ADVANCED CONTROL SYSTEM (EC-503 (C)) - Unit 3 Short Notes

UNIT 3: MOBILE COMMUNICATION SYSTEMS

I. FUNDAMENTALS OF CELLULAR SYSTEMS

A. Cellular Concept & Frequency Reuse

• Cellular Concept: Divides a large service area into small hexagonal cells. Each cell has a base station (BS). Frequency channels are reused in non-adjacent cells to increase capacity.

• Merits:

  • Increased capacity (more users).

  • Reduced transmitter power (smaller cells).

  • Localized traffic handling.

  • Robustness (single cell failure affects few users).

• Frequency Reuse Factor (Q): Ratio of bandwidth per cell to total system bandwidth.

$$Q = \frac{1}{N}$$

where **N** is the **cluster size** (number of cells using all available channels once).

• Cluster Size (N): Determined by geometry to maintain sufficient separation between co-channel cells.

$$N = i^2 + ij + j^2$$

where **i, j** are integer steps in hex grid.

*   Common N values: 3, 4, 7, 12, 19.

• Co-channel Cell Identification: For a 19-cell cluster (i=3, j=3), co-channel cells are located at a distance of $$\displaystyle D = \sqrt{3N} \cdot R $$, where R is cell radius.

  [!TIP] Exam Focus: Be prepared to draw a 19-cell cluster and circle/identify all co-channel cells (e.g., cell 1's co-channels are cells 1+19=20, etc., modulo 19).

B. Capacity and Trunking

• Capacity: Maximum number of users a system can support simultaneously.

  • Cellular Capacity: $$\displaystyle C = M \cdot S $$, where M = channels per cell, S = number of cells.

  • Trunking Theory: Uses Erlang B or C formulas to relate offered traffic (A), grade of service (GoS), and number of channels (K).

$$B(E, K) = \frac{\frac{E^K}{K!}}{\sum_{n=0}^{K} \frac{E^n}{n!}}$$

    where **B** = blocking probability (GoS), **E** = offered traffic in Erlangs.

• Grade of Service (GoS): Probability that a call is blocked (Erlang B) or delayed (Erlang C). Typical GoS = 2% blocking.

C. Capacity Expansion Techniques

D. Channel Assignment Strategies

• Fixed Channel Assignment (FCA): Each cell is permanently allocated a fixed set of channels.

  • Adv: Simple, low overhead.

  • Disadv: Inefficient, poor during heavy traffic.

• Dynamic Channel Assignment (DCA): Channels are allocated on-demand from a pool. BS requests channel from MSC.

  • Adv: Efficient, adaptable to traffic.

  • Disadv: Complex MSC control, high signaling overhead.

• Non-Fixed (Hybrid): Borrowing strategies (e.g., Borrowing with Channel Reservation).

II. HANDOFF AND MOBILITY MANAGEMENT

A. Handoff Necessity and Types

• Necessity: Maintain call continuity when mobile moves from one cell to another.

• Types:

  • Hard Handoff: Break-before-make. Resources in old cell released before connecting to new cell. (Used in GSM, FDMA/TDMA).

  • Soft Handoff: Make-before-break. Mobile connects to multiple BSs simultaneously. (Used in CDMA).

  • Mobile-assisted Handoff (MAHO): Mobile measures BS signal strength and reports to network. (Used in GSM).

  • Network-controlled Handoff (NCHO): Network measures and decides. (Older systems).

  • Mobile-controlled Handoff (MCHO): Mobile measures and decides autonomously. (Rare).

B. MAHO Technique and Queuing Concept

• MAHO Process:

  1. Mobile continuously monitors neighbor list (from BCCH).

  2. Measures Received Signal Strength (RSS) and Quality (BER) of serving & neighbor BSs.

  3. Sends measurement reports to current BS via SACCH.

  4. MSC evaluates and initiates handoff if threshold crossed.

• Queuing Concept: Handoff requests have higher priority than new calls. A queue for handoff requests can be used to reduce forced terminations.

C. Handoff Procedures

• GSM:

  1. Measurement & reporting (MAHO).

  2. MSC evaluates, selects target cell.

  3. Handoff Request to target BSC.

  4. Channel Assignment on target BS.

  5. Handoff Command sent to MS via current BS.

  6. MS switches to new channel, sends Handoff Complete.

• CDMA:

  • Soft Handoff: MS acquires pilot from new BS while still connected to old BS. Active set management. MSC combines signals (selection diversity).

  • Hard Handoff: Used for inter-system (e.g., CDMA to GSM).

III. RADIO WAVE PROPAGATION

A. Large-Scale Path Loss Models

• Free Space Propagation:

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

or in dB: $$\displaystyle P_r(d)[dBm] = P_t[dBm] + G_t[dB] + G_r[dB] - 20\log_{10}(f) - 20\log_{10}(d) - 32.44 $$

where f in MHz, d in km.

• Two-Ray Ground Reflection:

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

Critical distance: $$\displaystyle d_c = \frac{4\pi h_t h_r}{\lambda} $$. Beyond $$\displaystyle d_c $$, path loss is much steeper than free space.

• Foliage Losses: Additional attenuation when signal penetrates trees/vegetation. Approx. 0.5 dB/m at UHF.

• Propagation in Near-in-Distance: For $$\displaystyle d < d_c $$, path loss follows free-space model. For $$\displaystyle d > d_c $$, follows two-ray model.

• Mobile-to-Mobile Propagation: Both antennas near ground. Model similar to two-ray but with different effective heights.

• Hilly Terrain (Longley-Rice): Uses incident angle ($$\displaystyle \theta_i $$) and slope angle ($$\displaystyle \theta_s $$).

$$\theta_i = \tan^{-1}\left(\frac{h_d}{d}\right), \quad \theta_s = \tan^{-1}\left(\frac{H}{d}\right)$$

where $$\displaystyle h_d $$ = diffraction loss height, H = hill height.

B. Small-Scale Multipath Propagation

• Causes: Reflection, diffraction, scattering from objects.

• Effects: Multipath delay spread → Intersymbol Interference (ISI).

• Parameters:

  • Mean Excess Delay: $$\displaystyle \bar{\tau} = \frac{\sum_k P_k \tau_k}{\sum_k P_k} $$

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

C. Fading

• Clarke's Model (Rayleigh Fading): Assumes no LOS, many scatterers, isotropic. Envelope follows Rayleigh distribution, phase uniform.

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

where $$\displaystyle \sigma^2 $$ = average power.

• Fading Statistics:

  • Level Crossing Rate (LCR): Average rate at which fading envelope crosses a level R downward.

$$N_R = \sqrt{2\pi f_d} \rho e^{-\rho^2/2}, \quad \rho = R/\sqrt{2}\sigma$$

*   **Average Fade Duration (AFD)**: Mean time signal stays below a level R.

$$\bar{\tau} = \frac{1 - e^{-\rho^2}}{\sqrt{2\pi f_d} \rho}$$

D. Dispersion Parameters

• Coherence Bandwidth ($$\displaystyle B_c $$): Bandwidth over which channel impulse response is highly correlated. Approx. $$\displaystyle B_c \approx \frac{1}{5\sigma_\tau} $$ for flat fading.

• Maximum Symbol Rate for Minimal ISI:

$$R_s \leq B_c \quad \Rightarrow \quad R_s^{max} \approx \frac{1}{5\sigma_\tau}$$

> [!TIP] **Exam Problem**: Given $$\displaystyle B_c = 100 $$ kHz, $$\displaystyle R_s^{max} \approx 100 $$ kHz (or 200 kbps for binary). **Box this relation**.

• Doppler Spread ($$\displaystyle B_D $$): Spectrum broadening due to mobile motion. $$\displaystyle B_D = f_d = \frac{v}{\lambda} $$, where v = velocity.

• Coherence Time ($$\displaystyle T_c $$): Time duration over which channel is stationary. $$\displaystyle T_c \approx \frac{1}{B_D} $$.

• Delay Spread ($$\displaystyle \sigma_\tau $$): Time difference between first and last significant multipath component.

IV. MULTIPLE ACCESS TECHNIQUES

A. FDMA

• Frequency Management: Total bandwidth $$\displaystyle B_T $$ divided into $M$ channels of bandwidth $$\displaystyle B_c $$, with guard bands $$\displaystyle B_{guard} $$.

$$M = \frac{B_T - (M-1)B_{guard}}{B_c} \approx \frac{B_T}{B_c + B_{guard}}$$

> [!TIP] **Exam Problem**: Given $$\displaystyle B_T=12.5 $$ MHz, $$\displaystyle B_{guard}=10 $$ kHz, $$\displaystyle B_c=30 $$ kHz. Calculate M.

**Solution**:

$$M \approx \frac{12.5 \times 10^6}{30 \times 10^3 + 10 \times 10^3} = \frac{12,500}{40} = \boxed{312.5 \approx 312 \text{ channels}}$$

• Channel Assignment: Typically FCA.

B. TDMA

• Time-division of a frequency channel into slots.

• Multiple users share same frequency in time.

• Requires synchronization.

C. CDMA

• Spread Spectrum Fundamentals:

  • Direct Sequence (DSSS): Data multiplied by high-rate PN sequence (chip rate $$\displaystyle R_c $$). Signal bandwidth $$\displaystyle \approx R_c $$.

  • Frequency Hopped (FHSS): Carrier frequency hops according to PN sequence.

    • Slow Hopping: Multiple symbols per hop.

    • Fast Hopping: Multiple hops per symbol.

• CDMA System: Each user assigned a unique orthogonal PN code (e.g., Walsh codes). All users transmit same frequency, same time.

• Channels:

  • Forward (BS→MS): Uses Walsh codes for channelization. Pilot, sync, paging, traffic.

  • Reverse (MS→BS): Uses PN offset for user separation. Access, traffic.

• Power Control (Critical in CDMA):

  • Need: Near-far problem – strong signal masks weak ones. All signals must arrive at BS with similar power.

  • Mechanism: Open-loop (MS measures forward link) & Closed-loop (BS commands MS to adjust power, 800 bps control bits).

• Processing Gain ($$\displaystyle G_p $$): Ratio of spread bandwidth to data bandwidth.

$$G_p = \frac{R_c}{R_b} \quad (\text{linear}) \quad \text{or} \quad G_p[dB] = 10\log_{10}\left(\frac{R_c}{R_b}\right)$$

• BER for CDMA (MAI limited):

  For K users, matched filter receiver:

$$P_b \approx Q\left( \sqrt{\frac{E_b}{N_0 + (K-1)E_b}} \right) = Q\left( \sqrt{\frac{G_p \cdot E_b/N_0}{1 + (K-1)G_p \cdot E_b/N_0}} \right)$$

where $$\displaystyle Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-t^2/2} dt $$.

> [!TIP] **Exam Problem**: Given K=20, $$\displaystyle R_c=1.2288 $$ Mcps, $$\displaystyle R_b=13 $$ kbps, $$\displaystyle E_b/N_0=7.8 $$ dB, PN length=32768.

**Solution**:

1.  **Processing Gain**: $$\displaystyle G_p = \frac{1.2288 \times 10^6}{13 \times 10^3} = \boxed{94.5 \ (19.75 \ dB)} $$.

2.  $$\displaystyle E_b/N_0 $$ linear = $$\displaystyle 10^{7.8/10} = 6.03 $$.

3.  $$\displaystyle G_p \cdot E_b/N_0 = 94.5 \times 6.03 = 570 $$.

4.  BER: $$\displaystyle P_b \approx Q\left( \sqrt{\frac{570}{1 + 19 \times 570}} \right) = Q(\sqrt{0.005}) = Q(0.0707) \approx \boxed{0.472} $$ (very high due to MAI!).

• Advantages over FDMA/TDMA:

  • Soft capacity (graceful degradation).

  • Excellent抗干扰 (processing gain).

  • Privacy (pseudo-random codes).

  • Soft handoff.

  • Frequency reuse factor = 1.

D. OFDM

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

• Orthogonality: Subcarrier spacing = $$\displaystyle 1/T_s $$, where $$\displaystyle T_s $$ = symbol period. Prevents ICI.

• Advantages: Robust to frequency-selective fading (each subcarrier sees flat fading), efficient FFT implementation, flexible spectrum shaping.

• Disadvantages: High PAPR (Peak-to-Average Power Ratio), sensitive to frequency offset & phase noise.

E. MIMO

• Uses multiple antennas at both transmitter and receiver.

• Benefits:

  • Spatial Multiplexing: Increases data rate (capacity) linearly with min($$\displaystyle N_t, N_r $$).

  • Diversity: Improves reliability (space-time coding).

  • Beamforming: Increases SNR, reduces interference.

• Capacity (for rich scattering, i.i.d. channels):

$$C = \min(N_t, N_r) \cdot B \cdot \log_2(1 + \text{SNR}) \text{ bits/sec}$$

V. GSM AND CELLULAR STANDARDS

A. GSM System Architecture

• Block Diagram:

  
  MS → (Um) → BTS → (Abis) → BSC → (A) → MSC → (E) → HLR/VLR/AUC/EIR
  
                                 ↓
  
                               PSTN/ISDN
  
  

• Subsystems:

  • MS (Mobile Station): ME + SIM.

  • BSS (Base Station Subsystem): BTS + BSC + TC.

  • NSS (Network Switching Subsystem): MSC + HLR + VLR + AUC + EIR.

  • OSS (Operation Support Subsystem).

• Key Interfaces:

  • A: MSC ↔ BSC (SS7, 64 kbps).

  • Abis: BSC ↔ BTS (proprietary, 16/64 kbps).

  • Ater: BSC ↔ TC (for transcoding).

  • Um: MS ↔ BTS (radio, 200 kHz carrier spacing).

B. GSM Radio Subsystem

• Consists of MS and BTS (TRX, antennas, transcoding).

• Manages radio resources, handovers, power control, frequency hopping.

C. GSM Channels

• Traffic Channels (TCH):

  • TCH/F (Full Rate, 22.8 kbps net, 13 kbps speech after channel coding).

  • TCH/H (Half Rate, 11.4 kbps net).

• Control Channels (CCH):

  • BCCH (Broadcast Control): BS → MSs (system info).

  • CCCH (Common Control): MS ↔ BS (paging, access).

    • PCH (Paging), RACH (Random Access), AGCH (Access Grant).

  • DCCH (Dedicated Control):

    • SDCCH (Stand-alone Dedicated Control): Call setup, SMS.

    • SACCH (Slow Associated Control): Associated with TCH/FACCH. Power control, measurement reports (MAHO).

    • FACCH (Fast Associated Control): "Steals" TCH slot for urgent signaling (handoff). No extra capacity.

D. GSM Frame Structure

• TDMA Frame: 8 time slots (TS0-TS7), each 156.25 bit periods ≈ 577 µs.

• Multiframe:

  • Traffic Multiframe: 26 TDMA frames (26x8=208 slots). 1 TCH per 26 frames.

  • Control Multiframe: 51 TDMA frames (51x8=408 slots). Used for BCCH, CCCH, SDCCH.

• Superframe: 1326 TDMA frames (51x26 or 26x51). Repeats every ~6.12 sec.

• Hyperframe: 2,715,648 TDMA frames (~3.28 hours). Repeats all encryption sequences.

E. Multiple Access in GSM: FDMA/TDMA.

• $$\displaystyle B_T = 25 $$ MHz (EGSM 900) or 75 MHz (1800).

• $$\displaystyle B_c = 200 $$ kHz carrier spacing.

• $M \approx 124$ carriers (900 MHz band).

• Each carrier: 8 time slots → 8 users per carrier (theoretical).

F. Frequency Hopping in GSM

• Slow Frequency Hopping: Hopping rate = one TDMA frame (≈ 577 µs). Mobile hops to new frequency every frame.

• Purpose: Mitigate frequency-selective fading and co-channel interference.

• Hopping Sequence: Determined by Mobile Allocation (MA) and Hopping Sequence Number (HSN) in BSS.

VI. INTERFERENCE MANAGEMENT

A. Co-Channel Interference (CCI)

• Main Reason: Frequency reuse. Same channel reused in cells separated by distance D.

• Signal-to-Interference Ratio (S/I):

$$\frac{S}{I} = \frac{1}{\sum_{i=1}^{i_0} \left( \frac{D_i}{R} \right)^{-n}}$$

where $$\displaystyle i_0 $$ = number of 1st-tier co-channel cells, n = path loss exponent (3-4).

• Reduction Methods:

  1. Increase D/R ratio (use larger N → reduces capacity).

  2. Power Control: Reduce transmit power of mobiles/BSS.

  3. Antenna Tilting/Down-tilting: Focus energy, reduce spillover.

  4. Sectoring: Reduces $$\displaystyle i_0 $$ (e.g., 120° sector → $$\displaystyle i_0=2 $$ instead of 6).

  5. Cell Splitting: Smaller cells, lower transmit power.

B. Adjacent Channel Interference (ACI)

• Caused by imperfect receiver filters; leakage from adjacent channel.

• Worse than CCI because signal strength from adjacent channel can be much higher than desired signal (near-far).

• Reduction: Guard bands, high-quality filters, power control.

VII. ANTENNAS FOR MOBILE SYSTEMS

A. Cell-Site Antennas

• Types: Omni-directional (for small cells), Sector antennas (3×120°, 6×60°).

• Height: 30-100 m (to cover cell radius R).

• Radiation Pattern: Down-tilted to limit interference, focus on cell area.

• Unique Situations: Urban (mounted on rooftops/building tops), rural (tall towers), highway (high towers, narrow beams).

B. Mobile Antennas

• Types: Monopole (quarter-wave), whip, patch (for vehicles).

• Characteristics: Omni-directional in azimuth, low gain (0-3 dBi), vertically polarized.

• Diversity: Space diversity (two antennas spaced λ/2 apart) is common to combat fading.

VIII. ADVANCED TOPICS (Short Note Format)

A. Diversity Techniques

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

• Types:

  • Space Diversity: Multiple antennas separated by > λ/2.

  • Polarization Diversity: Two orthogonal polarizations (e.g., ±45°).

  • Frequency Diversity: Transmit same signal on different frequencies (FHSS).

  • Time Diversity: Repeat transmission at different times (channel coding, interleaving).

  • Angle Diversity: Multiple directional antennas pointing different directions.

• Combining Methods: Selection combining, maximal ratio combining, equal gain combining.

B. MIMO Systems

• Definition: Multiple transmit and receive antennas.

• Key Idea: Spatial multiplexing creates parallel channels, increasing capacity.

• Capacity Gain: In rich scattering, capacity ∝ min($$\displaystyle N_t, N_r $$).

• Challenges: Complex signal processing (V-BLAST, STC), channel estimation, correlation between antennas.

C. Orthogonal Frequency Division Multiplexing (OFDM)

• Principle: Serial-to-parallel conversion, modulate N orthogonal subcarriers.

• Orthogonality: $$\displaystyle f_k = k/T_s $$, $$\displaystyle k=0,1,...,N-1 $$. $$\displaystyle \int_0^{T_s} e^{j2\pi f_k t} e^{-j2\pi f_m t} dt = 0 \ (k \neq m) $$.

• Cyclic Prefix (CP): Copy end of symbol to front. Eliminates ISI and maintains orthogonality.

• Advantages: Robust to multipath, efficient FFT, flexible bandwidth allocation.

• Disadvantages: High PAPR, sensitive to Doppler/frequency offset.

• Applications: 4G LTE, 5G NR, Wi-Fi (802.11a/g/n/ac/ax), DVB-T, DSL.

[!TIP] Final Exam Strategy:

1. Draw diagrams for frequency reuse (19-cell), GSM architecture, CDMA block diagram.

2. Memorize key formulas: Erlang B, $$\displaystyle R_s^{max} \approx 1/(5\sigma_\tau) $$, FDMA M, CDMA $$\displaystyle G_p $$, BER.

3. Contrast concepts: Hard vs. Soft handoff, Flat vs. Freq-selective fading, FCA vs. DCA, Slow vs. Fast FH.

4. Units: Always check (kHz, MHz, µs, km). Convert consistently.

5. For numerical problems, write the formula first, substitute values, box final answer.