Symbol Error Rate vs. Bit Error Rate?

I'm feeling confused. Again referring to the chart in Figure 5.2-17 on
p.282 of [proakiscomm], these datapoints are for a 10^{-5} symbol error
rate. 

Why symbol error rate? It seems like this isn't comparing apples to
apples since an error in an M-bit symbol could be 1, 2, ..., or M
bit errors, thus the bit error rate could be different between any
two modulations.

It seems like what we'd rather do is compare based on equivalent
bit error rates. No? Comments?
-- 
%  Randy Yates                  % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC            %  sliding, it's magic."
%%% 919-577-9882                %  
%%%% <yates@ieee.org>           % 'Living' Thing', *A New World Record*, ELO
http://www.digitalsignallabs.com

Randy Yates <yates@ieee.org> writes:

> I'm feeling confused. Again referring to the chart in Figure 5.2-17 on
> p.282 of [proakiscomm], these datapoints are for a 10^{-5} symbol error
> rate. 

@BOOK{proakiscomm,
  title = "{Digital Communications}",
  author = "John~G.~Proakis",
  publisher = "McGraw-Hill",
  edition = "fourth",
  year = "2001"}

-- 
%  Randy Yates                  % "How's life on earth? 
%% Fuquay-Varina, NC            %  ... What is it worth?" 
%%% 919-577-9882                % 'Mission (A World Record)', 
%%%% <yates@ieee.org>           % *A New World Record*, ELO
http://www.digitalsignallabs.com

Randy Yates <yates@ieee.org> writes:

> I'm feeling confused. Again referring to the chart in Figure 5.2-17 on
> p.282 of [proakiscomm], these datapoints are for a 10^{-5} symbol error
> rate. 
>
> Why symbol error rate? It seems like this isn't comparing apples to
> apples since an error in an M-bit symbol could be 1, 2, ..., or M
> bit errors, thus the bit error rate could be different between any
> two modulations.
>
> It seems like what we'd rather do is compare based on equivalent
> bit error rates. No? Comments?

I have a similar question on Eb/N0. Why compare based on that when,
at the end of the day, what we're really concerned with is transmit
power? 

It seems like a better chart would be R/W versus transmit power for
a fixed data rate and for a specified bit error rate.
-- 
%  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC            %                    and kiss her interface, 
%%% 919-577-9882                %            til then, I'll leave her alone."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://www.digitalsignallabs.com

On Apr 3, 7:27&#4294967295;pm, Randy Yates <ya...@ieee.org> wrote:
> Randy Yates <ya...@ieee.org> writes:
> > I'm feeling confused. Again referring to the chart in Figure 5.2-17 on
> > p.282 of [proakiscomm], these datapoints are for a 10^{-5} symbol error
> > rate.
>
> > Why symbol error rate? It seems like this isn't comparing apples to
> > apples since an error in an M-bit symbol could be 1, 2, ..., or M
> > bit errors, thus the bit error rate could be different between any
> > two modulations.
>
> > It seems like what we'd rather do is compare based on equivalent
> > bit error rates. No? Comments?
>
> I have a similar question on Eb/N0. Why compare based on that when,
> at the end of the day, what we're really concerned with is transmit
> power?
>

the bottom line is the energy needed per bit transmitted compared to
the noise density in the receiver and thats what Eb/No tells you..

re QPSK vs BPSK....you can think of QPSK as 2 orthogonal BPSK streams,
for a given BW, you can use two BPSK transmitters (twice the power)
and send twice the data rate.. so the Eb/No is the same.
Mark

On Thu, 03 Apr 2008 19:27:22 -0400, Randy Yates <yates@ieee.org>
wrote:

>Randy Yates <yates@ieee.org> writes:
>
>> I'm feeling confused. Again referring to the chart in Figure 5.2-17 on
>> p.282 of [proakiscomm], these datapoints are for a 10^{-5} symbol error
>> rate. 
>>
>> Why symbol error rate? It seems like this isn't comparing apples to
>> apples since an error in an M-bit symbol could be 1, 2, ..., or M
>> bit errors, thus the bit error rate could be different between any
>> two modulations.
>>
>> It seems like what we'd rather do is compare based on equivalent
>> bit error rates. No? Comments?

Sklar's text also has a very similar plot (i.e., a
bandwidth-efficiency plane) in his book and he does use Pb rather than
Pm, or bit error vs symbol error rate.  The plots are, as one would
expect, very similar.   I think you'd have to ask the authors why they
preferred one over the other.

>I have a similar question on Eb/N0. Why compare based on that when,
>at the end of the day, what we're really concerned with is transmit
>power? 

The really nice thing about Eb/No is it makes different modulations
and code rates and any mix thereof comparable for power efficiency. If
the link is power limited or power is an important resource, then
Eb/No is one of the more useful metrics.   If throughput or spectral
efficiency is also important then SNR might be a better metric.  It
just depends on how you're trying to manage the optimizations.

>It seems like a better chart would be R/W versus transmit power for
>a fixed data rate and for a specified bit error rate.

That's not quite as generic since it would compare only a single data
rate case, although that would be interesting for that specific
comparison.  Eb/No can always be converted to SNR, though, and
sometimes that's useful as well.   It all depends on which resource is
most important:  bandwidth, power, etc.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org