Error Vector Magnitude (EVM)

For a given modulation constellation (say 16 QAM), is there a minimum
EVM (irrespective of how good the SNR is)? This may sound a it silly,
but I find that while simulating a 16 qam transceiver system on simple
AWGN channel (with no other impairments like phase noise, dc offset, iq
mismatch etc) , the evm value more or less flattens (close to 0.0027)
when Es/No is beyond 45 dB (below this evm steadily decrease with
increasing SNR) . Is there something wrong with my findings? Or is
there a fundamental minimum EVM for a given modulation scheme?

My suspicion is that, as the SER/BER approach 0, there is some error
floor. But I am not able to justify why the error itself doesn't
approach zero!

Could some one throw some lights on this

Galois wrote:
> For a given modulation constellation (say 16 QAM), is there a minimum
> EVM (irrespective of how good the SNR is)? This may sound a it silly,
> but I find that while simulating a 16 qam transceiver system on simple
> AWGN channel (with no other impairments like phase noise, dc offset, iq
> mismatch etc) , the evm value more or less flattens (close to 0.0027)
> when Es/No is beyond 45 dB (below this evm steadily decrease with
> increasing SNR) . Is there something wrong with my findings? Or is
> there a fundamental minimum EVM for a given modulation scheme?
>
> My suspicion is that, as the SER/BER approach 0, there is some error
> floor. But I am not able to justify why the error itself doesn't
> approach zero!
>
> Could some one throw some lights on this

In an ideal system with perfect timing recovery the EVM can go to zero.
In a real-world system it could be that a floor is present due to
timing jitter. Often in receivers or measurement gear the bit timing is
resolved only to within some fraction of a baud, say using a polyphase
filter with a bunch of phases per baud. The soft decisions can only get
to within one tick of the sampling instant, so a kind of quantization
jitter is created, spreading out the constellation points a bit.

John

One possibility is the finite precision of your simulation method.

For example, my Matlab's floating point system only goes down to 2e-16
(eps). It caused me some problems when I was trying to simulate some
non-linear systems.

Galois wrote:
...
> My suspicion is that, as the SER/BER approach 0, there is some error
> floor. But I am not able to justify why the error itself doesn't
> approach zero!
> 
> Could some one throw some lights on this

I believe that john touched on the lower limits to the error floor, ie 
the best performance you can expect in practice.  However I feel that 
this portion of the question is instead directed at the upper limit to 
the floor. ie why in the presence of absolute noise and no signal you 
still receive some correct bits.

This is simply due to the noise being unbiased with mean zero.  Most 
signaling methods, QAM included, have minimum energy.  This means that 
the signal constellation is not offset from zero, and instead is 
entirely centered around zero.

This means that even when there is no noise, just by chance the correct 
signal will be received.  The most noisy signal ,assuming simple +1/-1 
signalling (ie BPSK etc), will give correct results on average half the 
time.  This all assumes equal probability for a 0 or 1 to be sent (ie a 
-1 or +1 constellation point being sent).

For a given signal constellation, and a known noise distribution you can 
work out the average probabilities of a correct decision given no signal 
input.

The lower limit on error probability is generally considered to be 0.5. 
  This means that the correct bit will be detected on average half the 
time.  If the probability is by chance less than this (ie the output is 
wrong more often than right), then you can just flip the output bits 
from your receiver, and now you're at a better than 0.5 probability (ie 
the output is now right more often than wrong).

So the maximum bit error rate will always be 0.5

On 22 Nov 2005 04:54:11 -0800, "Galois" <ratnuu@gmail.com> wrote:

>For a given modulation constellation (say 16 QAM), is there a minimum
>EVM (irrespective of how good the SNR is)? This may sound a it silly,
>but I find that while simulating a 16 qam transceiver system on simple
>AWGN channel (with no other impairments like phase noise, dc offset, iq
>mismatch etc) , the evm value more or less flattens (close to 0.0027)
>when Es/No is beyond 45 dB (below this evm steadily decrease with
>increasing SNR) . Is there something wrong with my findings? Or is
>there a fundamental minimum EVM for a given modulation scheme?
>
>My suspicion is that, as the SER/BER approach 0, there is some error
>floor. But I am not able to justify why the error itself doesn't
>approach zero!
>
>Could some one throw some lights on this

In a simulation you won't be able to do better than the quantization
levels that are available in the sim.   In other words, you may be
measuring the precision of the simulator.   I would think, though,
that a carefully designed simulator with good transceiver models could
be achieved that results in zero or at least very, very low EVM.   It
might take some careful work to get there, but it's probably doable.
Have you looked at the numerical value's of the symbol magnitudes?
Are they limit cycling around particular values?

There is no theoretical lower bound on EVM.   With infinite precision
and ideal components a system could achieve an EVM of zero.
Practical systems, even simulations, may be limited by the components.
For any real system the rf components and quantization noise will
typically drive EVM.


Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Thank you all (Jon, Bevan, Eric all) for your comments and suggestions.

May be I should have described the problem setup a bit more specific.

For the simulation, I did have an RRC Tx pulse shaping filter and an
RRC Rx filter (matched filter in this case). I used an oversampling
factor of 4.  The RRC filters had a length of 81 taps (with
oversampling of 4) Ofcourse the whole transceiver simulated in a clear
(no radio imperfections, other than filter truncation and quantization,
due to the simulator as cited by Eric).

So, my earlier posted observation of a minimum EVM correspond to this
setup. I did spend some more time to analyse the problem and I found a
reasonable justification (to me atleast!) to the same.

1) The filter truncation causes some dispersion on the modulation
constellation. My feeling is that, the filter memory spreades/smears
the distortions across many samples. So, even in the absense of any
other linear/nonlinear distortions in the channel or Tx/Rx (as I have
assumed in this case). Due to this, the EVM does not decrease with
increased SNR (lower noise) BEYOND some SNR (for 81 tap, 4
oversampling, 16 qam it used to be about 45dB Es/No). But, when the
filter length is increased, the so 'observed' evm comes down. As
expected, the constellation dispersion also came down. Increasing the
oversampling as well, helped to reduce the 'absolute oberved evm floor'
, but largely, the filter length has a direct influence. I could bring
down the evm to as close to 1e-7 (with 10 fold filter length increase
with remaining setup the same)

2) I agree with Eric. There is a simulator precision problem, but that
is quite alright (since it is fairly small in terms of the minum
representable value) here.

Now, I want to throw this problem. If RRC filtering is used, is it
possible to arrive at a theoretical limit on EVM (in an otherwise clean
channel but AWGN) as a function of FilterLength. This is not terribly
important (or may be relevant), but isnt it possible to find it? Or is
there some known result already?

I would like to hear further thoughts/clarification on this.

Thanks once again for your time, interest and suggestions.

best regards
Ratna

On 22 Nov 2005 23:34:27 -0800, "Galois" <ratnuu@gmail.com> wrote:

>Thank you all (Jon, Bevan, Eric all) for your comments and suggestions.
>
>May be I should have described the problem setup a bit more specific.
>
>For the simulation, I did have an RRC Tx pulse shaping filter and an
>RRC Rx filter (matched filter in this case). I used an oversampling
>factor of 4.  The RRC filters had a length of 81 taps (with
>oversampling of 4) Ofcourse the whole transceiver simulated in a clear
>(no radio imperfections, other than filter truncation and quantization,
>due to the simulator as cited by Eric).
>
>So, my earlier posted observation of a minimum EVM correspond to this
>setup. I did spend some more time to analyse the problem and I found a
>reasonable justification (to me atleast!) to the same.
>
>1) The filter truncation causes some dispersion on the modulation
>constellation. My feeling is that, the filter memory spreades/smears
>the distortions across many samples. So, even in the absense of any
>other linear/nonlinear distortions in the channel or Tx/Rx (as I have
>assumed in this case). Due to this, the EVM does not decrease with
>increased SNR (lower noise) BEYOND some SNR (for 81 tap, 4
>oversampling, 16 qam it used to be about 45dB Es/No). But, when the
>filter length is increased, the so 'observed' evm comes down. As
>expected, the constellation dispersion also came down. Increasing the
>oversampling as well, helped to reduce the 'absolute oberved evm floor'
>, but largely, the filter length has a direct influence. I could bring
>down the evm to as close to 1e-7 (with 10 fold filter length increase
>with remaining setup the same)
>
>2) I agree with Eric. There is a simulator precision problem, but that
>is quite alright (since it is fairly small in terms of the minum
>representable value) here.
>
>Now, I want to throw this problem. If RRC filtering is used, is it
>possible to arrive at a theoretical limit on EVM (in an otherwise clean
>channel but AWGN) as a function of FilterLength. This is not terribly
>important (or may be relevant), but isnt it possible to find it? Or is
>there some known result already?
>
>I would like to hear further thoughts/clarification on this.
>
>Thanks once again for your time, interest and suggestions.

What is the excess bandwidth (alpha) of your RRC filter?   The
narrower the filter the longer the filter needs to be, so if you're
trying to use a low alpha (e.g., 0.15 or so) the system will probably
be more sensitive to truncating the FIR than for wider (alpha = 0.30
or so) filters.

So the sensitivity to truncating the FIR will also depend on the
steepness of the filter rolloffs.  Another way to look at it is that
the more energy you truncate off the FIR the more EVM you might
expect.   In my experience, though, reasonable filter lengths can make
EVM, or even BER distance from the matched filter bound, to be pretty
negligible.


Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Thanks Eric. Your point ofcourse is correct. I used 0.22 as alpha.
-Thanks
R

>Thanks Eric. Your point ofcourse is correct. I used 0.22 as alpha.
>-Thanks
>R
>
>

How can i calculate the "composite EVM" from the symbols constellation in
UMTS? is there a way to calculate it without make a chip re-construction ?
is there a way to calculate it from all the EVM of symbols from each code
?

Thank,
Tomer