---
title: "Numerical: co-channel distance for 7-cell reuse"
subject: "Wireless Communication"
chapter: 2
key: "semester_7/wireless_communication:cochannel-distance-seven-cell"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/cochannel-distance-seven-cell
site: BCT Engineering
---

# Numerical: co-channel distance for 7-cell reuse

Wireless Communication · Chapter 2: Cellular Mobile Communication Concepts

- Asked in: 2074 Bhadra, 4 marks
- Video: [Lecture 3: Proof of Frequency Reuse Factor](https://www.youtube.com/watch?v=GrUqu7ryRr4) — Learning Express
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/cochannel-distance-seven-cell
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-2

## Question

For a seven cell reuse pattern, find the minimum distance between centers of co-channel cells. Area of each cell is uniform and is equal to 23 square km.

## Short answer

Cell radius from hexagon area 23 km² is R=√(23/2.598)=2.975 km. With N=7, reuse ratio is √21=4.583, so the minimum co-channel distance is D=4.583×2.975=13.63 km.

## Answer

**Given:** N = 7, area of each hexagonal cell = 23 km².

**Step 1: Cell radius from hexagon area**
```text
A = (3√3/2) R² = 2.598 R²
R² = 23 / 2.598 = 8.853
R  = 2.975 km
```

**Step 2: Co-channel reuse ratio**
```text
Q = √(3N) = √21 = 4.583
```

**Step 3: Minimum co-channel distance**
```text
D = Q × R = 4.583 × 2.975 = 13.63 km
```

**Answer: The minimum distance between centres of co-channel cells is about 13.63 km.**

## Check yourself

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

1. The area of a hexagonal cell of radius R is:
   A. pi R^2
   B. (3 sqrt3 / 2) R^2 = 2.598 R^2
   C. 3R^2
   D. 6R^2
   Answer: B. Used to find R from the cell area. (Key point: Hexagon area)

2. With area 23 km^2, R is about:
   A. 8.85 km
   B. 4.8 km
   C. 1.5 km
   D. 2.975 km
   Answer: D. R^2 = 23/2.598 = 8.853, R = 2.975. (Key point: Cell radius)

3. For N = 7, Q is:
   A. sqrt(21) = 4.583
   B. 7
   C. 3.46
   D. 6
   Answer: A. Q = sqrt(3N). (Key point: Q for N=7)

4. The minimum distance between co-channel centres is:
   A. 23 km
   B. 4.58 km
   C. 13.63 km
   D. 8.85 km
   Answer: C. D = Q R = 4.583 x 2.975. (Key point: Distance)

## Related in Wireless Communication

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- [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

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