# Channel tracking in an OFDM system

Started by July 28, 2008
```Hello,

I am trying to design an adaptive equalizer for an OFDM system which has
an extremely low symbol rate. I have a question regarding this.

The transmitter and the receiver are moving wrt each other. For what
amount of relative motion between them in one OFDM symbol period (as a
fraction of the carrier wavelength) can I assume that the channel is
reasonably correlated across OFDM symbols?

The front end uses an isotropic antenna.

Any help is much appreciated.

Thank you,
Ananth
```
```On Jul 28, 11:20 am, "ananth.rs" <ananth...@gmail.com> wrote:
> Hello,
>
> I am trying to design an adaptive equalizer for an OFDM system which has
> an extremely low symbol rate. I have a question regarding this.
>
> The transmitter and the receiver are moving wrt each other. For what
> amount of relative motion between them in one OFDM symbol period (as a
> fraction of the carrier wavelength) can I assume that the channel is
> reasonably correlated across OFDM symbols?
>
> The front end uses an isotropic antenna.
>
> Any help is much appreciated.
>
> Thank you,
> Ananth

It depends on how much SNR hit you can tolerate.  You can try to use
a bounding technique based on the triangle inequality in this case.

Suppose we take a simple single-carrier with 1-tap channel and
equalization.
y_n = x_n * h + z_n
where h is the channel.  For simplicity, let the channel have unit
norm
||h|| = 1.

Now suppose let's consider an MMSE or zero-forcing equalization, let
the equalizer be:
g = 1/h
Then the equalizer output is:
q_n = g * y_n

If the channel h changes to h', then the error induced on the
equalizer output
if the equalizer g is not adapted can be bounded by the triangle
inequality.

Hope that helps.
Julius
```
```>Hello,
>
>I am trying to design an adaptive equalizer for an OFDM system which has
>an extremely low symbol rate. I have a question regarding this.
>
>The transmitter and the receiver are moving wrt each other. For what
>amount of relative motion between them in one OFDM symbol period (as a
>fraction of the carrier wavelength) can I assume that the channel is
>reasonably correlated across OFDM symbols?
>
>The front end uses an isotropic antenna.
>
>Any help is much appreciated.
>
>Thank you,
>Ananth
>

You can determine this based on the channel coherence time(depend on the
relative speed of motion and wavelength) as relative to the OFDM symbol
time.

You can check a good reference paper by Prof. Bernard Sklar. The title is