ECE4024 Chap.6 OFDM Design and Operation
OFDM Design and Operation
OFDM converts a frequency-selective channel into many narrowband subcarrier decisions when its timing, prefix and carrier-alignment conditions hold. This chapter follows the complete transmitter and receiver chain, derives the parameter links among bandwidth, sample time, useful duration and subcarrier spacing, and treats the cyclic prefix as both protection and overhead.
It also diagnoses the distinct effects of timing error, carrier offset and Doppler.
What this chapter covers
- 01
QAM mapping and parallel streams
- 02
IFFT generation of time-domain blocks
- 03
Orthogonal subcarrier spacing
- 04
Cyclic-prefix insertion and removal
- 05
FFT recovery and per-bin channel weights
- 06
Bandwidth, sample time and useful duration
- 07
Prefix efficiency and payload rate
- 08
Timing, carrier offset, Doppler and ICI
Worked example · free
Complete an OFDM parameter chain
- +1Sample period is T = 1/7.68 MHz = 0.130208 microseconds.
- +2Useful duration is 512T = 66.667 microseconds, so subcarrier spacing is 1/Tu = 15 kHz.
- +1Prefix duration is 64T = 8.333 microseconds.
- +1Total OFDM symbol duration is 66.667 + 8.333 = 75.000 microseconds.
- +2Prefix efficiency is 512/(512 + 64) = 0.8889, and overhead is 0.1111 or 11.11 percent.
- +1Check N times spacing: 512 x 15 kHz = 7.68 MHz.
Key terms
- Subcarrier orthogonality
- The cancellation of other subcarriers at each bin centre over the correct useful observation interval despite overlapping spectra.
- Useful duration
- The OFDM interval processed by the FFT after prefix removal, whose reciprocal is the subcarrier spacing.
- Prefix efficiency
- Useful samples divided by total transmitted samples in one block, quantifying the time cost of the cyclic prefix.
- Intercarrier interference
- Leakage among subcarriers caused when frequency or timing conditions destroy their orthogonality at the FFT output.
- Integer offset
- A carrier offset equal to a whole number of subcarrier spacings, which mainly relabels frequency bins under the ideal model.
- Fractional offset
- The noninteger part of carrier offset that spreads energy into neighbouring subcarriers and creates intercarrier interference.
OFDM Design and Operation FAQ
Why can OFDM subcarriers overlap without interfering?
Their spacing and observation interval make each other subcarrier land on a spectral zero at the desired bin centre. This cancellation depends on correct timing and frequency alignment, so overlap alone is not sufficient.
How long should the cyclic prefix be?
It should cover the relevant discrete channel memory or maximum delay under the model used. A longer prefix adds robustness but reduces time efficiency and payload rate because the copied samples carry no new information.
Why does OFDM simplify equalization?
With a sufficient prefix, the useful block follows a circular-convolution model. The FFT diagonalises that operation, leaving one complex channel coefficient and one equalizer weight per subcarrier rather than a long time-domain convolution.
What happens when Doppler is large?
Rapid channel variation and frequency shifts disrupt the assumed subcarrier orthogonality, producing intercarrier interference. Compare Doppler spread with subcarrier spacing and symbol duration with coherence time under the supplied criteria.
How do I avoid double-counting prefix overhead?
If a rate denominator already uses the total symbol duration including the prefix, do not multiply by prefix efficiency again. Use either a useful-rate expression with an efficiency factor or the full duration directly.
Exam move
Redraw the transmitter and receiver chain from memory, ensuring prefix removal comes before the FFT. Work full parameter chains rather than isolated formulas: bandwidth to sample time, FFT size to useful duration, reciprocal to spacing, channel delay to prefix and total duration to rate. Use N times subcarrier spacing as a check.
For impairments, distinguish insufficient prefix, timing inside the safe region, timing outside it, integer carrier offset, fractional offset and Doppler. Each breaks a different condition and calls for a different explanation. Build an OFDM parameter ledger with one row each for sampling rate, FFT size, sample interval, useful symbol time, subcarrier spacing, prefix samples, prefix time and total symbol time.
Derive rather than memorise the reciprocal pairs, then verify that FFT size times subcarrier spacing matches the sampled bandwidth under the stated allocation. Separate occupied data subcarriers from transform bins, because guards, direct current, pilots and control tones do not all carry payload.
When computing rate, count data-bearing tones and data-bearing OFDM symbols before multiplying by modulation bits and coding rate; divide by elapsed symbol or frame time only once. Draw the modulator from mapped complex symbols through the IFFT, parallel-to-serial conversion and cyclic-prefix insertion. Reverse the order at the receiver and place channel estimation before per-subcarrier equalization.
Explain orthogonality by the observation interval and frequency spacing, not by saying neighbouring spectra never overlap. For channel memory, compare the maximum relevant delay with prefix duration and state the consequence if the protection is too short.
Run separate diagnosis drills for timing offset, carrier-frequency offset and phase noise: identify which property is disturbed, what the FFT output looks like and which synchronization step targets it. Finally, contrast higher and lower subcarrier spacing. A shorter useful symbol can track latency or Doppler differently but changes prefix efficiency and tolerance to delay.
The answer should expose the trade-off instead of treating one numerology as universally robust.
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