[e2e] Collaboration on Future Internet Architectures

[David P. Reed]

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).