# Multiplexing and Data Rate Assignment

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Multiplexing CHAPTER 4 Outline * Frequency Division Multiplexing(FDM) * Synchronous Time Division Multiplexing * Statistical Time Division Multiplexing * Asymmetric Digital Subscriber Line(ADSL) Multiplexing * Set of techniques that allows the simultaneous transmission of multiple signals across a single link * allows several transmission sources to share a larger transmission capacity Link = physical path Channel = portion of a link that carries a transmission between a given pairs of lines 2 CATEGORY OF MULTIPLEXING WDM FDM TDM ADSL Frequency Division Multiplexing * FDM – numerous signals are combined for ransmission on a single communications line or channel. Each signal is assigned a different frequency (subchannel) within the main channel. * Useful bandwidth of medium exceeds required bandwidth of channel * e. g. broadcast radio and cable television * Channel allocated even if no data Frequency Division Multiplexing Diagram * Each signal is modulated to a different carrier frequency * Carrier frequencies separated by guard bands (unused bandwidth) – to prevent interference so signals do not overlap. 3 FDM System FDM is an analog multiplexing technique that combines signals. FDM process

FDM Demultiplexing Example 1 Assume that a voice channel occupies a bandwidth of 4 KHz. We need to combine three voice channels into a link with a bandwidth of 12 KHz, from 20 to 32 KHz. Show the configuration using the frequency domain without the use of guard bands. Solution Shift (modulate) each of the three voice channels to a different bandwidth, as shown in next figure Example 2 Five channels, each with a 100-KHz bandwidth, are to be multiplexed together. What is the minimum bandwidth of the link if there is a need for a guard band of 10 KHz between the channels to prevent interference? Solution

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For five channels, we need at least four guard bands. This means that the required bandwidth is at least 5 x 100 + 4 x 10 = 540 KHz, as shown in next Figure. 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. Analog Carrier Systems AT&T (USA) * Hierarchy of FDM schemes * Group 1. 12 voice channels (4kHz each) = 48kHz 2. Range 60kHz to 108kHz * Supergroup 1. 60 channel 2. FDM of 5 group signals on carriers between 420kHz and 612 kHz * Mastergroup 1. 10 supergroups Analog Hierarchy To maximize the efficiency infrastructure, multiplexed signals from lower bandwidth lines onto higher-bandwidth signals FDM of Three Voiceband Signals FDM Applications 1. Common used radio broadcasting – AM and FM * AM (530 – 1700KHz) – shared with all radio stations * FM uses a wider band (88 – 108MHz) – each station needs more bandwidth, 200KHz 2.

Television Broadcasting * Each TV channel has own bandwidth of 6 Mhz 3. 1st Generation of Cellular telephones * Voice signal 3KHz (300 – 3300Hz) channels * Bt = 10 x Bm , therefore each channel has 30KHz channels * each user has been allocated two 30KHz channel, therefore 60KHz. 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 ellular 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. Wavelength Division Multiplexing * Multiple beams of light at different frequency * Carried by optical fiber * A form of FDM (same concept) * Each colour of light (wavelength) carries separate data channel * 1997 Bell Labs * 100 beams * Each at 10 Gbps * Giving 1 terabit per second (Tbps) * Commercial systems of 160 channels of 10 Gbps now available * Lab systems (Alcatel) 256 channels at 39. 8 Gbps each * 10. 1 Tbps * Over 100km WDM Operation Same general architecture as other FDM * Number of sources generating laser beams at different frequencies * Multiplexer consolidates sources for transmission over single fiber * Optical amplifiers amplify all wavelengths * Typically tens of km apart * Demux separates channels at the destination * Mostly 1550nm wavelength range * Was 200MHz per channel * Now 50GHz Dense Wavelength Division Multiplexing * DWDM * No official or standard definition * Implies more channels more closely spaced that WDM * 200GHz or less TDM digital process that allows several connections to share the high bandwidth of a link ach connection occupies a portion of time in the link TDM is a digital multiplexing technique to combine data. TDM : Time Slots and Frames In a TDM, the data rate of the link is n times faster, and the unit duration is n times shorter. Time Division Multiplexing Example 5 Four 1-Kbps connections are multiplexed together. A unit is 1 bit. Find : (1) the duration of 1 bit before multiplexing, (2) the transmission rate of the link, (3) the duration of a time slot, and (4) the duration of a frame? Solution We can answer the questions as follows: 1. The duration of 1 bit is 1/1 Kbps, or 0. 001 s (1 ms). 2.

The rate of the link is 4 Kbps. 3. The duration of each time slot 1/4 ms or 250 ms. 4. The duration of a frame 1 ms. Interleaving • switches are synchronized and rotate at the same speed but opposite direction •process of sending a unit data onto the path when the connection on the multiplexing and de-multiplexing is open 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