From: tommala on
>On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote:
>
>> Hi everyone,
>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM
>> modulator(using only constellation points coordinates). I figured out
>> from wikipedia.org and "Digital Modulation Technique" that
constellation
>> points will have following coordinates(in the complex plane):
>> 1) (+-sqrt(Eb),0) for BPSK
>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3)
>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for
>> 16-QAM
>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK
>> and QPSK.
>> I think there is a mistake in constellation points representation
above.
>> Do You have any ideas?
>> Thank You in advance for any remarks.
>
>BPSK : . .
>
> . .
>QPSK :
> . .
>
>
> . . . .
>
> . . . .
>16-QAM:
> . . . .
>
> . . . .
>
>
>
>
>
>
>
>
>--
>www.wescottdesign.com
>
I know how constellations look but don't know how connect its points
coordinates with Eb.

Dilip Warrier can You write sth more about r.How it is related to Eb?
Maybe where can I find mathematical considerations of constellation points
if such exist.
From: Tim Wescott on
On Sun, 06 Dec 2009 14:10:17 -0600, tommala wrote:

>>On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote:
>>
>>> Hi everyone,
>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM
>>> modulator(using only constellation points coordinates). I figured out
>>> from wikipedia.org and "Digital Modulation Technique" that
> constellation
>>> points will have following coordinates(in the complex plane):
>>> 1) (+-sqrt(Eb),0) for BPSK
>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3)
>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for
>>> 16-QAM
>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK
>>> and QPSK.
>>> I think there is a mistake in constellation points representation
> above.
>>> Do You have any ideas?
>>> Thank You in advance for any remarks.
>>
>>BPSK : . .
>>
>> . .
>>QPSK :
>> . .
>>
>>
>> . . . .
>>
>> . . . .
>>16-QAM:
>> . . . .
>>
>> . . . .
>>
>>
>>
>>
>>
>>
>>
>>
>>--
>>www.wescottdesign.com
>>
> I know how constellations look but don't know how connect its points
> coordinates with Eb.
>
> Dilip Warrier can You write sth more about r.How it is related to Eb?
> Maybe where can I find mathematical considerations of constellation
> points if such exist.

Then you need to understand the connection between Eb and the position of
the point on the constellation. Once you do, you will both understand
exactly how to connect a constellation's point to the Eb for that case,
and you will understand why folks start using the word "average" when
they talk about the Eb of a 16-QAM signal.

So -- I assume you're transmitting these constellations on some sort of a
sinusoidal carrier, with the real axis mapped to the in-phase portion of
the signal, and the imaginary axis mapped to the quadrature portion of
the signal. If that is, indeed, what you're doing, and if you know where
a symbol lies on the complex plane, what is the energy of that symbol?

Until you can answer that question, you're not ready for any answers you
get from us. Once you _do_ answer that question, you may not need to
look to us for answers.

--
www.wescottdesign.com
From: Eric Jacobsen on
On 12/6/2009 1:10 PM, tommala wrote:
>> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote:
>>
>>> Hi everyone,
>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM
>>> modulator(using only constellation points coordinates). I figured out
>>> from wikipedia.org and "Digital Modulation Technique" that
> constellation
>>> points will have following coordinates(in the complex plane):
>>> 1) (+-sqrt(Eb),0) for BPSK
>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3)
>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for
>>> 16-QAM
>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK
>>> and QPSK.
>>> I think there is a mistake in constellation points representation
> above.
>>> Do You have any ideas?
>>> Thank You in advance for any remarks.
>> BPSK : . .
>>
>> . .
>> QPSK :
>> . .
>>
>>
>> . . . .
>>
>> . . . .
>> 16-QAM:
>> . . . .
>>
>> . . . .
>>
>>
>>
>>
>>
>>
>>
>>
>> --
>> www.wescottdesign.com
>>
> I know how constellations look but don't know how connect its points
> coordinates with Eb.
>
> Dilip Warrier can You write sth more about r.How it is related to Eb?
> Maybe where can I find mathematical considerations of constellation points
> if such exist.

Can you compute the SNR? Carrier to Noise ratio (C/N)?

If so, it's a pretty straightforward transformation from S/N or C/N to
Eb/No. The nature of the transformation is described in many textbooks.

Here are some hints:

Eb is a bit energy measurement. What's the relationship between the
total signal power and the amount of energy proportional to a single bit?

No is the noise power per unit Hz bandwidth. If you know the noise
power computed from the symbol constellation, that can be converted to
No pretty easily.

So, to compute SNR, you need to know the signal power and the noise
power. Eb and No can be computed from each of those, respectively.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
From: tommala on
>On 12/6/2009 1:10 PM, tommala wrote:
>>> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote:
>>>
>>>> Hi everyone,
>>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM
>>>> modulator(using only constellation points coordinates). I figured
out
>>>> from wikipedia.org and "Digital Modulation Technique" that
>> constellation
>>>> points will have following coordinates(in the complex plane):
>>>> 1) (+-sqrt(Eb),0) for BPSK
>>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3)
>>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2))
for
>>>> 16-QAM
>>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for
BPSK
>>>> and QPSK.
>>>> I think there is a mistake in constellation points representation
>> above.
>>>> Do You have any ideas?
>>>> Thank You in advance for any remarks.
>>> BPSK : . .
>>>
>>> . .
>>> QPSK :
>>> . .
>>>
>>>
>>> . . . .
>>>
>>> . . . .
>>> 16-QAM:
>>> . . . .
>>>
>>> . . . .
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> --
>>> www.wescottdesign.com
>>>
>> I know how constellations look but don't know how connect its points
>> coordinates with Eb.
>>
>> Dilip Warrier can You write sth more about r.How it is related to Eb?
>> Maybe where can I find mathematical considerations of constellation
points
>> if such exist.
>
>Can you compute the SNR? Carrier to Noise ratio (C/N)?
>
>If so, it's a pretty straightforward transformation from S/N or C/N to
>Eb/No. The nature of the transformation is described in many textbooks.
>
>Here are some hints:
>
>Eb is a bit energy measurement. What's the relationship between the
>total signal power and the amount of energy proportional to a single
bit?
>
>No is the noise power per unit Hz bandwidth. If you know the noise
>power computed from the symbol constellation, that can be converted to
>No pretty easily.
>
>So, to compute SNR, you need to know the signal power and the noise
>power. Eb and No can be computed from each of those, respectively.
>
>--
>Eric Jacobsen
>Minister of Algorithms
>Abineau Communications
>http://www.abineau.com
>

I can't compute SNR nor C/N. Even I don't have to.
The simulation has GUI in which user can choose (Eb/No)min; (Eb/No)max and
(Eb/No)step (Eb/No in [dB]).
The program compute in the loop for every i=Eb/No from (Eb/No)min to
(Eb/No)max BER as ratio=number of wrong received bits/number of total
transmitted bits.
In the loop I calculate Eb as Eb=No*pow(10,i/10)where No is constant
number e.g. 1 [W/Hz].
I assume Eb constant for every modulation.
And my problem is to correct connect Eb with point coordinates.

P.S.
signal power=Eb*bit rate
noise power=No*bandwidth

From: Tim Wescott on
On Sun, 06 Dec 2009 16:13:15 -0600, tommala wrote:

>>On 12/6/2009 1:10 PM, tommala wrote:
>>>> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote:
>>>>
>>>>> Hi everyone,
>>>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM
>>>>> modulator(using only constellation points coordinates). I figured
> out
>>>>> from wikipedia.org and "Digital Modulation Technique" that
>>> constellation
>>>>> points will have following coordinates(in the complex plane):
>>>>> 1) (+-sqrt(Eb),0) for BPSK
>>>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3)
>>>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2))
> for
>>>>> 16-QAM
>>>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for
> BPSK
>>>>> and QPSK.
>>>>> I think there is a mistake in constellation points representation
>>> above.
>>>>> Do You have any ideas?
>>>>> Thank You in advance for any remarks.
>>>> BPSK : . .
>>>>
>>>> . .
>>>> QPSK :
>>>> . .
>>>>
>>>>
>>>> . . . .
>>>>
>>>> . . . .
>>>> 16-QAM:
>>>> . . . .
>>>>
>>>> . . . .
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> www.wescottdesign.com
>>>>
>>> I know how constellations look but don't know how connect its points
>>> coordinates with Eb.
>>>
>>> Dilip Warrier can You write sth more about r.How it is related to Eb?
>>> Maybe where can I find mathematical considerations of constellation
> points
>>> if such exist.
>>
>>Can you compute the SNR? Carrier to Noise ratio (C/N)?
>>
>>If so, it's a pretty straightforward transformation from S/N or C/N to
>>Eb/No. The nature of the transformation is described in many textbooks.
>>
>>Here are some hints:
>>
>>Eb is a bit energy measurement. What's the relationship between the
>>total signal power and the amount of energy proportional to a single
> bit?
>>
>>No is the noise power per unit Hz bandwidth. If you know the noise
>>power computed from the symbol constellation, that can be converted to
>>No pretty easily.
>>
>>So, to compute SNR, you need to know the signal power and the noise
>>power. Eb and No can be computed from each of those, respectively.
>>
>>--
>>Eric Jacobsen
>>Minister of Algorithms
>>Abineau Communications
>>http://www.abineau.com
>>
>>
> I can't compute SNR nor C/N.

Translation "I'm not qualified to do what I'm trying"

> Even I don't have to.

Translation "and I don't care"

> The simulation has GUI in which user can choose (Eb/No)min;
> (Eb/No)max and (Eb/No)step (Eb/No in [dB]).
> The program compute in the loop for every i=Eb/No from (Eb/No)min to
> (Eb/No)max BER as ratio=number of wrong received bits/number of total
> transmitted bits.
> In the loop I calculate Eb as Eb=No*pow(10,i/10)where No is constant
> number e.g. 1 [W/Hz].
> I assume Eb constant for every modulation.

Translation "I expect to conduct my entire professional career dependent
on software that someone else writes, and I don't see a problem with that.

> And my problem is to correct
> connect Eb with point coordinates.
>
I think your problem is bigger than that.

--
www.wescottdesign.com