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Minimization of phase error fluctuation in OFDM equalizer

Started by danael May 29, 2009
I am designing ofdm equalizer.Ofdm frame contains: 
-19 symbols
-24 subcarriers per channel
-pilot symbols that are comb type arranged
-BPSK modulation 

The period of one frame (19symbols) is 625us,pilots are inserted every
four symbol in time direction and every four subcarrier in frequency
direction.

I made real measurements to determine the channel nature between base
station and receiving terminal

When I look at the subcarriers (right after FFT) on the constellation
graph, the subcarriers are rotated (along the time axis)- this is what I
expected.

On the basis on pilots in time direction,I am able to find the trend of
the rotation and by means of piece wise linear interpolation I compensate
this phase rotation.Now all the pilots are on the axis Re=0 (BPSK) however
data subcarriers fluctuate around axis Re=0 with peak-to-peak phase change
of +5/-5 degrees (phase error).

degrees
I
I      o                     o
I    o   o        o             o
+--X-------X-------X-------X--------->Symbols
I            o       o   o
I               o      o 
I
I

Fig.Phase distortion for one frame in time direction (across symbols)
after
    linear interpolation.X-pilots ,o-data subcarriers.


My problem is that the pilots don't reflect the true nature of the
channel.The frequency of channel change is too high to be represented by
the pilots.Higher order interpolation seems to have no sense as well since
the pilots are laid on almost straight line.

Additionally I made various test with the usage of ofdm signal
generator.In this case phase rotation may be neglected but the pilots still
don't reflect the true nature of the channel - the are laid on straigth
line again.

Does it mean I have reached maximum system preformance or the pilots are
arranged just to far from each other?

I have noticed that the frequency of this fluctuation is always in the
range of 4-8kHz. 
-1 frame period (19symbols) T=625us
-period of fluctuation Tf =8symbols
-1 symbol period Ts=T/19=33us

F=1/Tf=1/(8*Ts)=4kHz - frequency of phase fluctuation 

Does it make sense to use just 4-8kHz FIR filter to attenuate this
fluctuation (ie.to decrease phase error)?When the fluctuation freq. is
lower the pilots approximate the channel very well.

Daniel


On May 29, 7:52&#2013266080;am, "danael" <danielto...@hotmail.com> wrote:
[snip]
> > Does it mean I have reached maximum system preformance or the pilots are > arranged just to far from each other? > > I have noticed that the frequency of this fluctuation is always in the > range of 4-8kHz. > -1 frame period (19symbols) T=625us > -period of fluctuation Tf =8symbols > -1 symbol period Ts=T/19=33us > > F=1/Tf=1/(8*Ts)=4kHz - frequency of phase fluctuation > > Does it make sense to use just 4-8kHz FIR filter to attenuate this > fluctuation (ie.to decrease phase error)?When the fluctuation freq. is > lower the pilots approximate the channel very well. > > Daniel
You can think of this as a sampling problem. The pilots allow your receiver to periodically estimate (i.e. sample) and reconstruct the phase fluctuation. In your case, (I think) based on each pilot, you do either a piecewise constant approximation or a first-order interpolation. Based on the numbers you give above, unless you have a good parametric model, you are in the aliasing regime. This is because as you said the rate (bandwidth) of fluctuation is 4-8 kHz whereas you have only one pilot every 625us. That means your "sampling" is only 1600 Hz. Do you know if there's a way to model the fluctuations? Is it periodic? Does it have much jitter? Also consider the following. You can use a PLL to track a small amount of drift, but for larger values you're better off with an FLL since otherwise your PLL's loop bandwidth has to be so large that you get a lot of phase noise at the output of the PLL. But this insight comes only if the source of error turns out to be frequency drift or doppler, else you'll be using the FLL to solve the wrong problem. You have a very interesting problem! Julius
On May 29, 8:52&#2013266080;pm, "danael" <danielto...@hotmail.com> wrote:
> I am designing ofdm equalizer.Ofdm frame contains: > -19 symbols > -24 subcarriers per channel > -pilot symbols that are comb type arranged > -BPSK modulation > > The period of one frame (19symbols) is 625us,pilots are inserted every > four symbol in time direction and every four subcarrier in frequency > direction. > > I made real measurements to determine the channel nature between base > station and receiving terminal > > When I look at the subcarriers (right after FFT) on the constellation > graph, the subcarriers are rotated (along the time axis)- this is what I > expected. > > On the basis on pilots in time direction,I am able to find the trend of > the rotation and by means of piece wise linear interpolation I compensate > this phase rotation.Now all the pilots are on the axis Re=0 (BPSK) however > data subcarriers fluctuate around axis Re=0 with peak-to-peak phase change > of +5/-5 degrees (phase error). > > degrees > I > I &#2013266080; &#2013266080; &#2013266080;o &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; o > I &#2013266080; &#2013266080;o &#2013266080; o &#2013266080; &#2013266080; &#2013266080; &#2013266080;o &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; o > +--X-------X-------X-------X--------->Symbols > I &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080;o &#2013266080; &#2013266080; &#2013266080; o &#2013266080; o > I &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; o &#2013266080; &#2013266080; &#2013266080;o > I > I > > Fig.Phase distortion for one frame in time direction (across symbols) > after > &#2013266080; &#2013266080; linear interpolation.X-pilots ,o-data subcarriers. > > My problem is that the pilots don't reflect the true nature of the > channel.The frequency of channel change is too high to be represented by > the pilots.Higher order interpolation seems to have no sense as well since > the pilots are laid on almost straight line. > > Additionally I made various test with the usage of ofdm signal > generator.In this case phase rotation may be neglected but the pilots still > don't reflect the true nature of the channel - the are laid on straigth > line again. > > Does it mean I have reached maximum system preformance or the pilots are > arranged just to far from each other? > > I have noticed that the frequency of this fluctuation is always in the > range of 4-8kHz. > -1 frame period (19symbols) T=625us > -period of fluctuation Tf =8symbols > -1 symbol period Ts=T/19=33us > > F=1/Tf=1/(8*Ts)=4kHz - frequency of phase fluctuation > > Does it make sense to use just 4-8kHz FIR filter to attenuate this > fluctuation (ie.to decrease phase error)?When the fluctuation freq. is > lower the pilots approximate the channel very well. > > Daniel
What is the maximum Doppler frequency of the channel? Or what is the coherence time of the channel? (how quickly does it change significantly?) If the spacing of your pilots in the time-domain is larger than the coherence time, then you are undersampling the channel in the time- domain, and you can't accurately reconstruct it by any interpolation method (you get aliasing ambiguities). On the other hand, if the sampling in the time (and frequency) domains is adequate, then the optimal reconstruction filter is the 2D Wiener filter (otherwise known as MMSE estimator), which requires knowledge of the 2D covariance matrix of the channel. This does both optimal noise smoothing and the interpolation of the channel from the pilot positions to the data positions all in one step, based on the known smoothness of the channel (and the SNR) defined by the covariance matrix. It is superior to any other methods (linear, spline fitting, etc etc) assuming this second-order statistics of the channel is known (or can be reasonable estimated). -T