simple-minded non-OFDM signal design question

Randy Yates <yates@ieee.org> writes:

> Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
>
>> Randy Yates wrote:
>>
>>
>>>>>So I guess I have two questions: 1) Is it possible to design
>>>>>single-carrier systems (including the receiver) which are just as
>>>>>immune to multipath as multi-carrier systems?
>>>>
>>>>Certainly. Although it will require a huge amount of computation.
>>> Why? What sort of things would you have to do to a single-carrier
>>> signal to "get out the multipath?"
>>
>> The single carrier receiver will have to use an adaptive model of the
>> channel and apply some sort of the maximum likelihood algorithm for
>> the optimal demodulation. This is a heavy computational task.
>
> But is the computational complexity significantly greater than
> O(N*log(N))? That is the computational load an OFDM system must
> have from the git-go.

Perhaps an even better question would be, "Is this computational
complexity significant in today's technology?"
-- 
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Steve Underwood wrote:


> Well, I find the rant accurate, but the statement before misses a key 
> issue. 8-VSB seems like its about to become the dominant approach across 
> the world, because the Chinese just chosen a variant of it. They did 
> this because they believe they have sidestepped the patents for which 
> Americans are paying heavy royalties. The believed they couldn't do this 
> with DVB/T. In a world of heavy royalties, any crappy technology which 
> can sidestep them is often a much preferred solution.
> 
> Steve

Exactly. Thank you for the excellent comment.

VLV

Rune Allnor wrote:

> Randy Yates skrev:
> 
>>Is it possible to design
>>single-carrier systems (including the receiver) which are just as
>>immune to multipath as multi-carrier systems?
> 
> 
> The answer is no.

The answer is yes. Considering the same bandwidth.

VLV

Randy Yates wrote:


>>The single carrier receiver will have to use an adaptive model of the
>>channel and apply some sort of the maximum likelihood algorithm for
>>the optimal demodulation. This is a heavy computational task.
> 
> 
> But is the computational complexity significantly greater than
> O(N*log(N))? That is the computational load an OFDM system must
> have from the git-go.

Unfortunately, the complexity is going to be exponential. The number of 
operations will be at the order of size_of_the_alphabet raised to the 
power of the memory_of_the_channel (i.e. delay spread).

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Randy Yates wrote:

>>>The single carrier receiver will have to use an adaptive model of the
>>>channel and apply some sort of the maximum likelihood algorithm for
>>>the optimal demodulation. This is a heavy computational task.
>>
>>But is the computational complexity significantly greater than
>>O(N*log(N))? That is the computational load an OFDM system must
>>have from the git-go.
> 
> 
> Perhaps an even better question would be, "Is this computational
> complexity significant in today's technology?"

Perhaps an even better question would be "Who is going to pay?"

Consider QAM-16 at the rate of 100Mbit/s, i.e. 25 Mbaud. The delay 
spread will be at the order of 100ns, i.e. ~3 symbols. The number of 
operations will be 16^3 = 4096 per symbol, or ~100G ops per second.
This is not unfeasible however it is not practical either.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:

> Randy Yates wrote:
>
>>>>The single carrier receiver will have to use an adaptive model of the
>>>>channel and apply some sort of the maximum likelihood algorithm for
>>>>the optimal demodulation. This is a heavy computational task.
>>>
>>>But is the computational complexity significantly greater than
>>>O(N*log(N))? That is the computational load an OFDM system must
>>>have from the git-go.
>> Perhaps an even better question would be, "Is this computational
>> complexity significant in today's technology?"
>
> Perhaps an even better question would be "Who is going to pay?"
>
> Consider QAM-16 at the rate of 100Mbit/s, i.e. 25 Mbaud. The delay
> spread will be at the order of 100ns, i.e. ~3 symbols. The number of
> operations will be 16^3 = 4096 per symbol, or ~100G ops per second.
> This is not unfeasible however it is not practical either.

That's a great estimate, Vladimir. Thanks.

However I would change one significant thing - a TV channel only
requires about 20 Mb/s. That brings us down to 20 GOPS, but that's
still quite hefty - it is a definite economical impact.

To take a wild stab in the dark comparing to OFDM, let's say it uses
256 carriers each operating with QPSK, so that's 256 * 2 = 512
bits/FFT. Then at 20 Mb/s, that's about 40,000 FFTs/s. Then
the computational complexity C is 

  C = 40,000 * N * log(N)  
    ~= 80 MOPS.

That's a factor of 250 in complexity. Yowie!
-- 
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Randy Yates <yates@ieee.org> writes:

> To take a wild stab in the dark comparing to OFDM, let's say it uses
> 256 carriers each operating with QPSK, so that's 256 * 2 = 512
> bits/FFT. Then at 20 Mb/s, that's about 40,000 FFTs/s. 

That's wrong - ignore that. 
-- 
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On Sun, 01 Oct 2006 09:54:00 GMT, Oli Charlesworth
<catch@olifilth.co.uk> wrote:

>Rune Allnor said the following on 01/10/2006 06:29:
>> Randy Yates skrev:
>>> Is it possible to design
>>> single-carrier systems (including the receiver) which are just as
>>> immune to multipath as multi-carrier systems?
>> 
>> The answer is no.
>> 
>> The reason is that the physics of any multipath, narrow-band system
>> determines that there will be zones of destructive interefernce.
>> 
>> Consider a transmitter and reciever placed in an infinite half-space
>> above a plane reflecting surface, which has an arbitrary reflection
>> coefficient R. Assume the transmitter's position is (0,z) and the
>> receiever's position is (r,s)
>> 
>> The recieved signal x(t) will become
>> 
>> x(r,s,z,t) = x'(r,z,s,,t) + x"(r,z,s,t)
>> 
>> where x' is the direct signal and x" is the signal that has been
>> reflected from the ground.
>> 
>> The key is to realize that no matter how you choose r,z, and s,
>> there will always exist some geometrical configuration of transmitter
>> and reciever where x' + x" = 0, and no transmission is possible.
>
>This can only be true if you ignore the inverse-square law, surely?  The 
>reflected beam will always travel further, and therefore incur more 
>attentuation, and therefore will never be a 0dB echo.
>
>(Obviously when the transmitter-receiver separation is very great, the 
>difference in attenuation will be negligible.)

Broadcast transmissions are very often received Non-Line-of-Sight, and
in those conditions the direct path may be attenuated more than a
reflected path.   Nulls, genuine zero-energy nulls, are possible and
actually quite common under these conditions.

>> The reason why one uses multi-carrier systems, is that if
>> one channel suffers from destructive interference, some other
>> channel might come through.
>
>Randy's question was referring to a comparison between single-carrier 
>and multi-carrier systems with the same bandwidth (it wouldn't be a fair 
>comparsion otherwise).  If this is the case, then in identical multipath 
>conditions, they should each experience identical interference (which is 
>obvious if you consider that the spectral response of the channel will 
>be identical in each case).
>
>In a situation where the entire single-carrier bandwidth is nulled out 
>as you describe, then the entire multi-carrier bandwidth would be nulled 
>out as well, so there's no disadvantage.

And back to another of Randy's questions; I've often asserted that
there's no difference in capacity between single- and multi-carrier
transmissions.   Either can theoretically be made to work essentially
equally well under given conditions.   There are many ways of looking
at why OFDM becomes more attractive under certain conditions, much of
it having to do with the complexity of the equalization but
flexibility and adaptability considerations (and other things) also
come into play.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Eric Jacobsen <eric.jacobsen@ieee.org> writes:

> On Tue, 26 Sep 2006 03:31:14 GMT, Randy Yates <yates@ieee.org> wrote:
>
>>Randy Yates <yates@ieee.org> writes:
>>> [...]
>>
>>OK, let me tip my hand. 
>>
>>There are some folks/circles that are ragingly debating
>>whether the COFDM used in DVB/T is better than the US's
>>8VSB. I'm wondering if there is any real difference IF
>>the end-to-end systems are designed "properly."
>
> Oh, gag a maggot.

Wow, I hadn't heard that phrase since high-school, which dates
you and I both, Eric!

> I can't believe anybody still thinks that 8VSB is a good idea for
> anything, anywhere, under any circumstances.

Eric, 

First of all, I'm not trying to drum up support for 8VSB. As far as
I can tell, the situation is that we're stuck with it, so my questions
are more like, "What can we do with it now that we've got it?", or 
"Why can't we make it work as well as (C)OFDM?"

Secondly, this is really about some interesting comm theory (IMHO) and
not about heated standards battles. I have absolutely no joy or
interest in going (even if anyone would listen to me, which they
wouldn't because I'm nobody) to the ATSC or FCC about this. There's
about as much wisdom in that as there is in aspiring to be a lawyer...

> I've got some opinion on this, which I'll offer FWIW, but it's really
> just my opinion.   I've worked with both 8VSB and OFDM and am pretty
> familiar with both the ATSC and DVB-T standards.
>
> As far as I can tell the Grand Alliance, 

I guess you mean the ATSC? The Grand Alliance was some political party
back in 1600's England from what Google told me. (Yeah, I know - you're
being cute. OK.)

> from which we've been afflicted with 8VSB, was populated mostly by
> old farts who hadn't been exposed to much radio technology other
> than NTSC and other television standards.  The only two modulation
> techniques that were seriously considered, by my understanding, were
> 16-QAM and 8VSB.  The conclusion was that 8VSB was "superior" at
> least partly because it only needed a real-valued equalizer in the
> receiver and it was, therefore, simpler to implement.  And since
> 8VSB looks pretty familiar to somebody who's been looking at NTSC
> signals through their career, it probably was very comfortable for
> them to accept it.

That adds up.

> There's a reason you don't see n-VSB showing up anywhere else.   It
> pretty much just sucks, IMHO.  The Grand Alliance really didn't do us
> any favors by selecting that.

Well, you really didn't answer my question. You just basically said
"8VSB sucks." I'm not really contending against that assertion: maybe
it does. All I'm asking is "Why?"

It sounds like, from subsequent posts with Vladimir in this thread,
that the answer, basically, is that it takes a lot more computational
complexity to obtain the same performance with 8VSB as it does with
OFDM. Do you agree?
-- 
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http://home.earthlink.net/~yatescr

Randy Yates <yates@ieee.org> writes:

> It sounds like, from subsequent posts with Vladimir in this thread,
> that the answer, basically, is that it takes a lot more computational
> complexity to obtain the same performance with 8VSB as it does with
> OFDM. Do you agree?

And to be even more explicit, Vladimir postulated that such equivalent
performance would require a MLSE (Viterbi) and that such an algorithm
requires on the order of M^L calculations per symbol. 
-- 
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