- 2070 Bhadra · 3+4+3 marks
CCI/ACI, reuse ratio proof and channels per cell
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.
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.
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°):
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.
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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