ADVANCED CONTROL SYSTEM (EC-503 (C)) - Unit 2 Short Notes

Cellular System Fundamentals

Cellular Concept and Frequency Reuse

• Cellular Concept: Divides service area into small cells, each with a base station. Frequencies are reused in non-adjacent cells to increase capacity.

• Frequency Reuse: Same set of frequencies (channel group) used in cells separated by a sufficient distance to keep interference below a threshold.

• Reuse Factor (N): Number of cells in a cluster. Common values: 3, 4, 7, 9, 12, 19, etc.

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

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

where $R$ = cell radius.

[!TIP] For a hexagonal grid, co-channel cells are located at positions $(i, j)$ relative to a reference cell, where $i, j$ satisfy $$\displaystyle i^2 + ij + j^2 = N $$ (e.g., for $$\displaystyle N=7 $$, $(2,1)$ or $(1,2)$).

Cluster Design and 19-Cell Reuse

• A 19-cell cluster ($$\displaystyle N=19 $$) is common for large cells. Co-channel cells are at vectors like $(3,2)$, $(2,3)$, etc., satisfying $$\displaystyle 3^2 + 3\times2 + 2^2 = 19 $$.

• Diagram:

  DiagramSEARCH: 19-cell reuse pattern hexagonal
  • Center cell (0,0). First-tier co-channels at $(3,2)$, $(2,3)$, $(-1,4)$, etc., forming a larger hexagon.

Capacity and Trunking

• Erlang B Formula: Calculates probability of call blocking (Grade of Service, GoS) in a loss system with $C$ channels and offered traffic $A$ (in Erlangs).

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

• GoS: $$\displaystyle P_b $$ (e.g., 0.02 means 2% calls blocked).

• Capacity: Number of users supported = $C \times$ (traffic per user) / (GoS factor).

Capacity Expansion Techniques

Cell Site and Mobile Antennas

• Cell Site Antennas: High power, mounted on towers/tall buildings. Types: omni-directional, directional (sectorized). Unique situations: rooftop mounting, terrain-following.

• Mobile Antennas: Low power, omnidirectional, on vehicle roof. Challenges: multipath, Doppler, varying height.

Merits of Cellular Systems

• Frequency Reuse: Efficient spectrum use.

• Capacity: Supports many users via cell splitting/sectoring.

• Coverage: Seamless wide-area coverage via handoff.

• Robustness: Handles mobile environment with fading/interference management.

Radio Propagation

Large-Scale Propagation Models

• Free Space Propagation:

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

or in dB: $$\displaystyle P_r(\text{dBm}) = P_t(\text{dBm}) + G_t(\text{dBi}) + G_r(\text{dBi}) - 20\log_{10}(4\pi d/\lambda) $$.

Valid for $d \gg$ antenna far-field ($$\displaystyle d > \frac{2D^2}{\lambda} $$).

• Ground Reflection Model (2-ray):

$$P_r \propto \frac{h_t^2 h_r^2}{d^4}$$

(for large $d$).

Includes constructive/destructive interference due to path difference.

• Foliage Losses: Additional attenuation when signal penetrates trees. Approx. 0.05–0.1 dB/m at UHF.

• Near-in-Distance Propagation: Empirical models for short distances (e.g., $$\displaystyle d < 100 $$ m) where far-field assumptions fail.

• Mobile-to-Mobile Propagation: Both antennas low height; ground reflection dominant; often modeled with log-distance path loss.

Small-Scale Multipath Propagation

• Causes: Reflections, diffractions, scattering from buildings, terrain.

• Effects: Multipath delay spread → intersymbol interference (ISI). Doppler spread → time-varying fading.

Fading Phenomena

Clarke's Model for Flat Fading

• Assumes Rayleigh fading for non-LOS environments.

• Received signal: $$\displaystyle r(t) = \text{Re}\left[ \sum_{n=1}^{N} \alpha_n e^{j(2\pi f_c t + \theta_n)} \right] $$.

• For $N \to \infty$, in-phase and quadrature components are independent Gaussian (0, $$\displaystyle \sigma^2 $$). Envelope $$\displaystyle R = \sqrt{I^2+Q^2} $$ follows Rayleigh distribution:

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

• Phase $\theta$ uniform on $[0,2\pi)$.

Level Crossing Rate (LCR) and Fade Duration

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

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

where $$\displaystyle f_d = v/\lambda $$ max Doppler.

• Average Fade Duration: $$\displaystyle \bar{\tau} = \frac{1}{N_R} e^{\rho^2/2} $$ for $$\displaystyle \rho < 1 $$.

Fading Statistics

• Rayleigh: No LOS component.

• Rician: With LOS, envelope follows Rician distribution (K-factor = LOS power / scattered power).

Doppler Effects

• Doppler Shift: $$\displaystyle f_d = \frac{v}{\lambda} \cos\theta $$, where $\theta$ is angle between motion and wave direction.

• Doppler Spread: Range of frequencies $$\displaystyle [-f_d, f_d] $$.

• Coherence Time $$\displaystyle T_c $$: Time duration over which channel is approximately constant. Approx. $$\displaystyle T_c \approx \frac{9}{16\pi f_d} $$ (for $$\displaystyle J_0 $$ correlation).

Channel Parameters

• Coherence Bandwidth $$\displaystyle B_c $$: Frequency separation over which channel fade is correlated. Approx. $$\displaystyle B_c \approx \frac{1}{5\tau_{rms}} $$ (for 0.9 correlation), where $$\displaystyle \tau_{rms} $$ = RMS delay spread.

• Maximum Symbol Rate (to avoid ISI):

$$R_s \leq 2 B_c \quad \text{(for flat fading)}$$

Example: If $$\displaystyle B_c = 100 $$ kHz, $$\displaystyle R_s^{\max} = 200 $$ ksymbols/s.

• Delay Spread $$\displaystyle \tau_{rms} $$: RMS of multipath delays. Causes frequency selectivity.

• Dispersion Parameters: $$\displaystyle \tau_{rms} $$, $$\displaystyle B_c $$, $$\displaystyle f_d $$, $$\displaystyle T_c $$.

Special Propagation Scenarios (Hilly Terrain)

• Incident Angle $\phi$: Angle of arrival at mobile from direct path.

• Slope Angle $\theta$: Elevation angle of terrain relative to horizontal.

• For hilly terrain with cell site height $H$, mobile height $$\displaystyle h_m $$, distance $d$:

$$\tan \phi \approx \frac{H - h_m}{d}, \quad \theta \approx \arctan\left(\frac{\text{height difference}}{\text{horizontal distance}}\right)$$

Example: $$\displaystyle H=50 $$ m, $$\displaystyle h_m=3 $$ m, $$\displaystyle d=5 $$ km → $$\displaystyle \phi \approx \tan^{-1}(47/5000) \approx 0.54^\circ $$.

Channel Assignment and Handoff

Channel Assignment Strategies

Frequency Management

• Frequency Planning: Assign channel groups to cells to minimize co-channel interference (using $N$).

• Channel Borrowing: Under heavy load, a cell can borrow channels from a neighbor, provided it doesn’t cause new interference.

Handoff

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

• Types:

  • Mobile-Assisted Handoff (MAHO): Mobile measures neighbor BS signal strength and reports to network. Network decides.

  • Network-Controlled Handoff (NCHO): Network (BSC/MSC) measures and decides.

  • Mobile-Controlled Handoff (MCHO): Mobile decides based on measurements.

  • Hard Handoff (break-before-make): Used in FDMA/TDMA.

  • Soft Handoff (make-before-break): Used in CDMA (mobile can communicate with multiple BSs).

MAHO Technique

1. Mobile continuously monitors pilot channels of neighboring cells.

2. Reports neighbor set signal strengths to serving BS via reverse control channel.

3. BS evaluates and requests handoff to MSC if threshold crossed.

4. MSC assigns new channel and instructs target BS.

Queuing Concept in Handoff

• Handoff requests have higher priority than new calls to avoid dropping ongoing calls.

• Guard channels: Reserve a fraction of channels in each cell exclusively for handoffs.

• Queuing delay: Handoff requests may be queued if no channel available; must be served within handoff delay (< 1 sec).

Handoff in GSM and CDMA

• GSM: Hard handoff. Mobile measures BA list (neighbor cells) via SACCH. BSC decides and allocates new traffic channel.

• CDMA: Soft handoff. Mobile simultaneously holds traffic channels from multiple BSs. Active set managed by MSC. Handoff involves adding/removing BSs from active set without channel change (same frequency).

Multiple Access Techniques

FDMA (Frequency Division Multiple Access)

• Principle: Each user assigned a dedicated frequency band (channel).

• Channel Allocation: Total bandwidth $$\displaystyle B_T $$ split into $C$ channels of bandwidth $$\displaystyle B_c $$, with guard bands $$\displaystyle B_{guard} $$ between channels.

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

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

$$C \approx \frac{12.5 \times 10^3}{30 + 10} = 312.5 \approx 312 \text{ channels}.$$

TDMA (Time Division Multiple Access)

• Principle: Each user assigned a time slot in a repeating frame. Multiple users share same frequency.

• Frame Structure (GSM example):

  • TDMA Frame: 8 time slots (TS0–TS7), each 0.577 ms.

  • Multiframe: 26 TDMA frames (for traffic) or 51 (for control).

  • Superframe: 1326 TDMA frames.

  • Hyperframe: 2715648 TDMA frames (≈ 3.5 hours).

CDMA (Code Division Multiple Access)

• Spread Spectrum: User signal spread over wide bandwidth using pseudo-noise (PN) sequences.

• PN Sequences: Binary sequences with low autocorrelation (e.g., m-sequences, Gold codes). Length $L$ (e.g., $$\displaystyle 2^{15}-1=32767 $$ in IS-95).

• Forward Channel (BS → MS):

  • Pilot: Unmodulated PN sequence for synchronization & coherent demodulation.

  • Sync: System parameters.

  • Paging: Page messages to mobiles.

  • Traffic: User data + power control bits.

• Reverse Channel (MS → BS):

  • Access: Initial access (random).

  • Traffic: User data + power control bits.

• Power Control:

  • Open Loop: MS estimates path loss from forward pilot and adjusts transmit power.

  • Closed Loop: BS sends power control commands (↑/↓ 1 dB) on forward traffic channel (every 1.25 ms).

• Processing Gain $$\displaystyle G_p $$:

$$G_p = \frac{W}{R_b} = \frac{\text{chip rate}}{\text{bit rate}}$$

IS-95: $$\displaystyle W = 1.2288 $$ Mcps, $$\displaystyle R_b = 13 $$ kbps → $$\displaystyle G_p \approx 94.5 $$ (or 19.75 dB).

• Capacity: Approx. $$\displaystyle K \approx \frac{W}{R_b} \cdot \frac{E_b/N_0}{\text{required } E_b/N_0} $$ (in noise-limited case).

• Near-Far Problem: Strong nearby signal overwhelms weak distant signal due to same code. Solved by tight power control.

• Advantages over FDMA/TDMA:

  • Soft handoff,抗干扰, low probability of intercept, gradual degradation.

FHSS (Frequency Hopped Spread Spectrum)

• Principle: Carrier frequency changes rapidly according to PN sequence.

• Slow FH: Several symbols per hop; hop rate < symbol rate.

• Fast FH: Hop per symbol; hop rate > symbol rate.

• Advantage: Avoids narrowband interference/fading.

OFDMA (Orthogonal Frequency Division Multiple Access)

• Principle: Divide channel into many orthogonal subcarriers; assign subsets to users (FDMA+TDMA).

• Orthogonality: Subcarriers spaced by $$\displaystyle 1/T_s $$ (symbol duration) → no ICI.

• Advantage: Robust to multipath (with cyclic prefix), flexible resource allocation.

MIMO (Multiple Input Multiple Output)

• Principle: Use multiple antennas at TX and RX for:

  • Spatial Multiplexing: Parallel data streams → higher data rate.

  • Diversity Gain: Improved reliability (e.g., Alamouti code).

• Channel Capacity: $$\displaystyle C = \log_2 \det(\mathbf{I} + \frac{\rho}{n_t} \mathbf{H}\mathbf{H}^H) $$ (bps/Hz), where $\mathbf{H}$ is channel matrix.

GSM System

GSM Architecture and Subsystems

• MS (Mobile Station): Mobile + SIM.

• BSS (Base Station Subsystem):

  • BTS (Base Transceiver Station): Radio interface.

  • BSC (Base Station Controller): Manages BTSs, handoff, frequency allocation.

• NSS (Network Switching Subsystem):

  • MSC (Mobile Switching Center): Call switching, mobility management.

  • HLR (Home Location Register): Permanent user data.

  • VLR (Visitor Location Register): Temporary data for roaming users.

  • EIR (Equipment Identity Register): IMEI tracking.

  • AUC (Authentication Center): Security.

• OMC (Operation & Maintenance Center).

Interface Standards

• A: BSC ↔ MSC (circuit-switched).

• Abis: BSC ↔ BTS (proprietary).

• Ater: BSC ↔ MSC (packet data).

• Um: Mobile ↔ BTS (radio).

Logical Channels

Frame Structure (TDMA-based)

1. TDMA Frame: 8 time slots (TS0–TS7), each 0.577 ms.

2. Multiframe:

   • Traffic: 26 TDMA frames (26×8=208 slots) → 120 ms.

   • Control: 51 TDMA frames → 235 ms.

3. Superframe: 1326 TDMA frames (traffic+control mix) → 6.12 s.

4. Hyperframe: 2715648 TDMA frames → ≈ 3.5 hours (for encryption sequence).

GSM Radio Subsystem

• MS ↔ BTS via Um interface.

• Frequency Bands: 890–915 MHz (uplink), 935–960 MHz (downlink) (P-GSM).

• Modulation: GMSK (Gaussian Minimum Shift Keying).

• Channel Spacing: 200 kHz.

Multiple Access in GSM

• FDMA/TDMA: Each carrier (200 kHz) divided into 8 time slots (TDMA). Each user gets one slot per frame (or two for TCH/H).

CDMA Systems (IS-95)

System Overview

• Band: Uplink 824–849 MHz, Downlink 869–894 MHz.

• Channel Bandwidth: 1.25 MHz.

• Chip Rate: 1.2288 Mcps.

• Multiple Access: DS-CDMA (Direct Sequence).

Forward Channel (BS → MS)

• Pilot: Unmodulated PN (15-bit shift register, $$\displaystyle 2^{15} $$ chips). Used for:

  • Coherent demodulation (phase reference).

  • Active set management (searcher).

• Sync: 1.2 kbps, contains system parameters (PN offset, paging channel index).

• Paging: 9.6 kbps, pages mobiles.

• Traffic: 9.6/13/14.4 kbps (variable). Includes:

  • User data.

  • Power control subchannel (800 bps).

  • Turbo coding (optional).

Reverse Channel (MS → BS)

• Access: 1.2 kbps, for initial access (random). Uses long PN code (42 bits) for user identification.

• Traffic: 9.6/13/14.4 kbps. Includes:

  • User data + power control bits.

  • Reverse pilot (for coherent detection).

Power Control Mechanisms

• Open Loop: MS estimates path loss from forward pilot: $$\displaystyle P_{tx} = P_{rx} + \text{path loss estimate} $$. Fast (1 ms update).

• Closed Loop: BS measures $$\displaystyle E_b/N_0 $$, sends power control bit (↑/↓ 1 dB) every 1.25 ms on forward traffic channel. MS adjusts accordingly.

• Goal: Equalize $$\displaystyle E_b/N_0 $$ at BS for all users (near-far mitigation).

Processing Gain Calculation

$$G_p = \frac{W}{R_b} = \frac{1.2288 \times 10^6}{13 \times 10^3} \approx 94.5 \quad (19.75 \text{ dB})$$

Call Processing and Handoff Procedures

1. Call Setup: MS monitors pilot, selects strongest. Acquires sync, reads BCCH (paging channel). Registers with MSC via SDCCH.

2. Handoff:

   • MS measures pilot strengths of neighbor cells (active, candidate, neighbor sets).

   • Reports to BS via traffic channel (if in call) or access channel.

   • T_ADD (6 dB above active), T_DROP (6 dB below active) thresholds.

   • Soft Handoff: MSC adds new BS to active set when pilot > T_ADD. Drops when < T_DROP for time $$\displaystyle T_{DROP} $$.

   • Hard Handoff: If no common frequency, change frequency (rare).

Bit Error Probability Calculation (Example)

Given: $$\displaystyle K=20 $$ users, $$\displaystyle W=1.2288 $$ Mcps, $$\displaystyle R_b=13 $$ kbps, $$\displaystyle E_b/N_0 = 7.8 $$ dB, PN length $$\displaystyle L=32768 $$.

1. Processing Gain:

$$G_p = \frac{W}{R_b} = \frac{1.2288 \times 10^6}{13 \times 10^3} = 94.5 \quad (19.75 \text{ dB})$$

2. Single-user $$\displaystyle E_b/N_0 $$ (assuming perfect power control):

$$\left(\frac{E_b}{N_0}\right)_{\text{single}} = \frac{G_p \cdot (E_b/N_0)_{\text{total}}}{K} \quad ?$$

Actually, for DS-CDMA MAI:

$$\frac{E_b}{N_0} = \frac{G_p \cdot (E_b/N_0)_{\text{received}}}{1 + (K-1) \cdot \text{loading factor}}$$

But with perfect power control, each user’s $$\displaystyle E_b/N_0 $$ at BS is equal. Approx. single-user bound:

$$\left(\frac{E_b}{N_0}\right)_{\text{eff}} = \frac{G_p \cdot (E_b/N_0)_{\text{received}}}{K}$$

Given $$\displaystyle E_b/N_0 = 7.8 $$ dB (required for target BER), solve for BER using BPSK/QPSK formula:

$$P_b = Q\left(\sqrt{2 \cdot (E_b/N_0)_{\text{eff}}}\right)$$

But careful: Provided $$\displaystyle E_b/N_0 = 7.8 $$ dB is likely the required for target BER. With $$\displaystyle K=20 $$, actual $$\displaystyle E_b/N_0 $$ per user at BS is lower due to MAI.

Standard IS-95 model:

$$\left(\frac{E_b}{N_0}\right)_{\text{total}} = \frac{G_p \cdot (E_b/N_0)_{\text{received}}}{1 + (K-1) \cdot \frac{3}{2} \cdot \text{voice activity}}$$

Assuming voice activity 0.5, and $$\displaystyle G_p=94.5 $$, $$\displaystyle K=20 $$:

$$\left(\frac{E_b}{N_0}\right)_{\text{received}} = \frac{(E_b/N_0)_{\text{total}} \left[1 + (K-1) \cdot 1.5 \cdot 0.5\right]}{G_p}$$

But problem states "maximum $$\displaystyle E_b/N_0 $$ of 7.8 dB is provided" → likely received $$\displaystyle E_b/N_0 $$ per user after power control? Ambiguous.

Simplified: Assume $$\displaystyle E_b/N_0 = 7.8 $$ dB is the effective $$\displaystyle E_b/N_0 $$ for each user. Then for BPSK:

$$P_b = Q\left(\sqrt{2 \times 10^{7.8/10}}\right) = Q(\sqrt{2 \times 6.03}) = Q(3.47) \approx 2.7 \times 10^{-4}$$

Processing Gain = 94.5 (19.75 dB).

Interference Management

Co-channel Interference (CCI)

• Cause: Reuse of same frequency in adjacent clusters.

• SIR (Signal-to-Interference Ratio):

$$SIR = \frac{S}{\sum_{i=1}^{i_0} I_i}$$

where $$\displaystyle i_0 $$ = number of co-channel interferers (typically 6 for 1st tier).

Approx. for hexagonal cells:

$$SIR \approx \left( \frac{D}{R} \right)^n = \left( \sqrt{3N} \right)^n$$

where $n$ = path loss exponent (3–4).

• Reduction Methods:

  | Method | How | |--------|-----| | Increase N | Larger reuse distance (reduces capacity). | | Sectoring | 120° or 60° sectors reduce $$\displaystyle i_0 $$ (e.g., 120° → $$\displaystyle i_0=2 $$). | | Cell Splitting | Smaller cells → lower transmit power → reduced interference range. | | Power Control | Reduce TX power to minimum required. | | Antenna Tilting | Down-tilt to limit coverage to cell interior. |

Adjacent Channel Interference (ACI)

• Cause: Imperfect filtering → leakage from adjacent channels.

• Worse near cell site (mobile close to BS, high power on adjacent channel).

• Reduction: Increase guard bands, use high-quality filters, channel assignment (avoid adjacent channels in same cell/neighbors).

Near-Far Problem in CDMA

• Cause: CDMA users transmit on same frequency; strong nearby signal masks weak distant signal at receiver.

• Solution: Tight closed-loop power control (1 dB steps, 1.25 ms updates) to equalize received powers.

Diversity Techniques

Need for Diversity

• Mitigate fading by providing multiple independent signal paths.

Types

Implementation in Receivers

• Selection Diversity: Choose best branch.

• Equal Gain Combining: Coherent sum with equal weights.

• Maximal Ratio Combining: Weighted sum proportional to SNR → optimal.

Advanced Topics and Future Trends

MIMO Systems

• Spatial Multiplexing: Multiple independent data streams transmitted simultaneously from $$\displaystyle n_t $$ antennas. Capacity increases linearly with $$\displaystyle \min(n_t, n_r) $$.

• Diversity Gain: Improves reliability via coding across antennas (e.g., Alamouti STBC: 2 TX, 1 RX achieves diversity order 2).

• Channel Capacity (i.i.d. Rayleigh):

$$C = \min(n_t, n_r) \cdot \log_2(1 + \rho) \text{ bps/Hz}$$

OFDM (Orthogonal Frequency Division Multiplexing)

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

• Advantages in Multipath:

  • Guard Interval (Cyclic Prefix): Inserted to combat delay spread. Length $$\displaystyle \tau_g > \tau_{max} $$ (max delay spread) → eliminates ISI.

  • Narrowband Subcarriers: Each sees flat fading (if $$\displaystyle B_{subcarrier} \ll B_c $$).

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

Generations of Wireless Networks (1G to 5G)

Short Notes (as per exam)

• MIMO: Uses multiple antennas for spatial multiplexing (higher rate) and diversity (reliability). Requires rich multipath environment.

• OFDM: Multicarrier modulation with orthogonal subcarriers; cyclic prefix combats ISI; used in 4G/5G, Wi-Fi.

• Diversity (Spatial): Multiple receive antennas; selection combining simplest; MRC optimal. Requires antenna spacing > $\lambda/2$.