So the algorithm that tries to equalize receives signal quality, rather than received signal power. It's called distributed power control, or DPC. And DPC works as follows: we'll just illustrate it very conceptually at first and soon we'll go through a computation. The first thing that happens is that each of these transmitters here, in this case we're just going to focus on three. Is going to start transmitting to the cell tower. And they're all interfering with one another as you can see here, we have our in direct gains as we've pointed out before. And then the cell tower is going to measure the signal to interference ratios, from each of these transmitters. So it just takes that measurement has very strict ways of doing that by taking the received power and dividing it by noise that is outside the signal and it is going to send a message back to them telling each one of then what the required SIR is and each of these transmitters is going to use a basic formula similar to TPCL actually to adjust their power. 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. So, in the next segment, we'll walk through the computations of a few iterations of distributive power control which is the famous solution to the near far problem.
