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Now one of the issues with CDMA is clearly that everybody is talking at the same

Â time, the same frequency band. In other words, the frequency reuse vector is one.

Â And how do we deal with the resulting interference? Interference in the air for

Â cellular network is the first example in this course of something called negative

Â externality. Externality, here, roughly speaking, refers to the fact that your

Â happiness also depends on what other people do. Your signal, your cup of tea or

Â coffee is other transmission's poison, and this is what we call a negative

Â externality. Now, we will also later look at positive externalities in social and

Â technological networks. Sometimes people also call this the tragedy of commons. In

Â the later lecture, we will talk about, more tragedy of commons and how to deal

Â with that in social and tecnological networks. Now, one famous special case of

Â interference in the air is so-called near-far problem. If we go back to this

Â picture, you see that A mobile station a is much closer to the base station than

Â mobile station B. Okay? Your neighbor or your friend's, let's say, your friend's

Â iPhone might be much closer than your Android phone to the base station. Maybe

Â your friend is sitting right beneath the cell tower, the base station, and

Â therefore, the distance it traverses is much shorter, and the signal received at

Â the base station is much stronger than yours, and it can drown out your signal,

Â and that is what we call the near-far problem. Okay? The near user will

Â overwhelm the farther away users signal. Now, there was a simple solution provided

Â by Qualcomm in the late 80s that uses the idea of feedback control. Now, later,

Â we'll see much more complicated feedback control in the network. In this case, this

Â is a simple one hop from the base station to different mobile stations. The degree

Â of freedom here is exactly transmit power, and, it says that, well, adjust your

Â transmit power based on where you are. It's going to estimate first the channel

Â condition, for example, how much channel loss does your signal suffer? And then it

Â would reverse that, so if your channel of loss is a factor of two, okay, and the

Â other is a, a factor of 0.9 for example, okay? Then, I will tell you, look, you

Â should multiply your signal strength by a factor of two, and you should multiply by

Â a factor of one over 0.9, which is much smaller than two. Then, this power

Â adjustment would cancel out the effect of the channel attenuation, and then I would

Â have equalized received signal power from both of you and the base station. So this

Â is a simple algorithm. There's no iteration and it is through a central

Â command by the base station and it suffices to. achieve equalization of

Â received signal power. And without this feedback control to take off the near-far

Â problem, you would never be able to implement CDMA, because, the amount of

Â interference would be just too much. Now, what if you need to achieve a target

Â signal quality which might be different for different mobile stations? Not just

Â simply equalize all the received power and that was the challenge in the early 90s.

Â Now in order to make sense of that question, we'll have to provide a little

Â bit of symbol. ,, . Okay. Now, we're going to look at a very small

Â cell. There are only two mobile stations. Okay? Two iPhones, one and two, and one

Â base station. Even though there's one physical receiver, we're going to divide

Â it into two logical receivers. Okay? Receiver one and receiver two. And we will

Â look at four different channels, two of them are the so-called direct channels.,

Â these are the desired intended communication path. Of course, in the air,

Â there's no real physical pipe of a channel. So, by channel, we really mean a

Â logical link. What actually happens is just energy

Â propagating in the electromagnetic field and being picked up by antenna. We don't

Â have pipes as if we are, you know, drawing pipes, but actually don't. so these are

Â logical channels. And we say that there is a transceiver pair from the transmitter.

Â one t o the logical receiver one, and then, from transmitter to the logical

Â receiver two. So happens these, two logical receivers are physically

Â co-located at the same spot and then, what about interference? When Transmitter 1

Â talks, the energy propagates, okay? And part of a energy will be picked up by this

Â logical Receiver 2. This is a dot line to represent an interference channel and

Â there is the other interference channel and we will use the following symbol Gij

Â to denote the channel loss on the corresponding direct or interference

Â channel. Now somehow the community does touch with the term channel gain even

Â though this G is numbers between zero and one. So, it should be cloud channel loss,

Â let's say that called channel gains. Now, this is a little tricky. So, we go a

Â little slow here, it says Gij represents the channel gain from the transmitter of

Â logical tranceiver pair to the receiver of logical transceiver pair i. So, we're

Â going to use the terms user, transmitter receiver pair, or logical transceiver pair

Â interchangeably. For example, Gu11 is the channel from the transmitter of logical

Â pair one to the receiver of logical pair one. Let's say, well, that's a good

Â channel indeed. It is the direct channel for desired communication and so is in

Â general, G2 too. So in general, Gii are the direct channels. But when j is not

Â equal, equal to i, for example, G21 that says, this is from the transmitter of pair

Â one over here, to the receiver of pair two. And therefore, this is the channel

Â gain of an interference channel. G12 says this is from the transmitter of pair two

Â to the receiver of pair one. And, in general, G12 is not equal to G21,

Â necessarily. Now, ideally, of course, we want Gii's to be bigger than Gij's, where

Â j is not equal to i. And, indeed, with the help of those spreading codes, this ones

Â minus ones we do have usually, a Gii that's bigger than Gij's. However, there

Â could be many j's not equal to i. Okay, there could be tens of them. And, even

Â though each one provides just a l ittle bit of interference to your transmission,

Â they could add up. Okay. That is the cocktail party you should log

Â in. So, how do we capture the notion of received signal quality? If the quality's

Â high, you'll be able to talk more efficiently.

Â For example, you can talk faster and the receiver can still understand what you are

Â talking about. But sometimes, in cocktail party. because it's so noisy around, so

Â much interference, you have to slow down your conversation. Okay? You have to talk

Â slower. That is, fewer bits per second. So that the, the receiver can hear you

Â correctly. And the way we capture. this ratio, is through the so called SIR,

Â 9:25

Signal-to-interference ratio plus noise ratio. Now, what is the signal? I'm not

Â talking about a signal power at the transmitter side. I'm talking about the

Â signal power at the receiver side. So that is the transmit power which we denote by P

Â sub I'm going to say i, P sub i multiplied by the channel, that's the direct channel,

Â and getting to the receiver of pair i. That's the received power. Divided by,

Â because it's a ratio, the interference collected at the receiver, that is P sub j

Â times Gij. Okay? From. J transmitter, okay, to the same common

Â ith receiver and there are many of such j is not equal to i. Plus, at the ith

Â receiver, there's usually some noise term, n sub i. This is what we call the SIR

Â associated with the ith user. For example, in our previous case, however just two

Â users and therefore SIR1 is simply P1 G11 over P2 G12 plus n1 and also SIR2 is just

Â P2 times G2 over interference, which is P1 times G21 plus n2. Okay?

Â But in general, you have more than one term here in the denominator. Okay.

Â So now that we have the notation. Let's look at what kind of a function this SIR

Â is, SIR for each transceiver pair i, okay, the received signal differential ratio for

Â pair i is really a function of the entire vector with this notation on top of power

Â vector P. Okay? not just the function of your own power, but also a function of

Â other's po wer. That is the mathematical representation of

Â the very physical fact of interference in wireless communication. If there's no

Â other users easy to increase SIR for user one, I just increased P1, but of course

Â there are other users. A larger P1 helps SIR1, but it will also show up as a larger

Â denominator for the other SIRs that would hurt the other SIRs. Okay?

Â So First observation is that SIR is a function of the entire vector P.. Now,

Â second, what are the constants and what are your degrees of freedom. Because we're

Â talking about transmit power control, so obviously, the degree of freedom is the

Â vector p and that's what we want to design and optimize over. We are given all the

Â Gij's that is determined by the propagation environment. Okay, is this

Â indoors, is this outdoor, what kind of terrain is it, it is given by the location

Â of the transcievers. and that's not up to us to optimize. And we are given all these

Â receiver electronics and therefore their noise. So the Gs and n's are given

Â constants, the Ps are what we'll be calling the optimization variables in

Â transmit power control. So now our goal is to say all difference transceiver pairs

Â index by i will like to get certain SIR achieved. Okay?

Â So, the question is for a given set of Gs and n's, can we find such a vector P? Is

Â there such a vector P at all to achieve certain target SIR values.

Â And if there's more than 1, which one shall we pick? In the next module of the

Â video lecture, we will see the answers to these questions in a distributed mechanism

Â to coordinate interference in wireless cellular networks and that mechanism is

Â now in use in many wireless standards.

Â