UNIT 1: MOBILE COMMUNICATION - EXAM-FOCUSED NOTES

I. FUNDAMENTALS OF CELLULAR SYSTEMS & FREQUENCY REUSE

Core Concept & Need

• Cellular Concept: Divides a large service area into smaller cells, each with a base station (BS). Enables frequency reuse—using the same frequency channels in geographically separated cells—to increase system capacity and spectrum efficiency.

• Need: Overcomes limitations of single large coverage area (high power, limited channels). Allows universal coverage and capacity scaling.

Frequency Reuse

• Frequency Reuse Factor (N): Number of cells in a cluster. Same frequencies are reused only in cells separated by N cells.

• Reuse Ratio (D/R): Ratio of co-channel cell distance (D) to cell radius (R).

$$D = R \sqrt{3N}$$

$$\boxed{\frac{D}{R} = \sqrt{3N}}$$

• Cluster Size (N): Determined by integer pairs (i, j) representing shifts in hexagonal grid.

$$\boxed{N = i^2 + ij + j^2}$$

*   **Common Clusters:** N=7 (i=2,j=1), N=19 (i=3,j=1).

• System Capacity: Total channels C = M × S, where M = number of clusters in system, S = channels per cluster.

[!TIP] Exam Focus: You WILL be asked to draw a 19-cell cluster and locate co-channel cells for given (i,j). Practice the hexagonal grid with 60° angles.

Capacity Expansion Techniques

II. CHANNEL ASSIGNMENT & HANDOFF MANAGEMENT

Channel Assignment Strategies

Handoff (Handover)

• Necessity: Maintain call continuity when mobile moves between cells or signal degrades.

• Types:

  • Intra-cell: Within same cell (due to fading).

  • Inter-cell: Between cells (most common).

  • Inter-BSC / Inter-MSC: Between different controllers/switches.

  • Mobile-to-Mobile / Mobile-to-Fixed: Direction of handoff.

• Process:

  1. Measurement: Mobile measures BS signal strength (RSS). MAHO (Mobile-Assisted Handoff): Mobile reports measurements to BS.

  2. Decision: Network (BSC/MSC) decides based on thresholds.

  3. Execution: Allocate new channel, release old.

• Queuing for Handoff: Prioritize handoff requests over new call attempts to minimize forced termination probability. Handoff requests may be queued briefly if no channel available.

[!TIP] Exam Focus: MAHO vs. MAHO (Mobile-Assisted) vs. Network-controlled is a common distinction. Queuing concept is critical for reducing dropped calls.

III. MOBILE RADIO PROPAGATION & FADING

Large-Scale Path Loss (Shadowing)

• Free Space Model (Friis Equation):

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

Valid for **d >> λ, d << R<sub>c</sub>** (far-field, no ground reflection).

• Two-Ray (Ground Reflection) Model:

$$P_r(d) \propto \frac{1}{d^4} \text{ (for large d)}$$

**Critical Distance (d<sub>c</sub>):** Point where 2-ray crosses free-space.

$$\boxed{d_c = \frac{4\pi h_t h_r}{\lambda}}$$

• Log-Distance Path Loss Model:

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

*   **n:** Path loss exponent (free-space=2, urban~4).

*   **X<sub>σ</sub>:** Zero-mean Gaussian **shadow fading** (dB).

• Empirical Models:

  • Okumura-Hata: For 150-1500 MHz, 1-20 km. Urban, suburban, rural.

  • COST-231 Hata: Extension up to 2 GHz.

Small-Scale Multipath Propagation

• Causes: Reflection, Diffraction, Scattering.

• Key Parameters:

  • Delay Spread (τ_rms): RMS multipath spread.

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

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

  • Frequency Selective Fading: Occurs if signal bandwidth > B_c.

  • Flat Fading: Occurs if signal bandwidth << B_c.

• Doppler Shift & Spread:

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

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

    • Approx: $$\displaystyle T_c \approx \frac{1}{2f_d} $$ (50% correlation) or $$\displaystyle T_c \approx \frac{9}{16\pi f_d} $$.

  • Fast Fading: Channel changes within symbol duration (T_s < T_c).

  • Slow Fading: Channel constant over symbol duration (T_s >> T_c).

[!TIP] Exam Focus: Relate bandwidth to B_c for flat/selective fading. Relate symbol rate to T_c for fast/slow fading. The June 2025 question on coherence bandwidth is classic: Max symbol rate ≈ B_c for minimal ISI.

Fading Models & Statistics

• Clarke's Model (Rayleigh Fading):

  • Assumes no LOS component. In-phase (I) and quadrature (Q) components are zero-mean Gaussian.

  • Envelope (R) follows Rayleigh PDF:

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

*   **Phase (θ)** is uniform [0, 2π).

• Rician Fading: Includes a dominant LOS component. PDF has a Rician K-factor.

• Statistical Characterization:

  • Level Crossing Rate (LCR): Rate at which fading envelope crosses a given level.

  • Average Fade Duration (AFD): Mean time signal spends below a threshold.

IV. MULTIPLE ACCESS TECHNIQUES

CDMA Deep Dive (IS-95)

• Spread Spectrum: Data modulated by high-rate PN sequence (chips). Increases bandwidth.

• Processing Gain (G_p): Ratio of spread bandwidth to original data bandwidth. Measures interference rejection.

$$\boxed{G_p = \frac{W}{R_b} \text{ (linear)} \quad \text{or} \quad 10\log_{10}(G_p) \text{ (dB)}}$$

• IS-95 Channels:

  • Forward (Downlink): Pilot, Sync, Paging, Traffic.

  • Reverse (Uplink): Access, Traffic.

• Power Control:

  • Necessity: Near-far problem—strong nearby signals overwhelm weak distant ones.

  • Open-loop: Mobile estimates path loss from forward pilot.

  • Closed-loop: BS commands mobile to adjust power (800 Hz rate).

• Handoff: Soft Handoff (make-before-break, mobile in contact with multiple BSs). Hard Handoff (break-before-make, like FDMA/TDMA).

• Advantages: Universal frequency reuse (1), soft capacity, inherent security,抗干扰.

• Capacity: Interference-limited. Approx. voice load per cell: $$\displaystyle N \approx \frac{W}{R_b} \cdot \frac{1}{(E_b/N_0)_{req}} $$ (theoretical).

[!TIP] Exam Focus: Processing Gain calculation is frequent. Know IS-95 channel names (Pilot, Sync, Paging, Traffic, Access). Soft vs. Hard handoff is a key comparison point.

V. GSM ARCHITECTURE

Network Architecture (Block Diagram)

graph TD

    MS[Mobile Station] -->|Um (Radio)| BTS

    BTS -->|Abis| BSC

    BSC -->|A| MSC

    MSC --> VLR

    MSC --> HLR

    MSC --> AUC

    MSC --> EIR

    BSC --> TRAU

    TRAU --> MSC

    OSS[Operation & Support Subsystem] --> All

• MS: Mobile Equipment (ME) + SIM.

• BSS: BTS (radio), BSC (control), TRAU (transcoding/rate adaptation).

• NSS: MSC (switching), VLR (visitor DB), HLR (home DB), AUC (auth), EIR (equipment ID).

• OSS: O&M.

Logical Channels

Frame & Multiframe Structure

• TDMA Frame: 8 time slots (TS0-TS7), ~4.615 ms.

• 26-Multiframe: For TCH & SDCCH (26 TDMA frames = 120 ms).

• 51-Multiframe: For BCCH & CCCH (51 TDMA frames = 235 ms).

• Burst Types: Normal (TCH/SDCCH), Frequency Correction (FCCH), Synchronization (SCH), Access (RACH), Dummy.

[!TIP] Exam Focus: Draw GSM architecture with all subsystems. Tabulate logical channels with their purpose. Know 26 vs 51 multiframe association.

VI. ADVANCED TOPICS (Short Notes)

Orthogonal Frequency Division Multiplexing (OFDM)

• Principle: High-rate data stream split into N parallel low-rate streams, modulated on N orthogonal subcarriers.

• Implementation: IFFT at Tx, FFT at Rx.

• Advantages:

  • Robust to ISI (long symbol duration > delay spread).

  • Efficient spectrum use (overlapping orthogonal carriers).

• Disadvantages:

  • High PAPR (Peak-to-Average Power Ratio).

  • Sensitive to frequency offset/synchronization errors.

• Used in: 4G LTE, 5G NR, Wi-Fi, DVB-T.

Multiple Input Multiple Output (MIMO)

• Concept: Use multiple antennas at Tx and Rx.

• Key Gains:

  • Spatial Multiplexing (SM): Increase data rate (parallel streams).

  • Diversity Gain: Improve reliability (space-time coding like STBC).

• Types:

  • SM: MIMO channel matrix H with high rank → multiple independent data streams.

  • STBC: Encode data across antennas/time for diversity (e.g., Alamouti code).

• Used in: 4G/5G (massive MIMO), Wi-Fi 6/7.

Diversity Techniques (Spatial Focus)

• Goal: Combat fading by providing multiple independent signal replicas.

• Spatial Diversity:

  • Method: Use multiple antennas separated by λ/2 or more.

  • Combining Techniques:

    1. Selection Combining (SC): Choose antenna with highest SNR.

    2. Maximal Ratio Combining (MRC): Weighted sum of all signals → optimal SNR.

    3. Equal Gain Combining (EGC): Co-phased sum, equal gain.

• Other Types: Time, Frequency, Polarization, Angle diversity.

VII. INTERFERENCE & PERFORMANCE

Co-Channel Interference (CCI)

• Cause: Reuse of same frequency in adjacent cells (co-channel cells).

• SIR (Signal-to-Interference Ratio): For mobile at distance D from desired BS, and distances D_i from i interfering co-channel BSs:

$$SIR = \frac{S}{\sum_{i=1}^{i_0} I_i} = \frac{R^{-n}}{\sum_{i=1}^{i_0} D_i^{-n}}$$

where **n** = path loss exponent.

• Reduction Techniques:

  1. Increase D/R ratio (decrease N → fewer channels per cell, but better SIR).

  2. Cell Splitting/Sectoring (reduces number of interfering sources).

  3. Power Control (reduce Tx power of mobiles near BS).

  4. Directional Antennas (sectoring).

• Design Criterion: SIR must exceed threshold (e.g., 18 dB for good voice quality).

Adjacent Channel Interference (ACI)

• Cause: Imperfect filters causing adjacent channel leakage. Near-far effect exacerbates it.

• Reduction: Increase guard bands, better filters, power control.

System Performance Metrics

• Coverage Probability: Probability signal strength > threshold.

• Capacity: Erlangs/km² or channels/km².

• Grade of Service (GoS): Blocking probability (Erlang B) for new calls, dropping probability for handoffs.

VIII. SYSTEM COMPARISONS & EVOLUTION

FDMA vs. TDMA vs. CDMA

KEY FORMULAS QUICK REFERENCE

1. Cluster Size: $$\displaystyle N = i^2 + ij + j^2 $$

2. Co-channel Distance: $$\displaystyle D = R\sqrt{3N} $$

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

4. Critical Distance (2-ray): $$\displaystyle d_c = \frac{4\pi h_t h_r}{\lambda} $$

5. Coherence Bandwidth: $$\displaystyle B_c \approx \frac{1}{5\tau_{rms}} $$ (50%)

6. Doppler Spread: $$\displaystyle f_d = \frac{v}{\lambda} \cos \theta $$

7. Coherence Time: $$\displaystyle T_c \approx \frac{1}{2f_d} $$ (50%)

8. Processing Gain: $$\displaystyle G_p = W / R_b $$

9. CDMA Capacity (approx): $$\displaystyle N \approx \frac{W}{R_b} \cdot \frac{1}{(E_b/N_0)_{req}} $$

10. FDMA Capacity: $$\displaystyle N \approx \frac{B_T}{B_c} $$ (ignoring guard bands)

[!CAUTION] Common Pitfalls:

• Confusing coherence bandwidth with channel bandwidth. B_c is a property of the channel, not the signal.

• Mixing up delay spread (time) and Doppler spread (frequency).

• Forgetting that N in frequency reuse must be of the form $$\displaystyle i^2+ij+j^2 $$ (1,3,4,7,9,12,13,19...).

• In CDMA, processing gain is linear ratio, not dB unless specified.

• GSM 26-multiframe is for TCH/SDCCH, 51-multiframe for BCCH/CCCH.