ADVANCED CONTROL SYSTEM (EC-503 (C)) - Unit 4 Short Notes

Unit 4: Mobile Communication Systems

I. Cellular System Fundamentals

Frequency Reuse

• Concept: Reusing the same set of radio frequencies (channels) in geographically separated cells to support many users with limited spectrum.

• Necessity: Increases system capacity and coverage area without requiring more spectrum.

• Reuse Factor (N): Number of cells in a cluster. Each cluster uses all available channels exactly once.

• Cluster Size (N): Must satisfy $$\displaystyle N = i^2 + ij + j^2 $$, where $i, j$ are non-negative integers (e.g., 3, 4, 7, 12, 19...).

• Cellular Layout: Hexagonal grid is the standard model.

  DiagramSEARCH: 19-cell cluster hexagonal grid co-channel cells

• Co-channel Cells: Cells using the same frequency set.

  • Separation (Reuse Distance, D): Minimum distance between co-channel cells.

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

where $R$ = cell radius.

> **!TIP:** For a given $N$, larger $D$ reduces co-channel interference (CCI) but lowers capacity.

Cell Splitting & Sectoring

• Cell Splitting: Subdividing a congested cell into smaller cells (microcells/picocells). Increases capacity by reducing $R$ and $D$ (requires frequency plan adjustment).

• Sectoring: Using directional antennas (typically 120° or 60°) at a cell site to divide a cell into sectors. Each sector uses a separate frequency set.

  • Impact: Reduces CCI (as co-channel cells are farther apart in angular domain) and increases capacity by reusing frequencies in different sectors of the same cell site.

Capacity & Trunking

• Traffic Intensity (A): Offered load in Erlangs. $$\displaystyle A = \lambda H $$, where $\lambda$ = call arrival rate, $H$ = average call duration.

• Erlang B Formula (Blocking Probability): For loss systems (no queue).

$$P_b = \frac{\frac{A^c}{c!}}{\sum_{k=0}^{c} \frac{A^k}{k!}}$$

where $c$ = number of channels (trunks).

• Erlang C Formula (Delay Probability): For systems with queuing.

• Grade of Service (GoS): Measure of service quality, typically the probability of call blocking ($$\displaystyle P_b $$) or delay.

• Trunking Efficiency: Ability to handle a given traffic intensity with a limited number of channels. Higher $c$ for same $A$ gives lower $$\displaystyle P_b $$.

II. Radio Propagation and Fading

Propagation Models

1. Free Space Propagation:

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

Path loss: $$\displaystyle PL(d) \propto 20 \log_{10}(d) + 20 \log_{10}(f) + 20 \log_{10}\left(\frac{4\pi}{c}\right) $$.

2. Two-Ray Ground Reflection:

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

Dominates when $$\displaystyle h_t, h_r << d $$.

3. Foliage Losses: Additional attenuation when signal penetrates trees/vegetation. Empirical models exist (e.g., ITU model).

4. Near-in-Distance (NID): Region close to transmitter ($$\displaystyle d < h_t $$) where path loss exponent can be < 2.

5. Mobile-to-Mobile Propagation: Both antennas are low and near ground. Two-ray model often applies with effective antenna heights.

Small-Scale Multipath Propagation

• Causes: Reflection, diffraction, scattering from buildings, terrain, etc.

• Effects: Rapid signal fluctuations (fading), multipath delay spread.

• Delay Spread ($$\displaystyle \tau_{rms} $$): RMS difference in arrival times of multipath components.

  • Impact: Causes intersymbol interference (ISI) if symbol duration $$\displaystyle T_s \lesssim \tau_{rms} $$.

Fading Phenomena

• Clarke's Model (Rayleigh Fading): Assumes many scatterers, no LOS. Received envelope $r$ follows Rayleigh distribution:

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

Phase $\theta$ is uniform $[0, 2\pi)$. Power $$\displaystyle r^2 $$ follows **exponential distribution**.

• Fading Statistics:

  • Level Crossing Rate (LCR): Average rate at which fading envelope crosses a specified level $r$ in positive direction.

$$N_R = \sqrt{2\pi f_D} \rho e^{-\rho^2}, \quad \rho = \frac{r}{\sqrt{2}\sigma}$$

where $$\displaystyle f_D = \frac{v}{\lambda} $$ is max Doppler spread.

*   **Average Fade Duration (AFD):** Average time the signal stays below a level $r$.

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

Channel Dispersion Parameters

• Coherence Bandwidth ($$\displaystyle B_c $$): Bandwidth over which channel frequency response is highly correlated (flat fading). Approx. $$\displaystyle B_c \approx \frac{1}{5\tau_{rms}} $$ (for 50% correlation).

• Doppler Spread ($$\displaystyle f_D $$): Range of frequency shifts due to motion. $$\displaystyle f_D = \frac{v}{\lambda} |\cos \theta| $$, max when $$\displaystyle \theta=0 $$.

• Coherence Time ($$\displaystyle T_c $$): Time duration over which channel impulse response is invariant. Approx. $$\displaystyle T_c \approx \frac{9}{16\pi f_D} $$ (for 50% correlation).

• Relationship to Symbol Rate & ISI:

  • Flat Fading: $$\displaystyle T_s \ll T_c $$ and $$\displaystyle B_s \ll B_c $$. No ISI.

  • Frequency-Selective Fading: $$\displaystyle B_s > B_c \Rightarrow \tau_{rms} > T_s \Rightarrow $$ ISI occurs.

  !TIP: $$\displaystyle B_c $$ and $$\displaystyle T_c $$ are inversely related to delay spread and Doppler spread, respectively.

III. Antennas and Handoff Management

Antennas in Mobile Systems

• Cell-Site Antennas:

  • Types: Omnidirectional, directional (sectoring: 65°, 120°).

  • Placement: On towers/building rooftops. Height critical for coverage.

  • Unique Situations: Need for downtilt (mechanical/electrical) to reduce CCI; diversity (space, polarization) to combat fading.

• Mobile Antennas:

  • Types: Whip, helical, patch (for vehicles/handsets).

  • Characteristics: Low gain, omnidirectional (usually), vertically polarized.

Handoff Management

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

• Types:

  1. Hard Handoff: Break-before-make (GSM). Mobile disconnects from old BS before connecting to new.

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

  3. Mobile-Assisted Handoff (MAHO): Mobile measures signal strength/quality of neighboring cells and reports to network. Network-controlled decision.

  4. Network-Controlled Handoff (NCHO): Network (BSC/MSC) makes decision based on measurements from multiple BSs.

  5. Mobile-Controlled Handoff (MCHO): Mobile makes decision autonomously.

• MAHO Technique:

  1. Mobile continuously monitors ** pilot channels** (CDMA) or BSIC+BCCH (GSM) of neighbor cells.

  2. Measurements (e.g., RSSI, $$\displaystyle E_c/N_0 $$, BLER) are filtered.

  3. When threshold (e.g., neighbor signal > serving signal + hysteresis) crossed, measurement report sent to serving BS.

  4. Serving BS requests handoff to target BS via MSC/BSC.

  5. MSC/BSC allocates resources and commands handoff.

• Queuing Concept in Handoff: Prioritize handoff requests over new call attempts to avoid call drops (higher GoS for handoffs). Can be modeled as $M/M/c/c$ loss system with priority.

IV. Multiple Access and Multiplexing Techniques

Multiple Access Methods

• FDMA Calculations:

$$N_{ch} = \frac{B_T - B_{guard}}{B_c}$$

where $$\displaystyle B_T $$ = total bandwidth, $$\displaystyle B_{guard} $$ = total guard bandwidth, $$\displaystyle B_c $$ = channel bandwidth.

\boxed{N_{ch} = \left\lfloor \frac{B_T - B_{guard}}{B_c} \right\rfloor}

• TDMA Frame Structure: A frame consists of $N$ time slots. One slot per user per frame. Includes synchronization, guard times.

  DiagramSEARCH: GSM TDMA frame structure 8 timeslots

• CDMA:

  • Spread Spectrum: Transmit signal bandwidth $W$ >> information bit rate $$\displaystyle R_b $$.

  • PN Sequences: Pseudo-random binary sequences (e.g., m-sequences, Gold codes) with good autocorrelation.

  • Processing Gain (Spreading Factor):

$$G_p = \frac{W}{R_b} = \frac{T_{chip}}{T_{bit}}$$

    Determines resistance to interference and number of users.

*   **Forward Channel (BS→MS):** Uses **Walsh codes** (orthogonal) for channelization. Pilot, sync, paging, traffic channels.

*   **Reverse Channel (MS→BS):** Uses **PN sequences** (quasi-orthogonal) for channelization. Each user has unique PN offset.

*   **Power Control:** **Essential** due to near-far problem. Closed-loop power control (e.g., 800 bps in IS-95) adjusts MS/BTS transmit power to equalize received $$\displaystyle E_b/N_0 $$ at BS.

• Frequency Hopped Spread Spectrum (FHSS):

  • Principle: Carrier frequency changes ("hops") according to PN sequence over a wide band.

  • Slow FH: Several bits/symbol transmitted per hop.

  • Fast FH: Frequency changes every symbol or few bits.

  • Advantage: Avoids narrowband interference and jamming.

Multiplexing Overview: FDM, TDM, CDM (same as MA schemes), WDM (optical).

V. GSM and CDMA Systems

Global System for Mobile Communications (GSM)

• Architecture:

  • MS (Mobile Station): ME (Mobile Equipment) + SIM.

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

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

  DiagramSEARCH: GSM architecture block diagram MSC BSC BTS MS

• Interfaces:

  • Um: Air interface (MS-BTS).

  • Abis: BTS-BSC (TDM, proprietary).

  • A: BSC-MSC (SS7, ISUP).

• Traffic & Control Channels:

  • TCH (Traffic Channel): Full-rate (TCH/F, 13 kbps), Half-rate (TCH/H, 6.5 kbps).

  • CCH (Control Channel):

    • BCH (Broadcast): FCCH, SCH, BCCH.

    • CCH (Common): CCCH (PCH, AGCH, RACH).

    • DCCH (Dedicated): SDCCH, SACCH, FACCH.

• Frame Structure (TDMA):

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

  • Multiframe:

    • 26-Multiframe (TCH): 26 TDMA frames for traffic.

    • 51-Multiframe (CCH): 51 TDMA frames for control.

  • Superframe & Hyperframe: For encryption and hopping synchronization.

• Multiple Access: FDMA/TDMA. 200 kHz carrier spacing, 8 slots per carrier.

• Radio Subsystem: BTS + antennas + transcoders. Handles radio transmission/reception, channel coding/decoding, encryption.

CDMA Systems (IS-95)

• Forward Channel (1.25 MHz):

  • Pilot: Unmodulated PN sequence (for synchronization, coherent demod, handoff).

  • Sync: System time, PN offset.

  • Paging: Messages to idle MS.

  • Traffic: User data + power control bits.

  • Walsh Codes: Orthogonal codes (64 available, length 64 chips) separate channels.

• Reverse Channel (1.25 MHz):

  • Access: Initial access attempts.

  • Traffic: User data + power control bits.

  • PN Sequences: Each user assigned unique PN offset (2^15 possible).

• Processing Gain:

$$G_p = \frac{Chip\ Rate}{Data\ Rate} = \frac{1.2288\ Mcps}{13\ kbps} \approx 94.5 \ (or\ 19.75\ dB)$$

\boxed{G_p = \frac{W}{R_b}}

• Power Control:

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

  • Closed-loop: BS sends power control bits (1 bit per 1.25 ms) to MS (+1dB or -1dB). Frequency: 800 bps.

• Call Processing & Handoff:

  • Soft Handoff: MS acquires pilot from target BS, sends handoff request to serving BS. Serving BS requests MSC to add target BS to active set. MSC establishes link to target BS. When signal from serving BS degrades, it's dropped from active set.

• Bit Error Probability (BEP): For BPSK in AWGN, $$\displaystyle P_b = Q\left(\sqrt{2E_b/N_0}\right) $$. In CDMA, $$\displaystyle E_b/N_0 $$ is effectively increased by $$\displaystyle G_p $$ against noise, but multiple access interference (MAI) limits performance.

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

where $K$ = number of active users.

Generations (1G to 5G/6G):

VI. Capacity and Interference Management

Co-channel Interference (CCI)

• Sources: Reuse of same frequency in adjacent cells.

• Main Cause: Inadequate frequency reuse distance $D$ relative to cell radius $R$.

• Reduction Techniques:

  1. Increase $D$ (Increase $N$): Lowers capacity.

  2. Power Control: Reduce transmit power of mobiles/BTS to just meet link requirement.

  3. Antenna Tilting (Downtilt): Focuses energy within cell, reduces spillover.

  4. Sectoring: Increases effective $D$ in angular domain.

  5. Cell Splitting: Reduces $R$, allows smaller $D$ for same C/I.

Frequency Management & Channel Assignment

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

  • Adv: Simple, low overhead.

  • Disadv: Inefficient during non-uniform traffic; high blocking during peak in some cells.

• Dynamic Channel Assignment (DCA): Channels assigned on-demand from a common pool.

  • Adv: Better traffic balancing, higher capacity under variable load.

  • Disadv: Complex, high signaling overhead, need real-time interference measurement.

• Non-Fixed Algorithms:

  • Borrowing: Cells can borrow channels from neighbors if own pool exhausted (with permission).

  • Channel Segregation: Cells learn which channels have lowest interference and preferentially use them (self-organizing).

• Hybrid: Often FCA with borrowing (FCB).

Techniques to Expand Cellular Capacity

1. Cell Splitting: Reduce $R$ → more cells → more clusters → more total channels.

2. Sectoring: Replace omni antennas with directional (e.g., 3-sector → effective $N$ reduced by 3).

3. Microcells/Picocells: Very small cells (tens/hundreds of meters) for high-density areas.

4. Additional Spectrum: Allocate more bandwidth (e.g., 900 MHz → 1800 MHz → 2.1 GHz).

5. Overlay/Underlay: Use different cell sizes with same frequencies (careful power control).

VII. Advanced Wireless Technologies

Multiple Input Multiple Output (MIMO)

• Concept: Use multiple antennas at both transmitter (M) and receiver (N).

• Benefits:

  • Spatial Multiplexing: Transmit independent data streams → increase capacity (up to $\min(M,N)$ times).

  • Diversity: Multiple paths → increase reliability (lower BER).

  • Beamforming: Focus energy directionally → increase range/capacity.

• Challenges: Complex signal processing, channel estimation.

Orthogonal Frequency Division Multiplexing (OFDM)

• Principle: High-rate data stream split into many parallel low-rate subcarriers (orthogonal, overlapping).

• Advantages:

  • ISI Resistance: Long symbol duration $$\displaystyle T_s $$ > channel delay spread $$\displaystyle \tau_{max} $$. Use cyclic prefix.

  • Spectral Efficiency: Orthogonal subcarriers allow tight spacing (no guard bands).

  • Simple Equalization: Flat fading per subcarrier (single-tap equalizer).

  • Robust to frequency-selective fading.

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

Diversity Techniques

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

• Types:

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

  • Time Diversity: Same signal sent at different times (channel coding, interleaving).

  • Frequency Diversity: Same signal on different frequencies (FHSS, multi-carrier).

  • Polarization Diversity: Orthogonal polarizations (vertical/horizontal).

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

VIII. Calculations and Problem Solving

1. Symbol Rate from Coherence Bandwidth (Minimal ISI)

• Condition: For minimal ISI, symbol duration $$\displaystyle T_s > $$ delay spread $$\displaystyle \tau_{rms} $$.

  Using $$\displaystyle B_c \approx \frac{1}{5\tau_{rms}} $$ (50% correlation), then $$\displaystyle \tau_{rms} \approx \frac{1}{5B_c} $$.

  Maximum Symbol Rate:

$$R_s^{max} = \frac{1}{T_s^{min}} \approx 5 B_c$$

\boxed{R_s^{max} \approx 5 \times B_c}

*Example:* $$\displaystyle B_c = 100 $$ kHz → $$\displaystyle R_s^{max} \approx 500 $$ kbaud.

2. Number of Channels in FDMA

• Formula: $$\displaystyle N_{ch} = \frac{B_T - B_{guard}}{B_c} $$

  Example: $$\displaystyle B_T = 12.5 $$ MHz, $$\displaystyle B_{guard} = 10 $$ kHz, $$\displaystyle B_c = 30 $$ kHz.

$$N_{ch} = \frac{12.5 \times 10^6 - 10 \times 10^3}{30 \times 10^3} = \frac{12,490,000}{30,000} \approx 416.33 \Rightarrow \boxed{416\ \text{channels}}$$

3. IS-95 CDMA Parameters

• Given: $$\displaystyle K=20 $$ users, $$\displaystyle W=1.25 $$ MHz, $$\displaystyle R_b=13 $$ kbps, $$\displaystyle L_{PN}=32768 $$ ($$\displaystyle 2^{15} $$), $$\displaystyle E_b/N_0 = 7.8 $$ dB.

• Processing Gain:

$$G_p = \frac{W}{R_b} = \frac{1.25 \times 10^6}{13 \times 10^3} \approx 96.15 \ (19.83\ dB)$$

\boxed{G_p \approx 96.15}

• Bit Error Probability (BEP): Assuming Gaussian approximation for MAI.

$$\frac{E_b}{N_0}_{eff} = \frac{G_p \cdot E_b/N_0}{1 + (K-1)G_p \cdot E_b/N_0}$$

Convert $$\displaystyle E_b/N_0 = 7.8 $$ dB → linear: $$\displaystyle 10^{0.78} \approx 6.03 $$.

$$\frac{E_b}{N_0}_{eff} = \frac{96.15 \times 6.03}{1 + 19 \times 96.15 \times 6.03} \approx \frac{579.6}{1 + 11000} \approx 0.0527 \ (-12.8\ dB)$$

For BPSK: $$\displaystyle P_b = Q\left(\sqrt{2 \times 0.0527}\right) = Q(0.325) \approx 0.372 $$ (from Q-table).

\boxed{P_b \approx 0.372}

> **!TIP:** In CDMA, even with good $$\displaystyle E_b/N_0 $$, high $K$ causes MAI, drastically reducing $$\displaystyle E_b/N_0_{eff} $$.

4. Propagation: Incident & Slope Angle (Hilly Terrain)

• Given: $$\displaystyle H = 100 $$ m (hill height), $$\displaystyle h_t = 50 $$ m (BS antenna), $$\displaystyle h_r = 3 $$ m (MS antenna), $$\displaystyle d = 5 $$ km.

• Slope Angle ($$\displaystyle \theta_s $$): Angle of hill slope relative to horizontal.

$$\theta_s = \tan^{-1}\left(\frac{H}{d}\right) = \tan^{-1}\left(\frac{100}{5000}\right) = \tan^{-1}(0.02) \approx \boxed{1.15^\circ}$$

• Incident Angle ($$\displaystyle \theta_i $$): Angle at which signal arrives at mobile relative to horizontal.

$$\theta_i \approx \theta_s - \tan^{-1}\left(\frac{h_t - h_r}{d}\right)$$

First term: $$\displaystyle \tan^{-1}((h_t - h_r)/d) = \tan^{-1}(47/5000) \approx 0.54^\circ $$.

$$\theta_i \approx 1.15^\circ - 0.54^\circ = \boxed{0.61^\circ}$$

> **!TIP:** For mobile behind a hill, $$\displaystyle \theta_i $$ is small; diffraction loss is high. Use knife-edge diffraction model.

5. Other Key Formulas

• Reuse Distance: $$\displaystyle D = R\sqrt{3N} $$

• SIR in Cellular (for hexagonal, omni): $$\displaystyle \text{SIR} \approx \left(\frac{D}{R}\right)^n = \left(\sqrt{3N}\right)^n $$, where $n$ = path loss exponent (3-4).

• Erlang B (Recursive): $$\displaystyle P_b(0) = 1 $$; $$\displaystyle P_b(c) = \frac{A \cdot P_b(c-1)}{c + A \cdot P_b(c-1)} $$.

Summary of High-Frequency Exam Topics:

1. Draw & Explain: 19-cell cluster, co-channel cells, GSM architecture, CDMA forward/reverse channels.

2. Define & Differentiate: Slow/fast fading, flat/frequency-selective fading, $$\displaystyle B_c $$, $$\displaystyle T_c $$, $$\displaystyle f_D $$.

3. Explain with Diagrams: Frequency reuse, cell splitting/sectoring, MAHO, frame structure (GSM), spread spectrum/CDMA.

4. Compare: FDMA/TDMA/CDMA, FCA/DCA, slow/fast FH.

5. Numerical: $$\displaystyle N_{ch} $$ (FDMA), $$\displaystyle R_s^{max} $$ from $$\displaystyle B_c $$, CDMA processing gain & BEP, propagation angles.

6. List & Explain: Capacity expansion techniques, dispersion parameters, CCI reduction, antennas.

7. Short Notes: MIMO, OFDM, Diversity, Clarke's model, Trunking/GoS, Foliage losses, Near-in-distance.