The Remaining Problem
We’ve split data across subcarriers and made them orthogonal. But there’s still one issue.
Reflections can spill into the next symbol.
A reflected copy of symbol 1 arrives late and overlaps with symbol 2. This corrupts symbol 2’s data.
The Solution: Cyclic Prefix
Add guard time before each symbol. But not just any guard time.
Key idea: Copy the end of the symbol and put it at the beginning.
Why copy the end?
- An empty gap would break subcarrier orthogonality
- The receiver needs to see complete sine wave cycles
- By copying the end, the symbol wraps around on itself
- Any window of the correct length contains a valid symbol
How does this help?
The reflection from symbol 1 lands in the cyclic prefix of symbol 2, not in the actual data.
The receiver simply discards the prefix and extracts the clean symbol.
How Long Should the Prefix Be?
The cyclic prefix must be longer than the maximum reflection delay.
| Environment | Max Delay | Typical CP |
|---|---|---|
| Indoor WiFi | ~100 ns | 800 ns |
| Urban cellular | ~5 μs | 4.7 μs |
| Rural/hilly | ~20 μs | 16.7 μs |
If the reflection arrives within the CP duration, it won’t cause interference.
Worse environments need longer prefixes.
The Cost
The cyclic prefix is overhead. It carries no new information.
Example: WiFi 802.11a
- Symbol duration: 4 μs
- Cyclic prefix: 0.8 μs
- Overhead: 0.8 / 4.8 = 17%
We sacrifice some efficiency for immunity to reflections.
It’s a worthwhile trade-off. Without the CP, reflections would corrupt the data entirely.
Summary
Cyclic prefix = copy the end of symbol to the beginning as a guard time.
| Without CP | With CP |
|---|---|
| Reflections corrupt next symbol | Reflections hit the prefix |
| ISI problems | ISI eliminated |
| Maximum throughput | Slight overhead |
The cyclic prefix is the final piece that makes OFDM work in real-world multipath environments.