Data Communications & Computer Networks

Transcription

1 Data Communications & Computer Networks Chapter 3 Data Transmission Fall 2008 Agenda Terminology and basic concepts Analog and Digital Data Transmission Transmission impairments Channel capacity Home Exercises ACOE312 Data Transmission 1

2 Terminology and basic concepts 1. Terminology (1) Transmitter Receiver Medium Guided medium e.g. twisted pair, optical fiber Unguided medium e.g. air, water, vacuum ACOE312 Data Transmission 2

3 Terminology (2) Direct link No intermediate devices Point-to-point Direct link Only 2 devices share link Multi-point More than two devices share the link Terminology (3) Simplex One direction e.g. Television Half duplex Either direction, but only one way at a time e.g. police radio Full duplex Both directions at the same time e.g. telephone ACOE312 Data Transmission 3

4 Time-Domain Concepts Analog signal Varies in a smooth way over time Digital signal Maintains a constant level then changes to another constant level Periodic signal Pattern of signal is repeated over time Aperiodic signal Pattern of signal is not repeated over time Analogue & Digital Signals ACOE312 Data Transmission 4

5 Periodic Signals Sine Wave Square Wave Sine Wave characteristics Peak Amplitude (A) maximum strength of signal volts Frequency (f) Rate of change of signal Hertz (Hz) or cycles per second Period = time for one repetition (T) T = 1/f Phase (φ) Relative position in time ACOE312 Data Transmission 5

6 Varying Sine Waves s(t) = A sin(2πft +φ) Wavelength Distance occupied by one cycle Distance between two points of corresponding phase in two consecutive cycles λ=wavelength Assuming signal velocity v λ = v T λ f = v c =2,98*10 8 m/s (approximately 3*10 8 m/s) speed of light in free space ACOE312 Data Transmission 6

7 Frequency Domain Concepts Signal usually made up of many frequencies Components are sine waves Can be shown (Fourier analysis) that any signal is made up of component sine waves Can plot frequency domain functions Addition of Frequency Components (T=1/f) sin(2πft) (1/3) sin(2π(3f)t) (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] ACOE312 Data Transmission 7

8 Spectrum & Bandwidth Spectrum range of frequencies contained in signal Bandwidth (BW) Narrow band of frequencies containing most of the signal energy Absolute bandwidth: Width of the spectrum Effective bandwidth (or bandwidth): energy of signal contained in a narrow band of frequencies (usually expressed as the 3 db points) DC Component Component of zero frequency Frequency Domain Representations Fundamental frequency (f) Signal spectrum Absolute bandwidth= 3f-1f=2f (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] This signal has an infinite bandwidth. Its effective bandwidth is limited in a relatively narrow band of frequencies where the most energy of the signal is contained s(t)=1, -X/2<t<X/2 ACOE312 Data Transmission 8

9 Signal with DC Component Time Domain s(t) = 1 + (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] Frequency Domain Bandwidth Square wave Square wave signal consists of an infinite number of odd harmonics (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t) +(1/7)sin(2π(7f)t)]] (4/π)Σ[sin(2πkft)]/k for odd values of k ACOE312 Data Transmission 9

10 Data Rate and Bandwidth (1) Any transmission system has a limited band of frequencies This limits the data rate that can be carried Data Rate and Bandwidth (2) Suppose a digital transmission system is capable of transmitting signals with a BW of 4MHz. Let us attempt to transmit a square wave signal (i.e. a sequence of alternating 0s and 1s. What is the achievable data rate? ACOE312 Data Transmission 10

11 Data Rate and Bandwidth (3) Case 1: Assume that the square wave is approximated to this signal. (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] BW=f upper f lower = 5f f =4f If f=1mhz, then the BW=4MHz. Since T=1/f then signal period is 1/1MHz=1µs Since one bit occurs every 0.5T then Data rate=1/0.5t=2mbps So, for this particular example, for a BW of 4MHz, the Data Rate achieved is 2Mbps Data Rate and Bandwidth (4) Case 2: Assume that the square wave is approximated to this signal. (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] BW=f upper f lower = 5f f =4f If f=2mhz, then the BW=8MHz. Since T=1/f then signal period is 1/2MHz=0.5µs Since one bit occurs every 0.5T then Data rate=1/0.25t=4mbps So, for this particular example, for a BW of 8MHz, the Data Rate achieved is 4Mbps ACOE312 Data Transmission 11

12 Data Rate and Bandwidth (5) Case 3: Assume that the square wave is approximated to this signal. BW=f upper f lower = 3f f =2f (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] If f=2mhz, then the BW=4MHz. Since T=1/f then signal period is 1/2MHz=0.5µs Since one bit occurs every 0.5T then Data rate=1/0.25t=4mbps So, for this particular example, for a BW of 4MHz, the Data Rate achieved is 4Mbps Data Rate and Bandwidth (6) Conclusions In general, any digital waveform has infinite BW If a digital waveform is transmitted over any medium, the transmission system will limit the BW that can be transmitted For any given medium, the greater the BW transmitted, the greater the cost Limiting the BW creates distortions, which makes the task of interpreting the received signal more difficult The more limited the BW, the greater the distortion, and the greater the potential for error by the receiver ACOE312 Data Transmission 12

13 Analog and Digital Data Transmission 2. Analog and Digital Data Transmission Data Entities that convey information Signals Electric or electromagnetic representations of data Signaling is the physical propagation of the signal along a suitable medium Transmission Communication of data by propagation and processing of signals ACOE312 Data Transmission 13

14 Analog and Digital Data Analog Continuous values within some interval e.g. sound, video Digital Discrete values e.g. text, integers Acoustic Spectrum (Analog) (log scale) ACOE312 Data Transmission 14

15 Analog and Digital Signals Means by which data are propagated Analog signals Continuously variable Various media wire, fiber optic, space Speech bandwidth 100Hz to 7kHz Telephone bandwidth 300Hz to 3400Hz Video bandwidth 4MHz Digital signals Use two DC components (binary 0 and 1) Advantages & Disadvantages of Digital signals Advantages Cheaper Less susceptible to noise Disadvantages Greater attenuation Pulses become rounded and smaller Leads to loss of information ACOE312 Data Transmission 15

16 Attenuation of Digital Signals Components of Speech Frequency range (of hearing) 20Hz-20kHz Speech 100Hz-7kHz Easily converted into electromagnetic signal for transmission Sound frequencies with varying volume converted into electromagnetic frequencies with varying voltage Limit frequency range for voice channel Hz ACOE312 Data Transmission 16

17 Conversion of Voice Input into Analogue Signal Binary Digital Data From computer terminals etc. Two dc components Bandwidth depends on data rate ACOE312 Data Transmission 17

18 Conversion of PC Input to Digital Signal Data and Signals Usually use digital signals for digital data and analog signals for analog data Can use analog signal to carry digital data Modem Can use digital signal to carry analog data Compact Disc audio ACOE312 Data Transmission 18

19 Analog Signals Carrying Analog and Digital Data Digital Signals Carrying Analog and Digital Data Voice ACOE312 Data Transmission 19

20 Analog Transmission Analog signal transmitted without regard to content May be analog or digital data Attenuated over distance Use amplifiers to boost signal However, amplifiers or signal boosters also amplify noise Digital Transmission Concerned with content Integrity endangered by noise, attenuation etc. Repeaters are used A repeater receives digital signal, recovers the bit pattern (0 or 1) and retransmits new signal. Thus, attenuation is overcome Noise is not amplified ACOE312 Data Transmission 20

21 Advantages of Digital Transmission Digital technology Low cost large-scale and very-large scale integration technology Data integrity Longer distances over lower quality lines Capacity utilization High bandwidth links economical High degree of multiplexing easier with digital techniques Security & Privacy Encryption Integration Can treat analog and digital data similarly Economies of scale and convenience can be achieved by integrating voice, video and digital data Transmission Impairments ACOE312 Data Transmission 21

22 3. Transmission Impairments Signal received may differ from signal transmitted For Analog signals degradation of signal quality For Digital signals bit errors may occur Most significant transmission impairments are Attenuation and attenuation distortion Delay distortion Noise Attenuation Signal strength reduces with distance over any transmission medium Depends on medium Received signal strength: must be enough to be detected must be sufficiently higher than noise to be received without error Attenuation is an increasing function of frequency, i.e. the higher the frequency, the more the attenuation attenuation ACOE312 Data Transmission 22

23 Delay Distortion (DD) Only in guided media It occurs because the propagation velocity of a signal through a guided medium varies with frequency Received signal is distorted due to varying delays experienced at its constituent frequencies DD is particularly critical for digital signals some of the signal components of one bit may spill over into other bit positions, causing intersymbol interference, which limits the maximum data rate over a transmission channel Noise (1) Additional signals inserted between transmitter and receiver Noise is the major limiting factor in communication system performance Noise can be divided into 4 main categories Thermal Intermodulation Crosstalk Impulse noise ACOE312 Data Transmission 23

24 Noise (2) Thermal Due to thermal agitation of electrons in all electronic devices Uniformly distributed across the bandwidth Also referred to a white noise Intermodulation Signals that are the sum and difference of original frequencies sharing the same transmission medium Example: mixing of signals at f1 and f2 may produce energy at f1±f2, which could interfere with an intended signal at (f1+f2) or (f1-f2) Crosstalk Unwanted coupling between signal paths Antennas or wires may pick up other unwanted signals, eg. phone line Impulse Non continuous, consisting of irregular pulses or noise spikes of short duration but of high amplitude e.g. External electromagnetic interference, such as lightning Channel capacity ACOE312 Data Transmission 24

25 4. Channel Capacity As we have seen so far, there is a variety of impairments that distort or corrupt a signal. To what extent do these impairments limit the maximum achievable data rate? Channel Capacity is the maximum rate at which data can be transmitted over a communication channel. Data rate In bits per second (bps) Rate at which data can be communicated Bandwidth In cycles per second, or Hertz Constrained by transmitter and medium Nyquist Bandwidth Assume a noise-free channel If rate of signal transmission is 2B, then a signal with frequencies no greater than B is sufficient to carry signal rate or, given bandwidth B, highest signal rate is 2B Given a binary signal, the maximum data rate supported by a channel of bandwidth B Hz is 2B bps Maximum data rate, C, can be increased by using M signal levels Nyquist formula: C= 2 B log 2 M in bps (bits per second) However, receiver must be able to distinguish one of M possible signal elements. Noise and other transmission impairments limit the practical value of M. ACOE312 Data Transmission 25

26 Shannon Capacity Formula Nyquist s formula indicates that doubling BW, doubles the data rate in a noise-free channel. In practice, noise is always present. So, let us consider the relationship between data rate, noise and error rate. Faster data rate shortens each bit duration so a burst of noise affects more bits So, at a given noise level, the higher the data rate, the higher the error rate Signal-to-Noise ratio (SNR or S/N) expressed in decibels SNR db= 10 log 10 (Signal power/noise power) Max channel Capacity is C=B log 2 (1+SNR) in bps (bits per second) This formula is for error-free capacity and assumes white noise. In practice, data rate is lower than C. A few things about Decibels (1) It is customary to express gains, losses and relative levels in decibels because Signal strength often falls off exponentially, so loss is easily expressed in terms of the decibel, which is a logarithmic unit The net gain or loss in a cascaded transmission path can be calculated with simple addition and subtraction The decibel (db) is a measure of the ratio between two signal levels. The decibel gain is given by G db =10 log 10 (Output power / Input power) G db =10 log 10 (P out /P in ) ACOE312 Data Transmission 26

27 A few things about Decibels (2) Gain is expressed in positive db values (G db ) Loss is expressed in negative db values (L db ) E.g. A gain of 3dB means that the power has halved and this is a loss of power. (Why?) Power Ratio db Power Ratio db A few things about Decibels (3) Note that db is a measure of relative, not absolute difference. The db is also used to measure the difference in Voltage Since P = V 2 /R Where, P=Power dissipated across resistance R v = Voltage across resistance R Then G db = 10 log 10 (P out /P in ) = 10 log 10 [(V 2 out /R) /(V2 in /R)] = 20 log 10 (V out /V in ) Similarly L db = 20 log 10 (V in /V out ) ACOE312 Data Transmission 27

28 Example on channel capacity Suppose that the spectrum of a noise-free channel is between 3 MHz and 4 MHz and SNR db =24 db. What is the maximum achievable data rate? How many signal levels are required to achieve this rate? Solution of example Bandwidth, B=4 MHz 3 MHz = 1 MHz = 10 6 Hz. SNR db =24 db = 10log 10 (SNR) Therefore, SNR=10 (24/10) = = Using Shannon s formula, C=B log 2 (1+SNR), C=10 6 log 2 ( ) = 7.98 x 10 6 ~ 8 Mbps Based on Nyquist s formula, C=2B log 2 M in order to achieve a data rate of 8MBps in a channel bandwidth of 1MHz, then we need M signal levels, where M is equal to: 8x10 6 = 2x10 6 log 2 M => 4 = log 2 M => M=2 4 =16 ACOE312 Data Transmission 28

29 Home Exercises Exercises (1) Q1. What is the theoretical maximum channel capacity for the following PSTN channel of a signal-to-noise ratio of 13dB? Assume white thermal noise is only present on the channel. S(f) in db f (Hz) Q2. Consider a signal f(t)=3sin(3000πt)+sin(9000πt) injected through a noisy channel of a signal-to-noise ratio of 20dB. What is the maximum data rate achieved? ACOE312 Data Transmission 29

30 Exercises (2) Q3. A modem to be used with a PSTN network uses a modulation scheme with eight levels per signalling element. Assuming the same channel bandwidth as in Q1, but a noiseless channel, find the maximum possible data rate. Q4. Given a channel with an intended capacity of 20 Mbps, the bandwidth of the channel is 3 MHz. Assuming white thermal noise, what signal to noise ratio in decibels is it required to achieve this capacity? Q5. Fill in the missing elements in the following table Decibels Losses Gains 2 10 Useful log identities log a B=X => a X =B log a B = (log 10 B)/(log 10 a) ACOE312 Data Transmission 30

31 Required Reading Stallings Chapter 3 Tanenbaum Chapter 2.1 ACOE312 Data Transmission 31