GSM Cell Planning Study Guide - Hexagonal Tessellation

1 Introduction to GSM Cell Planning

GSM (Global System for Mobile Communications) cell planning is the systematic process of designing and deploying cellular network infrastructure to provide optimal coverage, capacity, and quality of service. It involves determining the number, location, and configuration of base stations (BTS) to serve a given geographical area efficiently.

Key Objective: Maximize system capacity while minimizing infrastructure costs and interference, ensuring seamless connectivity for mobile subscribers.

Why Cell Planning Matters

Spectrum Efficiency: Limited frequency spectrum must be reused efficiently
Cost Optimization: Balance between network quality and infrastructure investment
Quality of Service: Maintain acceptable signal strength and minimize dropped calls
Future Expansion: Design scalable networks for growing subscriber base
Interference Management: Control co-channel and adjacent channel interference

2 The Cellular Concept & Hexagonal Tessellation

The fundamental principle of cellular communications, introduced by Bell Labs in 1947, is to divide the coverage area into hexagonal cells that tessellate perfectly without gaps or overlaps. This geometry provides the most efficient coverage with the fewest number of cells.

7-Cell Cluster Hexagonal Tessellation

The diagram below shows a true hexagonal tessellation forming a 7-cell cluster. Click on any cell to see its co-channel relationships and understand the reuse pattern.

2

Cell 2

3

Cell 3

1

Cell 1

C

Center

4

Cell 4

6

Cell 6

5

Cell 5

Center Cell

Cluster Cells (N=7)

Co-Channel Cells

Frequency Reuse Distance:
D = R × √(3N)
Where R = cell radius, N = cluster size (number of cells per cluster)

Hexagonal Geometry & Cluster Size (N)

The cluster size determines how frequently channels can be reused. Valid cluster sizes follow the hexagonal grid geometry where cells tessellate perfectly:

N = i² + ij + j²
Where i, j are non-negative integers (co-channel reuse parameters)
Move i cells along chain, turn 60°, move j cells to find co-channel cell

i	j	N (Cluster Size)	Reuse Ratio Q	Common Use
1	0	1	1.73	Omni-directional
1	1	3	3.00	3-cell reuse
2	0	4	3.46	4-cell reuse
2	1	7	4.58	Standard 7-cell (GSM)
2	2	12	6.00	12-cell reuse
3	0	9	5.20	9-cell reuse
3	1	13	6.24	Large cells
3	2	19	7.55	Dense urban

Tessellation Property: Regular hexagons are the only regular polygons (along with squares and triangles) that can tessellate the plane without gaps. Among these, hexagons provide the largest area-to-perimeter ratio, making them optimal for minimizing boundary effects and interference.

3 Frequency Planning & Reuse Patterns

Frequency planning is the strategic allocation of available spectrum to cells to maximize capacity while controlling interference. The co-channel reuse ratio (D/R) is critical for system performance.

Co-Channel Reuse Ratio

Q = D/R = √(3N)
Q = Co-channel reuse ratio (typically 4.6 to 11.0 for GSM)

Interactive Frequency Reuse Calculator

Cluster Size (N)

Cell Radius R (km)

Total Channels (C)

Reuse Distance D

9.17 km

Reuse Ratio Q

4.58

Channels per Cell

142

Important: Lower Q values (tighter reuse) increase capacity but also increase co-channel interference. GSM typically uses Q ≥ 4.6 for acceptable voice quality (C/I ≥ 9 dB).

Channel Allocation Strategies

Strategy	Description	Advantages	Disadvantages
Fixed Channel Allocation (FCA)	Permanent assignment of channels to cells	Simple, predictable	Inflexible, inefficient
Dynamic Channel Allocation (DCA)	Channels assigned on demand	High efficiency, adaptive	Complex, higher signaling
Hybrid Channel Allocation (HCA)	Fixed + dynamic channels	Balance of both	Moderate complexity
Borrowing Channel Allocation (BCA)	Borrow from adjacent cells	Handles hotspots	Increased interference risk

4 Cell Types & Hierarchical Architecture

Modern GSM networks employ a hierarchical cell structure (HCS) to balance coverage and capacity across different environments.

Cell Hierarchy

Macro
1-30 km

Micro
0.1-1 km

Pico
<100 m

Cell Type	Radius	Transmit Power	Application	Frequency Band
Macro Cell	1-30 km	20-40 W	Wide area coverage, highways	900 MHz (better propagation)
Micro Cell	0.1-1 km	1-5 W	Urban areas, streets	1800/1900 MHz
Pico Cell	<100 m	0.1-1 W	Indoors, hotspots	1800/1900/2100 MHz
Umbrella Cell	>30 km	High	Overlay for fast moving users	900 MHz

HCS Benefit: The layered approach allows frequency reuse at different layers. Micro cells can reuse frequencies allocated to distant macro cells due to physical separation and building attenuation.

5 Link Budget & Coverage Planning

Link budget calculations determine the maximum allowable path loss and thus the cell radius. This is fundamental to coverage planning.

Basic Link Budget Equation

MAPL = P_t + G_t + G_r - L_f - L_b - S_margin - R_s
MAPL = Maximum Allowable Path Loss (dB)

Link Budget Calculator

TX Power (dBm)

TX Antenna Gain (dBi)

RX Antenna Gain (dBi)

Feeder Loss (dB)

Body Loss (dB)

Shadow Margin (dB)

Receiver Sensitivity (dBm)

Frequency (MHz)

MAPL (Uplink)

154 dB

Cell Radius (km)

5.2 km

Using Okumura-Hata model for urban areas

Propagation Models

Model	Frequency Range	Environment	Accuracy
Okumura-Hata	150-1500 MHz	Macro cells, urban/suburban	±10 dB
COST-231 Hata	1500-2000 MHz	Extended for PCS/DCS	±10 dB
Walfisch-Ikegami	800-2000 MHz	Urban micro cells	±7 dB
Ray Tracing	Any	Micro/pico cells	±3 dB (site-specific)

6 Capacity Planning & Traffic Engineering

Capacity planning ensures the network can handle the expected subscriber load during busy hours. Erlang-B and Erlang-C formulas are used to dimension the network.

Erlang-B Formula (Blocked Calls Cleared)

B(N, A) = (A^N/N!) / (Σ_k=0^N A^k/k!)
Where A = offered traffic (Erlangs), N = number of channels, B = blocking probability

Erlang-B Capacity Calculator

Number of Channels (N)

Blocking Probability (%)

Traffic per User (mErl)

Supported Traffic

21.9 E

Supported Users

876

Utilization

73%

GSM Specific Capacity Factors

Time Slots: 8 per carrier (200 kHz), 1 for control, 7 for traffic
Half-Rate: Doubles capacity to 14 calls per carrier (lower voice quality)
Frequency Hopping: Improves C/I ratio, allows tighter reuse
Discontinuous Transmission (DTX): Reduces interference, saves MS power
Power Control: Reduces interference, extends battery life

Traffic Profile: Business districts peak during working hours (9-17), residential areas peak in evenings (19-23). Cell planning must account for these temporal variations.

7 Interference Management

Interference is the primary limiting factor in GSM capacity. The Carrier-to-Interference ratio (C/I) must be maintained above thresholds for acceptable service quality.

Types of Interference

Type	Source	GSM Requirement	Mitigation
Co-Channel	Same frequency, distant cells	C/I ≥ 9 dB	Reuse distance, power control
Adjacent Channel	Neighboring frequencies	C/A ≥ -9 dB (200 kHz)	Channel spacing, filtering
Intermodulation	Non-linearities in PA	Spurious < -70 dBc	Linear amplifiers, isolators
Co-Site	Same site, different sectors	Isolation > 30 dB	Antenna separation, filters

C/I Ratio Calculation

C/I = (R^-γ) / (Σ D_i^-γ)
Where γ = path loss exponent (typically 3-4), R = cell radius, D_i = distance to interferers

C/I Calculator

Reuse Ratio Q (D/R)

Path Loss Exponent (γ)

Number of Interferers

18.7 dB

✓ Acceptable for GSM voice (requires >9 dB)

8 Sectorization & Antenna Configuration

Sectorization divides a cell into angular sectors using directional antennas, reducing the number of interfering cells and improving C/I ratio, allowing tighter frequency reuse.

Sector Configurations

Configuration	Sectors	Antenna Pattern	Interfering Cells	Gain vs Omni
Omni	1	360°	6	Baseline
Bi-sector	2	180°	3-4	+3 dB C/I
Tri-sector (Standard)	3	120°/65°	2	+4.5 dB C/I
6-sector	6	60°/33°	1	+7 dB C/I

Sectorization Gain:
C/I improvement ≈ 10 log₁₀(6/n)
Where n = number of interfering cells in the first tier (2 for 3-sector, 1 for 6-sector)

Practical Impact: 3-sector sites are most common in GSM. They reduce interference by ~4.5 dB, allowing a 7-cell cluster to perform like a 4-cell cluster in terms of capacity, effectively increasing system capacity by 75%.

Antenna Downtilt

Electrical and mechanical downtilt control the coverage pattern and reduce interference to distant co-channel cells:

Mechanical Downtilt: Physically tilting the antenna (0-15°)
Electrical Downtilt: Phase shifting elements (0-10° typically)
Combined Effect: Reduces coverage overlap, improves C/I in dense deployments

9 The Cell Planning Process

Systematic cell planning follows a structured methodology from initial analysis to final optimization.

Planning Phases

1

Pre-Planning & Data Collection

Traffic forecasts, coverage requirements, terrain analysis, clutter classification, existing infrastructure audit

2

Nominal Cell Planning

Initial site selection, cluster planning, frequency allocation, coverage prediction using propagation models

3

Detailed Cell Planning

Site survey, antenna specification, height optimization, azimuth/downtilt planning, neighbor list definition

4

Implementation & Verification

Equipment installation, drive testing, coverage verification, parameter tuning, performance benchmarking

5

Optimization & Maintenance

Performance monitoring, handover optimization, capacity expansion, interference resolution, ongoing tuning

Key Planning Tools

Planet (Aircom): Industry standard for RF planning
Atoll (Forsk): Multi-technology planning (2G/3G/4G/5G)
Asset (TEOCO): Coverage and capacity optimization
MapInfo/ARCGIS: Geographical data processing
Matlab/Python: Custom algorithms and analysis

10 Key Takeaways & Summary

Core Principles

Hexagonal tessellation enables efficient coverage
Frequency reuse creates the cellular concept
Trade-off between capacity and quality (C/I)
Hierarchical cells balance coverage/capacity

Critical Formulas

D = R√(3N)
N = i² + ij + j²
Q = √(3N)
Erlang-B for capacity

Design Targets

C/I ≥ 9 dB (co-channel)
C/A ≥ -9 dB (adjacent)
Blocking ≤ 2% (Erlang-B)
Edge coverage ≥ -90 dBm

Exam Tips: Focus on understanding the relationship between cluster size (N), reuse distance (D), and co-channel interference (C/I). The hexagonal tessellation geometry is fundamental—remember that N = i² + ij + j² determines valid cluster sizes. Be prepared to calculate system capacity using Erlang-B tables and determine appropriate cell radius from link budgets. Remember that sectorization improves C/I by reducing the number of interfering cells in the first tier.

GSM Cell Planning