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# Guard interval and ISI-free OFDM transmission

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This experiment illustrates the ISI-free transmission of OFDM systems under this condition:

The guard time exceeds the channel's maximum delay spread: ${T}_{G}\ge {\tau }_{\mathrm{max}}$ .

OFDM symbols are generated by an IFFT with size $N$. A guard interval (GI) is appended at the start of each symbol. This cyclic prefix comprises the last ${N}_{G}$ samples of each symbol.

## Start

In this example the guard time is ${T}_{G}=0.8\mu s$ . Further settings from IEEE 802.11ac are used.

 Number of subcarriers, FFT size $N=64$ Discrete length of the guard interval ${N}_{G}=16$ Data subcarriers ${N}_{C}=52$ Pilot subcarriers ${N}_{P}=4$ Extended OFDM symbol period ${{T}^{\prime }}_{S}=4\mu s$ Guard interval duration ${T}_{G}=\frac{{N}_{G}{{T}^{\prime }}_{s}}{N+{N}_{G}}=0.8\mu s$

The simulation uses a single echo channel and starts with ${\tau }_{\mathrm{max}}=0.8\mu s$ (echo delay). This results in an ISI-free detection.

ISI free detection for ${\tau }_{\mathrm{max}}={T}_{G}=0.8\mu s$ .

## Experiment

Now, modify the echo delay. When restarting the simulation the channel estimation and equalizer initialization is performed.

Simulation - Setup (F12): modify “Echo delay” ( ${\tau }_{\mathrm{max}}$ ) and click on “OK”.

Approve the ISI free condition ${T}_{G}\ge {\tau }_{\mathrm{max}}$ for different echo delays.

ISI for ${\tau }_{\mathrm{max}}>{T}_{G}$ : ${\tau }_{\mathrm{max}}=0.85\mu s$ and ${\tau }_{\mathrm{max}}=1\mu s$

Note that the transmission sampling time is $0.05\mu s$ and thus the echo delay can be adjusted in this granularity, e.g. ${\tau }_{\mathrm{max}}=0.75,0.80,0.85,0.90\mu s$.

The initial setup uses 52 data QPSK symbols (2 bit) per OFDM symbol (4us). This yields to a source symbol duration of ${T}_{D}=0.0769\mu s$  and a bit rate of 26 Mbit.

## Next steps

Now select a different OFDM configuration in Simulation - Setup (F12).

Is this transmission ISI-free?

Check the ISI-free condition ${T}_{G}\ge {\tau }_{\mathrm{max}}$ !