Communication Network and Transmission (EC-503 (A)) Notes

1. Cellular System Fundamentals

Cellular Concept and Frequency Reuse

Cellular concept: Divide service area into small regions called cells, each with a base station. Frequency bands are reused in non-adjacent cells to increase capacity.
Frequency reuse factor: \( \frac{1}{N} \), where \( N \) is the cluster size (number of cells using distinct frequency sets). Common patterns:
- 4/12 pattern: \( N = 4 \), co-channel distance \( D/R = \sqrt{3N} = \sqrt{12} \approx 3.46 \).
- 3/9 pattern: \( N = 3 \), \( D/R = \sqrt{9} = 3 \).
- 19-cell reuse pattern: \( N = 19 \) (achieved with \( i=3, j=2 \) in hexagonal geometry, \( N = i^2 + ij + j^2 \)). Co-channel cells are located at displacements \( (\pm i, \pm j) \) and permutations.
Merits:
- Increased capacity via frequency reuse.
- Reduced transmitter power and interference.
- Enables handoff and mobility.
- Efficient use of spectrum.

[!TIP]

For a 19-cell cluster (\( N=19 \)), co-channel cells are at relative positions: \( (3,2), (2,3), (-3,2), (-2,3), (3,-2), (2,-3), (-3,-2), (-2,-3) \) and their reflections. Always verify \( N = i^2 + ij + j^2 \).

Capacity and Trunking

Erlang B formula (loss system, no queue):

\[ \boxed{E_B(N, A) = \frac{\frac{A^N}{N!}}{\sum_{k=0}^{N} \frac{A^k}{k!}}} \]

where \( N \) = number of channels, \( A \) = offered traffic intensity (Erlangs).
Erlang C formula (delay system with queue):

\[ \boxed{E_C(N, A) = \frac{\frac{A^N}{N!} \frac{N}{N-A}}{\sum_{k=0}^{N-1} \frac{A^k}{k!} + \frac{A^N}{N!} \frac{N}{N-A}}} \]
Grade of Service (GOS): Probability that a call is blocked (Erlang B) or delayed (Erlang C). Target GOS typically ≤ 2%.

Cell Splitting and Sectoring

Cell splitting: Divide congested cells into smaller cells (microcells/picocells). Reduces cell radius \( R \), increases number of cells per area by factor \( (R_{\text{old}}/R_{\text{new}})^2 \). Requires additional base stations and frequency plan adjustment.
Sectoring: Replace omnidirectional antennas with directional antennas (e.g., 120° or 60° sectors). Reduces co-channel interference by limiting the number of interfering cells, effectively increasing \( N \) without reducing \( R \).

Channel Assignment Strategies

Fixed Channel Assignment (FCA): Each cell has a fixed set of channels. Simple but inflexible; channels may be idle in some cells while blocked in others.
Dynamic Channel Assignment (DCA): Channels assigned on demand from a pool. Better utilization but requires complex control and signaling.
Non-fixed algorithms:
- Borrowing: Cells can borrow channels from neighbors under congestion, with coordination to avoid interference.
- Channel segregation: Cells learn channel usage patterns over time and prefer less-used channels.

2. Propagation and Channel Characteristics

Large-Scale Propagation Models

Free space propagation:

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

Path loss (dB): \( PL(d) = 32.45 + 20\log_{10}(f_c) + 20\log_{10}(d) \), \( f_c \) in MHz, \( d \) in km.
Two-ray ground reflection:

\[ P_r \propto \frac{h_t^2 h_r^2}{d^4} \quad \text{for} \quad d \gg \sqrt{h_t h_r} \]

Breakpoint distance \( d_b = \frac{4\pi h_t h_r}{\lambda} \). Path loss exponent changes from 2 to 4 beyond \( d_b \).
Foliage losses: Additional attenuation due to trees/vegetation. Approx: \( L_f (\text{dB}) = 0.45 f^{0.285} d^{0.5} \), \( f \) in MHz, \( d \) in meters.
Near-in-distance (close-in reference) model:

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

\( d_0 \) = reference distance (1–100 m), \( n \) = path loss exponent (2–6), \( X_\sigma \) = log-normal shadowing.
Mobile-to-mobile propagation: Both antennas at mobile heights (\( h_{t,m}, h_{r,m} \approx 1–3 \) m). Path loss exponent \( n \approx 4–6 \) due to low antennas and obstruction.
Hilly terrain:
- Incident angle \( \theta_i \): Angle between incident ray and horizontal at diffraction point.
  
  \[ \theta_i = \tan^{-1}\left(\frac{H - h_t}{d_1}\right) \]
- Slope angle \( \beta \): Angle of hill slope.
  
  \[ \beta = \tan^{-1}\left(\frac{H}{d_1}\right) \]
  
  where \( H \) = hill height, \( h_t \) = transmitter antenna height, \( d_1 \) = horizontal distance from transmitter to hill. Assume hill at midpoint for calculation if not specified.

Small-Scale Multipath Propagation

Causes: Reflection (buildings, water), diffraction (edges, corners), scattering (rough surfaces, foliage).
Multipath delay spread \( \Delta \tau \): Time difference between first and last received multipath. Causes intersymbol interference (ISI) if \( \Delta \tau \) comparable to symbol period \( T_s \).

Channel Parameters

Coherence bandwidth \( B_c \): Bandwidth over which channel impulse response is highly correlated.

\[ \boxed{B_c \approx \frac{1}{\Delta \tau}} \quad (\text{for } 50\% \text{ correlation}) \]
Doppler spread \( f_D \): Spectrum broadening due to motion.

\[ f_D = \frac{v}{\lambda} = \frac{v f_c}{c} \]

where \( v \) = velocity, \( \lambda \) = wavelength, \( c \) = speed of light.
Coherence time \( T_c \): Time duration over which channel is invariant.

\[ \boxed{T_c \approx \frac{1}{2f_D}} \quad (\text{for } 50\% \text{ correlation}) \]

Fading Characteristics

Condition	Fading Type
\( B_s \ll B_c \)	Flat fading (all frequencies fade similarly)
\( B_s > B_c \)	Frequency-selective fading (different frequencies fade independently)
\( T_s \ll T_c \)	Slow fading (channel constant over symbol duration)
\( T_s > T_c \)	Fast fading (channel varies within symbol duration)

where \( B_s \) = signal bandwidth, \( T_s \) = symbol period.

Clarke's Model for Flat Fading

Assumes Rayleigh distribution for envelope \( R \):

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

where \( \sigma^2 \) = average power of in-phase and quadrature components.
Phase \( \theta \) uniformly distributed over \( [0, 2\pi) \).
Level crossing rate (LCR) for threshold \( \rho \):

\[ \boxed{N_R(\rho) = \sqrt{2\pi f_D} \, \rho \, e^{-\rho^2/2}} \]

where \( \rho \) = normalized threshold (\( \rho = R_{\text{th}} / \sigma \)).

Dispersion Parameters

Delay spread \( \Delta \tau \): RMS delay spread from power delay profile.
Coherence bandwidth \( B_c \approx 1/(5\Delta \tau) \) (90% correlation) or \( 1/\Delta \tau \) (50%).
Doppler spread \( f_D = v f_c / c \).
Coherence time \( T_c \approx 1/(2f_D) \) (50% correlation).

3. Multiple Access Techniques

Frequency Division Multiple Access (FDMA)

Principle: Assign each user a unique frequency band (channel). Guard bands between channels prevent interference.
Channel count:

\[ \boxed{N = \left\lfloor \frac{B_T + B_{\text{guard}}}{B_c + B_{\text{guard}}} \right\rfloor} \]

where \( B_T \) = total bandwidth, \( B_c \) = channel bandwidth, \( B_{\text{guard}} \) = guard band per adjacent channel pair.

Time Division Multiple Access (TDMA)

Principle: Users share same frequency but transmit in different time slots.
Frame structure: A frame contains multiple time slots; each user assigned a slot per frame. Example: GSM uses 8-slot TDMA frames.

Code Division Multiple Access (CDMA)

Spread spectrum (direct sequence): Each user’s data multiplied by a unique pseudo-noise (PN) sequence with chip rate \( W \gg R_b \).
Processing gain:

\[ \boxed{G_p = \frac{W}{R_b}} \]
IS-95 channels:
- Forward (base → mobile):
  - Pilot: unmodulated PN sequence for coherent detection and handoff.
  - Synchronization: 1.2 kbps, for timing and paging channel sync.
  - Paging: 9.6 kbps, for paging messages.
  - Traffic: variable rate (1.2–9.6 kbps), orthogonal Walsh codes.
- Reverse (mobile → base):
  - Access: 600 bps, for initial call setup.
  - Traffic: variable rate, with unique PN codes (non-orthogonal).
Power control:
- Near-far problem: Close users overpower distant ones due to path loss differences.
- Open loop: Mobile estimates path loss from forward pilot and sets initial power.
- Closed loop: Base station sends 600 bps power adjustment commands to mobile.
Advantages over FDMA/TDMA:
- Soft capacity (gradual degradation).
-抗干扰能力强 (interference limited).
- Secure (spread spectrum).
- Soft handoff possible.

Frequency Hopped Spread Spectrum (FHSS)

Principle: Carrier frequency changes rapidly according to PN sequence.
Slow frequency hopping: One frequency per symbol (or per few symbols).
Fast frequency hopping: Multiple frequency hops per symbol.

Orthogonal Frequency Division Multiplexing (OFDM)

Divide wideband channel into many narrowband orthogonal subcarriers. Each subcarrier experiences flat fading. Use cyclic prefix to combat ISI. High spectral efficiency, used in 4G/5G and Wi-Fi.

Multiple Input Multiple Output (MIMO)

Use multiple antennas at transmitter and receiver. Provides:
- Spatial multiplexing: Increase data rate.
- Diversity: Improve reliability.
- Beamforming: Directional transmission.

4. GSM System

Architecture

Block diagram:
```
MS ↔ BTS ↔ BSC ↔ MSC ↔ PSTN

        ↓        ↓

        BSC      HLR/VLR/AUC/EIR
```
- MS: Mobile Station.
- BTS: Base Transceiver Station (radio equipment).
- BSC: Base Station Controller (manages multiple BTS, handoff, frequency allocation).
- MSC: Mobile Switching Center (call switching, mobility management).
- HLR: Home Location Register (permanent subscriber data).
- VLR: Visitor Location Register (temporary data for visiting subscribers).
- AUC: Authentication Center (security).
- EIR: Equipment Identity Register (stolen/defective MS identification).
Interfaces:
- A: BSC ↔ MSC.
- Abis: BTS ↔ BSC.
- Um: MS ↔ BTS (air interface).

Radio Subsystem

Cell site antennas: Typically sectorized (120° or 60°) to reduce interference. Mounted on towers/buildings.
Mobile antennas: Omnidirectional, low gain. Unique situations: inside vehicles, buildings (penetration loss).

Channels

Traffic Channels (TCH):
- Full rate: 13 kbps (voice).
- Half rate: 6.5 kbps (doubles capacity).
Control Channels:
- BCCH: Broadcast Control Channel (downlink) – system info.
- CCCH: Common Control Channel (uplink/downlink) – call access.
- DCCH: Dedicated Control Channel – point-to-point signaling.
- SACCH: Slow Associated Control Channel – linked to TCH, carries measurement reports, SMS.
- FACCH: Fast Associated Control Channel – steals TCH bits for urgent signaling (e.g., handoff).

Frame Structure

TDMA frame: 8 time slots (each 156.25 bits), duration 4.615 ms.
Multiframe:
- Traffic: 26 TDMA frames (26 × 8 = 208 slots) – 12 used for TCH, rest for control.
- Control: 51 TDMA frames (51 × 8 = 408 slots) – for BCCH, CCCH, etc.
Burst types:
- Normal: 116 data bits, 26 training bits, 6.25 guard bits.
- Frequency correction: all-0 sequence for mobile synchronization.
- Synchronization: 64-bit sequence for frame timing.
- Access: 16-bit random access for initial contact.

5. CDMA System (Detailed)

IS-95 CDMA System

Bandwidth: 1.25 MHz per carrier.
Chip rate: 1.2288 Mcps.
Data rates: 1.2, 2.4, 4.8, 9.6 kbps (variable rate).

Forward Channel Structure

Pilot: Continuous, unmodulated PN sequence ( Walsh code 0). Used for coherent detection, handoff measurement, and phase reference.
Synchronization: 1.2 kbps, carries system time and paging channel Walsh codes.
Paging: 9.6 kbps, carries paging messages to mobiles.
Traffic: Variable rate, assigned unique Walsh codes (1–63). Uses convolutional coding (rate 1/2, constraint length 9) and interleaving.

Reverse Channel Structure

Access: 600 bps, used for initial call setup (random access). PN codes from long code mask.
Traffic: Variable rate, assigned unique PN sequences (offset by user’s ESN). Uses same coding as forward.

Power Control

Near-far problem: Without control, close mobiles’ signals overwhelm distant ones at the base station.
Open loop: Mobile measures forward pilot strength and sets initial transmit power: \( P_{\text{tx}} = P_{\text{pilot}} + \text{constant} \).
Closed loop: Base station measures SNR, sends 600 bps power adjustment commands (±1 dB steps) to mobile every 1.25 ms.

Performance Analysis

Processing gain:

\[ \boxed{G_p = \frac{W}{R_b} = \frac{1.2288 \times 10^6}{R_b}} \]

For \( R_b = 13 \) kbps, \( G_p = 94.53 \) (≈19.8 dB).
Bit error probability (reverse link, with power control and \( K \) users):

\[ \boxed{P_b = Q\left( \sqrt{ \frac{2 \cdot (E_b/N_0)}{1 + (K-1)(E_b/N_0)/G_p } } \right)} \]

where \( E_b/N_0 \) is per-user SNR after despreading, \( K \) = number of users.
Capacity: Approximately \( K \approx \frac{G_p}{(E_b/N_0)_{\text{required}}} \) for large \( G_p \) and perfect power control.

Call Processing and Handoff

Call processing:
1. Mobile monitors pilot channels, selects best cell.
2. Sends access message on access channel.
3. Base station assigns traffic channel (Walsh code) and adjusts power.
4. Transition to traffic channel.
Handoff: Soft handoff – mobile can communicate with multiple base stations simultaneously; signals are combined. No interruption.

6. Handoff and Mobility Management

Handoff Necessity

Maintain call continuity when mobile moves out of current cell’s coverage or experiences interference.

Types of Handoff

Intra-cell: Change channel within same cell (due to interference or capacity).
Inter-cell: Change cell under same MSC.
Inter-MSC: Change cell under different MSC (requires inter-MSC signaling).
Hard handoff: Break-before-make (GSM, FDMA/TDMA). Resources released in source before acquiring in target.
Soft handoff: Make-before-break (CDMA). Mobile maintains connections with multiple base stations during transition.

Mobile Assisted Handoff (MAHO)

Mobile measures signal strength (or SNR) of serving and neighboring cells (via pilot channels in CDMA or BCCH in GSM).
Reports measurements to BSC/MSC periodically or when threshold crossed.
Queuing concept: Handoff requests given priority over new call requests to minimize dropped calls. Handoff queue may be used if no channel immediately available.

Handoff Procedures

GSM: Hard handoff. Mobile measures neighboring cell signal strengths (via BA list), reports to BSC. BSC decides, instructs target BTS to prepare, then hands over.
CDMA: Soft handoff. Mobile continuously measures pilot strengths; when a new pilot exceeds a threshold (T_ADD), mobile sends a handoff request to base station. Base station adds the new traffic channel; mobile combines signals from multiple base stations (selection or maximal ratio combining). When a pilot drops below T_DROP, it is removed.

7. Interference Management and Capacity Expansion

Co-Channel Interference (CCI)

Cause: Reuse of same frequency in geographically separated cells.
Reduction techniques:
- Frequency reuse optimization: Increase \( N \) (reduces capacity).
- Cell splitting: Smaller cells reduce co-channel distance for same \( N \).
- Sectoring: Directional antennas reduce number of interfering cells in first tier.
- Power control: Reduce transmit power to limit interference range.
- Directional antennas: Increase front-to-back ratio, reduce interference from non-desired directions.

Adjacent Channel Interference (ACI)

Cause: Imperfect receiver filters, near-far effect (close transmitter on adjacent channel bleeds into receiver).
Reduction: Sufficient frequency separation, high-quality filters, power control.

Capacity Expansion Techniques Summary

Cell splitting: Reduce cell radius, increase number of cells.
Sectoring: Use directional antennas (e.g., 3 × 120° or 6 × 60°).
Microcells/picocells: Deploy small cells in high-traffic hotspots (e.g., indoors, urban).
Multiple access scheme selection: CDMA offers higher capacity than FDMA/TDMA in interference-limited scenarios due to soft capacity and processing gain.
Tight frequency reuse: Use \( N=1 \) or \( N=3 \) with aggressive interference management (sectoring, power control).

8. Advanced Topics

Diversity Techniques

Spatial: Multiple antennas separated in space (e.g., MIMO).
Polarization: Dual-polarized antennas (vertical/horizontal).
Frequency: Same signal transmitted on multiple frequencies.
Time: Same signal transmitted in multiple time slots.

MIMO Systems

Spatial multiplexing: Multiple data streams transmitted simultaneously from multiple antennas, increasing capacity linearly with min(\( n_t, n_r \)).
Diversity gain: Improved reliability via space-time coding (e.g., Alamouti).
Beamforming: Directional transmission to desired user, reducing interference.

OFDM

Principle: Serial data stream divided into parallel low-rate streams, each modulated on orthogonal subcarriers.
Advantages: Robust against frequency-selective fading, efficient FFT implementation, cyclic prefix eliminates ISI.
Applications: 4G LTE, 5G NR, Wi-Fi (802.11a/g/n/ac/ax).

Wireless Network Generations

1G: Analog (AMPS, NMT), voice only.
2G: Digital (GSM, CDMA), voice + low-rate data (SMS).
3G: UMTS, CDMA2000, mobile broadband (up to 2 Mbps).
4G: LTE, OFDMA, all-IP, high data rates (100 Mbps mobile, 1 Gbps stationary).
5G: NR, massive MIMO, mmWave, network slicing, ultra-low latency, high capacity.

9. Calculations and Problem Solving

Coherence Bandwidth to Maximum Symbol Rate

Problem: If \( B_c = 100 \) kHz, maximum symbol rate for minimal ISI?
Solution:

\[ \boxed{R_s^{\text{max}} \approx B_c = 100 \text{ kHz}} \]

For flat fading, require \( B_s \ll B_c \), so symbol rate \( R_s = 1/T_s \) should satisfy \( R_s \lesssim B_c \).

FDMA Channel Count with Guard Bands

Problem: \( B_T = 12.5 \) MHz, \( B_{\text{guard}} = 10 \) kHz, \( B_c = 30 \) kHz. Find \( N \).
Solution:

\[ N = \left\lfloor \frac{B_T + B_{\text{guard}}}{B_c + B_{\text{guard}}} \right\rfloor = \left\lfloor \frac{12.5 \times 10^6 + 10 \times 10^3}{30 \times 10^3 + 10 \times 10^3} \right\rfloor = \left\lfloor \frac{12.51 \times 10^6}{40 \times 10^3} \right\rfloor = \left\lfloor 312.75 \right\rfloor = 312 \]

\boxed{N = 312 \text{ channels}}

CDMA Processing Gain and Bit Error Probability

Problem: IS-95, \( K=20 \) users, \( W=1.25 \) MHz, chip rate \( 1.2288 \) Mcps, \( R_b=13 \) kbps, \( E_b/N_0 = 7.8 \) dB. Find processing gain and \( P_b \).
Solution:

\[ G_p = \frac{W}{R_b} = \frac{1.25 \times 10^6}{13 \times 10^3} = 96.15 \quad (19.8 \text{ dB}) \]

Convert \( E_b/N_0 = 7.8 \) dB → linear: \( 10^{7.8/10} = 6.03 \).

Using formula with MAI:

\[ \text{SNR} = \frac{E_b/N_0}{1 + (K-1)(E_b/N_0)/G_p} = \frac{6.03}{1 + 19 \times 6.03 / 96.15} = \frac{6.03}{1 + 1.191} = \frac{6.03}{2.191} = 2.752 \]

\[ P_b = Q(\sqrt{2 \times 2.752}) = Q(\sqrt{5.504}) = Q(2.346) \approx 0.0095 \]

\boxed{G_p = 96.15}, \boxed{P_b \approx 0.0095}

Hilly Terrain: Incident and Slope Angles

Problem: \( H=100 \) m, \( h_t=50 \) m, \( h_r=3 \) m, \( d=5 \) km. Assume hill at midpoint (\( d_1 = d/2 = 2.5 \) km).
Solution:

\[ \theta_i = \tan^{-1}\left(\frac{H - h_t}{d_1}\right) = \tan^{-1}\left(\frac{50}{2500}\right) = \tan^{-1}(0.02) = 1.145^\circ \]

\[ \beta = \tan^{-1}\left(\frac{H}{d_1}\right) = \tan^{-1}\left(\frac{100}{2500}\right) = \tan^{-1}(0.04) = 2.290^\circ \]

\boxed{\theta_i = 1.145^\circ}, \boxed{\beta = 2.290^\circ}

[!TIP]

In hilly terrain calculations, clearly state assumptions (e.g., hill at midpoint). If the hill position is unspecified, assume midpoint for simplicity.