So, we just looked at what was initially proposed solution to the near-far problem and we said it was called the TPC or transmit power control algorithm. The TPC algorithm tries to do is to equalize the received signal power, but, it turns out that signal power isn't really what we need the calls to be equalizing. We need to equalize something else, which is called the signal quality. Now, quality is different than power, because quality takes interference into account. So when we looked at the TPC algorithm, we were only concerned with what issue the transmitters were sending, so this one was sending may be 2 milliwatts and this guy closer to the station was send 1 milliwatt if the station was over here or something. And, while we, we were looking at this person's link to the transmitter and this person's link to the transmitter. And we said, while this person needs to then increase his power to 4 milliwatts and this person cuts it down to 0.5 milliwatts I'm just making these numbers up, then everything might be okay. The problem is that when this person increases up to 4 millawatts that he's causing extra interference to this transmitter right over here. So we kind of have a vicious cycle, where as this person increases his power and this person would have higher interference, then he might have to increase his power, which would cause this person more interference. Then he might have to increase his power and so on and it'd be a vicious repetitive cycle or an arms race if you will to the maximum transfer of power. So we need a way to do that, and we'll look at now, exactly what signal quality really is and we'll define this. So suppose we have three transmitters, A, B, and C, and they're all looking to transmit to a base station. Now we can consider the receivers on the single base station as co-located. So this is receiver A, receiver B, and receiver C. Even though they're all going to a point on the base station, just look at them as three separate places on the base station. So if we look at receiver, if we look at transmitter B for a second, let's focus on him first. We have a few parameters here. The first one is the direct channel. So B has a direct channel right to his receiver B. This is transmitter B, this is receiver B. And that's where he wants to get his signal, so he wants to get it to receiver B. But now, if you look at these receiver, what we also have to take into consideration is the fact that A and C are going to cause interference. So, this is the direct channel, and this is the indirect or interference channel. And direct here really means desire to indirect this undesired, and this is also an indirect as well. And, we have the same exact thing for each of the other transmitters and receiver pairs. So for A, he has a direct channel and his interference comes from interfering channels with channels B and C. And then in addition, each of these receivers themselves are going to have some amount of internal noise. It's just basically random fluctuations of electrical signal. We won't go into it in much detail, but each receiver has a certain amount of a noise that is within it as well. So, this leads us to define what's is known as the signal to interference ratio. And we'll look at exactly how that is computed when we look at the next algorithm, but basically, we want to take all this good stuff and divide it by all this bad stuff. So the good stuff is the direct signal. Now, the bad is the interfering signal. We can call that the interference. In this diagram right here, we can see for B, the interference would be this arrow coming through, as well as this arrow coming through. Plus, we have some noise in the receiver that we have to get over. So, every transmitter needs a certain signal to interference ratio or SIR, and SIR is how we quantify signal quality. So, when we try to equalize signal quality rather than signal power, we're trying to equalize the desired signal to interference ratios. So now, suppose we have three phones that are standing close to one another and each of them has some desired signal to interference ratio that they all want to pick. So, this phone first sees some it, that he's lower than his desired signal to interference ratio, so we increase this power. Now, that causes interference for this phone, and this phone. So now, each of them increase their powers, which then causes this phone to increase his power, again. Causing this phone to increase his power, causing this phone to increase his power, and it becomes a really vicious cycle again, as we said. So the question we have to ask is, is there a way to avoid this arms race? Is there a way that we can follow some sort of a courtesy procedure on each of these phones so that no one will ever come up and transmit too loud? And the answer is, yes. That is possible to do provided that the signal to interference ratios are feasible. So we want the desired SIRs, the SIRs that each of these guys choose and that they want to get to, to be feasible. And as long as they're feasible, then we can have a solution and we can find a set of transmit powers for each of these phones to send that. Such that all of these signal interference ratios will be satisfied at the same time.
