Multipath Question and OFDM

OFDM is touted as a multipath-resistant modulation, but I have a simple
scenario that seems to challenge that assertion.

Consider the situation in which the received signal consists of the
direct path plus a reflected path that is exactly 180 degrees out of
phase at the center frequency and at (or near) the same signal strength
as the direct path.

This is going to cause a deep null. However, isn't it true that this
null will have a rate-independent width? That is, whether we're
transmitting 100 Mb/s or 10 kb/s, the null bandwidth remains constant,
does it not?

If so, then any signal rate (or modulation scheme) that results in an
OFDM bandwidth less than the null width is going to fail regardless of
"multipath-resistant" nature of OFDM. Right? (I believe this multipath
and bandwidth scenario is called "flat fading."

Assuming all this is correct, then isn't it true that the designer of
an OFDM system has to ensure the bandwidth is sufficiently large to
take advantage of the multi-carrier nature of OFDM? 
-- 
%  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

Randy Yates wrote:

> OFDM is touted as a multipath-resistant modulation,

Popular fallacy.
OFDM is a wideband modulation which allows simple suboptimal receivers.

> but I have a simple
> scenario that seems to challenge that assertion.
> Assuming all this is correct, then isn't it true that the designer of
> an OFDM system has to ensure the bandwidth is sufficiently large to
> take advantage of the multi-carrier nature of OFDM? 

Of course. It works exactly the same way as a radar: the bandwidth of a 
signal must be wide enough to resolve the differences in the path 
lengths. This is the fundamental feature regardless of the type of 
modulation.

BTW, it takes a lot of bandwidth to be multipath resistant: ~tens of MHz 
for outdoors and ~hundreds of MHz for indoors.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:

> Randy Yates wrote:
>
>> OFDM is touted as a multipath-resistant modulation,
>
> Popular fallacy.
> OFDM is a wideband modulation which allows simple suboptimal
> receivers.

What bloody good is a "simple suboptimal receiver" that fails in
the presence of multipath?!?

> BTW, it takes a lot of bandwidth to be multipath resistant: ~tens of
> MHz for outdoors and ~hundreds of MHz for indoors.

Is that the sort of bandwidth that the new standards based on OFDM
use? For example, DVT-B and 802.16a?
-- 
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <yates@ieee.org>           % 'Waterfall', *Face The Music*, ELO
http://www.digitalsignallabs.com

Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
> [...]
> OFDM is a wideband modulation which allows simple suboptimal
> receivers.

Suboptimal in what sense?
-- 
%  Randy Yates                  % "Bird, on the wing,
%% Fuquay-Varina, NC            %   goes floating by
%%% 919-577-9882                %   but there's a teardrop in his eye..."
%%%% <yates@ieee.org>           % 'One Summer Dream', *Face The Music*, ELO
http://www.digitalsignallabs.com

On Dec 12, 12:28&#4294967295;pm, Randy Yates <ya...@ieee.org> wrote:
> OFDM is touted as a multipath-resistant modulation, but I have a simple
> scenario that seems to challenge that assertion.

OFDM (with cyclic prefix) allows one-tap equalization - in other words
the channel equalization process requires only one complex multiply
per subcarrier. This results in a simple receiver - compared to time-
domain EQ (e.g. Rake receiver) or the equivalent in the frequency
domain involving matrix multiplication.
It also makes the channel estimation process (e.g. using pilot
symbols) simple.

Note there are many other modulation technologies that can be
considered as generalizations of OFDM, or a combination of OFDM with
frequency coding - such as MC-CDMA, SC-FDMA (=DFT-precoded OFDM), etc.
Each requires a guard interval to allow simple removal of ISI, which
should be in the form of a cyclic prefix (rather than, say, zero
padding) in order for the EQ to be one-tap.

> If so, then any signal rate (or modulation scheme) that results in an
> OFDM bandwidth less than the null width is going to fail regardless of
> "multipath-resistant" nature of OFDM. Right? (I believe this multipath
> and bandwidth scenario is called "flat fading."
>
> Assuming all this is correct, then isn't it true that the designer of
> an OFDM system has to ensure the bandwidth is sufficiently large to
> take advantage of the multi-carrier nature of OFDM?

Yes - OFDM in itself does not guarantee that frequency diversity can
be achieved. However if the bandwidth is large enough for frequency
diversity, OFDM is a simple way of implementing it.

-T

On Dec 12, 8:19 am, Randy Yates <ya...@ieee.org> wrote:
>
> Cyclic convolution? Orthogonalizes the operation? What do these mean?
> Is cyclic convolution the same as circular convolution?

Cyclic convolution = circular convolution.

Recall that the DFT is the correct transform for periodic (circular,
cyclic)
signals, so you learned that if you were to compute a linear, non-
cyclic
convolution using DFTs or FFTs, then you have to do this overlap-add.

Now you have to do it backwards, in a way!

> PDP? Last I knew, that was the prefix for a line of Digital Equipment
> Corporation computers.

Power Density Profile.

Randy Yates wrote:
> Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
> 
>>[...]
>>OFDM is a wideband modulation which allows simple suboptimal
>>receivers.
> 
> 
> Suboptimal in what sense?

In the sense that OFDM is not approaching the channel capacity limit, 
being wasteful both in power and in bandwidth. However they are buying 
the implementation simplicity for that.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Randy Yates wrote:


>>BTW, it takes a lot of bandwidth to be multipath resistant: ~tens of
>>MHz for outdoors and ~hundreds of MHz for indoors.
> 
> Is that the sort of bandwidth that the new standards based on OFDM
> use? For example, DVT-B and 802.16a?

While ago, when working on my thesis, I was surprised by that fact, too. 
Many systems advertised as multipath resistant evidently don't have 
enough bandwidth for that.

As for the modulations, my preference is the frequency hopped scheme. It 
is simple, robust and efficient in the implementation. The bandwidth can 
be made as wide as required.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Fri, 12 Dec 2008 05:49:55 -0800 (PST), Tom <tom.derham@gmail.com>
wrote:

>On Dec 12, 9:37&#4294967295;pm, Randy Yates <ya...@ieee.org> wrote:
>> Tom <tom.der...@gmail.com> writes:
>> > [...]
>> > OFDM (with cyclic prefix) allows one-tap equalization - in other words
>> > the channel equalization process requires only one complex multiply
>> > per subcarrier.
>>
>> Why? This seems to be presuming some relationship between total
>> bandwidth and number of subcarriers. Otherwise, consider the
>> scenario in which a single subcarrier's bandwidth is so great
>> that a fade is not flat even within that subcarrier.
>
>Remember that detection at the receiver is done over finite size
>blocks of samples corresponding to one OFDM symbol length.
>The response of the DFT at an evaluated frequency is a sinc function
>where nulls lie in all the other subcarriers. So there is no energy
>spread from one subcarrier into the others (orthogonality).
>There is no ability to resolve other frequencies between two
>subcarriers - due to the finite length of the DFT input. So a single
>subcarrier is "flat fading" by definition.
>In fact, in order to get the very low coherence bandwidth that you
>describe (i.e. where the actual channel is frequency selective between
>the frequencies corresponding to adjacent subcarriers), it would
>require the channel length (maximum multipath delay) to be longer than
>the OFDM symbol length! This is not allowed to happen since the guard
>interval length (which is normally much shorter than the OFDM symbol
>length) must be at least as long as the channel length.
>
>-T

And that does have an effect on dictating the width of the
subcarriers.    Generally as the range gets longer and the channel
delay spread (PDP) gets longer, the subcarriers have to get narrower.
So one does have to make the subcarriers narrower as the delay spread
gets longer in order to maintain flat fading in each subcarrier.    So
Randy's question was pretty good, actually, and I think the answers
have been a little misleading in a way.

It *is* possible to have a subcarrier wider than the channel nulls,
and then you'll need more EQ taps per subcarrier since the fading per
subcarrier is no longer flat.  That does mean that the whole idea of
keeping the delay spread contained within the cyclic prefix has been
violated, but it can be done (and some systems are actually designed
that way).

For examples:

UWB - very short range, very wide subcarriers (MHz).
802.11 - LAN range, medium-width subcarriers (360kHz)
DVB-T - Long range, narrow subcarrier (~1-2kHz)

The symbol rate per subcarrier just has to be low enough to cover the
channel delay spread in order to use a single coefficient EQ.   Just
like a single-carrier system.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

> Randy Yates wrote:
> >>BTW, it takes a lot of bandwidth to be multipath resistant: ~tens of
> >>MHz for outdoors and ~hundreds of MHz for indoors.
>

Hi Randy,
while comparing the pros and cons of OFDM to other systems..here are
two other factors to consider:

1) resistance to impulse and burst noise

2) PAR or peak to average ratio of the Tx signal in the transmitter
and the impact this has on the hardware design re to linearity and
power consumption..

these are two of the downsides to OFDM as far as I know..

Mark