ELEC5508 Chap.3 Diversity and OFDM
Diversity and OFDM
This chapter separates reliability from equalisation. Diversity creates independently fading chances across time, frequency or antennas, while OFDM reorganises a frequency-selective channel into parallel subcarriers. The cyclic prefix protects the useful FFT window only when it covers channel memory, and pilot density must respect coherence in both time and frequency. Correlation is the boundary linking these topics.
Repeating a symbol across highly correlated branches does not create the same reliability as using independent fades, and placing pilots too sparsely assumes correlation that the channel may not possess. OFDM simplifies the channel into per-subcarrier gains but does not remove fading. Coding, mapping or combining must still spread information if frequency diversity is desired.
Synchronisation also remains essential because timing and carrier offsets can break orthogonality even when prefix length is correct.
What this chapter covers
- 01
Diversity order and independent branches
- 02
Correlation and covariance rank
- 03
Time, frequency and antenna diversity
- 04
OFDM transforms and orthogonal subcarriers
- 05
Cyclic-prefix sizing and overhead
- 06
Pilot placement and one-tap equalisation
Worked example · free
Size a cyclic prefix
- +1Spacing is 2.4 MHz divided by 192, or 12.5 kHz.
- +1Useful time is 1/12.5 kHz, or 80 microseconds.
- +1Sample time is 80/192 = 0.4167 microseconds.
- +1Round 18/0.4167 upward to 44 samples, giving 18.33 microseconds.
- +1Overhead is 18.33/98.33 = 18.64%.
Key terms
- Diversity order
- The number of independently fading dimensions governing high-SNR error decay.
- Antenna diversity
- Reliability gain from combining or coding across spatially distinct channel branches.
- OFDM
- Multicarrier modulation that uses transforms to create orthogonal narrowband subchannels.
- Pilot
- A known transmitted value used to estimate or track the channel.
- One-tap equalisation
- Per-subcarrier correction using one complex gain after OFDM diagonalisation.
Diversity and OFDM FAQ
Does every extra antenna add diversity?
No. Diversity depends on independent channel dimensions, not hardware count alone. Strong correlation can reduce covariance rank, so several antennas may behave like fewer independent branches. Antenna placement and propagation geometry determine the effective gain.
Why does OFDM need a cyclic prefix?
The prefix absorbs multipath channel memory before the useful FFT window. If its duration covers the relevant delay spread, linear convolution appears circular over the useful samples and each subcarrier can be equalised with one complex coefficient.
Does OFDM itself provide frequency diversity?
OFDM exposes frequency-selective gains across subcarriers. A symbol gains frequency diversity only when coding, repetition or mapping spreads its information across independently faded frequencies. Sending unrelated uncoded symbols on separate subcarriers does not protect each symbol from its own fade.
What checks prevent common OFDM design errors?
Calculate subcarrier spacing, useful symbol time, sample time, required prefix samples and prefix overhead in that order. Round the prefix upward when a whole number of samples is required, then verify that its duration covers the intended channel memory. Keep that delay check separate from Doppler and frequency-offset checks: a long prefix does not stop the channel varying within a symbol.
Next compare subcarrier width with coherence bandwidth and the symbol or pilot interval with coherence time. If claiming diversity, identify the coding, repetition or mapping that spreads information across independent fades. When comparing schemes, hold total transmitted energy fixed and distinguish diversity slope from power gain, coding gain and synchronisation effects.
Exam move
Keep diversity and OFDM in separate columns: reliability mechanism versus equalisation structure. Recompute spacing, symbol time, sample time and prefix samples until the rounding and units are automatic. For diversity, make a three-row table for time, frequency and antennas. In each row name the independence condition, the physical cost and the receiver operation.
Add covariance rank as the test that distinguishes nominal branches from effective diversity. Practise explaining why a repeated observation across correlated paths provides less protection than independently faded observations. For OFDM, draw the transmitter and receiver chain from subcarrier symbols through IFFT, prefix insertion, channel, prefix removal and FFT. Annotate what can fail at each boundary.
Work prefix problems in the same order every time: bandwidth divided by subcarrier count, reciprocal spacing, sample time, delay divided by sample time, round upward, then compute overhead. After solving, test delay and Doppler separately. Prefix length addresses channel memory; it does not repair rapid variation or frequency offset. For laboratory questions, predict the constellation and BER effect before running the model.
Hold transmitted energy constant when comparing repetition, space-time coding or antenna cases, and explain whether a curve change represents diversity slope, power gain, coding gain or a synchronisation defect. Finish by deciding how pilots should be spaced across time and frequency from the two coherence scales.
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