Re: [Discuss-gnuradio] information theory -- follow up (off topic)

[Eric Blossom]

On Wed, Mar 12, 2003 at 06:00:14PM -0800, address@hidden wrote:
> Apologies, but I felt compelled to post this... it took me a bit to find it.
> >From Simon Haykin's Comm Systems Text, he describes the result of one of
> Shannon's key theories, dubbed "The Shannon Limit."
> 
> -----
> The information capacity of a continuous channel of bandwidth B Hertz,
> perturbed by additive white Gaussian noise of power spectral density No/2
> and limited in bandwidth to B, is given by:
> 
> C = B log(base2) (1 + P/(NoB) ), 
> 
> with C in bits/second, where P is the average transmitted power.
> 

There is a fundamental assumption in Shannon's model that there is a
single transmitter and a single receiver and that the noise is
Gaussian.  All the excitement that David Reed is probably talking
about (sorry, haven't read the Salon article yet), is related to
"MIMO" systems, "Multiple Input Multiple Output".  Note that in a
direct sequence spread spectrum system, the interferers (those with
other spreading codes) can reasonably be modeled as Gaussian noise.

The exciting part is that although the capacity between any two nodes
falls off because of the increase in noise, the aggregate throughput
of the network continues to grow as you add nodes.  There are usually
some assumptions about node density and an assumption of 1/(r*r) fall
off in power.  In reality there are greater losses due to buildings,
etc, allowing a *higher* aggegrate throughput.  Other things that are
not intuitively obvious that help the capacity of the system include
multi-path and motion of the nodes.

Matt or Tim Shepard can add more if they're listening.  They've both
done substantial theoretical work and modeling in these kinds of
networks.

Eric