Ch. 8 Multiplexing

1. Ch. 8 Multiplexing

2. Ch. 8 Multiplexing • 8.1 Frequency-Division Multiplexing • 8.2 Synchronous Time-Division Multiplexing • 8.3 Statistical Time-Division Multiplexing • 8.4 Asymmetric Digital Subscriber Line • 8.5 xDSL

3. 8.1 Frequency-Division Multiplexing • FDM--Definition • The division of a transmission facility into two or more channels by splitting the frequency band transmitted by the facility into narrower bands, each of which is used to constitute a distinct channel.

4. 8.1 Frequency Division Multiplexing (p.2) • FDM-- Figure 8.4 • Incoming signals are each modulated using a different carrier frequency (N sources.) • The channels are separated by guard bands, which are unused portions of the spectrum. • The spectrum of the composite signal is shown in Figure 8.4b. • The receiver consists of bandpass filters and demodulators, centered around each carrier frequency.

5. 8.1Frequency Division Multiplexing (p.3) • Examples of FDM • Example 8.1 Broadcast and cable TV • Three source signals: black-and white video, color information, and audio. • All three fit in a 6 M Hz bandwidth. • Each of these can be treated as 1 channel (Table 8-1) and multiplexed together. • Example 8.2 Voiceband Signals • 4 k Hz bandwidth (effective bandwidth 300 to 3400 Hz). • SSBSC--single sideband, suppressed carrier. • Use 64k Hz, 68k Hz, and 72k Hz carriers (Fig. 8-5).

6. 8.1 Frequency Division Multiplexing (p.4) • Analog Carrier Systems (Table 8.1) • FDM --earliest carrier system and still is common. • AT&T (North American Standard) • Group--12 voice channels • Supergroup--5 groups (60 voice channels) • Mastergroup-10 supergroups (600 voice channels)

7. 8.1 Frequency Division Multiplexing (p.5) • Wavelength Division Multiplexing • Multiple beams of light are transmitted at different frequencies on the same fiber. • 1997--Bell Labs demonstrated 100 beams each operating at 10 G bps, for a total data rate of 1 trillion bits per second (1 terabit per sec). • Commercial systems with 160 and 256 channels are currently available.

8. 8.1 Frequency Division Multiplexing (p.6) • Problems with FDM carrier systems: • Crosstalk and intermodulation noise. • Must demodulate all signals for switching. • Inflexible.

9. 8.2 Time-Division Multiplexing • TDM--Definition • The division of a transmission facility into two or more channels by allotting the facility to several different information channels, one at a time.

10. 8.2 Time-Division Multiplexing(p.2) • STDM--Definition • A method of TDM in which time slots on a shared transmission line are assigned to I/O channels on a fixed, predetermined basis. • Each channel could carry a bit, byte, or block, depending on implementation. • In general, start and stop bits are stripped off, if asynchronous terminals are being multiplexed. • See Fig. 8.6.

11. 8.2 Time Division Multiplexing (p.3) • STDM Link Control • Blocks of bits are the input sources (eg. HDLC). • Flow control, error control, etc. will be handled before and after the multiplexers. • Framing • There is some framing required. • Added-digit framing--a single bit is added to each frame; the bits will form a repetitive pattern.

12. 8.2 Time Division Multiplexing (p.4) • Pulse Stuffing • Suppose that the outgoing data rate of the multiplexer, excluding framing bits, is higher than the sum of the maximum instantaneous incoming rates. • Excess capacity is used by stuffing extra dummy bits or “pulses” into each incoming signal until its rate is raised to that of a locally-generated clock signal. • Solves problems of synchronization among data sources.

13. 8.2 Time Division Multiplexing (p.5) • Example 8.3 --STDM-- (Fig.8.8) • Digital and Analog Sources • Source 1 Analog • 2 kHz bandwidth (16 kbps). • Source 2 Analog • 4 kHz bandwidth (32 kbps). • Source 3 Analog • 2 kHz bandwidth (16 kbps). • Sources 4-11: Digital • Each of the eight sources is a 7200 bps synchronous data stream.

14. 8.2 Time Division Multiplexing (p.6) • Example 8.3 --STDM-- (Fig.8.8) (cont.) • Analog sources • Sampled and encoded using 4 bits. • Gathered into one 16-bit buffer . • Result is a 64 k bps multiplexed information stream. • Resulting analog source frame is Source 1 (4 bits), Source 2 (4 bits), Source 3 (4 bits), Source 2 (4 bits). • Digital sources • Each is increased to 8 k bps using pulse stuffing. • TDM signal: 64 k bps + 8 x 8 k bps =128 k bps. • Extra Study Question: What would a frame look like?

15. 8.2 Time Division Multiplexing (p.7) • Digital Carrier Systems • Standards • North American and ITU-T are different. • Table 8.3 (DS-1 through DS-4; Levels 1-5)

16. 8.2 Time Division Multiplexing (p.8) • DS-1 Transmission Format (Fig. 8-9) • Frame Structure (193 bits) • 8 bits/channel • 24 channels • 1 framing bit. • Data Rate • 193 bits/frame x 8 k frames/sec =1.544 Mbps.

17. 8.2 Time Division Multiplexing (p.9) • DS-1 Transmission Format (Fig. 8-9)(cont.) • Voice • Uses bit robbing. • Every sixth frame has one bit "robbed" for control signaling from each channel. • Data • Bit 8 is used for control signaling (8,000 bps.) • Bit 1-7 used for 56 kbps service. • Bit 2-7 used for 9.6, 4.8, and 2.4 kbps service.

18. 8.2 Time Division Multiplexing (p.10) • SONET/SDH • An optical transmission interface. • Signal Hierarchy--Table 8.4. • Frame Formats--Fig.8.10 and 8.11.

19. 8.3 Statistical TDM • Statistical TDM--Definition • A method of TDM in which time slots on a shared transmission line are allocated to I/O channels on demand (dynamically.) • Also known as asynchronous TDM.

20. 8.3 Statistical TDM (p.2) • More efficient than synchronous TDM in some cases, since some synchronous TDM slots go unused. • Synchronous TDM is more like "reserved seating" and Statistical TDM is "open seating". • Definition: • The "aggregate" data rate is the nominal data rate of all the sources combined; it is generally larger than the actually data rate on the multiplexed line.

21. 8.3 Statistical TDM (p.3) • Architecture • Each I/O line has a buffer (eg, UARTs.) • The buffers are scanned for new characters. • Address information is added and the result is placed in an outgoing block (ie, a FIFO queue). • Two multiplexors could exchange blocks using a data link protocol such as HDLC. • See Fig. 8.12 and 8.13.

22. 8.3 Statistical TDM (p.4) • Performance • Problem: Peak load may exceed the transmission line data rate between the MUX’s. • Solution: Buffer is used to hold incoming characters from terminals. • Example: Table 8-6 • Input: number of bits from the sources in 1 msec. • Output: number of bits transmitted in 1 msec. • Backlog: length of buffer--bits that have to wait. • Increasing the transmission data rate reduces the backlog.

23. 8.3 Statistical TDM (p.5) • Performance Model Example • I = number of input sources= 10. • R= data rate of each source = 1,000 bps. • IR= aggregate data rate = 10, 000 bps. • M=outgoing transmission line rate (in bps.) • case 1: 5000 bps • case 2: 7000 bps • K= M/(IR) • case 1: 5000/10,000 = .5 • case 2: 7000/10,000 = .7 • a= amount of time each source is active = .5

24. 8.3 Statistical TDM (p.6) • Single Server Queue Performance Model • What is the delay through the queue? • What is the average length of the queue? • What is the probability of overflow? • Assumptions for Statistical TDM: • Random (Poisson) arrivals. • Constant "service" time. • FIFO Queue . • Table 8.7 Formulas for Single-Server Queue.

25. 8.3 Statistical TDM (p.7) • Queue Parameters • l= arrival rate of "messages" (per second). • Ts= mean service time for each arrival (secs/message). • r= fraction of time facility is busy (utilization.) • N= no. of messages in system (buffer size). • Tr= average time a message is in the system (delay). • Formulas • See Table 8.7

26. 8.3 Statistical TDM (p.8) • Statistical TDM as a Queue: • Arrival rate into the queuing system: • l= a IR = .5 x 10,000 bps = 5,000 bps. • Service time of each arrival: • Ts = 1/M • Utilization • r = l Ts = a I R/M = a/K = l/M • case 1: r1 = 5,000 bps/5,000 bps = 1 • case 2: r2 = 5,000 bps/7,000 bps = .71

27. 8.3 Statistical TDM (p.8) • Performance Curves • Fig. 8.14a.Buffer Size vs. Utilization • As r increases, the average number of messages waiting in the queue increases. • Fig. 8.1b. Mean Delay vs. Utilization • Three curves for different M’s. • As M increases, delay decreases (fixed r). • As r increases, delay increases.

28. 8.3 Statistical TDM (p.9) • Performance Curves (cont.) • Fig. 8.15--Probability of Overflow vs. Max Buffer Size • Probability of overflow decreases with an increase in Max Buffer Size ( for a fixed r). • Decreasing r will decrease the probability of overflow.

29. 8.3 Statistical TDM (p.10) • Recall Example • case 1: r1 =1 • case 2: r2 =.71 • Which one has a reasonable delay? • Which one has a reasonable average buffer size? • Which one has a reasonable maximum buffer size?

30. 8.3 Statistical TDM (p.11) • Cable Modem • Two channels--one in each direction. • Channels are shared--type of statistical multiplexing.

31. 8.4 Asymmetric Digital Subscriber Line • ADSL Design (Fig. 8.17) • ADSL provides more capacity down-stream than upstream. • Although originally conceived for video-on-demand, it is being used for Internet access. • Lowest 25kHz are reserved for voice (POTS) • Separate Upstream and Downstream (FDM). • Overlapping Upstream and Downstream (FDM with echo cancellation.) • Discrete Multitone Transmission (DMT) is used.

32. 8.5 xDSL • ADSL is one of several schemes for high-speed transmission on a subscriber line. • Other schemes are summarized in Table 8.8 • High Data Rate Digital Subscriber Line • Single Line Digital Subscriber Line • Very High Data Rate Digital Subscriber Line