UNIT 4: WIRELESS CHANNEL AND SYSTEM DESIGN

I. WIRELESS SYSTEMS OVERVIEW AND FUNDAMENTALS

Evolution of Wireless Communication (1G to 5G)

[!TIP] Exam Focus: Know key differentiators: 1G (analog), 2G (digital voice/SMS), 3G (mobile broadband), 4G (all-IP), 5G (three use cases).

Types of Wireless Services & Requirements

Economic & Social Impact

• Economic: Trillions in GDP contribution, enables digital economy, creates new industries (app economy, IoT services).

• Social: Connects remote areas, enables remote work/education, emergency services, but also raises concerns about digital divide, privacy, and health.

Key Technical Challenges

1. Spectrum Scarcity: Limited licensed spectrum → need for high efficiency (modulation, MIMO, spectrum sharing).

2. Multipath & Fading: Causes signal strength fluctuations (fading) and ISI → requires equalization, diversity, OFDM.

3. User Mobility & Doppler: Frequency shift ($$\displaystyle f_d = \frac{v f_c}{c} $$) → limits coherent detection, requires channel tracking.

4. Interference: Co-channel, adjacent-channel → requires careful cell planning, power control, advanced receivers.

5. Power Constraints: Battery life limits device functionality → low-power design, sleep modes.

6. Security & Privacy: Wireless medium is inherently open → requires encryption, authentication.

Spectrum Limitations & Impact on System Design

• Regulatory: ITU allocates global bands (e.g., 700 MHz for 4G/5G), national regulators license them.

• Impact:

  • Modulation: Higher-order QAM (e.g., 256-QAM) for spectral efficiency but less robust to noise/fading.

  • Multiple Access: FDMA/TDMA (2G), CDMA (3G), OFDMA (4G/5G) to share limited bands.

  • Cell Planning: Frequency reuse pattern (e.g., 1/3 reuse in LTE) to maximize reuse while managing interference.

II. WIRELESS CHANNEL CHARACTERISTICS AND PARAMETERS

A. Large-Scale Propagation Models

• Path Loss: Average signal power decay with distance.

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

  • Log-Distance Path Loss: $$\displaystyle PL(d)[dB] = PL(d_0)[dB] + 10n \log_{10}\left(\frac{d}{d_0}\right) + X_\sigma $$, where $n$ = path loss exponent (2-6), $$\displaystyle X_\sigma $$ ~ $$\displaystyle \mathcal{N}(0, \sigma^2) $$ (shadowing).

• Shadowing (Large-Scale Fading): Slow variations due to obstacles. Modeled as log-normal distribution: $$\displaystyle P(PL > x) = \frac{1}{2} \text{erfc}\left(\frac{x - \mu}{\sqrt{2}\sigma}\right) $$.

B. Small-Scale Propagation & Multipath

Causes of Multipath:

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

• Diffraction: Around edges/obstacles (sharp corners).

• Scattering: From rough surfaces, small objects, foliage.

Time-Variant Multipath Channel Model (Two-Path Model):

Received signal: $$\displaystyle r(t) = \sum_{i=0}^{1} a_i e^{j\phi_i} s(t - \tau_i) $$

• $$\displaystyle a_i $$: amplitude of $$\displaystyle i^{th} $$ path.

• $$\displaystyle \tau_i $$: delay of $$\displaystyle i^{th} $$ path.

• $$\displaystyle \phi_i $$: phase (includes path phase + Doppler shift).

• Channel impulse response: $$\displaystyle h(t, \tau) = \sum_{i} a_i(t) e^{j\phi_i(t)} \delta(\tau - \tau_i(t)) $$.

Parameters Characterizing Multipath Channels:

1. Delay Spread:

   • Excess Delay: $$\displaystyle \tau_i - \tau_0 $$ (relative to first path).

   • RMS Delay Spread: $$\displaystyle \sigma_\tau = \sqrt{\overline{\tau^2} - (\overline{\tau})^2} $$, where $$\displaystyle \overline{\tau} = \frac{\sum P_i \tau_i}{\sum P_i} $$, $$\displaystyle \overline{\tau^2} = \frac{\sum P_i \tau_i^2}{\sum P_i} $$, $$\displaystyle P_i = a_i^2 $$.

2. 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 $$\displaystyle B_c \approx \frac{1}{\sigma_\tau} $$.

   Relation: $$\displaystyle \boxed{B_c \propto \frac{1}{\sigma_\tau}} $$ (Large $$\displaystyle \sigma_\tau $$ → small $$\displaystyle B_c $$ → frequency-selective fading).

3. Doppler Shift & Spread:

   • Doppler Shift (single path): $$\displaystyle f_d = \frac{v f_c}{c} \cos\theta $$, where $\theta$ = angle between mobile direction and wave arrival.

   • Doppler Spread ($$\displaystyle B_d $$): Range of Doppler shifts due to motion in different directions. Maximum $$\displaystyle f_{d,\max} = \frac{v f_c}{c} $$.

4. Coherence Time ($$\displaystyle T_c $$): Time duration over which channel is invariant. Approx. $$\displaystyle T_c \approx \frac{1}{f_d} $$ (for 50% correlation).

   Relation: $$\displaystyle \boxed{T_c \propto \frac{1}{f_d}} $$ (High speed → large $$\displaystyle f_d $$ → small $$\displaystyle T_c $$ → fast fading).

5. Small-Scale Fading Classification:

   • Flat vs Frequency-Selective: Based on $$\displaystyle B_c $$ vs signal bandwidth $$\displaystyle B_s $$.

     • Flat: $$\displaystyle B_s << B_c $$ (or $$\displaystyle \sigma_\tau << 1/B_s $$) → no ISI.

     • Frequency-Selective: $$\displaystyle B_s > B_c $$ (or $$\displaystyle \sigma_\tau > 1/B_s $$) → ISI.

   • Fast vs Slow: Based on $$\displaystyle T_c $$ vs symbol period $$\displaystyle T_s $$.

     • Fast: $$\displaystyle T_s > T_c $$ (or $$\displaystyle f_d > 1/T_s $$) → channel changes within symbol.

     • Slow: $$\displaystyle T_s << T_c $$ (or $$\displaystyle f_d << 1/T_s $$) → channel constant over symbol.

Statistical Models for Small-Scale Fading:

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

• Rician Fading: Dominant LOS component (power $$\displaystyle K\sigma^2 $$). Amplitude follows Rician distribution:

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

where $A$ = amplitude of specular (LOS) component, $$\displaystyle I_0 $$ = modified Bessel function. **Rician $K$-factor:** $$\displaystyle K = \frac{A^2}{2\sigma^2} $$ (power ratio of LOS to scattered). $$\displaystyle K=0 $$ → Rayleigh; $K \to \infty$ → AWGN.

• Impact of Doppler: Causes time-variation in fading envelope (Doppler spectrum). For Rayleigh, Jakes' model gives classic Doppler spectrum: $$\displaystyle S(f) = \frac{2}{\pi f_{d,\max} \sqrt{1 - (f/f_{d,\max})^2}} $$ for $$\displaystyle |f| \le f_{d,\max} $$.

C. Channel Effects on Signal Reception

• Delay-Dispersive Fading (Frequency-Selective): Causes Intersymbol Interference (ISI) → increases error probability. Mitigated by equalization, OFDM.

• Frequency-Dispersive Fading (Fast Fading): Causes deep fades at specific frequencies → increases error probability in flat fading channels. Mitigated by diversity, coding, interleaving.

• Impact on Modulation: Coherent detection (PSK, QAM) requires accurate channel estimation; non-coherent (FSK) more robust but less spectrally efficient.

III. CHANNEL MODELING AND MEASUREMENT

A. Classification of Channel Models

B. Statistical Channel Models

• WSSUS Model (Wide-Sense Stationary Uncorrelated Scattering): Assumes channel is WSS in time and uncorrelated in delay. Key parameters:

  • Delay Power Spectrum (DPS): $P(\tau)$ → gives power vs excess delay.

  • Scattering Function: $$\displaystyle S(\tau, f_d) $$ → 2D function of delay and Doppler.

  • Condensed Parameters: RMS delay spread $$\displaystyle \sigma_\tau $$, RMS Doppler spread $$\displaystyle \sigma_{f_d} $$.

• Tapped-Delay Line (TDL) Model: Discretizes delay axis. $$\displaystyle h(t) = \sum_{i=0}^{N-1} a_i(t) e^{j\phi_i(t)} \delta(t - \tau_i) $$. Each tap is a complex Gaussian process (Rayleigh) or Rician.

C. Deterministic Channel Modeling

• Ray Tracing: Computes EM waves along all possible paths (direct, reflected, diffracted) using geometry and material properties. Accurate but computationally intensive.

  Efficiency: Uses image theory, ray bundling, and pre-processing of environment database.

• Scattering from Rough Surfaces:

  • Kirchhoff Theory: Assumes surface roughness small compared to wavelength. Uses stationary phase approximation.

  • Perturbation Method: For small roughness heights, treats surface as small perturbations on a smooth surface.

D. Channel Sounding and Measurement Techniques

• Purpose: Measure channel impulse response $h(t, \tau)$ or transfer function $H(t, f)$.

• Time Domain (Pulse Sounding): Transmit short pulse, measure received signal. Directly gives $h(\tau)$ but requires high peak power.

• Frequency Domain (Swept Frequency): Transmit tone at discrete frequencies, measure amplitude/phase → construct $H(f)$. Good dynamic range.

• Network Sounders: Use existing communication signals (e.g., pilots in LTE) for channel estimation.

• Correlation-Based Methods: Transmit pseudo-random sequence (PN), correlate with received to get impulse response. Good noise suppression.

IV. TRANSCEIVER DESIGN AND MODULATION

A. Wireless Transceiver Block Diagram

[RF Front-End] → [Down-converter] → [ADC] → [Equalizer] → [Demodulator] → [Decoder] → Data

      ↑                                                              ↓

[Antenna] ← [Up-converter] ← [DAC] ← [Modulator] ← [Encoder] ← [Source]

• RF Front-End: Amplification, filtering, frequency conversion.

• Equalizer: Compensates for ISI (frequency-selective fading).

• Diversity Processor: Combines multiple signal branches.

• Characteristics: Must balance performance (BER), flexibility (multi-standard), cost, power consumption.

B. Modulation Techniques Overview

Spectral Efficiency Comparison (MSK vs QPSK):

• Both have 2 bits/symbol.

• MSK: Continuous phase, narrower main lobe, lower sidelobes → better out-of-band radiation, suitable for nonlinear amplifiers.

• QPSK: sharper transitions, higher sidelobes → needs linear amplifier or filtering.

C. Impact of Modulation on System Performance

• AWGN Channels: BER expressions known (e.g., QPSK: $$\displaystyle P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) $$).

• Fading Channels:

  • Flat Fading: Signal multiplied by fading coefficient $h$. Average BER for coherent QPSK in Rayleigh: $$\displaystyle P_b \approx \frac{1}{2}\left(1 - \sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\right) $$, $$\displaystyle \bar{\gamma} = E_b/N_0 $$.

  • Frequency-Selective Fading: ISI dominates → BER depends on equalizer performance.

• Coherent vs Non-Coherent:

  • Coherent (PSK, QAM): Needs channel estimation (pilots), better performance.

  • Non-Coherent (FSK, DPSK): No estimation needed, 3 dB worse in AWGN, more robust to fast fading.

V. EQUALIZATION TECHNIQUES

A. Need for Equalization

In frequency-selective fading, channel impulse response has multiple taps → ISI. Equalizer at receiver inverts or mitigates channel effect to recover transmitted symbols.

B. Classification of Equalizers

1. Linear Equalizers (LE): Inverts channel linearly. Types:

   • Zero-Forcing (ZF): Forces $$\displaystyle h * c = \delta $$ → amplifies noise at deep fades.

   • Minimum Mean Square Error (MMSE): Balances ISI and noise enhancement.

2. Decision-Feedback Equalizer (DFE): Feedforward filter (like LE) + feedback filter (cancels past ISI using detected symbols). Non-linear, avoids noise enhancement, but error propagation.

3. Blind Equalization: Operates without training sequence. Uses Constant Modulus Algorithm (CMA) which minimizes $$\displaystyle E\left[(|y|^2 - R)^2\right] $$, where $R$ = constant modulus. Preferred when: Training overhead is high (e.g., continuous data transmission), or channel varies slowly.

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

C. Equalizer Structures & Comparison

Adaptive Algorithms:

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

• RLS (Recursive Least Squares): Faster convergence, higher complexity.

D. Maximum Likelihood Sequence Detection (Viterbi)

• Principle: Finds most likely transmitted sequence given received signal through trellis of channel states.

• Application: For channel with memory $L$ (taps), state = last $L$ symbols. Viterbi algorithm finds path with maximum metric (e.g., Euclidean distance).

• Complexity: $$\displaystyle O(M^L) $$ per symbol, where $M$ = constellation size. Reduction: Use reduced-state sequence estimation (RSSE).

VI. DIVERSITY TECHNIQUES

A. Concept of Diversity

• Idea: Provide multiple independent (or partially correlated) copies of signal to receiver → probability all fade deeply is very low.

• Role: Combats small-scale fading (fast fading). Increases average SNR, reduces BER.

B. Types of Diversity

C. Diversity Combining Methods

Given $L$ branches with signals $$\displaystyle z_i = h_i s + n_i $$, where $$\displaystyle h_i $$ = channel gain, $$\displaystyle n_i $$ = noise.

1. Selection Combining (SC): Choose branch with highest $$\displaystyle |z_i| $$ or SNR. Simple, 1-2 dB worse than MRC.

2. Maximal Ratio Combining (MRC): Weighted sum: $$\displaystyle z_{MRC} = \sum_{i=1}^L w_i z_i $$, where $$\displaystyle w_i = h_i^*/\sigma_n^2 $$. Optimal (maximizes SNR). Requires channel knowledge per branch.

3. Equal Gain Combining (EGC): $$\displaystyle w_i = e^{-j\angle h_i} $$ (unit magnitude). Simpler than MRC, near-optimal if amplitudes similar.

Performance (Rayleigh fading, MRC): Average output SNR = $L \cdot \bar{\gamma}$, where $\bar{\gamma}$ = avg SNR per branch. BER improves exponentially with $L$.

VII. ADVANCED AND SYSTEM-SPECIFIC TOPICS

A. Antennas for Mobile Stations

• Design Constraints: Small size ($\ll \lambda$), low cost, low profile, omnidirectional (usually), efficiency vs. size trade-off.

• Common Types:

  • Monopole/Whip: Simple, quarter-wave, omnidirectional.

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

  • Helical: Circular polarization, used in satellite phones.

  • Array Antennas: For MIMO/diversity (e.g., 2x2 in smartphones).

• Impact: Antenna efficiency directly affects link budget; pattern affects diversity gain; MIMO antennas enable spatial multiplexing.

B. Data Services in Cellular Communication

• Circuit-Switched (CS): Dedicated channel for entire call (2G voice, early data via CSD).

• Packet-Switched (PS): Shared channel, on-demand (GPRS/EDGE "2.5G", UMTS, LTE, 5G). More efficient for bursty data.

• Evolution:

  • GPRS (2G): ~40 kbps, always-on PS.

  • EDGE (2G): ~200 kbps, enhanced modulation (8PSK).

  • HSPA (3G): ~10 Mbps (downlink), shared channel.

  • LTE (4G): All-IP, OFDMA, ~100 Mbps mobile.

  • 5G NR: eMBB (enhanced mobile broadband), URLLC (ultra-reliable low-latency), mMTC (massive machine-type).

• QoS for Data: Differentiated services (latency, throughput, reliability) via scheduling, QoS Class Identifiers (QCI) in LTE/5G.

C. Multiple Access Techniques: TDMA vs CDMA

FDMA: Each user gets dedicated frequency band (1G analog). OFDMA: Combines OFDM with FDMA/TDMA (4G/5G) → flexible resource allocation.

KEY FORMULAS & CONCEPTS BOXED

• Free-Space Path Loss: $$\displaystyle PL(d) = \left( \frac{4\pi d f_c}{c} \right)^2 $$

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

• Doppler Shift: $$\displaystyle f_d = \frac{v f_c}{c} \cos\theta $$

• RMS Delay Spread: $$\displaystyle \sigma_\tau = \sqrt{\overline{\tau^2} - (\overline{\tau})^2} $$

• Coherence Bandwidth: $$\displaystyle B_c \approx \frac{1}{\sigma_\tau} $$ (order of magnitude)

• Coherence Time: $$\displaystyle T_c \approx \frac{1}{f_d} $$ (order of magnitude)

• Rician K-factor: $$\displaystyle K = \frac{\text{LOS power}}{\text{Scattered power}} $$

• MRC Output SNR: $$\displaystyle SNR_{out} = \sum_{i=1}^L SNR_i $$

[!CAUTION] Common Pitfalls:

1. Confusing delay spread (time domain) with coherence bandwidth (frequency domain) — they are inversely related.

2. Thinking fast fading is only about Doppler — it's about $$\displaystyle T_c $$ vs $$\displaystyle T_s $$.

3. Assuming CDMA capacity is infinite — it's interference-limited, not user-limited.

4. Forgetting that equalizers combat ISI (frequency-selective fading), not deep fades themselves (use diversity for that).

5. Mixing up micro (within cell, antenna spacing) and macro (between BSs, soft handoff) diversity.