Assumptions to be made while simulating for a wireless channel

Dear comp.dsp,

I am going to try to learn a bit more about the wireless channel
(specifically using OFDM) by first creating a set of symbols and
perform a transmit and receive. It is a simple begining I want to
make, and I will probably use GNU Octave and, later, when I do know
the basics, shift to IT++.

My doubts are:

1. Let us say I am going to use just BPSK over OFDM. Then, I can level
shift the BPSK to +1 and -1, divide it into blocks of Nfft each (where
Nfft is the number of subcarriers), take ifft and prepend the cyclic
prefix (don't know how much yet), add some Gaussian white noise, and
retrieve the samples after doing an IFFT. Now, since I haven't assumed
a multipath channel, I needn't really do channel estimation, as I know
the point where the actual symbol starts. Is this assumption correct?

2. How do I simulate the fading? Is it simply using a Rayleigh random
variable multiplying my samples before going through AWGN, for slow
fading?

3. What would be the right way to estimate my channel, if I assume
that the channel is a tapped-delay FIR filter? If I understand
estimation theory correctly, the best way would be to use known pseudo-
random sequence and do a least squares estimate, invert the channel
response and obtain the equalized result. Is this correct?

Thanks a lot!

Kumar

On Feb 27, 10:09 pm, "Kumar Appaiah" <kumar.appa...@gmail.com> wrote:
> Dear comp.dsp,
>
> I am going to try to learn a bit more about the wireless channel
> (specifically using OFDM) by first creating a set of symbols and
> perform a transmit and receive. It is a simple begining I want to
> make, and I will probably use GNU Octave and, later, when I do know
> the basics, shift to IT++.
>
> My doubts are:
>
> 1. Let us say I am going to use just BPSK over OFDM. Then, I can level
> shift the BPSK to +1 and -1, divide it into blocks of Nfft each (where
> Nfft is the number of subcarriers), take ifft and prepend the cyclic
> prefix (don't know how much yet), add some Gaussian white noise, and
> retrieve the samples after doing an IFFT. Now, since I haven't assumed
> a multipath channel, I needn't really do channel estimation, as I know
> the point where the actual symbol starts. Is this assumption correct?

Right. If you don't simulate any channel dispersion and just have
additive noise, there's nothing to equalize, except for maybe
filtering the data to remove some of the noise if possible.

> 2. How do I simulate the fading? Is it simply using a Rayleigh random
> variable multiplying my samples before going through AWGN, for slow
> fading?

That's one way to do it.

> 3. What would be the right way to estimate my channel, if I assume
> that the channel is a tapped-delay FIR filter? If I understand
> estimation theory correctly, the best way would be to use known pseudo-
> random sequence and do a least squares estimate, invert the channel
> response and obtain the equalized result. Is this correct?

Again, that's one way to do it. You can use a number of different
algorithms for making an equalizer, such as LMS or least squares. If
the channel is non-time-varying and you have a model for it, then you
can solve for a fixed optimal filter. However, this isn't practical
(in practice you won't know the exact transfer function of the
channel, and it will likely vary over time), so for a more realistic
simulation, you should probably use some adaptive algorithm like LMS
or recursive least-squares to estimate the channel's transfer
function. One way of helping the filter to adapt to the channel is by
using a training sequence of known symbols, such as a PN sequence,
before you actually start transmitting data. After the training is
complete, you would switch the filter to "decision-directed" mode,
which uses the output of your demodulator as the filter's reference
signal. Most adaptive filtering textbooks would have some sort of
material on this topic.

Jason

On Feb 28, 6:55 pm, cincy...@gmail.com wrote:
> > 3. What would be the right way to estimate my channel, if I assume
> > that the channel is a tapped-delay FIR filter? If I understand
> > estimation theory correctly, the best way would be to use known pseudo-
> > random sequence and do a least squares estimate, invert the channel
> > response and obtain the equalized result. Is this correct?
>
> Again, that's one way to do it. You can use a number of different
> algorithms for making an equalizer, such as LMS or least squares. If
> the channel is non-time-varying and you have a model for it, then you
> can solve for a fixed optimal filter. However, this isn't practical
> (in practice you won't know the exact transfer function of the
> channel, and it will likely vary over time), so for a more realistic
> simulation, you should probably use some adaptive algorithm like LMS
> or recursive least-squares to estimate the channel's transfer
> function. One way of helping the filter to adapt to the channel is by
> using a training sequence of known symbols, such as a PN sequence,
> before you actually start transmitting data. After the training is
> complete, you would switch the filter to "decision-directed" mode,
> which uses the output of your demodulator as the filter's reference
> signal. Most adaptive filtering textbooks would have some sort of
> material on this topic.

Thanks for  the pointers. I shall move refer to some material related
to this. I guess you are referring to the decision feeedback
equalizer.

One more thing. For a time varying FIR channel, as you say, the
coefficients vary with time with some correlation. So, would
simulating channel which moves around (I mean varies statistically
according to) a power delay profile be a good idea?

Thanks.

Kumar