Then they'll readjust their power levels accordinginly.
And now, this is going to cause different types of interference in different types
of channel gains. And then, we're going to measure the SIRs
again, and send the SIRs back, and adjust their powers again, and so on.
So the next way is an iterative algorithm, and it will keep going on just
like this. Iterative means it's going to take
multiple steps, and eventually, we hope that the algorithm will converge which it
will converge, as we said, provided that the SIRs are feasible.
And again, by feasible we mean compatible, or that they can all be
satisfied simultaneously. So a good word for this would be
compatible [SOUND], for feasible. And, in fact, in addition to Converging
to a set of power levels that will work and that will achieve these desired
signal, interference ratios. They're also going to be optimal in the
sense that they're at the smallest power levels as possible.
So, the reason the higher power levels are bad, just to give you an idea is
that, the more power your cell phone uses to transmit, the more its batteries are
going to drain. So you want to always be setting it at
the lowest power you can while still achieving that SIR value.
And additionally, it's just not good to waste energy when you don't have to.
So that's another thing as well. So before we continue on to this example,
first let's point out a few of the values that we will be working with in the first
thing about each of the examples that you will see throughout this course is that
they're going to be much, much smaller than a real system.
So a real system in a real cellular are going to have many many many more devices
than you're going to see and we're going to be working with here, but we're
constrained by what we can write on a single piece of paper, and additionally,
it will illustrate the main ideas just by considering a smaller example.
So, now in this table over here, we're showing each of the three transmitters on
this side, A, B, and C and then the receivers as well.
And this, each of these values, is what we call a gain.
And the direct gains are from, for instance, from A to A, from B to B, and
from C to C. Those are the [SOUND] direct Channel gain
so we can write that here direct this is direct and this is direct.
And what this is really saying from A to A being point 9 is that whatever transmit
power we start with over here its multiplied by point 9.
And that is what it gets received at over here.
And we look at these as gain values, but since there less than one, we know that
is going to be less than what we transmitted at by the time we get to the
receiver because we're multiplying, so its really an attenuation but we look at
them as gain just strictly speaking for, in mathematical terms.
So then from B to B it's 0.8,so B has not as good of a direct channel gain as A
because you the direct channel gain to be as high as possible and C has 0.9 just
like as A does. Now we looking for the interfering gain,
for instance we can say from A strating with A to B, from A to B is 0.1, so this
value over here B 0.1. from A to C we have 0.2, so this couples
down here 0.2 of that. So wherever transmittive power we're at
we multiply it by 0.2 and we get how much power is going to come into the receiver
from as a result of A. So we want the indirect channel gains so
each of these dotted lines are indirect. And I'm not going to write all of the
indirect, I'm not going to write indirect six times.
And I don't need to write indirect six times, you get the idea.
So, we want the indirect gains to be as small as possible, whereas we want the
direct gains to be as high as possible. We can't always get all we want and then
from B we know B couples into A as 0.1 and B couples into C as 0.2 C couples to
A a 0.2 and C couples to B as 0.1 one thing we should know is that this table
is not symmetric And symetric would mean that going from B to A is the same thing
as going from A to B. So for many of the values here it
actually is symetric but for instance if you look at from C to B and B to C there
not the same cause we have point 1 and 0.2.
And the reason they're not the same is that different transmitters are going to
have different effects on different receivers.
Now, the next set of values that we need are based upon the links themselves.
So link A, link B, and link C have different parameters.
First is the target SIR, At the receiver. The target signal to interference ratio.
So A wants to get to 1.8, B wants to get to 2.0, and C wants to get to 2.2.
And now, in terms of noise, as we said, each noise is going to have a certain
amount of power. We're in a fraction of a milliwatt here.
A has 0.1 milliwatts noise, B has 0.2 milliwatts noise, and C has 0.3
milliwatts noise. So, you can see that they have different
necessities for different signal qualities, which'll depend upon the
specific phone and. Things along those lines, but
additionally, the receivers themselves are going to have different noises too,
and C is the worst in terms of noise, whereas A is the best.
Christopher BrintonLecturer
Mung ChiangProfessor
