Multiplexing and Spread Spectrum

• Explain why links are multiplexed and name the three basic methods
• Design FDM systems, including guard bands and the analog hierarchy
• Calculate slot, frame and link rates for synchronous TDM
• Handle unequal rates; explain T-1/E-1 lines and statistical TDM
• Explain FHSS and DSSS and why they spread the bandwidth

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Lecture 9: Multiplexing and Spread Spectrum

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• A link's capacity is usually far more than one user needs
• Multiplexing lets n signals share one link: one cable, one fibre, one radio band
• A multiplexer (MUX) combines them; a demultiplexer (DEMUX) separates them at the far end
• Inside the link, each signal travels on its own channel

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Lecture 9: Multiplexing and Spread Spectrum

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• Each source modulates its own carrier (AM or FM, Lecture 8), at a different frequency
• The modulated signals are added into one composite signal on the link
• Channels are separated by guard bands
• The demultiplexer uses filters to split the channels, then demodulates each

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Lecture 9: Multiplexing and Spread Spectrum

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• Given: three voice channels, 4 kHz each; a link band from 20 to 32 kHz
• Total needed: 3 × 4 = 12 kHz; the link offers exactly 12 kHz
• Shift voice 1 to 20–24 kHz, voice 2 to 24–28 kHz, voice 3 to 28–32 kHz
• Receiver: three band-pass filters, then shift each back down to 0–4 kHz

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• Ex. 6.2: n channels need n − 1 guard bands between them
• Minimum link bandwidth = 5 × 100 + 4 × 10 = 540 kHz
• Ex. 6.3: digital channels can share FDM after modulation
• Four 1 Mbps channels in 1 MHz: 250 kHz each, so 4 bits per hertz: 16-QAM

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Lecture 9: Multiplexing and Spread Spectrum

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Try it: plan an FDM band

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Lecture 9: Multiplexing and Spread Spectrum

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• Telephone companies once multiplexed voice in levels, each built from the one below
• Group: 12 voice channels × 4 kHz = 48 kHz
• Each level adds guard bands, so bandwidth grows a little faster than the channel count
• Replaced by digital TDM (T-lines, E-lines) and fibre

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Lecture 9: Multiplexing and Spread Spectrum

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• Ex. 6.4: AMPS, the 1980s North American mobile system
• Two 25 MHz bands: one for sending, one for receiving (full duplex by FDM)
• Each user needs 30 kHz in each direction
• 25 MHz / 30 kHz = 833.33 → 832 channels; 42 for control → 790 simultaneous calls

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Lecture 9: Multiplexing and Spread Spectrum

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Lecture 9: Multiplexing and Spread Spectrum

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• WDM is FDM for light: each signal uses a different wavelength (colour)
• A prism or diffraction grating combines the beams into one fibre and separates them again
• Each wavelength carries its own high-speed data stream
• DWDM packs wavelengths very closely, giving terabits per second per fibre

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Lecture 9: Multiplexing and Spread Spectrum

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• TDM is digital: inputs share the link by taking turns in time
• Each input gets a time slot; one round of slots is a frame
• In synchronous TDM every input owns a fixed slot in every frame
• The link must be n times faster than each input, so slots are n times shorter

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Lecture 9: Multiplexing and Spread Spectrum

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• Find the input unit duration first: 1 / input rate
• The frame lasts exactly that long; the slot is 1/n of it
• Link rate = frame rate × bits per frame
• Work all three before checking the answers on the right

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Lecture 9: Multiplexing and Spread Spectrum

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• The MUX visits the inputs in a fixed order, like a rotating switch: interleaving
• The DEMUX rotates in step, so each slot goes to the right output with no address
• If an input is idle, its slot is sent empty
• Bursty traffic (web, chat) leaves many slots empty

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Lecture 9: Multiplexing and Spread Spectrum

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• Synchronous TDM is easy when all inputs have the same rate
• Multilevel: split a fast input into several slower streams
• Multiple-slot: give a fast input more slots per frame
• Pulse stuffing: pad slow inputs with dummy bits up to a common rate

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Lecture 9: Multiplexing and Spread Spectrum

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• The receiver must know where each frame starts
• One or more framing (synchronising) bits are added per frame, in a known pattern such as 0101…
• Ex. 6.10: four sources, 250 characters/s each, 1 character per slot, 1 sync bit per frame
• Overhead: 8,250 − 8,000 = 250 bps for synchronisation

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Lecture 9: Multiplexing and Spread Spectrum

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Lecture 9: Multiplexing and Spread Spectrum

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• DS-0 = one digital voice channel: 8,000 samples/s × 8 bits = 64 kbps (Lecture 5's PCM)
• T-1 carries 24 DS-0s in synchronous TDM
• One frame per sample period (125 µs): 24 bytes + 1 framing bit
• Higher levels multiplex lower ones, adding overhead each time

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Lecture 9: Multiplexing and Spread Spectrum

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• Europe and most of the world, including Bangladesh, use E-lines instead of T-lines
• E-1: 32 time slots of 64 kbps = 2.048 Mbps
• 30 slots carry voice; the others carry framing and signalling
• Recall Lecture 6: E-1 lines use HDB3 line coding; T-1 uses AMI with B8ZS

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Lecture 9: Multiplexing and Spread Spectrum

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• Slots are given only to inputs that have data; no empty slots
• Each slot must carry an address (and, for variable-length slots, a length)
• The link can be slower than the sum of all inputs, because not all are busy at once
• The idea behind packet switching (Lecture 10)

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Lecture 9: Multiplexing and Spread Spectrum

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Try it: synchronous vs statistical TDM

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Lecture 9: Multiplexing and Spread Spectrum

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• 1 · FDM planner: channels, guard bands, link bandwidth
• 2 · Synchronous TDM: watch inputs interleave; slot, frame and link rates
• 3 · Statistical TDM: how many slots does synchronous TDM waste?
• 4 · Spread spectrum: FHSS hop pattern and DSSS chips

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• Multiplexing saves bandwidth; spread spectrum deliberately expands it
• Each station's signal is spread over a band much wider than it needs: BSS ≫ B
• Spreading follows a pseudo-random code, independent of the data
• Hard to jam, hard to eavesdrop, and many users can share the band

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Lecture 9: Multiplexing and Spread Spectrum

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• The carrier hops among M frequencies, staying Th seconds on each
• A pseudo-random code generator chooses the next frequency
• Only a receiver with the same code and starting point can follow the hops
• Bandwidth used ≈ M × B; several stations can hop independently in the same band

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Lecture 9: Multiplexing and Spread Spectrum

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Try it: hop around the jammer

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Lecture 9: Multiplexing and Spread Spectrum

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• Each data bit is replaced by n chips from a spreading code
• Chip = bit XOR code: a 1 sends the code inverted, a 0 sends it as is
• The chip rate is n times the bit rate, so the bandwidth grows about n times
• The receiver multiplies by the same code to get the bits back; others see noise

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Lecture 9: Multiplexing and Spread Spectrum

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Try it: spread and despread with DSSS

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Lecture 9: Multiplexing and Spread Spectrum

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• DSSS chip rate = bit rate × chips per bit
• 802.11b at 1 Mbps: 11 Mchips/s, in a 22 MHz channel
• FHSS hop duration = 1 / hop rate
• Bluetooth: 1,600 hops per second, so 625 µs per hop

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Lecture 9: Multiplexing and Spread Spectrum

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Md Mahbub E Noor

Lecture 9: Multiplexing and Spread Spectrum

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Lecture 9: Multiplexing and Spread Spectrum

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• Multiplexing lets n channels share one link; FDM and WDM by frequency, TDM by time
• FDM link bandwidth = n·B + (n − 1)·guard; WDM is FDM for light
• Synchronous TDM: link = n × input rate; slot = unit time / n; add framing bits
• T-1 = 24 × 64 kbps + 8 kbps framing = 1.544 Mbps; E-1 = 32 × 64 kbps = 2.048 Mbps
• Statistical TDM uses addresses; FHSS and DSSS spread bandwidth for security

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Lecture 9: Multiplexing and Spread Spectrum

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