OFDM transmission step-by-step

 


OFDM transmission: step-by-step example

This OFDM tutorial walks through an example transmission via a frequency-selective channel and illustrates an ISI free detection. This practical course aims to illustrate OFDM basics leaving aside the complexity of multi carrier theory. The mission is to process a simple example of data transfer.

Basic OFDM system. A setup of 8 subcarriers and a cyclic prefix (CP) with discrete length of 2 is used. Noise and time-variant effects are neglected.
Echochannel Transfer function of a two paths channel
Frequency-selective channel - impulse response and transfer function of a two-paths channel.

Channel estimation

Before data can be transmitted a pilot sequence is sent to initialize the equalizer according to the channel.

OFDM signals when a pilot sequence is sent.
Initially a pilot sequence is sent. The equalizer coefficients are determined.

We step through the transmit chain following the parallel signal blocks.

End-to-end data transmission

Now a data sequence is processed in the same way but the detected signal is equalized.
Again, we step through the transmit chain following the parallel signal blocks.

All signals of an OFDM data transmission.
OFDM data transmission. The detected data are perfect as no noise was considered: d ( i )=d( i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqads gagaqbamaabmaabaGaamyAaaGaayjkaiaawMcaaiabg2da9iaadsga daqadaqaaiaadMgaaiaawIcacaGLPaaaaaa@3EEC@ .

OFDM transmission implements ISI free detection
OFDM transmission implements ISI free detection.

Now carry out the OFDM step-by-step lab experiment.

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In this experiment an OFDM data transmission via a frequency-selective channel is established. Using example values we walk through the signal chain, OFDM symbols and equalizer coefficients. Finally a data sequence can be detected ISI-free. Check the tutorial.

Channel estimation

Initially a pilot sequence d ( i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaads gacaGGOaGaamyAaiaacMcaaaa@3A4A@ is sent for channel estimation and equalizer initialization.

Received OFDM pilot symbol w(i) Two-path channel transfer function
The spectral representation of the pilot OFDM symbol w(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadE hacaGGOaGaamyAaiaacMcaaaa@3A5D@ represents the channel transfer function.

The equalizer coefficients are the reciprocal of w(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadE hacaGGOaGaamyAaiaacMcaaaa@3A5D@ .

End-to-end data transmission

Now a data sequence is sent. Continue the simulation (6 steps). Step through the transmit chain:

d(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaads gacaGGOaGaamyAaiaacMcaaaa@3A4A@ A block containing 8 data symbols (representing 16 bits) is generated and serial-to-parallel converted.
u(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw hacaGGOaGaamyAaiaacMcaaaa@3A5B@ It IFFT-transforms to an OFDM symbol.
s(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaado hacaGGOaGaamyAaiaacMcaaaa@3A59@ The guard interval (GI) is added, i.e. the OFDM symbol is extended by a cyclic prefix containing the last single symbols.
r(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadk hacaGGOaGaamyAaiaacMcaaaa@3A58@ The received symbol is degenerated by the channel.
v(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadA hacaGGOaGaamyAaiaacMcaaaa@3A5C@ The OFDM symbol is obtained by removing the guard interval, i.e. the first two single symbols.
w(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadE hacaGGOaGaamyAaiaacMcaaaa@3A5D@ (After further 8 steps.) It FFT-transforms to the spectral representation of the OFDM symbol.
d (i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqads gagaqbaiaacIcacaWGPbGaaiykaaaa@3A56@ The equalized signal represents the 8 data symbols.
Data symbols sent Data symbols detected OFDM transmission implements isi free detection
The data symbols are detected error free: d (i)=d(i) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqads gagaqbaiaacIcacaWGPbGaaiykaiabg2da9iaadsgacaGGOaGaamyA aiaacMcaaaa@3E8C@ . OFDM transmission implements ISI free detection.

Note that in this case no noise is present.

Next steps

The app recurrently transmits a fixed data sequence.

This simulation app implements a simple OFDM data transmission over a frequency-selective channel.

The app stops after the first symbol of the pilot sequence is sent.

Now a data sequence d( i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaads gadaqadaqaaiaadMgaaiaawIcacaGLPaaaaaa@3A7A@ is sent.

Key Action
F5 Process one simulation step.
F6 Process 10 simulation steps.

Mouse Action

Left click on Equalizer.

 Eq

Equalizer

Left click on Coefficients.

Coefficients Measure

coefficients

Right click on d ( i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqads gagaqbamaabmaabaGaamyAaaGaayjkaiaawMcaaaaa@3A86@

Equalizer

select measure

Select Constellation diagram.

select constellation diagram

constellation diagram

Left click on bullet representing the digital source.

source

And switch to Random.

digital signal properties

Left click on Two-path channel.

Echo

Modify the channel to simulate time selective channel variation.

Two-path channel properties

Simulation - Setup (F12)

simulation setup

Modify the initial echo delay of the channel and press OK to restart the simulation.