Lec 07 _ Link budget, Fading margin, Outage — Transcript

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1. 0:08Good morning, let us begin, this is lecture number 7 and a quick recap of what we have
2. 0:18covered in the last lecture would be helpful for us. In the last lecture we talked about
3. 0:24antennas a little bit from the systems perspective the usefulness of an isotropic antenna.
4. 0:30The one of the things that characterizes is the scale factors which we represent as the
5. 0:36area of an isotropic antenna again it is a conceptual term basically it is something
6. 0:41that is helpful for us in terms of the characterizing of the wireless link. So, the area of an isotropic
7. 0:48antenna if we take it as a reference lambda squared by 4 pi, lambda being the wavelength
8. 0:54of the carrier frequency then we derived 2 very important expressions.
9. 1:02One was the representation of the transmission equation the transmitted power minus the path
10. 1:11loss being the received signal power again this is an equation that would be represented
11. 1:16in dB and I am sure you are comfortable with that way of looking at it because again intuitively
12. 1:23when you look at it as path transmitted power minus path loss that gives you the total power
13. 1:28that is received. So, if we characterized it in this fashion the path loss itself for
14. 1:33free space propagation is 4 pi d by lambda square d is the distance between the transmitter
15. 1:39and receiver. And this is what we used as our baseline and
16. 1:44that helps us characterize the transmission from the antenna to some point which we call
17. 1:52as d break, we assume that the transmission is line of sight. So, therefore, a typical
18. 1:59a AWGN type of transmission can be assumed n equal to 2 free space path loss the only
19. 2:04impairment will be AWGN. Then beyond that there could be other of other impairments
20. 2:10which cause the signal to attenuate more quickly. So, therefore, we see, so this is received
21. 2:17signal power versus the distance we see that initially it decays as a square law and then
22. 2:25eventually at a higher exponent.
23. 2:27So, this is some of the elements that we had discussed in the last class. We also made
24. 2:33a few other observations that typically an antenna would be characterized in terms of
25. 2:39its elevation angle theta and the azimuthal angle phi transmitted and received gains are
26. 2:45the same we are also interested in the pattern of radiation, we typically have for mobiles
27. 2:55omni directional radiation this is different from isotropic which radiates in all directions
28. 2:59omni directional is; omni directional in the azimuthal plane. Then we also mentioned that
29. 3:05the base stations do not radiate in all 360 degrees they radiate with this specific pattern
30. 3:12once you have a pattern then you can talk about a 3 dB bandwidth of the radiation pattern
31. 3:17and that more or less defines how which is be the area where the radiation will be focused.
32. 3:24So, they equation that we have for us is very much dependent on the transmitted power now
33. 3:33there is another point another aspect that I would like you to be very familiar with
34. 3:38and be confident of using because transmitted power is what comes out of your power amplifier.
35. 3:46Now, after the power amplifier if you go back and look at the original diagrams or any of
36. 3:52the diagrams of a base station you will find that there is an antenna the antenna typically
37. 3:58gives you some gain. So, that contributes to the effectiveness of the signal that you
38. 4:03have transmitted. So, Pt times the gain of the antenna is actually what you will see
39. 4:10going out of into the air. So, typically we define a quantity called EIRP effective or
40. 4:17equivalent isotropic radiated power more commonly known as effective isotropic radiated power.
41. 4:23So, this is like saying if I compare this with an isotropic radiator what would be the
42. 4:28power of the radiator be that basically tells you this is this is the maximum radiation
43. 4:33the in that we can expect from this antenna, but we keep in mind that this antenna going
44. 4:39to radiate only in a particular direction. So, this is a way of characterizing the maximum
45. 4:45power output of the antenna. So, Pt times Gt is a very useful quantity now in many cases
46. 4:51the antenna has to be connected to the power amplifier by means of cables that will introduce
47. 4:56some losses for you. So, before you get to the antenna there is some loss. So, that also
48. 5:01has to be accounted for in link budgets they are called the feeder losses its L subscript
49. 5:07f in a wonder what is where is that what is feeding what it is a power amplifier feeding
50. 5:11the antenna the cable that is feeding it and there are losses in those. So, that will have
51. 5:16to be taken out. So, the effective isotropic radiated power
52. 5:20which is what I would like you to keep in mind as we look at the link budget equation
53. 5:27it will be the transmitted power that is coming out of the power amplifier times the gain
54. 5:32which would be a dB term antennas typically we can have 20 dB gain or 15 dB gain depending
55. 5:39upon the type of antenna, you have designed. So, that will be the Gt that that is a positive
56. 5:44factor and then there is a negative factor which takes away from the calculation which
57. 5:50is the losses that we encounter in the system. So, this is quick summary of what we have
58. 5:55discussed in the last class, we also started to talk about Molisch chapter example 3 point
59. 6:04one I hope you had a chance to look at it we will just quickly summarize the key factors
60. 6:10from that example, but before that let me just ask if there are any questions on the
61. 6:15points that we have covered so far, Radiated power , EIRP the how the losses come into
62. 6:22the picture and how to characterize the breakpoint model.
63. 6:28Let us move on. So, today’s lecture, we will touch upon some aspects starting from
64. 6:33the example we will also talk a little bit about fading margin I want you to start thinking
65. 6:40slightly differently about a fading model and it is more in terms of a statistical quantity
66. 6:47and not as a deterministic quantity because fading is something that we cannot anticipate
67. 6:52or we cannot tell ahead of time it is a statistical impairment then as I mentioned yesterday we
68. 6:58will talk a little bit about parabolic antennas we do not use it on a handset or on a base
69. 7:03station, but it is used for any type of microwave backhaul which is also part of the cellular
70. 7:10system. Then a comment about noise figure again most
71. 7:13of you are familiar with the understanding of noise figure, but I thought it would be
72. 7:18helpful for us to also get an insight into the impact of noise figure on the system,
73. 7:25I thought we will spend a few minutes on that after that we will talk about noise limited
74. 7:30systems which is what we have been talking about we basically are saying that there is
75. 7:34no impairment the only impairment is the losses that you encounter because of distance between
76. 7:39the transmitter and receiver that would be a noise limited system compared to a interference
77. 7:44limited system and that leads us into the cellular concept.
78. 7:47So, that is the role out of the plan that we have reading assignment we will definitely
79. 7:56encourage you to look at Molisch chapter 3 because that will complete the discussion
80. 7:59that we have had. So, far please also read Rapaport number chapter 2 because that introduces
81. 8:05cellular concept that is the next topic that we are touching upon and as I mentioned the
82. 8:12cellular concept was introduced by a person by name MacDonald and his original paper and
83. 8:18you know very rarely do we go back and read original papers we do not go back and read
84. 8:22Shannon’s paper or maxwell’s because it all happened you know years ago, but this
85. 8:27happened quite recently in our lifetime. So, it is good to go and see what was the thinking
86. 8:31how did he actually come up with a cellular concept what was the problem that he was trying
87. 8:36to solve. So, I am sure you will enjoy reading it please do take the time to do that it will
88. 8:40be uploaded in module. So, let us begin with the discussion for today
89. 8:46and we will again answer any questions that come about.
90. 8:52Molisch chapter 3.1 example 3.1 I am assuming that you had a chance to look at it, but let
91. 8:58us take a quick look the effective radiated power isotropic radiated power would be the
92. 9:04power output from the transmitter I think that was given to us as 45 dBm that is a 10
93. 9:11dB antenna gain and a 5 dB feeder loss. So, if you take all of that into account the total
94. 9:18EIRP is 50 dBm that is our transmit sign. Then we move over to the receive side I am
95. 9:29sure you would have now. So, basically we are trying to see how much path loss can we
96. 9:33encounter. So, this is transmitted power this is received power and what is the loss in
97. 9:40between. So, what is the receive level that I need to achieve P min is given to us as
98. 9:45minus 102 dBm and we have told that we must account for a 12 dB fading margin. So, which
99. 9:54way do I go with the fading margin the minimum receiver sensitivity is minus 1 or 2 I am
100. 9:59must make sure that I am coming at a signal level higher 12 dB higher in order for me
101. 10:04to have the 12 dB margin. So, if I add 12 dB; that means, the minimum received signal
102. 10:10power it is not sensitivity since your receiver would still receive at minus 1 or 2, but you
103. 10:14have to design your system. So, that the minimum received power including the margin is at
104. 10:19minus the 90 dBm. So, transmit minus receive is 140 dB we are
105. 10:26given that the d break is at 100 meters. So, the path loss still d break is 72 dB notice
106. 10:31how much of the energy you have already lost by the time you reach 100 meters and the remaining
107. 10:38distance accounts for the 68 dB and given that n is equal to 3.5 I am sure the calculation
108. 10:47is straightforward the distance comes out to be 8.8 kilometers.
109. 10:52So, EIRP, received signal power, receiver sensitivity, margin, path loss what is in
110. 11:01between is path loss any questions let me give you a way to visualize this a whatever
111. 11:10we have been talking about and I feel that this is a good way for us to as engineers
112. 11:18to visualize the system.
113. 11:21So, here is a simplified way of visualizing the link budget you have the transmitter that
114. 11:30you can assume that as the output will be the power amplifier that gives you a signal
115. 11:34at a certain level. Then you have the cables that connect you to the antenna that will
116. 11:39cause a drop in the power because the that is the losses then the antenna gain it may
117. 11:45boosted back to its original power or maybe boosted even beyond what the original power
118. 11:49was that that is the level at which you transmit. The other end you have the thermal noise floor,
119. 11:57thermal noise floor plus the noise figure basically tells you where your noise power
120. 12:05level is going to be located. Beyond that you know that you must have a minimum signal
121. 12:10to noise ratio that is going to be your receiver sensitivity. Now what else can happen on the
122. 12:18receive side? You may have an antenna gain antenna gain will boost the antenna boost
123. 12:23the receive signal sing. So, that gives you a plus there may be antenna connector losses.
124. 12:28So, you must account for that that will cause an additional gap most of the time they cancel
125. 12:32each other and therefore, you do not see much of a gain; however, as I told you yesterday
126. 12:36you may be holding the other phone in a way that actually causes additional gain. So,
127. 12:42which means that you know there is an additional loss that you have to account for.
128. 12:46Now, where is the margin coming in? Margin must come above receiver sensitivity. So,
129. 12:54basically whatever is the we after you accounted for all the losses and the gains if this is
130. 12:59your receiver sensitivity if you now want to include a margin you say I cannot receive
131. 13:04at this level I must receive at a level slightly higher that will be the acceptable received
132. 13:10signal power. So, that the difference between the transmitted level and what you can accept
133. 13:15with the margin is what we want to account what we account for as path loss though the
134. 13:21path loss itself has got may have 2 components or 3 depending upon the model that you have
135. 13:26used, we have used the simplest model where you have a single break point which is line
136. 13:31a line of sight or free space propagation up to d break and then a higher path loss
137. 13:36exponent post the d break. So visualize it as signal level gain, loss,
138. 13:45path loss, receive antenna, gain margin and basically you sort of go up and down, but
139. 13:52make sure that you have got moving in the right direction. So, that then you get your
140. 13:56path loss calculations very correctly. Any questions on why something is up why it is
141. 14:03down and probably very intuitive, but if there was something that is not clear that is k
142. 14:09times t Boltzmann constant times t. So, that basically sets your electronic noise floor
143. 14:15right and the if you multiply it by the bandwidth of the receiver that tells you basically where
144. 14:22you will have to set your threshold beyond that there is noise that your receiver will
145. 14:27add that that gives you the that is the additional noise level. So, from the what is the ambient
146. 14:33noise for the particular receiver bandwidth that you are looking at that gives you this
147. 14:37threshold additional noise that your receiver electronics will add that gives you the noise
148. 14:43reference point or Pn a noise power level in your the receiver. So, very important,
149. 14:50but this is a calculation that we had done in the previous lecture.
150. 14:53So, basically it will be K T B that will be this line plus noise figure gives you Pn that
151. 15:01is this line good now I want to want I want you to look at one more aspect.
152. 15:09So, here is a base station you can see the base station here and let us assume that you
153. 15:16are a mobile that is moving in an arc with a certain distance d very simple scenario
154. 15:23except that there is a building here. So, when you are at the position A you are able
155. 15:29to see the base station quite clearly. So, the receive signal power is high as you move
156. 15:34to b still slightly you start to see a drop then between b and c there is a complete drop
157. 15:42in signal level there is a obstruction then when you go back towards d the signal goes
158. 15:48up very very simple scenario. Now, this is what happens in reality as well
159. 15:56because there are obstructions things that we don’t necessarily know or plan for those
160. 16:02cause a degradation in the signal. So, when I move from A to D, I cannot assume that the
161. 16:09signal level is going to be what it is there at any one of those points I have to say that
162. 16:14there is a possibility of fluctuation of the signal level and it is something that I have
163. 16:19no control over. So, what I have to say is there is a notion of an average signal level
164. 16:27Pr bar average signal level, now Pr is a random variable which is got some distribution around
165. 16:37Pr bar. So, again we will introduce a notation a little
166. 16:41bit more formally, but just sort of think about it. So, the whole idea of our discussion
167. 16:47is to say that I have a received signal power.
168. 16:50The; or you can think of it as average path loss average signal power is corresponds to
169. 16:55average path loss as well. So, average path loss is what I expect to see, but there is
170. 17:01a statistical variation and just for ease of visualization I have shown it as a Gaussian
171. 17:07distribution around that in and very often it actually fits a model that is close to
172. 17:13Gaussian. So, it is good for us to sort of use that as a baseline model.
173. 17:18So, if I design my system to have a path loss that is aligned with path loss bar I have
174. 17:27designed it for average path loss and if I did tell you that the definition of outage
175. 17:33means the signal is not of acceptable quality the outage scenario is when the signal goes
176. 17:39below the there is receive the acceptable quality. So, outage basically means that the
177. 17:45path loss it your actually seeing is greater than path loss max and you have designed path
178. 17:50loss max for your scenario as PL bar what is the probability of outage Gaussian distribution
179. 17:58what is the probability of power voltage. Integrate
180. 18:02Integrate from PL bar to infinity with respect to the whole thing what is it is one half.
181. 18:07So, fifty percentage of the time we are going to be an outage now that is not a acceptable
182. 18:13situation. So, what would you then rather do and say that no I am I cannot design my
183. 18:19system for 50 percentage outage I must design it for ninety percentage outage or ninety
184. 18:24percent outage, so 95 percent of the time if the signal should be of acceptable quality.
185. 18:29So, which means that I cannot design the path loss to be PL bar I must allow for a design
186. 18:36that is greater than PL bar. So, if I have moved my design point or the path loss allowed
187. 18:43to this levels basically I am I have designed for this point then the lightly hood of outage
188. 18:49decreases because only if the path loss exceeds the green line I am going to run into outage.
189. 18:54So, you can notice that the shaded region is what pushes me into outage.
190. 19:00so the whole notion of margins this is not some fix number or some rule of thumb which
191. 19:06somebody says no its 10 dB is 20 dB, no, it is a statistical understanding of the channel
192. 19:11and saying that the larger the margin the better is going to be or lower is going to
193. 19:18be my probability of outage. So, again these are all interesting things for you to keep
194. 19:24in mind, but I wanted you to start thinking about the whole notion of margins the fading
195. 19:31aspect and how do you account for it and of course, now keep in mind that this fading
196. 19:36comes from 2 sources one is shadowing which we saw the building type of obstruction and
197. 19:41then the other one is the multipath and constructive and destructive addition of those signals.
198. 19:47So, that is the second element that I want you to keep in mind.
199. 19:51So, why do we need fading margin I would expect you to answer it in a very precise manner
200. 19:56referred to outage its being a statistical quantity and the way to handle the statistical
201. 20:02aspect is to allow for margins and at the end of the day what we can achieve is a is
202. 20:08percentage outage you cannot guarantee 100 percentage, I would also encourage you to
203. 20:13look at Molisch example 3.2 it I will just give you the parameters again I am sure you
204. 20:20can refer to it. This is a problem which very similar to 3.1,
205. 20:26but it is a very good practice let me just highlight the points that are important for
206. 20:32us and do take the time to. So, the carrier frequency is given to us as 900 megahertz
207. 20:41very close to the previous case the transmitter gain given as 8 dB the receiver gain minus
208. 20:532 dB; that means, it is an antenna that is inside and you are holding it in a funny ways
209. 20:58is a gain is minus 2. The feeder losses at the transmitter side
210. 21:04we are given as 2 dB and the noise figure of the receiver is given as 8 dB we do need
211. 21:16to understand the baud rate. So, it is a system with a bandwidth of 25 kilo hertz which also
212. 21:28tells me that my baud rate is 25 symbols per second. So, the equivalent bandwidth that
213. 21:35I need for my translation from e B by I am not to Ps by Pn that is taken to be 25 kilo
214. 21:41hertz as well I want to achieve Ps by Pn of 18 dB Ps by Pn of 18 dB and we are told that
215. 21:56us to use a breakpoint model with the d break of 10 meters. Again maybe just a quick comment
216. 22:04on this previous example was 100 meters now you may wonder why do you take ten meters
217. 22:10is just to check whether we are doing the math correctly no when will you get ten meters
218. 22:14only line of sight. Urban areas.
219. 22:16Urban areas or your; you know mounting it in a campus environment without too much of
220. 22:22a height the antenna. So, basically after 10 meters you are going to hit obstruction
221. 22:27when we look at 100 meters in some rural area or you know where you put the antenna on top
222. 22:31of a very tall mast. So, 100 meters it sees without any obstruction. So, again it is not
223. 22:37just another exercise there is a reason behind the points that are mentioned beyond the d
224. 22:43break we are asked to use a path loss exponent of 3.8 and introduce a fading margin of 10
225. 22:55dB. The question that is being asked is what is
226. 23:02the transmitted power EIRP that is the question and usually this is how this is a more important
227. 23:10type of question that arises given all these scenarios what is the received signal power
228. 23:18oh sorry transmitted signal power what I want to guarantee is the signal to noise ratio
229. 23:24at the receiver Ps by Pn and I want to it give a fading margin as well. So, what should
230. 23:31be my transmitted power? So, again keeping in mind that we are talking about EIRP, you
231. 23:38can adjust the EIRP by increasing the gear the gain of the antenna and reducing the power
232. 23:42amplifier output or it does not matter again what we are asked here is only the EIRP. So,
233. 23:47that is enough to get a question. we need a distance to the receiver
234. 23:52Well the basically it says I must change Ps by Pn after in distance when we have distance
235. 23:58well if you were told the transmitted power you can calculate you probably need the distance
236. 24:08is a very good question you do need the distance of the cell it is there in the in the problem.
237. 24:12So, this is very good example for us to take a look at and solve and if there are any questions
238. 24:18we will clarify it in the class, but I think once you get the basic feel for it this should
239. 24:23not be a problem at all. I want to spend a few minutes talking about
240. 24:31parabolic antennas again as I mentioned these are used in a number of applications and communications.
241. 24:37So, let me just take a minute to sort of get you excited about wireless because this is
242. 24:43you know something very very good for us. So, as I mentioned earlier the area of an
243. 24:49isotropic antenna is lambda squared by 4 pi and we always characterize the gain of an
244. 24:58antenna in the following fashion you take the gain of your own antenna that that you
245. 25:08have and compare it to the gain of an isotropic antenna. So, basically it is equivalent area
246. 25:18that is what will be the area that what will be the effective received signal power or
247. 25:23the gain of your antenna divided by A iso this like saying you know what is your gain
248. 25:28relative to the gain of a isotropic antenna and if you were to express it in dB you will
249. 25:37also see a dB I represented there and it that says it is dB with respect to an isotropic
250. 25:44radiator. So, typically the gain of an antenna will be 8 dB or correctly speaking it should
251. 25:51be 8 dBi. So the effective area of a parabolic antenna
252. 25:57the cross section is a circle, so the effective area of a parabolic antenna. So, basically
253. 26:04this is parabolic antenna this would be pi d squared by 4 and if you remember this is
254. 26:19effective area. So, the entire area does not contribute. So, basically there is an efficiency
255. 26:24factor that must be accounted for and typically it is in the forty efficiently forty percentage
256. 26:32to 80 percentage range depending upon how smoothly you have done it how perfectly you
257. 26:36have made the parabolic reflector all of that accounts for it. So, if I now were to ask
258. 26:43for the gain of a parabolic antenna G of a parabolic antenna this would be eta times
259. 26:54pi d squared by 4 into 1 over lambda squared by 4 pi so basically the effective area of
260. 27:05a parabolic antenna divided by the area of an isotropic antenna. So, this basically I
261. 27:12am sorry. What is eta?
262. 27:15The eta the efficiency of a parabolic reflector would be any antenna is in that range. So,
263. 27:22the cross sectional area times the efficiency of the antenna gives you the effective effectiveness
264. 27:28of the antenna. So, this is given by eta times pi d by lambda whole squared. So, this is
265. 27:40typically how you would characterize the gain of a parabolic antenna and what I want to
266. 27:47share with you is a example of a parabolic antenna the largest parabolic antenna that
267. 27:53we have built and some amazing stuff that has happened with then.
268. 27:57So, when you get a chance please do look up something known as the NASA deep space network,
269. 28:05NASA deep space network consists of 3 antennas and they are located in 3 different parts
270. 28:12of the world and one of the interesting elements that you would notice is the is the size of
271. 28:21the antenna.
272. 28:22So, this is what the antenna looks like one of the antennas looks like it is sitting in
273. 28:28the desert because you know does not want to have a minimum amount of interference from
274. 28:34other sources the diameter of this antenna is seventy meters if you have gone to the
275. 28:40stadium and you look at 100 meter track from one end to the other this is almost the size
276. 28:44of that. So, it is a huge antenna and it weighs 2.7 million kilograms 2 points and that is
277. 28:53the dish is what that is how much it weighs because it is basically metal and you can
278. 28:58think of what it takes to build this type of an antenna in 1960s basically this was
279. 29:04when NASA was doing their deep space mission they knew that they were going to launch a
280. 29:10spacecraft that will go into beyond out of the solar system they needed to track it.
281. 29:14So, basically they design a 3 antenna system where you know 3 parts of the world one in
282. 29:19Spain, one in Australia, one in the US and it is as a communications engineer when you
283. 29:25when you when you actually go and see when you go and study these things absolutely fascinated
284. 29:31by what it can do. So, let us just look at the specifications
285. 29:35of this it achieved an efficiency of 50 percent when you design such a large parabolic dish
286. 29:43it cannot be a single sheet of metal it is individual sheets of metal then that are stitched
287. 29:47together. So, of course, you do not get a perfect finish. So, the this is about 50 percent
288. 29:51is what and the diameter is 70 meters that is a huge antenna and it was it can operate
289. 30:02in a wide range of a of carrier frequencies basically it was designed for 2 gigahertz
290. 30:08to 4 gigahertz and probably the record that its set was for a spacecraft called pioneer
291. 30:1610, pioneer 10 look it up very interesting it is a spacecraft that went out of our solar
292. 30:22system many many years; many many years ago, but the last communication from pioneer 10
293. 30:29by the pioneer 10 had an 8 watt transmitter just 8 watts and the last communications was
294. 30:36when pioneer 10 was at a distance of 1.6 into 10 power 10 kilometers from ground station
295. 30:45and the deep space network actually picked it up and decoded the signal.
296. 30:50It is one of those things where you know you say oh this is absolutely amazing because
297. 30:54the eight watts is lower than most of these bulbs and just imagine that is the power at
298. 31:02which you transmit from a distance of 10 power 10 kilometers and actually the space network,
299. 31:08but the amazing thing about it is not that that is one element of it I want you to one
300. 31:15more element of this one is the error correcting codes. Of course, this able to achieve this
301. 31:21because of the error correcting code I am sure you have studied forward error correction
302. 31:26right and your studied reed Solomon codes very very powerful codes, but the interesting
303. 31:33thing is when pioneer 10 was launched reed Solomon codes were not yet invented.
304. 31:37So, what did they do after reed Solomon codes were invented and they were verified and they
305. 31:43were proven to be the most powerful codes from the ground station they actually programmed
306. 31:48the microprocessor on board to do reed Solomon code. So, in space when it was outside you
307. 31:54know gone past mars and Jupiter they actually programmed it to do reed Solomon code. So,
308. 32:00then it switched over from convolutional codes that it was doing to reed Solomon codes and
309. 32:04then actually was able to communicate and that is how the last communication was with
310. 32:09ground. So, again wireless communications is about
311. 32:12some absolutely fascinating stuff and hopefully you will get excited and read, but how things
312. 32:19is a little bit less ambitious we are you know 3 kilometers 2 kilometers is what we
313. 32:23want to communicate reed Solomon is good, but convocation course is good as well. So,
314. 32:28I think it is we come back to ground and start talking about terrestrial cellular. So, but
315. 32:34I thought its always interesting for you to get a perspective that this is absolutely
316. 32:39exciting stuff you can do things which are it looks like science fiction, but you know
317. 32:45that that is wireless communication So, let us move on to our understanding of
318. 32:51noise figure because this is also important because it helps us keep the practical aspects
319. 32:59in mind can you give me the definition of noise figure what is noise figure as text
320. 33:06book define Input SNR.
321. 33:09Input SNR, thank you. So, basically it is SNR at input.
322. 33:14Let me this write it in short form SNR input by SNR output now if this number is greater
323. 33:22than one that automatically tells you that the output SNR is less than input SNR. So,
324. 33:27in other words somehow your receiver has added to the noise that is already present in the
325. 33:33system. So, the total noise at a receiver which we I have understood it to be K T B
326. 33:42F, K is the Boltzmann constant T is the ambient temperature B is the bandwidth and F is the
327. 33:52noise figure that is how you have calculated and that is how we have done it
328. 33:55Now, I want you to visualize this in a very interesting and novel manner to split is as
329. 34:01K T B that is ambient noise right ambient noise without the receiver this is what is
330. 34:10there if you would look at the bandwidth that is present for you plus K T B F minus 1 K
331. 34:23T B F minus 1. So, this is what is referred to as whatever is there in the ambient this
332. 34:29is what got additionally added because of your receiver. So, this T times F minus 1
333. 34:38is a very important quantity because there call this as the effective temperature of
334. 34:43your receiver effective temperature and this total K T B F minus 1 is the effective noise
335. 34:51temperature of your receiver or the effective contribution of the noise it is as if your
336. 34:55operate receiver was operating not at ambient, but at a slightly higher temperature and you
337. 34:59want to sort of account for that. So, ambient noise plus this noise together is the effective
338. 35:06temporal have total noise and at the end of the day is K T B F, so no confusions about
339. 35:11that. But let us see if we can understand this a
340. 35:15little bit better in terms of the figure on the left hand corner. So, think of it as a
341. 35:21simple amplifier amplifiers also add noise. So, this whole issue of noise figure can be
342. 35:28easily understood in the context of an amplifier. An amplifier with gain G input signal power
343. 35:35Si input noise power Ni and there is some additional noise which shows up at the output
344. 35:41which I call it as Na. What will be the total signal power at the output? Si times G. What
345. 35:51is the total noise power at the output? G Ni plus Na. Na is the power noise power that
346. 35:59of the signal that is added at the other side. So, let us write down the definition of SNR
347. 36:05input by SNR at the output, SNR at input would be Si by Ni divided by SNR at output would
348. 36:15be G times Si divided by G times Ni plus Na.
349. 36:25Now do some simple juggling of the expression factor out the G this can be written as I
350. 36:37just change color. So, it is easy for us to see Si by Ni divided by Si by Ni plus Na divided
351. 36:49by G this has 2 important implications if you wanted to reflect the noise of the amplifier
352. 36:58to the input side what should be the power level we should be Na divided by G because
353. 37:03that would also get amplified by the amplifier. So, this gives us a good way to visualizing
354. 37:07is there was already Ni power Ni noise power present Na by g also got added and then together
355. 37:15this thing got amplified and that is how we got this a got this a expression.
356. 37:20Now, take it one more step basically a factor out Ni on both sides. So, it let me use one
357. 37:28more color let me use green. So, this can be written as Si by Ni, I am going to factor
358. 37:36out Ni. So, then I get Si by Ni divided by 1 plus Na by G Ni. So, Si by Ni will of course,
359. 37:50cancel that gives me a very very important result the that the noise figure is one plus
360. 37:56Na by G Ni or Na by G is equal to F minus 1 times Ni that is a very very useful way
361. 38:14to visualize. And again this F minus 1, why is F minus 1 coming into the picture because
362. 38:21one component comes from ambient that is already present. Now what is a newly getting added
363. 38:26depends on F minus 1 but together the effect of the total noise is F I can split it just
364. 38:34for visualization in this fashion everybody is clear on this on this aspect.
365. 38:42So, now, we move to the realistic situation where you do not have just one amplified,
366. 38:49but you have several cascade of components which will give you the following aspect.
367. 38:56So, the first system let us say has got gain G1 with noise power N1 G2 N2 G3 N3. So, the
368. 39:07way to visualize this, this switch scenario is I want to look at the total noise total
369. 39:16noise. So, total noise will be Ni that is what is coming in at the input first stage
370. 39:24if I want to reflect it to the input side it will be N1 by G1 then it will be N2 by
371. 39:31G1 G2 plus N3 by G1 G2 G3 and so on plus dot, dot, dot again if reflect all of them to the
372. 39:43input side. What is N1 by G1? It will be F1 minus 1 correct times Ni.
373. 40:00What will N2 by G2 be? It will be F2 minus 1 times Ni and 3 by G3 will be F3 minus 1
374. 40:13times Ni. So, now, if I were to rewrite the equation and you know pull out the Ni factor
375. 40:22and then look at the effective noise this is what we get and this is the famous equation
376. 40:27that you would have been familiar with which says that the overall noise figure when I
377. 40:32have a cascade is equal to F1; that means, if there was no other components F1 that is
378. 40:40traditionally how we have understood receivers to function, but if there are cascaded terms
379. 40:45the second one will contribute F2 minus 1 divided by G1 F3 minus 1 by G1 G2…
380. 40:57So, the noise the interpretation of this expression is F1 I cannot do anything about F1 is basically
381. 41:06the if I did not have a cascaded system the noise figure of my front end becomes a noise
382. 41:11figure of my receiver; however, if I have a cascaded system the noise added by these
383. 41:17subsequent sections are down or inside downgraded to some extent by the gain of the preceding
384. 41:25terms. Why is that? Noise at a certain level if the preceding stage has already amplified
385. 41:32my signal by G1 is like saying keeping g at the signal the same level and suppressing
386. 41:36the noise tool by G1. So, second stage noise is suppressed by G1,
387. 41:41third stage noise is suppressed by G1 G2 if you keep the input signal level at the same
388. 41:46point. So, this is a very very useful visualization and again this is for cascaded systems and
389. 41:56if you do have to work with it.
390. 41:57So, when you take a look at any practical receiver the whole idea of this discussion
391. 42:02was to make sure you we come to this stage you will see that there is an antenna and
392. 42:07this is the way we describe and RF filter 3 lines representing the high frequency, the
393. 42:16low frequency and the middle frequency if I cancel out the high and free low I what
394. 42:21I am left with is a band pass filter. So, this is basically a band pass filter because
395. 42:25it allows the middle frequencies to pass does not tell us what those middle frequencies
396. 42:29are, but it tells you that one minutes if you look at this you know that is a band pass
397. 42:33filter the first electronic stage that you will counter after the band pass will be a
398. 42:39low noise amplifier and the reason for that is because this is what is going to decide
399. 42:46the overall noise figure of the system, all subsequent electronic components are going
400. 42:51to be suppressed in terms of their noise contributions by the gain of the low noise amplifier. So,
401. 42:58the LNA is very very crucial in our design maybe a simple example will give us a way
402. 43:05to appreciate that. Let us look at case one case one I have to
403. 43:11design a receiver with 80 dB gain; G is equal to 80 dB. So, I have to have a lot of a gain
404. 43:19stages to get the signal to the received level and the noise figure that I have is 10 dB.
405. 43:27So, what will it have, what will it do this is a receiver that will degrade whatever is
406. 43:32my input noise of signal to noise ratio by a factor of 10 dB. So, again now I have a
407. 43:39case 2 scenario, case 2; I have I am going to design it as a cascaded system I am going
408. 43:47to have G1 very very modest 10 dB gain only, but it is a very low noise amplifier I have
409. 43:58gotten it to be noise figure of 3 dB followed by a second stage where I have a gain of 70
410. 44:08dB I have to get overall gain 80 dB. So, I have got second stage of 70 dB.
411. 44:14And this is less like the previous one noise figure of 10 dB at a glance they do not look
412. 44:21too different you know 80 dB; 80 dB first one 10 dB noise figure this one you may say
413. 44:28oh first stage you did a very good design, but second stage look you messed it up by
414. 44:32putting a 10 dB noise figure amplifier stage are you know stage. So, which means that well
415. 44:37way dominate this is a cascaded system. So, therefore, the effectiveness or the effective
416. 44:44noise figure is 3 dB corresponds to 2 plus 10 dB corresponds to 10. So, its 10 minus
417. 44:521 divided by 10 the again of the first stage is 10. So, the effective F effective or I
418. 45:01think we use the term overall is 2.9. Much different from the earlier case this corresponds
419. 45:12to 4.6 dB. So, without doing much you have actually improved your performance of your
420. 45:18receiver by 5 dB and 5 dB is worth a lot in cellular systems those of you are doing research
421. 45:24know that even 1 dB makes a huge difference. So, that is important element that I want
422. 45:31you to keep in mind. The next point that I wanted you to think
423. 45:38we have talked about fading margin.
424. 45:40I want you to quickly introduce the concept of a noise limited system. So, all that we
425. 45:46have learnt so far I want you to put it together in a single framework. So, the framework is
426. 45:52that we do have a certain noise floor over which we do not have too much control over.
427. 46:00So, notice that basically the red line tells us the noise floor means all the clever designs
428. 46:10that we have done cascaded systems and all of that together tells us this is where my
429. 46:15noise level is basically its K T B, K T B F on top of that you must maintain a minimum
430. 46:24signal to noise ratio SNR min that tells us that you have to have the received signal
431. 46:31level at least at the blue line. On top of that if you want to introduce a
432. 46:35margin that blue line will shift a little further up assuming that you know you know
433. 46:40what the impact is. So, that is where you say that that is. Now the received signal
434. 46:46power starting from the close to the base station or to the mobile or from the mobile
435. 46:51to the base station starts off at a high level and decays with some exponent again I have
436. 46:56just shown it as a single line it may have a breakpoint does not matter it decays with
437. 47:01distance with some exponent now at some point this green line is going to cross over the
438. 47:06blue line; that means, your received signal power is going to be below what you consider
439. 47:11as the minimum received signal power for your system it is receiver sensitivity if it is
440. 47:16there are no margins it will be higher if there are margins. But at some point it is
441. 47:20going to cross the blue line and that is going to be the maximum range that you can cover
442. 47:26with your system with a given amount of reliability. This is a picture of all that we have talked
443. 47:33about so far, is this picture clear, any anything that is not clear about this picture. Because
444. 47:41if this picture is clear then we are ready to talk about the next concept which says
445. 47:47that if I have another base station that is using the same frequency that is the purple
446. 47:54line.
447. 47:55Now, the purple line is going to decay as distance from the this base station is going
448. 48:01and it will count the distance from this base station from the right side and you find that
449. 48:07at some point this purple base line will also cut the blue line, but probably long before
450. 48:14it cut the blue line it actually intersected the green line. Now that point of intersection
451. 48:19between the green line and the purple line what does that tell you, if I am a mobile
452. 48:25sitting at that distance from I am equidistant from both base stations assuming both are
453. 48:30transmitting in the same power level I am receiving this base station signal with the
454. 48:35same power as this base station this is desired signal this is interference I have no idea
455. 48:40what this base station is talking about what is my signal to impairment ratio.
456. 48:461 1 or 0 dB almost none of our communication
457. 48:52systems work at that level. So, which means that I this I cannot even come as far as the
458. 48:57intersection point, I have to stop at that point where my green line is it has to be
459. 49:03only at a sufficiently high level above the purple line the minute it gets less no communications
460. 49:09will not work. So, whatever was your that minimum signal to noise ratio now has to be
461. 49:15defined in terms of signal to interference plus noise ratio SNR is signal to interference
462. 49:20plus noise you do not care whether its interference or noise or both, but the effect of impairment
463. 49:25the denominator term with respect to the numerator term has to be at a certain level.
464. 49:29So, this tells we that what used to be d max previously now may be much much smaller this
465. 49:36is an interference limited system compared to a noise limited system. So, when I start
466. 49:42using multiple base stations with the same frequency I run into an interference limited
467. 49:48scenario. So, what is a limited interference limited scenario when does it arrives that
468. 49:52comes from MacDonalds concept that is called the cellular concept as he envisioned it is
469. 49:57a paper that was written in 1979, it will be uploaded in module take a look at it we
470. 50:02will discuss it in detail in class. It is absolutely from an engineering perspective
471. 50:06it is brilliant piece of work very very elegant very simple and you say well I would have
472. 50:11thought about it that is good, that is a way you should have people should write papers
473. 50:16and come up with new concepts. Thank you.