On Nov 10, 1:52 am, Andrew FPGA <andrew.newsgr...@gmail.com> wrote:

> I mean, I'm totally convinced that an integer ratio
> is what you need to demod the ofdm symbol with least loss of
> orthogonality, but how do you figure out how to change the sampling
> rate such that an integer ratio is achieved?

Sample rate mismatches will have the effect of stretching/shrinking
the symbol in the FFT bins, and will introduce a predictably varying
phase error in each carrier across the symbol. By examining this phase
error you can infer the sample rate error and correct it in a closed
loop.

EB

> It seems to me that if you're trying to optimize the hardware for an
> OFDM system, you will want to closely match the number of carriers in
> your symbol (guard + pilot + information) to the size of your FFT.

Why? The FFT size can't be smaller than the number of data symbols per
OFDM symbol, but I can't see why the FFT couldn't be larger. FFT
larger means zero padding in the frequency domain, which is
oversampling in the time domain. That seems fine to me?
(sure it means an FFT thats larger than necessary, so wasted
computation. Oh, hang on, opps, I reread your question and you said
"optimise the hardware", so I think this was actually what you were
saying, in which case I agree!)

> With that understood, it seems that in order to minimize interference
> between the carriers due to spectral leakage, you need to ensure that
> they are orthogonal in the FFT size - ie, you have an integer number
> of _cycles_ of each carrier in the transformed symobl. To achieve
> this, you need to match the sample rate of the received symbol to the
> sample rate of the transmitted symbol. This is usually done with some
> sort of clock tracking loop and resampling/interpolation since you
> can't rely on the TX and RX rates to match in the face of
> manufacturing variations, temperature differences and doppler effects.

I reckon in order to demodulate properly you need to estimate the
carrier frequency offset, be phase locked to the carrier(required for
coherent detection), and know when the ofdm symbol starts in time. One
may also need to correct for distortions added by the channel
(equalisation). But bugger me if I can see the link between that, and
choosing a sampling rate that is an integer multiple of the ofdm
symbol duration. I mean, I'm totally convinced that an integer ratio
is what you need to demod the ofdm symbol with least loss of
orthogonality, but how do you figure out how to change the sampling
rate such that an integer ratio is achieved?

Regards
Andrew

On Nov 5, 6:59 pm, Andrew FPGA <andrew.newsgr...@gmail.com> wrote:
> Hi,
> I'm trying to understand how synchronision might work in an OFDM
> receiver with respect to the consequences it has for how the baseband
> or IF signal is sampled. I have tried to read widely, but the IEEE
> literature around OFDM synchronisation never seems to mention the
> sample rate or the hardwarey aspects. Below is brief background to try
> and illustrate where I am coming from, followed by three specific
> questions that I am finding it difficult to answer.
>
> Background
> Broadly speaking, my understanding is that there are 3 "aspects" that
> need to be synchronised in the receiver.
> 1) Timing synchronisation - the receiver needs to know the time
> instant when the symbol starts. (I have seen various correlation based
> methods for this).
> 2) Carrier Frequency Offset (CFO) - Assuming a hetrodyne receiver
> there will be a local oscilator (LO) mixing the incoming signal down
> to an IF. The LO will have some frequency offset compared to the
> transmitter. For OFDM this offset causes a loss of orthogonality for
> the subcarriers, so the CFO must be corrected for.
> 3) Carrier phase offset.
>
> The Question:
> 1) Once the Carrier Frequency Offset has been estimated, how do we
> correct for it? Once the LO has mixed the signal down it seems to me
> that orthogonality has been lost and little can be done. So does the
> receiver modify the frequency of the LO to ensure it is kept frequency
> locked to the transmitter carrier frequency? Practically speaking how
> could the LO frequency be changed? I suppose standard frequency
> synthesis techniques are used (e.g. PLL, NCO...)
>
> 2) If my digital receiver is sampling the baseband signal, I'm
> beginning to think this sampling rate is completely independent of the
> synchronisation issues mentioned in 1,2,3. The key is to sample at
> more than twice the nyquist rate, and that is all I have to do to
> reconstruct the baseband signal? The sampling rate has nothing to do
> with synchronisation?
>
> 3) What about if my digital receiver is sampling at IF, again is the
> only requirement that I sample at the Nyquist rate? I don't need to
> somehow change my sample rate based on the CFO estimated by my digital
> processing in the receiver?
>
> Regards
> Andrew

The July 2007 IEEE Proceedings issue has a tutorial article on OFDM
synchronization. It might be useful to look at it. Particularly for
the strategies used in implementations, even if you don't take the
time to follow the details of every equation. For example, one of the
motivations for using OFDM is to be able to perform equalization as N
simple one-tap equalizers instead of a single time domain N-tap
equalizer implemented at N**2 or N**3 complexity. Given the simple
equalization structure, it is feasible to only make coarse frequency
and delay corrections explicitly and let the one-tap equalizer make
the final fine corrections. This becomes even more important in multi-
user MIMO implementations which require different corrections in
different user's bins.

Dale B. Dalrymple
http://dbdimages.com
Http://stores.lulu.com/dbd

On Nov 7, 12:38 am, "mnentwig" <mnent...@elisanet.fi> wrote:
> >>Have you forgotten that the sample rate of the Rx and Tx must match as
>
> well?
> No, that is not true. I need an integer number of samples per period,
> everything else just ends up as zero-padding inside the FFT.
>
> -mn

I'm interested in exploring this further because it seems to be a
fundamental misunderstanding on my part.

It seems to me that if you're trying to optimize the hardware for an
OFDM system, you will want to closely match the number of carriers in
your symbol (guard + pilot + information) to the size of your FFT.
With that understood, it seems that in order to minimize interference
between the carriers due to spectral leakage, you need to ensure that
they are orthogonal in the FFT size - ie, you have an integer number
of _cycles_ of each carrier in the transformed symobl. To achieve
this, you need to match the sample rate of the received symbol to the
sample rate of the transmitted symbol. This is usually done with some
sort of clock tracking loop and resampling/interpolation since you
can't rely on the TX and RX rates to match in the face of
manufacturing variations, temperature differences and doppler effects.

OTOH, if hardware efficiency is not one of your goals and you have
processing to spare, then you can afford to oversample your recieved
symbol and throw it (with padding) into a huge DFT. In that case the
oversampling will provide some buffer between the carriers, although I
think you may still see spectral leakage if the TX and RX aren't
related by integer ratios.

EB

>Ok, I think the following is a another graphical way 
Yes, that's the way I see it (or upconversion, depending on the sign).

>Why does the sample rate need to be an integer number of samples per
>OFDM symbol? and what does this really mean given that symbol duration
>will be spread in time by the channel?

Let me put it in other words:
You want an integer number of samples for each OFDM symbol. Otherwise
there is not a full symbol length inside the FFT, and orthogonality
suffers....

>...
>that a non-integer number of samples will cause
>spectral leakage - which is effectively one sub-carrier spreading into
>all others.

right.

>So practically speaking, and in general terms how does one ensure we
>sample at a rate that is an integer number of samples per OFDM symbol?

As above, have a full OFDM symbol inside the FFT. Sorry if I made up a
complicated explanation for something very simple :)

>I don't understand how oversampling helps to suppress adjacent
>channels. 

The more oversampling I have, the more bins will I use in the FFT (which
is BTW quite expensive). So adjacent channels (neighboring frequencies)
will show up in the FFT as subcarriers that I'm not interested in.
With a lower rate they alias on top of my signal, even before the FFT.

>>we may see energy from the adjacent channel.
That is correct... Zero-padding wasn't accurate, but I think it's clear.
In an implementation I'd use a digital filter before the FFT, and
decimate, since I don't care about the information in the adjacent
channels.

>If energy from adjacent channels spills into our channel bandwidth, I
>can't see how sampling faster would help to remove it?

That's just plain old aliasing problem, as in any other non-OFDM system.

Cheers

Markus

Hi Mn,
Thanks for your post. It has exposed me to a different view so that is
great, and has really got me thinking.

> Simply multiply the IQ sample stream with exp(-i*omega*t), a rotating
> unity phasor.
Ok, I think the following is a another graphical way of thinking about
this: the rx LO with omega CFO will downconvert the passband signal to
baseband - but the now baseband frequency spectrum will not quite be
centered around DC, it will be centered around omega rad/s. So you are
saying to correct for the CFO we simply down-convert again, but this
time do it digitally i.e. as part of the baseband processing? no?
(assuming we have an estimate for the CFO, correcting for the CFO
sounds easy - I'm not saying estimating CFO is easy, leave that
problem for later).

> Any rate will do, that has an
> integer number of samples per symbol.
> Essentially, higher rate gives zero padding in the frequency domain.

Why does the sample rate need to be an integer number of samples per
OFDM symbol? and what does this really mean given that symbol duration
will be spread in time by the channel?

If I think in terms of the fourier transform and spectral leakage, I
suppose I can see that a non-integer number of samples will cause
spectral leakage - which is effectively one sub-carrier spreading into
all others.
So practically speaking, and in general terms how does one ensure we
sample at a rate that is an integer number of samples per OFDM symbol?

Your zero padding comment makes perfect sense! I buy it because I am
familiar with zero padding in the time domain causing higher rate of
sampling of the frequency domain, and by considering Fourier
Transform's duality principle.

> But some oversampling is needed, because you cannot suppress adjacent
> channels sufficiently in the analog domain.

I don't understand how oversampling helps to suppress adjacent
channels. By oversampling we are just extending the frequency range
which we are observing with the demod FFT. The resultant frequency
domain zero padding just extends into the adjacent channel - so in
fact we may not see zeros there - we may see energy from the adjacent
channel.

If energy from adjacent channels spills into our channel bandwidth, I
can't see how sampling faster would help to remove it?

Cheers
Andrew

>>Have you forgotten that the sample rate of the Rx and Tx must match as
well?
No, that is not true. I need an integer number of samples per period,
everything else just ends up as zero-padding inside the FFT.

-mn

On Nov 5, 7:59 pm, Andrew FPGA <andrew.newsgr...@gmail.com> wrote:
> Hi,
> I'm trying to understand how synchronision might work in an OFDM
> receiver with respect to the consequences it has for how the baseband
> or IF signal is sampled. I have tried to read widely, but the IEEE
> literature around OFDM synchronisation never seems to mention the
> sample rate or the hardwarey aspects. Below is brief background to try
> and illustrate where I am coming from, followed by three specific
> questions that I am finding it difficult to answer.
>
> Background
> Broadly speaking, my understanding is that there are 3 "aspects" that
> need to be synchronised in the receiver.
> 1) Timing synchronisation - the receiver needs to know the time
> instant when the symbol starts. (I have seen various correlation based
> methods for this).
> 2) Carrier Frequency Offset (CFO) - Assuming a hetrodyne receiver
> there will be a local oscilator (LO) mixing the incoming signal down
> to an IF. The LO will have some frequency offset compared to the
> transmitter. For OFDM this offset causes a loss of orthogonality for
> the subcarriers, so the CFO must be corrected for.
> 3) Carrier phase offset.
>
> The Question:
> 1) Once the Carrier Frequency Offset has been estimated, how do we
> correct for it? Once the LO has mixed the signal down it seems to me
> that orthogonality has been lost and little can be done. So does the
> receiver modify the frequency of the LO to ensure it is kept frequency
> locked to the transmitter carrier frequency? Practically speaking how
> could the LO frequency be changed? I suppose standard frequency
> synthesis techniques are used (e.g. PLL, NCO...)
>
> 2) If my digital receiver is sampling the baseband signal, I'm
> beginning to think this sampling rate is completely independent of the
> synchronisation issues mentioned in 1,2,3. The key is to sample at
> more than twice the nyquist rate, and that is all I have to do to
> reconstruct the baseband signal? The sampling rate has nothing to do
> with synchronisation?
>
> 3) What about if my digital receiver is sampling at IF, again is the
> only requirement that I sample at the Nyquist rate? I don't need to
> somehow change my sample rate based on the CFO estimated by my digital
> processing in the receiver?
>
> Regards
> Andrew

Have you forgotten that the sample rate of the Rx and Tx must match as
well? If they don't then the carriers in the OFDM symbol lose
orthogonality in your FFT. The systems I've worked on also had a
synchronization & tracking loop in the Rx to align the sample rates.

EB

>The Question:
>1) Once the Carrier Frequency Offset has been estimated, how do we
>correct for it?

Simply multiply the IQ sample stream with exp(-i*omega*t), a rotating
unity phasor.
Nothing is lost, in theory you can recover from CFO without information
loss and in reality it may be only limited by the quality of the CFO
estimate.

> 2) If my digital receiver is sampling the baseband signal, I'm
> beginning to think this sampling rate is completely independent of
the...

It's purely an implementation question. Any rate will do, that has an
integer number of samples per symbol.
Essentially, higher rate gives zero padding in the frequency domain.
But some oversampling is needed, because you cannot suppress adjacent
channels sufficiently in the analog domain.

>3) What about if my digital receiver is sampling at IF, again is the
>only requirement that I sample at the Nyquist rate? I don't need to
>somehow change my sample rate based on the CFO estimated by my digital
>processing in the receiver?

No, you don't need to. Just run at a fixed rate. Note that "Nyquist rate"
relates to the bandwidth, not the frequency (i.e. for a 1 MHz wide signal
at 70 MHz IF the limit is 1M complex samples/s - bandpass sampling).
In reality one needs oversampling, as mentioned.

-mn

PS: This may clarify or confuse, don't know:
When the receiver moves at extremely high speeds (for example) towards the
transmitter, the symbol duration will in fact shorten. Then one would need
to adapt the rate to get the desired number of samples per symbol. So the
idea of changing the rate is not completely unfounded.
But AFAIK this effect is so small that it is negligible.

Hi,
I'm trying to understand how synchronision might work in an OFDM
receiver with respect to the consequences it has for how the baseband
or IF signal is sampled. I have tried to read widely, but the IEEE
literature around OFDM synchronisation never seems to mention the
sample rate or the hardwarey aspects. Below is brief background to try
and illustrate where I am coming from, followed by three specific
questions that I am finding it difficult to answer.

Background
Broadly speaking, my understanding is that there are 3 "aspects" that
need to be synchronised in the receiver.
1) Timing synchronisation - the receiver needs to know the time
instant when the symbol starts. (I have seen various correlation based
methods for this).
2) Carrier Frequency Offset (CFO) - Assuming a hetrodyne receiver
there will be a local oscilator (LO) mixing the incoming signal down
to an IF. The LO will have some frequency offset compared to the
transmitter. For OFDM this offset causes a loss of orthogonality for
the subcarriers, so the CFO must be corrected for.
3) Carrier phase offset.

The Question:
1) Once the Carrier Frequency Offset has been estimated, how do we
correct for it? Once the LO has mixed the signal down it seems to me
that orthogonality has been lost and little can be done. So does the
receiver modify the frequency of the LO to ensure it is kept frequency
locked to the transmitter carrier frequency? Practically speaking how
could the LO frequency be changed? I suppose standard frequency
synthesis techniques are used (e.g. PLL, NCO...)

2) If my digital receiver is sampling the baseband signal, I'm
beginning to think this sampling rate is completely independent of the
synchronisation issues mentioned in 1,2,3. The key is to sample at
more than twice the nyquist rate, and that is all I have to do to
reconstruct the baseband signal? The sampling rate has nothing to do
with synchronisation?

3) What about if my digital receiver is sampling at IF, again is the
only requirement that I sample at the Nyquist rate? I don't need to
somehow change my sample rate based on the CFO estimated by my digital
processing in the receiver?

Regards
Andrew