---
title: "CCI/ACI, reuse ratio proof and channels per cell"
subject: "Wireless Communication"
chapter: 2
key: "semester_7/wireless_communication:cci-aci-reuse-duplex-channels"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/cci-aci-reuse-duplex-channels
site: BCT Engineering
---

# CCI/ACI, reuse ratio proof and channels per cell

Wireless Communication · Chapter 2: Cellular Mobile Communication Concepts

- Asked in: 2070 Bhadra, 3+4+3 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/cci-aci-reuse-duplex-channels
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-2

## Question

Explain the difference between co-channel and adjacent channel interference. Prove that the co-channel reuse ratio is given by Q = √(3N), where N = i² + ij + j² is the cluster size. If 20 MHz of total spectrum is allocated for a duplex (i.e. bidirectional) wireless cellular system and each simplex (i.e. one-way) channel has 25 KHz of bandwidth, find a) The number of duplex channels, and b) The total number of channels per cell, assuming a cluster size of N = 4.

## Short answer

Co-channel interference comes from cells sharing the same frequency, adjacent channel interference from neighbouring frequencies leaking through filters. The co-channel reuse ratio is Q = √(3N). With 20 MHz total and 25 kHz simplex channels: 400 duplex channels; per cell (N = 4) = 100 duplex channels.

## Answer

#### Co-channel vs adjacent channel interference
**Co-channel interference (CCI)** is caused by signals from other cells that use the *same* frequency. **Adjacent channel interference (ACI)** is caused by signals on *neighbouring* frequencies that leak into the passband of the wanted channel.

| Point | Co-channel interference | Adjacent channel interference |
|---|---|---|
| Source | Co-channel cells (same frequency) | Neighbouring frequency channels |
| Cause | Frequency reuse | Imperfect receiver filters |
| Can more transmit power fix it? | No; S/I is independent of transmit power and depends on D/R | No; a strong nearby adjacent-channel user makes it worse (near–far effect) |
| Main measure | S/I = Qⁿ/i₀ | Selectivity of filters |
| Reduction | Larger N (larger D/R), sectoring, directional antennas | Better filtering, careful channel assignment, guard bands, power control |
| Relation to cluster | Depends on reuse ratio Q = D/R | Avoid adjacent channels in the same cell |

#### Proof that Q = √(3N)
To reach the nearest co-channel cell, move *i* cells along a chain of hexagons, turn 60° and move *j* cells. The centre-to-centre distance of adjacent hexagons is √3R. Applying the cosine rule (the angle between the two moves is 120°):

```text
D² = (i√3R)² + (j√3R)² − 2(i√3R)(j√3R)cos120°
   = 3R²(i² + ij + j²) = 3R²N
D  = R√(3N)
Q  = D/R = √(3N)
```

#### Channel calculation
Given: total spectrum = 20 MHz, simplex channel = 25 kHz, so a duplex channel needs 2 × 25 = 50 kHz.

```text
a) Duplex channels = 20 MHz / 50 kHz
                   = 20 000 kHz / 50 kHz = 400

b) Channels per cell (N = 4) = 400 / 4 = 100
```

**Answer: a) 400 duplex channels; b) 100 duplex channels per cell.**

## Check yourself

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

1. Co-channel interference is caused by:
   A. Other cells using the same frequency, a result of frequency reuse
   B. Thermal noise in the receiver
   C. Leakage from neighbouring frequencies due to poor filters
   D. Doppler shift
   Answer: A. CCI comes from co-channel cells; ACI comes from adjacent frequencies leaking in. (Key point: CCI versus ACI)

2. Which measure mainly reduces adjacent channel interference?
   A. Better filtering, careful channel assignment and guard bands
   B. Increasing D/R
   C. Larger cluster size
   D. Cell splitting
   Answer: A. ACI is due to imperfect receiver filters and near-far effect, so filtering and assignment help. (Key point: ACI reduction)

3. With 20 MHz total and 25 kHz simplex channels, how many duplex channels are there?
   A. 400
   B. 100
   C. 200
   D. 800
   Answer: A. A duplex channel needs 50 kHz, so 20 000/50 = 400. (Key point: Duplex channels)

4. With 400 duplex channels and N = 4, how many channels are in each cell?
   A. 1600
   B. 400
   C. 80
   D. 100
   Answer: D. Channels per cell = 400/4 = 100. (Key point: Channels per cell)

## 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
- [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
- [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 co-channel reuse ratio](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-reuse-cochannel-reuse-ratio) — Wireless Communication, chapter 2
- [Prove Q = √3N; optimal N for 15 dB S/I (n = 4)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Areuse-ratio-optimal-n-n4) — Wireless Communication, chapter 2