---
title: "Numerical: cluster size and users in service area"
subject: "Wireless Communication"
chapter: 2
key: "semester_7/wireless_communication:cluster-size-users-service-area"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/cluster-size-users-service-area
site: BCT Engineering
---

# Numerical: cluster size and users in service area

Wireless Communication · Chapter 2: Cellular Mobile Communication Concepts

- Asked in: 2073 Magh, 6 marks
- Video: [How to Calculate Cluster Size in Cellular Network](https://www.youtube.com/watch?v=NeddPLdVI68) — HowTo
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/cluster-size-users-service-area
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-2

## Question

Determine: a) the cell cluster size b) the number of cell clusters in the service area c) the maximum number of users in service area at any instant. [No data is given for this question in the paper as printed.]

## Short answer

Assuming typical values (area 1765 km², R=1.5 km, S=660, S/I=18 dB, n=4), N=7 satisfies the requirement. Then, 302 cells, about 43 clusters. Maximum simultaneous users = (660/7)×302 ≈ 28,400.

## Answer

The paper as printed does not give the data for this question, so a typical set of values is **assumed** below to show the full method:

- Service area = 1765 km², cell radius R = 1.5 km (hexagonal cells)
- Required S/I = 18 dB, path loss exponent n = 4, omnidirectional antennas (i₀ = 6)
- Total available duplex channels S = 660 (e.g. 33 MHz with 2 × 25 kHz per duplex channel)

#### a) Cell cluster size
Find the smallest valid N (N = i² + ij + j²) with S/I = (√(3N))ⁿ / i₀ ≥ 18 dB:
```text
N = 3 : (√9)⁴ / 6  = 13.5  → 11.30 dB ✗
N = 4 : (√12)⁴ / 6 = 24.0  → 13.80 dB ✗
N = 7 : (√21)⁴ / 6 = 73.5  → 18.66 dB ✓
```
**N = 7.**

#### b) Number of cell clusters in the service area
```text
Area of one cell = 2.598 R² = 2.598 × 1.5² = 5.846 km²
Number of cells  = 1765 / 5.846 = 301.9 ≈ 302 cells
Number of clusters = 302 / 7 = 43.1 ≈ 43 clusters
```

#### c) Maximum number of users at any instant
```text
Channels per cell = 660 / 7 = 94.3 ≈ 94
Max users = 94 × 302 = 28 388
(or by clusters: 43 × 660 = 28 380)
```
**About 28 400 users can be served simultaneously** (one user per channel).

General method: (1) choose N from the S/I requirement, (2) number of cells = area / (2.598 R²), clusters = cells / N, (3) maximum simultaneous users = (S/N) × number of cells = M × S.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The cluster size is chosen as:
   A. The largest valid N
   B. The smallest valid N = i^2+ij+j^2 meeting the required S/I
   C. Any N
   D. N = S
   Answer: B. Here N = 7 gives 18.66 dB; N = 4 gives only 13.8 dB. (Key point: Choosing N)

2. N = 4 is rejected because:
   A. It is not a valid cluster size
   B. It has too few channels
   C. It gives 18.7 dB
   D. S/I = 13.8 dB, below 18 dB
   Answer: D. N = 4 is valid but fails. (Key point: Why not N=4)

3. With area 1765 km^2 and a cell area of 5.846 km^2, the number of cells is about:
   A. 302
   B. 43
   C. 1765
   D. 28 388
   Answer: A. 1765/5.846 = 301.9. (Key point: Cells)

4. The number of clusters is:
   A. 302 x 7
   B. 302
   C. 302/7 = about 43
   D. 94
   Answer: C. Cells divided by N. (Key point: Clusters)

5. With 660 channels and N = 7, channels per cell is:
   A. 660
   B. about 94
   C. 7
   D. 4620
   Answer: B. 660/7 = 94.3. (Key point: Channels per cell)

6. Maximum simultaneous users is:
   A. 660
   B. 302
   C. 94
   D. about 28 400 (channels per cell x cells)
   Answer: D. 94 x 302 = 28 388. (Key point: Max users)

## Related in Wireless Communication

- [Numerical: 32-cell system area and channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-32-cells-capacity) — Wireless Communication, chapter 2
- [Numerical: 12-cell system capacity at 2% GOS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-capacity-12-cell-system) — Wireless Communication, chapter 2
- [Numerical: maximum cell radius using Hata model](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ahata-max-cell-radius) — Wireless Communication, chapter 3
- [Numerical: users supported and market penetration](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amarket-penetration-erlang) — Wireless Communication, chapter 2, asked 2×
- [Numerical: N-TDMA simultaneous users](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Antdma-simultaneous-users) — Wireless Communication, chapter 7
- [Numerical: co-channel distance for 7-cell reuse](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acochannel-distance-seven-cell) — Wireless Communication, chapter 2

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