[e2e] Collaboration on Future Internet Architectures
David P. Reed
dpreed at reed.com
Fri May 4 11:40:06 PDT 2007
Nothing magic about MIMO in this regard.
Lachlan Andrew wrote:
> On 03/05/07, David P. Reed <dpreed at reed.com> wrote:
>> the standard analysis
>> presumes that the noise process is independent at each receiver, an
>> overly non-physical and way-too-conservative-assumption by a factor
>> likely o(M^k) where k is >= 1.
>
> Thermal noise in the radio fround-end is almost certain to be
> independent at each receiver. If all other noise can be averaged out,
> this noise will still exist, and give the standard assumption.
I agree, but thermal noise in the radio front-end is a controllable of
the radio design of the front-end - it's not a limit on capacity that
depends either on the number of radios or on the environment in which
the radios operate.
There is no obvious reason in our analysis that is intended to cover all
possible realizable radio systems, to hold the receiver design constant
(including its internal noise process, which is not actually "thermal" -
in the strict sense of being caused by "temperature" - which is not a
physical quantity, just a statistical measure of actual physical
processes.) Thermal noise is any statistical input whose behavior
relates to temperature - in electronic receivers (based on QED effects)
it is due to various statistics of electrons in condensed matter
systems. Those statistics are bulk properties that can be varied by
choosing metals or semiconductors or other exotic materials. Thermal
noise in a superconductor is different in quality than thermal noise in
a semiconductor or in a copper wire.
If we are considering all possible receivers, we should stop at the
process that interacts with the electromagnetic field - be it a wire or
plate antenna, or a SQUID.
>
>> The per-node capacity in this hypothetical conservative model is thus
>> Cap[node] = o(W*log(S/N))...
>
> ... if we have a single receiver. That is why David Tse's work is all
> MIMO.
You didn't follow my derivation. If the total system capacity of M
radios is o(M*W*log(S/N)), then the per-node capacity is o(W*log(S/N)).
Simple division has nothing to do with MIMO.
In fact, there is nothing magic about MIMO systems at all - the magic
arises from the shape of space, which means that the waveform output by
an antenna is a 3D waveform, so that the signals from ANY two antennas
are orthogonal in 3-space. That's equivalent to saying that the only
thing that can interfere with a photon is the photon itself - a basic
axiom of quantum mechanics that goes back to the beginning of the 20th
century.
This orthogonality is the basis (get the pun) of MIMO systems, but it is
exploitable by any system that samples space-time in multiple distinct
points. (of course you have to have think in 4D vector spaces, rather
than in scalar functions of time to get the point).
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