Multimedie- och kommunikationssystem, lektion 5

Kap 6: Digital transmission.

Fysiskt medium. Modulation. Nyquists och Shannons kapacitetsgränser.

Figure 6.3 Copper wire transmission media: (a) two wire and multiwire open lines; (b) unshielded twisted pair (UTP);

Figure 6.3 Copper wire transmission media: (c) shielded twisted pair (STP); (d) coaxial cable.

Figure 6.4 (b) Optical fiber transmission modes.

Figure 6.2 Effect of attenuation, distortion, and noise on transmitted signal.

Figure 6.7 Sources of signal impairment.

Example 6.3

Asynchronous transmission

Exempel på asynkron serie-kommunikation: RS232C (”com-porten”)

NRZ = Non-return to zero.

In NRZ-L the level of the signal is dependent upon the state of the bit.

In NRZ-I the signal is inverted if a 1 is encountered.

Bit synchronization

RZ encoding

Figure 4.10

Manchester encoding

Figure 4.11

Differential Manchester encoding

Figure 6.15 Synchronous transmission clock encoding methods: (a) Manchester; (b) differential Manchester.

Figure 4.12

Bipolar AMI encoding

Example 6.6: Clock rate deviation

Figure 5.26

Analogue amplitude modulation

Figure 5.29

Analogue

frequency modulation

Digitala modulationsmetoder

Binär signal ASK = Amplitude Shift Keying (AM) FSK = Frequency Shift Keying (FM) PSK = Phase Shift Keying (PSK)

Exempel 1:

Till höger visas fyra symboler som används av ett s.k. 4PSK modem (PSK=Phase Shift Keying). De fyra symbolerna representerar bitföljderna 00, 01, 11 resp 10.

1 0 -1 0 a) Nedan visas utsignalen från det sändande modemet. Vilket meddelande, dvs vilken bitsekvens, överförs?

Svar

: 11 00 10 10.

b) Tidsaxeln är graderad i tusendels sekunder. Vad är symbolhastigheten i baud eller symboler/sekund?

Svar: 1/1ms = 1000 symber per sekund = 1kbaud.

c) Vad är bithastigheten i bit per sekund (bps)?

Svar: 2000bps.

0.5

1 1.5

2 time [millisecond] 2.5

3 3.5

4 00 1 0 -1 0 0.5

time [milliseconds] 1 01 1 0 -1 0 0.5

time [milliseconds] 1 11 1 0 -1 0 0.5

time [milliseconds] 1 10 1 0 -1 0 0.5

time [milliseconds] 1

Exempel 2

: Nedan visas åtta symboler som används av ett s.k. 8QAM-modem (QAM=Quadrature Amplitude Modulation). Symbolerna i övre raden representerar bitföljderna 000, 001, 011 resp 010 (från vänster till höger). Undre raden representerar 100, 101, 111 resp 110.

000 001 011 010 2 2 2 2 0 0 0 0 -2 0 2 0.005

100 0.01

-2 0 2 0.005

101 0.01

-2 0 2 0.005

111 0.01

-2 0 2 0.005

110 0.01

0 0 0 0 -2 0 0.005

0.01

-2 0 0.005

0.01

-2 0 0.005

0.01

-2 0 0.005

0.01

Forts exempel 2:

a) Nedan visas utsignalen från det sändande modemet. Vilket meddelande, dvs vilken bitsekvens, överförs?

Modulatorns utsignal 2 0 -2 0 0.005

0.01

0.015

0.02

0.025

Tid [sekunder] 0.03

0.035

0.04

b) Tidsaxlarna är graderad i sekunder. Vad är symbolhastigheten i baud eller symboler/sekund?

c) Vad är bithastigheten i bit per sekund (bps)?

Digital modulation

 För att överföra

N

bit/symbol krävs

M

=2

N

 Vid

M

symboler överförs

N

=log 2

M

bit/symbol.  Baudrate

f s

= antal symboler per sekund. Enhet: baud eller symboler/sekund.

 Symbollängd

T s

= 1/

f s

.

f s

= 1/

T s

 Bitrate

R

= datahastighet. Enhet: bps eller bit/s.



R= f s

log 2

M

Table 5.1 Bit and baud rate comparison

Modulation Units Bits/Symbol ASK, FSK, 2-PSK Bit 1 4-PSK, 4-QAM 8-PSK, 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM 256-QAM Dibit Tribit Quadbit Pentabit Hexabit Septabit Octabit 2 3 4 5 6 7 8 Baud rate N N N N N N N N Bit Rate N 2N 3N 4N 5N 6N 7N 8N

Example 12

Compute the baud rate for a 72,000-bps 64-QAM signal.

Solution

A 64-QAM signal has 6 bits per signal unit since log 2 64 = 6. Thus, 72000 / 6 = 12,000 baud

Figure 5.9

B PSK constellation

Figure 5.11

The 4-PSK characteristics

Figure 5.16

16-QAM constellations

Figure 5.13

Relationship between baud rate and bandwidth in ASK, PSK, QAM (not FSK) without pulse shaping

Vid många modulationsformer t.ex. s.k. ASK, PSK, och QAM är signalens bandbredd = symbolhastigheten.

Vid FSK är bandbredden vanligen större.

Bandbredden kan minskas genom s.k. pulsformning.

Maximal kanalkapacitet enligt Nyquist

Example 6.4: Nyquist maximum data rate

Shannons regel

Kanalkapaciteten C är max antal bit per sekund vid bästa möjliga modulationsteknik och felrättande kodning:

C = B log

2

(1+S/N)

, där B är ledningens bandbredd i Hertz (oftast ungefär lika med övre gränsfrekvensen), S är nyttosignalens medeleffekt i Watt och N (noice) är bruseffekten i Watt.

Example 6.5: Shannon information capacity

Figure 6.4

FDM (Frekvensdelningsmultiplex, frequency division multiplex)

Exempel på FDM-teknik: ADSL-modem, kabel-TV-modem, trådlös kommunikation.

Figure 6.5

FDM demultiplexing example

Example 3

Four data channels (digital), each transmitting at 1 Mbps, use a satellite channel of 1 MHz. Design an appropriate configuration using FDM

Solution

The satellite channel is analog. We divide it into four channels, each channel having a 250-KHz bandwidth. Each digital channel of 1 Mbps is modulated such that each 4 bits are modulated to 1 Hz. One solution is 16 QAM modulation. Figure 6.8 shows one possible configuration.

Figure 6.8

Example 3

Example 4

The Advanced Mobile Phone System (AMPS) uses two bands. The first band, 824 to 849 MHz, is used for sending; and 869 to 894 MHz is used for receiving. Each user has a bandwidth of 30 KHz in each direction. The 3 KHz voice is modulated using FM, creating 30 KHz of modulated signal. How many people can use their cellular phones simultaneously?

Solution

Each band is 25 MHz. If we divide 25 MHz into 30 KHz, we get 833.33. In reality, the band is divided into 832 channels.

6.2 WDM

Wave Division Multiplexing (Fiber optics)

Figure 6.10

WDM = Wave division multiplexing

En laser per kanal Fiberkabel

Figure 6.11

Prisms in WDM multiplexing and demultiplexing

Figure 6.12

TDM, Tidsmultiplex (Time Division multiplex)

Note:

TDM is a digital multiplexing technique to combine data.

Figure 6.13

TDM frames

Note:

In a TDM, the data rate of the link is n times faster, and the unit duration is n times shorter.

Figure 6.14

Interleaving

Example 6

Four channels are multiplexed using TDM. If each channel sends 100 bytes/s and we multiplex 1 byte per channel, show the frame traveling on the link, the size of the frame, the duration of a frame, the frame rate, and the bit rate for the link.

Solution

The multiplexer is shown in Figure 6.15.

Figure 6.15

Example 6

Example 7

A multiplexer combines four 100-Kbps channels using a time slot of 2 bits. Show the output with four arbitrary inputs. What is the frame rate? What is the frame duration? What is the bit rate? What is the bit duration?

Solution

Figure 6.16 shows the output for four arbitrary inputs.

Figure 6.16

Example 7

Figure 6.18

DS hierarchy

Figure 6.19

T-1 line for multiplexing telephone lines

Table 6.2 E line rates

E Line Rate (Mbps) E-1 2.048

E-2 E-3 E-4 8.448

34.368

139.264

Voice Channels 30 120 480 1920