Transmision impairments and capacity — Transcript

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1. 0:00ep100 data communication and computer
2. 0:04networks some illustration in this
3. 0:06material are collected from the book by
4. 0:08foron data Communications and networking
5. 0:10published by
6. 0:11mcrill given a transmission medium we
7. 0:14would like to know what is the ultimate
8. 0:17data rate that we can use the medium for
9. 0:21this ultimate rate is often referred to
10. 0:22as the transmission capacity of the
11. 0:26medium in order to come to an expression
12. 0:29to compute
13. 0:30the transmission capacity we have to
14. 0:32first look at what happens to the signal
15. 0:35as it propagates for medium the first
16. 0:37transmission quality we consider is
17. 0:39called attenuation it's a dampening it
18. 0:42means that you send a signal into a
19. 0:44medium but the signal will lose energy
20. 0:46in the medium no link is perfect and we
21. 0:49can look at the ratio of the input power
22. 0:52to the output power this is often
23. 0:54expressed in decibels so you see here
24. 0:56the expression we take the logarithm of
25. 0:59the ratio of the input and output powers
26. 1:01and you multiply it by by 10 for example
27. 1:04if you have input power of 120 Ms and
28. 1:07now receive out 30 m then you have an
29. 1:10attenuation of roughly
30. 1:1260b when we talk about power and
31. 1:15sensitivity tenation we it's often very
32. 1:17convenient to count in decibels for
33. 1:20instance by halfing the power of a
34. 1:22signal it means that it has lost 3db in
35. 1:25its
36. 1:26strength we can also represent power
37. 1:28levels relation to to reference power
38. 1:31level so that zero Deb means that the
39. 1:33power is the same as the reference level
40. 1:36you can see that because p in P out that
41. 1:39ratio is one and logarithm of one is
42. 1:41zero this is used for transmit the
43. 1:43output power and receive input
44. 1:45sensitivity so we measure it in decibel
45. 1:47wat or in decibel mwatt that means that
46. 1:51we have either a reference value of one
47. 1:55wat or of 1 M as the Expressions show
48. 1:57here it's only used for convenience if
49. 2:00we have a sender power expressed in say
50. 2:03uh
51. 2:04dbm then we can subtract off the
52. 2:07attenuation in decel from that power and
53. 2:09then we will get the receiver
54. 2:14power transmission quality is affected
55. 2:17also by something we call
56. 2:20Distortion if you look at the composite
57. 2:22signal as sent in such as as a signal
58. 2:25that is created to represent data then
59. 2:29you can look look at it as different
60. 2:30tones that are superimposed on one
61. 2:32another these different frequencies
62. 2:34these different tones propagate with
63. 2:37different speeds for the medium so when
64. 2:40they get at the receiver they get
65. 2:43superimposed or summed up in a different
66. 2:46way than they were generated at the
67. 2:47center and this is the
68. 2:49Distortion the result is that the signal
69. 2:51changes form or shape as it propagates
70. 2:54with the
71. 2:56medium we also have that the aen ation
72. 3:00might be frequency dependent so that
73. 3:03certain frequencies are dampened much
74. 3:05more than others we talk about the low
75. 3:08pass if the higher frequencies are
76. 3:11attenuated more than low ones and we
77. 3:13talk about the high pass if the lower
78. 3:15frequencies are attenuated more than the
79. 3:17high frequencies or band pass if there's
80. 3:20attenuation in the in the lower and the
81. 3:23higher region but there is a span
82. 3:25between these two regions where the
83. 3:26transmission can propagate with little
84. 3:29attenuation
85. 3:31transmission quality is affected by the
86. 3:33attenuation by the Distortion but
87. 3:35there's also noise added to the
88. 3:38signal this illustrates here that this a
89. 3:40waveform transmitted from point one and
90. 3:43then there's some noise generated from
91. 3:45the outside that's added to the signal
92. 3:48so that theed signal looks different
93. 3:50than what has been
94. 3:51sent noise is an uniside signal that's
95. 3:54added to transmitted signal the most
96. 3:57common form is what we call thermal
97. 3:58noise the this is due to the random
98. 4:01motion of electrons in the
99. 4:03medium of the signal frequenc and
100. 4:04amplitude and can be considered to be
101. 4:06added to the signal we call the Noise
102. 4:09White if it contains all frequencies
103. 4:11with equal power the signal to noise
104. 4:14ratio SNR is the ratio between the
105. 4:17signal that we sent into the medium over
106. 4:21the noise power that is added in the
107. 4:23medium this RTI is often also measured
108. 4:26in decibel so what can you do to handle
109. 4:29the signal
110. 4:31degradations you can compensate foration
111. 4:34by amplification but it amplifies both
112. 4:36the added noise as well as the signal
113. 4:38the amplifier is not perfect also and
114. 4:41could add its own
115. 4:42noise you could put a receiver that
116. 4:46receives the
117. 4:47signal generates back the data that was
118. 4:51carried by the signal and then generate
119. 4:53a new signal with the data going out
120. 4:55this is called
121. 4:56regeneration and this cleans off any
122. 4:59noise that have been added to the signal
123. 5:02but the receiver may make additional
124. 5:05errors and these errors of course
125. 5:07propagated over in the outgoing uh
126. 5:12medium we can have noise filters that
127. 5:15filter out unused parts of the channel
128. 5:17bandwidth that's not used for the actual
129. 5:20transmission and we can protect against
130. 5:22Distortion by equalizing the signals
131. 5:24that's being received meaning that we
132. 5:27could separate the signal the composite
133. 5:29signal into its different
134. 5:31sub frequencies and then adjust them
135. 5:35time and amplitude wise and put them
136. 5:38together again so that we compensate for
137. 5:40for the different propagation speeds
138. 5:42that the different frequencies had and
139. 5:43the different attenuations that the
140. 5:45different frequencies had in the medium
141. 5:47there's also other disturbances such as
142. 5:49cross talk which means that signals that
143. 5:52are pulled along with one another for
144. 5:54instance the unshielded twisted pair
145. 5:56cables signals in the pairs made leak
146. 5:59out and inducing a signal in another
147. 6:02pair this is protected against by
148. 6:05shielding the cables and reducing the
149. 6:06leakage the transmission capacity is the
150. 6:10ability of a medium to transmit data it
151. 6:14relates to the bandwidth of the medium
152. 6:16so which is a distance between the
153. 6:17highest and lowest frequency of signals
154. 6:20that may be transmitted through the
155. 6:21medium often with a attenuation of at
156. 6:25most
157. 6:263db this bandwidth limits the channels
158. 6:29ability to carry data if we increase the
159. 6:32bandwidth of the medium or we choose
160. 6:34another medium which has a higher
161. 6:36bandwidth than another then we can also
162. 6:38get a higher
163. 6:39capacity if there weren't for the noise
164. 6:42we would have an infinite capacity of a
165. 6:44medium so the noise is the main limiter
166. 6:46of the capacity we need to introduce
167. 6:49some terms the bit rate already
168. 6:52mentioned this is the number of bits
169. 6:54that can be transmitted by medium per
170. 6:56second the board rate is the number of
171. 6:58signal elements per second since we the
172. 7:01signal elements are the waveforms that
173. 7:04represent the data so if we have two
174. 7:08signal elements such as a high or a low
175. 7:11amplitude then we can represent each
176. 7:13element with one bit the more signal
177. 7:16elements we have the less different they
178. 7:18will be and thus at the receiver it will
179. 7:21be easier with more signal elements to
180. 7:23misinterpret the signal and make a
181. 7:26mistake than if you have fewer Elements
182. 7:28which are more distinct from one another
183. 7:30the name board comes from a French
184. 7:33researcher Emil bordo there a simple
185. 7:36expression for capacity it says if you
186. 7:38have a board rate of R symbols per
187. 7:41second and you have L symbols then you
188. 7:45take second logarithm of L and multiply
189. 7:50it by board rate and you get the
190. 7:53capacity the Nyquist bit rate cmax here
191. 7:57is the maximum bit rate on an Ideal chck
192. 7:59channel so the board rate is limited to
193. 8:02to B but L is not limited at all if you
194. 8:06have a noiseless channel because if
195. 8:08there's no noise then you could have L
196. 8:11going to Infinity the receiver will
197. 8:13still be able to distinguish the signal
198. 8:15elements from one another and therefore
199. 8:17you can increase the capacity by having
200. 8:18just the largest set of signal elements
201. 8:21but in reality the noise will make S
202. 8:25signals indistinguishable from one
203. 8:27another and therefore there is a limit
204. 8:30to this
205. 8:31capacity this limit was formulated by
206. 8:34Claud
207. 8:35Shannon uh he's often referred to as the
208. 8:38father of information Theory so you see
209. 8:41here that you
210. 8:43have an expression that is not very
211. 8:46different from the Nyquist heartley law
212. 8:49it's the capacity is equal to the
213. 8:51bandwidth not twice the bandwidth the
214. 8:53bandd is
215. 8:54here times the second logarithm of an
216. 8:58expression which is one plus the signal
217. 9:01to noise ratio and here the signal to
218. 9:03noise ratio is the actual ratio between
219. 9:06the two Powers not the logarithm not
220. 9:09expressed in
221. 9:12DB this is the highest capacity that you
222. 9:15can get with the channel if you have
223. 9:17white noise on the channel added White
224. 9:21Noise let's take an example it might be
225. 9:24silly take the human ear we have an
226. 9:27auditory bandd of roughly 20
227. 9:31khz uh the ear can have a dynamic range
228. 9:35of 130 DB where signal at 130 Deb is the
229. 9:38pain level of our
230. 9:41ears so question is what is the noise
231. 9:43levels that we have around us a
232. 9:45conversation is around 60 DB traffic
233. 9:49noise 70 maybe about to 85 DB of course
234. 9:52it can get
235. 9:54higher so we try to estimate the signal
236. 9:57to noise ratio for say music that we
237. 10:00listen to so we have a signal of 90 DB
238. 10:03the background noise is traffic of 70 DB
239. 10:07that means that we have 20 DB of signal
240. 10:09to noise ratio that corresponds to 100
241. 10:13times and that means that the capacity
242. 10:15with the signal to noise ratio will
243. 10:17correspond to 133 kilobit per second
244. 10:21which is basically what you can get with
245. 10:22an MP3
246. 10:28transmission