Wireless Communication (EC-802 (B)) - Unit 1 Short Notes

UNIT 1: WIRELESS COMMUNICATION FUNDAMENTALS AND CHANNEL MODELING

I. INTRODUCTION AND FUNDAMENTALS

Wireless Services and Requirements

• Types of Services:

  • Voice: Circuit-switched, low data rate, stringent latency (e.g., traditional cellular calls).

  • Data: Packet-switched, variable rate (e.g., web browsing, email).

  • Multimedia: High data rate, bandwidth-intensive, requires QoS (e.g., video streaming, video calls).

  • IoT (Machine-Type): Low power, low data rate, massive connectivity, often delay-tolerant.

• Economic & Social Impact: Ubiquitous connectivity, enables new business models (apps, sharing economy), bridges digital divide, but raises privacy/security concerns and requires massive infrastructure investment.

Evolution of Wireless Communication (1G to 5G & Beyond)

Key Technical Challenges

• Multipath Propagation: Signals arrive via multiple paths causing constructive/destructive interference → Fading (signal level fluctuations) and Inter-Symbol Interference (ISI).

• User Mobility: Causes Doppler Shift/Spread ($$\displaystyle f_d = v/\lambda $$) → Fast Fading (channel changes within symbol duration).

• Spectrum Limitations: Scarcity (finite resource), Regulation (ITU, national bodies), Interference (co-channel, adjacent channel).

• Power Constraints: Battery life limits for mobile devices → need for low-power circuit design and protocols.

Wireless Channel as a Linear Time-Variant (LTV) System

• Characterized by time-variant impulse response $h(t, \tau)$.

  • $t$: Time-varying due to mobility/scattering changes.

  • $\tau$: Delay due to multipath propagation.

• Output $$\displaystyle y(t) = \int_{-\infty}^{\infty} h(t, \tau) x(t-\tau) d\tau $$.

• Implication: Signal design must combat time-variation (fast fading) and dispersion (delay spread). Receiver requires channel estimation and adaptive processing (equalization, diversity).

II. WIRELESS CHANNEL CHARACTERIZATION AND MODELING

Large-Scale Fading (Path Loss & Shadowing)

• Path Loss: Average signal power attenuation with distance $d$.

  • Free-Space Path Loss: $$\displaystyle PL(d) = \left(\frac{4\pi d}{\lambda}\right)^2 $$ or $$\displaystyle PL(d)[dB] = 20\log_{10}\left(\frac{4\pi d}{\lambda}\right) $$.

  • Log-Distance Path Loss Model: $$\displaystyle PL(d)[dB] = PL(d_0)[dB] + 10n \log_{10}\left(\frac{d}{d_0}\right) + X_\sigma $$.

    • $n$: Path Loss Exponent (environment-dependent, e.g., 2=free space, 4=urban).

    • $$\displaystyle X_\sigma $$: Shadowing (log-normal random variable, 0 mean, $\sigma$ std dev in dB).

• Shadowing (Slow Fading): Caused by large obstacles (buildings, hills). Modeled as log-normal distribution (normal in dB domain).

Small-Scale Fading (Multipath)

• Causes: Multipath propagation, mobile speed, surrounding object motion.

• Time-Varying Impulse Response: $$\displaystyle h(t, \tau) = \sum_{i=1}^{L} \alpha_i(t) \delta(\tau - \tau_i(t)) $$, where $$\displaystyle \alpha_i(t) $$ are complex gains.

• Fading Distributions:

  • Rayleigh Fading: No dominant line-of-sight (LOS) component. Amplitude $R$ is Rayleigh: $$\displaystyle f_R(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)} $$, $r \ge 0$. Phase $\theta$ is uniform $[0, 2\pi)$. Power $$\displaystyle R^2 $$ is exponential.

  • Rician Fading: With a dominant LOS component. Amplitude follows Rician distribution:

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

    where $A$ is the deterministic LOS amplitude, $$\displaystyle I_0 $$ is modified Bessel function. **Rician K-factor:** $$\displaystyle K = A^2/(2\sigma^2) $$ (measures fading severity, $$\displaystyle K=0 $$ → Rayleigh, $K \to \infty$ → AWGN).

*   **Nakagami-m Fading:** More general model. Amplitude PDF: $$\displaystyle f_R(r) = \frac{2m^m}{\Gamma(m)\Omega^m} r^{2m-1} e^{-m r^2/\Omega} $$.

    *   $m$: fading figure ($$\displaystyle m=1 $$ → Rayleigh, $m \to \infty$ → AWGN).

    *   $\Omega$: average power $$\displaystyle E[R^2] $$.

Critical Channel Parameters

• Delay Spread & Coherence Bandwidth:

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

  • RMS Delay Spread: $$\displaystyle \sigma_\tau = \sqrt{\frac{\sum_k P(\tau_k)(\tau_k - \bar{\tau})^2}{\sum_k P(\tau_k)}} $$, where $$\displaystyle \bar{\tau} = \frac{\sum_k P(\tau_k)\tau_k}{\sum_k P(\tau_k)} $$.

  • Coherence Bandwidth ($$\displaystyle B_c $$): Frequency range over which channel is flat (correlated). Approx: $$\displaystyle B_c \approx \frac{1}{5\sigma_\tau} $$ (for 50% correlation) or $$\displaystyle B_c \approx \frac{1}{\sigma_\tau} $$.

  • Impact: If symbol period $$\displaystyle T_s < \sigma_\tau $$ → frequency-selective fading/ISI → need for equalization/OFDM.

  [!TIP] Exam Focus: Derive relationship: $$\displaystyle B_c \propto 1/\sigma_\tau $$. ISI occurs when $$\displaystyle T_s \ll \sigma_\tau $$.

• Doppler Shift & Coherence Time:

  • Maximum Doppler Shift: $$\displaystyle f_d = \frac{v}{\lambda} = \frac{vf_c}{c} $$, where $v$ is mobile speed, $\lambda$ wavelength, $$\displaystyle f_c $$ carrier freq.

  • Doppler Spread ($$\displaystyle B_D $$): Range of Doppler frequencies due to multipath angles. $$\displaystyle B_D \approx 2f_d $$ for isotropic scattering.

  • Coherence Time ($$\displaystyle T_c $$): Time duration over which channel is static (correlated). Approx: $$\displaystyle T_c \approx \frac{1}{f_d} $$ (for 50% correlation) or $$\displaystyle T_c \approx \frac{9}{16\pi f_d} $$ (from Jakes' model).

  • Doppler PSD (Jakes' Model): For uniform scattering, $$\displaystyle S(f) = \frac{2}{\pi f_d \sqrt{1 - (f/f_d)^2}} $$, $$\displaystyle |f| \le f_d $$.

  • Impact: If $$\displaystyle T_s > T_c $$ → fast fading (channel changes per symbol) → need for channel tracking.

Channel Models

• Narrowband (Frequency-Flat) Fading:

  • Assumption: $$\displaystyle B_{signal} \ll B_c $$ (delay spread negligible). Channel appears as single-tap LTV: $$\displaystyle y(t) = h(t)x(t) + n(t) $$.

  • Applicability: Narrowband systems (e.g., 2G GSM), where symbol period $\gg$ delay spread.

• Wideband (Frequency-Selective) Fading:

  • Assumption: $$\displaystyle B_{signal} > B_c $$ (delay spread significant). Channel has multiple resolvable taps in impulse response.

  • Applicability: Broadband systems (4G/5G, WLAN), high data rates → short symbol periods.

• Directional Channel Models:

  • Characterize angular spread and Direction-of-Arrival (DoA). Essential for MIMO and beamforming systems.

  • Modeled using angular power spectrum $P(\phi)$.

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

  • Assumptions:

    1. Wide-Sense Stationary (WSS): Statistics invariant to time shift $t$.

    2. Uncorrelated Scattering (US): Scattering components with different delays are uncorrelated: $$\displaystyle R_h(\tau_1, \tau_2; \Delta t) = P(\tau_1)\delta(\tau_1-\tau_2)r_h(\Delta t) $$.

  • Condensed Parameters: Fully described by PDP $P(\tau)$ and Doppler PSD $S(f)$ (or delay-Doppler scattering function).

  • Diagram:

    DiagramCANVAS: A 2D plot with delay (τ) on x-axis and Doppler frequency (f) on y-axis. Intensity/color represents scattering function magnitude. Shows a concentrated "cloud" along τ-axis for PDP and f-axis for Doppler spectrum.

• Time-Variant Two-Path Model:

  • Simplest model for fast fading: $$\displaystyle h(t) = a_1 e^{j2\pi f_{d1}t} + a_2 e^{j2\pi f_{d2}t} $$.

  • Captures Doppler shifts and time-variation. Useful for analysis of phase/frequency effects.

Deterministic Channel Modeling

• Ray Tracing:

  • Computes propagation paths (reflection, diffraction) using geometric optics in a detailed 3D environment map.

  • Efficiency: Computationally intensive (ray launching, intersection tests). Accuracy depends on scene database fidelity. Used for site-specific planning.

• Scattering from Rough Surfaces:

  • Kirchhoff Theory (Perturbation): Assumes surface roughness small compared to wavelength. Scattered field derived from surface integral using tangent plane approximation. Valid for slightly rough surfaces.

  • Physical Optics & Stationary Phase: For large, smooth surfaces. Uses far-field approximation and method of stationary phase to evaluate integrals.

Channel Sounding and Measurement

• Purpose: Obtain real-world PDP, Doppler spectrum, directional characteristics to validate/calibrate models.

• Measurement Methods:

  • Time-Domain:

    • Pulse Sounding: Transmit short pulse, measure impulse response directly. Limited by pulse width and dynamic range.

    • Correlation-Based (PN Sequence): Transmit spread spectrum sequence, correlate at receiver → high resolution, good dynamic range.

  • Frequency-Domain:

    • Swept Frequency (Network Analyzer): Measure $$\displaystyle S_{21} $$ over wide band → IFFT gives PDP. High accuracy, slow.

    • Multicarrier (OFDM): Use pilot subcarriers in OFDM system → estimate channel frequency response → PDP.

  • Spatial/Directional: Use antenna arrays to measure DoA and angular spread.

III. TRANSCEIVER DESIGN AND COUNTERMEASURES

Wireless Transceiver Architecture

graph LR

    A[Source] --> B[Channel Encoder]

    B --> C[Interleaver]

    C --> D[Modulator]

    D --> E[Upconverter/RF]

    E --> F[Antenna]

    F --> G[Wireless Channel]

    G --> H[Antenna]

    H --> I[Downconverter/RF]

    I --> J[Demodulator]

    J --> K[Equalizer]

    K --> L[Deinterleaver]

    L --> M[Channel Decoder]

    M --> N[Destination]

• Impact of Modulation:

  • Spectral Efficiency: Bits/s/Hz (e.g., QPSK=2, 16-QAM=4).

  • Power Efficiency: Required $$\displaystyle E_b/N_0 $$ for target BER (e.g., BPSK best, M-QAM worse).

  • Complexity: MSK (constant envelope, non-coherent detection possible) vs. QPSK (coherent required, linear amplifier needed). MSK has ~1.5 dB worse $$\displaystyle E_b/N_0 $$ than QPSK for same BER but better power efficiency due to constant envelope.

Impact of Channel Impairments on Reception

• Delay Spread/Frequency-Selective Fading: Causes ISI → error floor even at high SNR.

• Fast Fading: Channel varies within frame → deep fades cause burst errors.

• Error Probability: In fading channels, average BER is much higher than in AWGN for same average SNR. Requires diversity/coding to achieve reliable communication.

Equalization Techniques

• Purpose: Compensate for ISI by inverting channel frequency response.

• Classification:

  • Linear: ZF (forces $$\displaystyle H_{eq}H=1 $$ → noise enhancement), MMSE (minimizes MSE → trade-off).

  • Nonlinear: DFE (Feedback filter cancels past ISI, less noise enhancement than ZF).

  • Training-Based: Uses known training sequence for initial tap setting.

  • Blind Equalization: No training sequence (e.g., Constant Modulus Algorithm - CMA). Preferred when training overhead is high, channel non-stationary, or reverse link capacity limited.

  • Decision-Directed: Uses detected symbols as "training" after convergence.

• Fractional Spaced Equalizer (FSE):

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

  • Advantages: Avoids timing sensitivity, can correct for carrier phase offset, better performance when sampling not at optimum instant.

• Viterbi Detector (MLSE):

  • Optimal for ISI channels with finite memory (e.g., $L$ taps → $$\displaystyle M^L $$ states for M-ary modulation).

  • Uses Viterbi Algorithm to find maximum likelihood sequence through trellis. High complexity ($$\displaystyle O(2^L) $$) but best performance.

• Comparison: ZF (simple, noise enhancement) < MMSE/DFE (better) < MLSE (optimal, complex). FSE > symbol-spaced for timing robustness.

Diversity Techniques

• Fundamental: Provide multiple independent fading replicas → reduce probability of deep fades.

• Microdiversity: Local diversity (within a small area, e.g., at a mobile or base station). Uses antenna spacing ($\gg \lambda$) to achieve uncorrelated branches.

• Macrodiversity: Larger scale (between geographically separated base stations). Used in cellular systems (soft handoff), reduces shadowing impact.

• Diversity Combining:

  • Selection Combining (SC): Pick branch with highest SNR. Simple, ~$N$-dB gain for $N$ branches.

  • Maximal Ratio Combining (MRC): Weighted sum ($$\displaystyle w_i = h_i^* $$). Optimal for maximizing SNR. Gain $$\displaystyle \approx 10\log_{10}N $$ dB.

  • Equal Gain Combining (EGC): Same as MRC but unit weights. Near-optimal, simpler.

• How it Improves Reception: Converts deep Rayleigh fades into less severe fading (e.g., with $N$ i.i.d. branches, combined envelope distribution has heavier tail → lower outage probability).

IV. SYSTEM ASPECTS AND ENABLING TECHNOLOGIES

Spectrum Management and Limitations

• Regulatory: ITU-R allocates global bands, national bodies (FCC, TRAI) assign licenses.

• Impact of Scarcity/Fragmentation:

  • Drives need for high spectral efficiency (MIMO, OFDM, advanced coding).

  • Motivates flexible spectrum access (cognitive radio, dynamic spectrum sharing).

  • Causes interference management challenges (ICIC in LTE).

Multiple Access Techniques

• TDMA (Time Division Multiple Access):

  • Principle: Users share frequency but occupy distinct time slots in a frame.

  • Frame Structure: Frame = $N$ time slots. Each user assigned one slot per frame.

  • Pros: Simple, low complexity, no intra-cell interference.

  • Cons: Rigid, guard times waste capacity, high latency.

• CDMA (Code Division Multiple Access):

  • Principle: All users share same frequency/time, separated by orthogonal spreading codes (e.g., Walsh codes). Each data bit multiplied by high-rate code (chip rate $$\displaystyle >> $$ data rate).

  • Near-Far Problem: Strong nearby signal overwhelms weak distant signal at receiver → requires power control.

  • Soft Capacity: Capacity is interference-limited, not fixed number of codes.

  • **Pros:**抗干扰, soft handoff, frequency diversity.

  • Cons: Complex receiver (RAKE), requires precise power control, self-interference.

• Comparison:

  | Feature | TDMA | CDMA | | :--------------- | :---------------------------- | :---------------------------- | | Capacity | Hard limit (slots/frame) | Soft, interference-limited | | Complexity | Low (simple sync) | High (despreading, power ctrl)| | Interference | Minimal intra-cell | MAI dominant | | Handoff | Hard handoff | Soft handoff | | Synchronization| Tight slot sync | Code sync, less critical |

Data Services in Cellular Communication

• Evolution: Circuit-Switched (voice-centric, dedicated channel) → Packet-Switched (data-centric, shared channel, IP-based).

• Key Requirements:

  • Throughput: High peak/average data rates (Mbps to Gbps).

  • Latency: Low for real-time apps (URLLC: <1ms).

  • Reliability: High packet success rate (e.g., 99.999% for industrial IoT).

  • Mobility: Support for high-speed users (e.g., trains).

Antennas for Mobile Stations

• Design Constraints: Small size ($\ll \lambda$), low cost, user interaction (hand/grip effects), multipath environment, efficiency.

• Common Types:

  • Monopole: Simple, quarter-wave, needs ground plane.

  • PIFA (Planar Inverted-F Antenna): Compact, used in phones. Meandered shape for miniaturization.

  • Loop Antennas: Omnidirectional, less affected by user hand, but narrow bandwidth.

• Impact: Low gain → reduces link budget; narrow bandwidth → limits high-data-rate services; radiation pattern affected by user → unpredictable performance.

Advanced Topic: Antenna Parameters (Rayleigh Distance)

• Rayleigh Distance ($$\displaystyle R_R $$): Distance beyond which far-field radiation pattern is established. For antenna of largest dimension $D$ and wavelength $\lambda$:

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

• Derivation: From Fraunhofer diffraction condition. Approx: $$\displaystyle R_R \gg \frac{2D^2}{\lambda} $$ for plane wave assumption.

• Example: Square antenna, gain $$\displaystyle G = 20 $$ dBi = 100.

  • For square patch, $$\displaystyle G \approx \frac{4\pi A}{\lambda^2} \eta $$, assume efficiency $\eta \approx 0.8$.

  • $$\displaystyle A = D^2 = \frac{G \lambda^2 \eta}{4\pi} = \frac{100 \times \lambda^2 \times 0.8}{4\pi} \approx 6.37 \lambda^2 $$ → $D \approx 2.52 \lambda$.

  • $$\displaystyle R_R = \frac{2D^2}{\lambda} = \frac{2 \times (6.37 \lambda^2)}{\lambda} = 12.74 \lambda $$.

  [!TIP] Exam Focus: Remember $$\displaystyle R_R \propto D^2/\lambda $$. High gain (large $D$) or low $\lambda$ (high freq) → larger far-field distance.