GSM Capacity Calculations

Quick Refresher

Before we calculate, let’s recall what these terms mean:

• Spectrum - The chunk of radio frequencies the operator owns (e.g., 7 MHz)
• Carrier - One 200 kHz slice of that spectrum (a single channel)
• Cell - The area covered by one tower
• Cluster - A group of cells that together use all the carriers once
• Carriers per cell - How many carriers a single tower gets to use

With frequency reuse, each cell only gets some of the carriers. Neighboring cells get different ones to avoid interference.

The Big Question

You’re a mobile operator. You’ve been given spectrum. How many phone calls can each cell handle?

This is the fundamental capacity question in cellular networks.

The Three-Step Chain

Capacity flows through three conversions:

$\text{Spectrum} \rightarrow \text{Carriers} \rightarrow \text{Carriers per cell} \rightarrow \text{Calls per cell}$

Each step is simple. Let’s walk through them.

Step 1: Spectrum → Carriers

Your spectrum gets divided into carriers. Each GSM carrier is 200 kHz wide.

$\text{Total carriers} = \frac{\text{Spectrum (MHz)}}{0.2 \text{ MHz}}$

Think of it like cutting a rope into pieces. A 7-meter rope cut into 0.2-meter pieces gives you 35 pieces.

Example: You have 7 MHz of spectrum.

$\text{Carriers} = \frac{7}{0.2} = 35 \text{ carriers}$

Step 2: Carriers → Carriers per Cell

You can’t use all carriers in every cell. That would cause interference between neighboring cells using the same frequency.

With frequency reuse, carriers are divided among cells in a cluster.

$\text{Carriers per cell} = \frac{\text{Total carriers}}{\text{Cluster size}}$

Example: 35 carriers with a 7-cell cluster.

$\text{Carriers per cell} = \frac{35}{7} = 5 \text{ carriers}$

Each cell gets 5 carriers. Neighboring cells get different carriers.

If you get a fractional result, round down. You can’t have half a carrier.

Step 3: Carriers per Cell → Calls per Cell

Each carrier supports 8 users via TDMA (8 time slots per frame).

$\text{Calls per cell} = \text{Carriers per cell} \times 8$

Example: 5 carriers per cell.

$\text{Calls} = 5 \times 8 = 40 \text{ calls}$

Control Channel Overhead

Not all 8 slots carry voice. Some slots are reserved for control channels:

• BCCH - Broadcast channel (cell info)
• CCCH - Common control (paging, access)
• SDCCH - Signaling during call setup

Typically, 1-2 carriers worth of slots go to control.

$\text{Speech calls} = \text{Total slots} - \text{Control slots}$

For a cell with 5 carriers (40 slots), expect roughly 32-38 speech calls after control overhead.

The Complete Formula

Putting it all together:

$\text{Speech calls per cell} = \left( \frac{\text{Spectrum}}{0.2} \div \text{Cluster size} \right) \times 8 - \text{Control}$

What About “2× Spectrum”?

When you see 2×7 MHz, it means:

• 7 MHz for uplink (phone → tower)
• 7 MHz for downlink (tower → phone)

For capacity calculations, use just one direction (they’re paired). So “2×7 MHz” means you work with 7 MHz.

Worked Example 1

A GSM operator is allocated 2×7 MHz of spectrum. The technical parameters are:

• TDMA and FDD
• 8 time slots per TDMA frame
• Carrier bandwidth = 200 kHz
• Cluster size = 7 cells

(i) What is the number of carriers per cell? (ii) What is the maximum number of speech calls possible in a cell?

Solution:

(i) Carriers per cell:

$\text{Total carriers} = \frac{7 \text{ MHz}}{0.2 \text{ MHz}} = 35$

$\text{Carriers per cell} = \frac{35}{7} = \textbf{5 carriers}$

(ii) Speech calls per cell:

$\text{Total slots} = 5 \times 8 = 40$

After subtracting control channel overhead: ~38 speech calls

Worked Example 2

A GSM operator is allocated 2×8 MHz of spectrum. The technical parameters are:

• TDMA and FDD
• 8 time slots per TDMA frame
• Carrier bandwidth = 200 kHz
• Cluster size = 7 cells

(i) What is the number of carriers per cell? (ii) What is the maximum number of speech calls possible in a cell?

Solution:

(i) Carriers per cell:

$\text{Total carriers} = \frac{8 \text{ MHz}}{0.2 \text{ MHz}} = 40$

$\text{Carriers per cell} = \frac{40}{7} = 5.71 \rightarrow \textbf{5 carriers}$

We round down - you can’t have a fraction of a carrier.

(ii) Speech calls per cell:

$\text{Total slots} = 5 \times 8 = 40$

After subtracting control channel overhead: ~38 speech calls

Worked Example 3

A GSM operator is allocated 2×6 MHz of spectrum. The technical parameters are:

• TDMA and FDD
• 8 time slots per TDMA frame
• Carrier bandwidth = 200 kHz
• Cluster size = 7 cells

(i) What is the number of carriers per cell? (ii) What is the maximum number of speech calls possible in a cell?

Solution:

(i) Carriers per cell:

$\text{Total carriers} = \frac{6 \text{ MHz}}{0.2 \text{ MHz}} = 30$

$\text{Carriers per cell} = \frac{30}{7} = 4.28 \rightarrow \textbf{4 carriers}$

(ii) Speech calls per cell:

$\text{Total slots} = 4 \times 8 = 32$

After subtracting control channel overhead: ~30 speech calls

Why This Matters

This calculation answers real business questions:

• Network planning: How many cells do we need for 10,000 users?
• Spectrum value: Is buying 1 MHz more spectrum worth it?
• Technology comparison: How does GSM capacity compare to 3G?

Every extra MHz of spectrum or every improvement in cluster size directly translates to more revenue for operators.

Key Numbers to Remember