---
title: "Frequency reuse and co-channel reuse ratio"
subject: "Wireless Communication"
chapter: 2
key: "semester_7/wireless_communication:frequency-reuse-cochannel-reuse-ratio"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/frequency-reuse-cochannel-reuse-ratio
site: BCT Engineering
---

# Frequency reuse and co-channel reuse ratio

Wireless Communication · Chapter 2: Cellular Mobile Communication Concepts

- Asked in: 2072 Magh, 6 marks
- Video: [Frequency Reuse Factor | Co-Channel Interference & Signal To Interference Ratio](https://www.youtube.com/watch?v=JfIIiecbEg8) — ECIT Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/frequency-reuse-cochannel-reuse-ratio
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-2

## Question

What do you understand by frequency reuse concept? Define co-channel reuse ratio in details.

## Short answer

Frequency reuse assigns the same channel set to cells far enough apart to limit co-channel interference, increasing capacity. The co-channel reuse ratio Q = D/R = √(3N) for hexagons, where N = i²+ij+j². Larger Q reduces interference but lowers capacity; it directly determines S/I = Qⁿ / i₀.

## Answer

**Frequency reuse** is the technique of using the same set of radio channels in different cells that are far enough apart, so that co-channel interference stays within a tolerable limit. It lets a cellular system with a limited spectrum serve a very large number of users.

#### Frequency reuse concept
- The total *S* duplex channels are divided into *N* groups. Each cell in a group of *N* neighbouring cells (a **cluster**) gets *k = S/N* channels, so a cluster uses the full spectrum once.
- The cluster is then repeated across the service area. Cells with the same letter (same channel set) are **co-channel cells**.
- Each base station uses low power and antennas placed so that coverage stays roughly inside its own cell.
- For hexagonal cells, cluster size is N = i² + ij + j² (i, j = 0, 1, 2, …), so N = 1, 3, 4, 7, 9, 12, …
- If the cluster is repeated *M* times, total capacity is C = M·k·N = M·S. Smaller N means more repetitions and more capacity, but co-channel cells come closer and interference increases.
- The **frequency reuse factor** is 1/N, since each cell gets 1/N of the channels.

```text
      B   C          B   C
    G   A   D  ...  G   A   D
      F   E          F   E
   cluster 1 (N=7)  cluster 2
  Cell A in both clusters uses the same channel set
```

#### Co-channel reuse ratio
The **co-channel reuse ratio** *Q* is the ratio of the distance *D* between the centres of the nearest co-channel cells to the cell radius *R*:

```text
Q = D / R = √(3N)
```

- D = R√(3N) for hexagonal geometry, so *Q* depends only on cluster size.
- **Large Q** (large N): co-channel cells are far apart, so co-channel interference is low and transmission quality is better, but each cell has fewer channels and capacity is lower.
- **Small Q** (small N): more channels per cell and higher capacity, but more co-channel interference.
- *Q* links directly to signal-to-interference ratio. With path loss exponent *n* and *i₀* first-tier interferers: S/I ≈ (√(3N))ⁿ / i₀ = Qⁿ / i₀.

| N | Q = √(3N) |
|---|---|
| 3 | 3.00 |
| 4 | 3.46 |
| 7 | 4.58 |
| 12 | 6.00 |

**Example:** for an S/I requirement of 18 dB with n = 4 and i₀ = 6, N = 7 (Q = 4.58) gives S/I = 4.58⁴/6 ≈ 73.5 = 18.66 dB, which is acceptable.

## Check yourself

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

1. What is the main idea of frequency reuse in a cellular system?
   A. Giving every cell a unique frequency band so there is never interference
   B. Using the same channels in different cells far enough apart that co-channel interference is tolerable
   C. Using one high-power base station for the whole area
   D. Switching channels in a cell every few seconds
   Answer: B. Reusing the same channel set in distant cells lets limited spectrum serve many users while keeping interference acceptable. (Key point: Frequency reuse idea)

2. With S total duplex channels divided over a cluster of N cells, how many channels does each cell get?
   A. S/(N-1)
   B. S/N
   C. S x N
   D. N/S
   Answer: B. Each cell in the cluster gets k = S/N channels, so the cluster uses the full spectrum once. (Key point: Channels per cell)

3. For hexagonal cells, the co-channel reuse ratio Q is given by:
   A. Q = sqrt(3N)
   B. Q = 3N
   C. Q = N/3
   D. Q = sqrt(N)
   Answer: A. Q = D/R = sqrt(3N) for hexagonal geometry, so it depends only on cluster size. (Key point: Co-channel reuse ratio)

4. What happens when the cluster size N is made smaller?
   A. Capacity rises but co-channel interference increases
   B. Q rises and interference falls
   C. Capacity falls and interference rises
   D. Neither capacity nor interference changes
   Answer: A. A smaller N gives more channels per cell and more reuse (higher capacity) but co-channel cells come closer, so interference grows. (Key point: Effect of small N)

## Related in Wireless Communication

- [CCI vs ACI and co-channel reuse ratio proof](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acci-aci-prove-reuse-ratio) — Wireless Communication, chapter 2
- [Derivation of co-channel reuse ratio](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aderive-cochannel-reuse-ratio) — Wireless Communication, chapter 2
- [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
- [Frequency reuse and channel assignment strategies](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-reuse-channel-assignment) — Wireless Communication, chapter 2
- [CCI/ACI, reuse ratio proof and channels per cell](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acci-aci-reuse-duplex-channels) — Wireless Communication, chapter 2
- [Co-channel and adjacent channel interference](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acochannel-adjacent-interference-terms) — Wireless Communication, chapter 2

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