\displaystyle B_s \ll B_c $$ → flat fading.

Fading Statistics & Models

• Small-Scale Fading: Rapid fluctuations over $\lambda/2$ distance (due to multipath).

• Large-Scale Fading: Slow variations due to shadowing (log-normal).

• Rayleigh Fading (No LOS): Envelope $r$ follows Rayleigh distribution:

  \boxed{p(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)}}

  Phase $\phi$ uniform $[0,2\pi)$. Average power $$\displaystyle E[r^2] = 2\sigma^2 $$.

• Rician Fading (With LOS component $A$): Envelope PDF:

  \boxed{p(r) = \frac{r}{\sigma^2} e^{-(r^2+A^2)/(2\sigma^2)} I_0\left( \frac{rA}{\sigma^2} \right)}

  where $$\displaystyle I_0 $$ = modified Bessel function. Rician K-factor $$\displaystyle K = A^2/(2\sigma^2) $$. $$\displaystyle K=0 $$ → Rayleigh; $K \to \infty$ → AWGN.

• Nakagami-m Fading: More general, PDF:

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

  where $$\displaystyle \Omega = E[r^2] $$, $m$ = fading figure ($$\displaystyle m=1 $$ → Rayleigh).

• Impact on BER: Fading causes deep fades (high BER). Average BER requires integration over fading distribution. For BPSK in Rayleigh:

  \boxed{P_b = \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right)}

  where $$\displaystyle \bar{\gamma} = E[E_b/N_0] $$.

4.0 WIRELESS CHANNEL MODELING & MEASUREMENT

Stochastic Channel Modeling

• Narrowband (Flat Fading): $$\displaystyle h(t) = \alpha(t) e^{j\phi(t)} $$, constant over bandwidth.

• Wideband (Frequency-Selective): Modeled as tapped-delay line with $L$ taps.

• Directional Channel Models: Include angle-of-arrival (AoA) and angle-of-departure (AoD). Power azimuth spectrum (PAS) often Laplacian or Gaussian.

• WSSUS Model (Wide-Sense Stationary Uncorrelated Scattering):

  • Assumptions:

    1. Channel is wide-sense stationary (statistics invariant to time shift).

    2. Scattering components are uncorrelated in delay ($$\displaystyle R_h(\tau_1,\tau_2) \propto \delta(\tau_1-\tau_2) $$).

  • Condensed Parameters:

    • Delay Spread $$\displaystyle \tau_{rms} $$ (time dispersion).

    • Doppler Spread $$\displaystyle f_d $$ (frequency dispersion).

    • Coherence Bandwidth $$\displaystyle B_c \approx 1/\tau_{rms} $$.

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

  • Scatter Function $$\displaystyle S(\tau, f_D) $$: Delay-Doppler power distribution.

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WSSUS is key: It simplifies channel simulation by assuming uncorrelated scattering in delay. Violated in directional channels with clustered paths.

Deterministic Channel Modeling

• Ray Tracing:

  1. Build 3D environment database (walls, buildings).

  2. Launch rays from transmitter, trace reflections/diffractions.

  3. Sum contributions at receiver.

  Efficiency: Computationally intensive; uses image theory for reflections, UTD for diffraction. Accelerated by bounding volume hierarchies.

• Electromagnetic Theories:

  • Kirchhoff Theory: For large, smooth surfaces (specular reflection).

  • Perturbation Theory: For rough surface scattering (small roughness $$\displaystyle \sigma_h \ll \lambda $$). Scattering coefficient depends on surface height variance and correlation length.

Channel Sounding & Measurement

• Purpose: Estimate channel impulse response $h(t,\tau)$ to extract parameters (delay spread, Doppler, AoA).

• Time-Domain Measurement (Pulse Sounding):

  Transmit short pulse $p(t)$, receive $$\displaystyle y(t) = h(t,\tau) * p(t) $$. Deconvolution yields $h(t,\tau)$.

  Limitation: Requires high peak power, susceptible to noise.

• Frequency-Domain (Swept-Time):

  Transmit chirp (swept-frequency signal). Measure transfer function $H(f,t)$, inverse FFT → $h(t,\tau)$.

• Parameter Extraction: From measured $h(t,\tau)$:

  • Compute power delay profile $$\displaystyle P(\tau) = E[|h(t,\tau)|^2] $$.

  • Calculate $$\displaystyle \tau_{rms} $$, $$\displaystyle B_c $$ from $P(\tau)$.

  • Doppler spectrum from time variation of complex amplitudes.

5.0 SIGNAL PROCESSING FOR FADING CHANNELS: EQUALIZATION & DIVERSITY

Equalization Techniques

• Need: Frequency-selective fading causes ISI (symbols overlap). Equalizer compensates channel distortion.

• Classification:

  | Type | Principle | Example | Complexity | |------|-----------|---------|------------| | Linear | Minimize MSE or ZF | ZF: $$\displaystyle G = H^{-1} $$; MMSE: $$\displaystyle G = (H^H H + \sigma_n^2 I)^{-1} H^H $$ | Low | | Nonlinear | Use decisions to cancel ISI | DFE: Feedforward + Feedback filter | Medium | | MLSE | Maximum likelihood sequence estimation | Viterbi algorithm | High |

• Fractional-Spaced Equalizer (FSE):

  • Samples at $T/2$ (or $T/M$, $$\displaystyle M>1 $$) instead of symbol rate $T$.

  • Advantage: Avoids timing sensitivity, better for channels with non-minimum phase.

  • Structure: $M$-times oversampled filter, decimated to symbol rate.

• Blind Equalization vs. Decision-Directed:

  • Decision-Directed: Uses detected symbols as training after initial training phase. Sensitive to error propagation.

  • Blind: No training needed; uses constant modulus algorithm (CMA) or Godard algorithm.

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  When to use blind? In non-stationary channels or where training overhead is costly (e.g., bursty data).

• Viterbi Detector (MLSE):

  • Finds most likely sequence through trellis of channel states.

  • Metric: $$\displaystyle M(\mathbf{r}) = \sum_{n} |r_n - \sum_{k=0}^{L} h_k s_{n-k}|^2 $$.

  • Optimal for known channel $$\displaystyle h_k $$, but complexity grows exponentially with $L$ (memory).

Diversity Techniques

• Principle: Provide multiple independent copies of signal to combat fading.

• Microdiversity (within cell site):

  • Space: Multiple antennas at same location (separation > $\lambda/2$).

  • Time: Repeated transmissions over time (channel varies).

  • Frequency: Spread signal over bandwidth > coherence bandwidth.

  • Polarization: Orthogonal polarizations (vertical/horizontal).

• Macrodiversity (between cell sites):

  • Used in cellular systems (e.g., soft handoff in CDMA).

  • Combines signals from multiple BSs via microdiversity at MS or centralized combining.

• Combining Methods:

  | Method | Principle | SNR Penalty | Complexity | |--------|-----------|-------------|------------| | Selection | Choose branch with highest instantaneous SNR | ~3 dB loss | Low | | Equal Gain (EGC) | Coherent sum with equal weights | ~1 dB loss | Medium | | Maximal Ratio (MRC) | Weight by $\sqrt{\text{SNR}}$; optimal | 0 dB loss | High (needs channel estimation) |

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Key Insight: MRC maximizes output SNR: $$\displaystyle \text{SNR}_{\text{out}} = \sum_{i=1}^{N} \text{SNR}_i $$. Selection simplest but not optimal.

6.0 TRANSCEIVER ARCHITECTURE & MODULATION

Wireless Transceiver Block Diagram

Source → Source Encoder → Channel Encoder → Interleaver → Modulator → RF Front-end → Antenna

                                                                      ↓

Antenna → RF Front-end → Demodulator → Deinterleaver → Channel Decoder → Source Decoder → Destination

• Impact of Modulation:

  • Spectral Efficiency $$\displaystyle \eta = \frac{\log_2 M}{T_s B} $$ (bits/s/Hz).

  • BER: Coherent detection (BPSK, QPSK) better than non-coherent (FSK).

  • Robustness: Constant envelope modulations (MSK, GMSK) resistant to nonlinearities.

Modulation in Fading Channels

• Coherent vs. Non-Coherent:

  • Coherent: Requires channel estimation (pilots). Better performance.

  • Non-Coherent: No estimation needed (DPSK, FSK). ~3 dB penalty.

• Spectral Efficiency Comparison: MSK vs. QPSK

  • MSK (Minimum Shift Keying): Continuous phase, $$\displaystyle \Delta f = \pm 1/(4T_s) $$.

    $$\displaystyle \eta_{\text{MSK}} = 1 $$ bps/Hz (since $$\displaystyle B \approx 1.5/T_s $$).

  • QPSK: $$\displaystyle \eta_{\text{QPSK}} = 2 $$ bps/Hz (same $B$ as BPSK).

  \boxed{\eta_{\text{QPSK}} = 2 \eta_{\text{MSK}}}

  QPSK has higher efficiency but more sensitive to nonlinearities.

• Modulation Choice:

  • Flat Fading: BPSK/QPSK with equalization/diversity.

  • Frequency-Selective Fading: OFDM (multi-carrier) or single-carrier with equalization.

Performance Analysis

• AWGN Channel: For BPSK,

  \boxed{P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)}

• Fading Channels: Average BER by integrating over fading distribution $$\displaystyle f_\gamma(\gamma) $$:

  \boxed{P_b = \int_0^\infty P_b(\gamma) f_\gamma(\gamma) d\gamma}

  For Rayleigh with MRC diversity ($N$ branches):

  \boxed{P_b = \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right)^N}

  where $$\displaystyle \bar{\gamma} = E_b/N_0 $$ per branch.

7.0 SYSTEM-LEVEL ASPECTS & MULTIPLE ACCESS

Cellular System Fundamentals

• Frequency Reuse: Cluster size $$\displaystyle N = i^2 + ij + j^2 $$ (hexagonal grid). Reuse factor $1/N$.

• Cell Splitting: Divide congested cells into smaller ones (reduce $R$, increase $N$).

• Sectoring: Use directional antennas (e.g., 120° sectors) to reduce interference, effectively increase $N$.

• Handoff Strategies:

  • Mobile-assisted (MAHO): MS measures BS signals, network decides.

  • Network-controlled: BS measures, MSC decides.

  • Hard vs. Soft: Hard (break-before-make, TDMA); Soft (make-before-break, CDMA).

Multiple Access Techniques

• TDMA Frame Structure (e.g., GSM):

  
  [Sync | Control | Traffic Slot 1 | ... | Traffic Slot N]
  
  

  Each slot = 156.25 bits (0.577 ms).

• CDMA:

  • Spreading Codes: Walsh codes (orthogonal) for downlink; PN sequences (quasi-orthogonal) for uplink.

  • Processing Gain $$\displaystyle G_p = W/R $$ (spreading bandwidth / data rate). Higher $$\displaystyle G_p $$ → better抗干扰.

  • Capacity: $$\displaystyle N \approx \frac{W}{R} \cdot \frac{1}{E_b/N_0} $$ (approx). Near-far problem requires power control.

Data Services in Cellular Communication

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Evolution Trend: From circuit-switched (dedicated channel) to packet-switched (shared resources), enabling always-on, high-speed data. 5G introduces network slicing for diverse services.

EXAM-READY SUMMARY OF HIGH-FREQUENCY TOPICS

1. Coherence Bandwidth & Delay Spread:

   $$\displaystyle B_c \propto 1/\tau_{rms} $$. $$\displaystyle \tau_{rms} $$ from power delay profile. Determines flat vs. selective fading.

2. Doppler Shift Derivation:

   $$\displaystyle f_d = \frac{v}{\lambda} \cos \theta $$. Maximum $$\displaystyle f_{d,\max} = v/\lambda $$.

3. Small-Scale Fading Models:

   Rayleigh (no LOS), Rician (LOS present, K-factor), Nakagami-m (general).

4. WSSUS Model:

   Uncorrelated scattering in delay, wide-sense stationary. Parameters: $$\displaystyle \tau_{rms} $$, $$\displaystyle f_d $$, $$\displaystyle B_c $$, $$\displaystyle T_c $$.

5. Channel Sounding:

   Time-domain (pulse), frequency-domain (chirp). Extract $h(t,\tau)$.

6. Diversity:

   Micro (space/time/freq) vs. Macro (BS sites). Combining: Selection, EGC, MRC (optimal).

7. Equalization:

   Blind (CMA) vs. Decision-Directed. Fractional-spaced (oversampling). Viterbi = MLSE.

8. Antennas for MS:

   Omnidirectional, low gain, size constrained ($\lambda/4$).

9. Data Services Evolution:

   GSM (circuit) → GPRS (packet) → LTE (all-IP) → 5G (slicing).

10. TDMA vs. CDMA:

    TDMA: synchronous, fixed slots. CDMA: asynchronous, code-limited, soft handoff.