Guard interval and ISI-free OFDM transmission

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.

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

The guard time exceeds the channel's maximum delay spread: $T_{G} \geq τ_{\max}$ .

Guard time and channel's maximum delay spread.

Start

In this example the guard time is $T_{G} = 0.8 μ s$ . 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	${T^{'}}_{S} = 4 μ s$
Guard interval duration	$T_{G} = \frac{N_{G} {T^{'}}_{s}}{N + N_{G}} = 0.8 μ s$

The simulation uses a two-path channel and starts with a maximum excess delay $τ_{\max} = 0.8 μ s$ . This results in an ISI-free detection.

ISI free detection for

τ_{\max} = T_{G} = 0.8 μ 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” (

τ_{\max}

) and click on “OK”.

Approve the ISI free condition $T_{G} \geq τ_{\max}$ for different echo delays.

ISI for

τ_{\max} > T_{G}

τ_{\max} = 0.85 μ s

and

τ_{\max} = 1 μ s

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

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

Next steps

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

Guard interval - alternative simulation setup

Is this transmission ISI-free?

Check the ISI-free condition $T_{G} \geq τ_{\max}$ !

This simulation app implements an OFDM transmission using a guard interval.

It starts with an ISI-free detection as the condition is valid:

T_{G} \geq τ_{\max}

Guard time $T_{G} = 0.8 μ s$ .
Channel echo delay $τ_{\max} = 0.8 μ s$ .

Constellation diagram: ISI-free if

T_{G} \geq τ_{\max}

and ISI if

T_{G} < τ_{\max}

Mouse	Action
Simulation - Setup (F12)	Modify the initial echo delay $τ_{\max}$ of the channel and press OK to restart the simulation.
Simulation - Setup (F12)	Select a different OFDM configuration and change the echo delay $τ_{\max}$ .

Mouse

Action

Simulation - Setup (F12)

Modify the initial echo delay $τ_{\max}$ of the channel and press OK to restart the simulation.

Simulation - Setup (F12)

Select a different OFDM configuration and change the echo delay

τ_{\max}