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# Multiplexing

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### Multiplexing

1. 1. Multiplexing• The combining of two or more information channels onto a common transmission medium.• Basic forms of multiplexing: – Frequency-division multiplexing (FDM). – Time-division multiplexing (TDM) – Code-division multiplexing (CDM)28/01/2003 1
2. 2. FDM • Frequency Division Multiplexing – The deriving of two or more simultaneous, continuous channels from a transmission medium by assigning a separate portion of the available frequency spectrum to each of the individual channels. • FDMA (frequency-division multiple access): The use of frequency division to provide multiple and simultaneous transmissions.28/01/2003 2
3. 3. • Transmission is organized in frequency channels, assigned for an exclusive use by a single user at a time• If the channel is not in use, it remains idle and cannot be used by others• There are channeling frequency plans elaborated to avoid mutual co-channel and adjacent-channel interference among neighboring stations• The use of a radio channel or a group of radio channels requires authorization (license) – for each individual station or for group of stations28/01/2003 3
4. 4. FDM (Frequency Division Multiplexing) PowerFrequency FDMA BcBm Time Frequency channel Example: Telephony Bm = 3-9 kHz 28/01/2003 4
6. 6. Transmitter Emissions • Transmitter output components – Fundamental (wanted) signal – Harmonic emissions Ideal Real – Master oscillator 1.2 (fundamental & harmonics) Output spectrum 1 – Non-harmonically related 0.8 spurious 0.6 0.4 – Noise 0.2 0 1 2 3 4 5 6 7 8 9 10 Frequency (relative)28/01/2003 6
7. 7. Receiver response • Fundamental channel • Spurious channels – Intermediate frequency Ideal – Image frequency 1.2 – Channels received via 1 LO harmonicsResponse 0.8 0.6 – Intermodulation 0.4 channels 0.2 0 1 2 3 4 5 6 7 Frequency 8 9 1028/01/2003 7
8. 8. Intermodulation• 2 or more signals, nonlinear circuit• Intermodulation products: Fi = CkFk• {Ck} positive/negative integers or zero• {Fk} frequencies of signals applied• Order of Intermod. Product = | C k|• 3rd order (2F1-F2, 2F2-F1), also 5th and 7th28/01/2003 8
9. 9. • Non-ideal wideband linear systems are frequently treated by expressing the output (Y) of the system as a power series: Y a0 a1 X a2 X 2 a 3 X 3 ... a n X n ...• where X is the total input signal, and the coefficients a are presumed to be real and independent on X.• Assume, for simplicity, that input consists of three elementary signals: X A(t ) cos( 1 t) B(t ) cos( 2 t ) C(t ) cos( 3 t)28/01/2003 9
10. 10. • Some simple calculations will show that the output of the system Y, in addition to the linearly transposed input signals, contains the following spectral components:• 1st order Multiplied version of the input signal a1[ A(t ) cos( 1t ) B(t ) cos( 2 t ) C (t ) cos( 3t )]28/01/2003 10
11. 11. • 2nd order• a) Distorted version of the modulating signals a2 2 a a A (t ); 2 B 2 (t ); 2 C 2 (t ) 2 2 2• b) 2nd harmonics a2 2 a2 2 a2 2 A (t ) cos(2 1t ); B (t ) cos(2 2t ); C (t ) cos(2 3t ) 2 2 2• c) Sum and difference a 2 A(t ) B(t ) cos( 1 2 )t a 2 A(t )C (t ) cos( 2 3 )t a 2 B(t )C (t ) cos( 3 1 )t28/01/2003 11
12. 12. 3rd ordera) Distorted modulating signal 3 3 3 3 a3 A (t ) cos( 1t ); a3 B3 (t ) cos( 2t ); a3C 3 (t ) cos( 3t ) 4 4 4b) 3rd harmonics 1 1 1 a3 A3 (t ) cos(3 1t ); a3 B3 (t ) cos(3 2t ); a3C 3 (t ) cos(3 3t ) 4 4 4c) Crossmodulation 3 3 3 a3 A2 (t ) B (t ) cos( 2t ); a3 A(t ) B 2 (t ) cos( 1t ); a3 A(t )C 2 (t ) cos( 1t ) 2 2 2 3 3 3 a3 A2 (t )C (t ) cos( 3t ); a3 B(t )C 2 (t ) cos( 2t ); a3 B 2 (t )C (t ) cos( 3t ) 2 2 2d) Intermodulation 3 3 3 a3 A2 (t ) B(t ) cos ( 2 2 1 ; a3 A(t ) B 2 (t ) cos ( 1 2 2 ; a3 A2 (t )C (t ) cos ( 3 2 1 4 4 4 3 3 3 a3 A(t )C 2 (t ) cos ( 1 2 3 ; a3 B 2 (t )C (t ) cos ( 3 2 2 ; a3 B(t )C 2 (t ) cos ( 2 2 3 4 4 428/01/2003 12
13. 13. Non-essential channels F Y X28/01/2003 13
14. 14. F-D Separation Concept28/01/2003 14
15. 15. Theoretical Cells & Cell Clusters Various combinations possible28/01/2003 15
16. 16. Frequency and Distance Separation Separation acceptable Distance separation L+FDR= Separation unacceptable Frequency separation28/01/2003 24
17. 17. F-D Separation: 1D (Line) 1 2 1 2 1 2 Separation by (reuse distance) 1 zone 2 channels 1 2 3 1 2 3 1 2 zones 3 channels n zones (n +1) channels28/01/2003 25
18. 18. F-D Separation: 2D (Surface)Reuse distance = 1 4 channels Reuse distance = 2 9 channels n zones (n +1)2 channels 228/01/2003 26
19. 19. Cell clusters 7 3 Various combinations possible28/01/2003 27
20. 20. F-D Separation: 3D (Space) 9 4 >8 9 > 27 4 9 1 zone 8 channels 2 zone 27 channels n zones (n+1)3 channels28/01/2003 28
21. 21. Ideal Lattices • Bound-less, regular, plane lattice • Each station located at a node • All nodes occupied (no "holes") • All stations identical (omnidirectional) • Uniform propagation (no terrain obstacles) • Uniform EM environment • One set of channels regularly re-used28/01/2003 29
22. 22. Equipment deficiency: example Spectrum “blocked” by typical UHF-TV terrestrial transmitter due to receiver’s deficiencies (“FCC 20 Taboos”) 18 Area * No. of channels No of channels denied 16 14 ideal: 1% 12 co-ch: 23% 10 Real other: 77% 8 6 4 2 Ideal 0 0 50 100 150 200 250 300 350 Distance from transmitter, km28/01/2003 31 Dixon64
23. 23. Serial-to-Parallel Converter OFDM Serial-to-Parallel Converter F1 Sub-Ch 1 • Orthogonal Frequency Division Multiplexing (OFDM) Signal Processing – The channel is split into a Demodulation F2 Sub-Ch 2 number of sub-channels – Each sub-channel transmits a part of the original information – Each sub-channel adjusted to its environment (S/N) – Reduces multipath & selective FN Sub-Ch N fading – Allows for higher speeds Digital – Requires smart signal Modulation processing – Used in 802.11a(USA), DTTB(Eu), Hyperplan(Eu),Delogne P, Bellanger M: The Impact of Signal Processing on an Power Line Coms. standards.Efficient Use of the Spectrum, Radio Science Bulletin June 1999, 23-28LeFloch B, Alard M, Berrou C: Coded Orthogonal Frequency DivisionMultiplex, Proc of IEEE June 1995, 982-996 28/01/2003 32
24. 24. TDM• Time Division Multiplex: A single carrier frequency channel is shared by a number of users, one after another. Transmission is organized in repetitive “time-frames”. Each frame consists of groups of pulses - time slots.• Each user is assigned a separate time-slot.• TDD – Time Division Duplex provides the forward and reverse links in the same frequency channel.28/01/2003 33
25. 25. TDM TDM Power density Time-frameFrequency Time Time slot Example: DECT (Digital enhanced cordless phone) Frame lasts 10 ms, consists of 24 time slots (each 417 s) 28/01/2003 34
26. 26. SDM• Space Division Multiple Access controls the radiated energy for each user in space using directive antennas – Sectorized antennas – Adaptive antennas28/01/2003 35
27. 27. CDMA or SS • Code Division Multiple Access or Spread Spectrum communication techniques – FH: frequency hoping (frequency synthesizer controlled by pseudo-random sequence of numbers) – DS: direct sequence (pseudo-random sequence of pulses used for spreading) – TH: time hoping (spreading achieved by randomly spacing transmitted pulses) – Other techniques • Hybrid combination of the above techniques (radar and other applications) • Random noise as carrier28/01/2003 36
28. 28. CDMA - FH SSFrequency Power density CDMA Bm Bc Transmission is organized in time- Time frequency “slots”. Each link is Time-frequency slot assigned a sequence of the slots, according to a specific code. Used e.g. in Bluetooth system 28/01/2003 37
29. 29. DS SS communications basics Originalinformation Spreading Original signal Spread signal Propagation effects Transmission Unwanted signals + Noise Reconstructed De-spreading information Spread signal+ Reconstr. signal28/01/2003 38
30. 30. SS: basic characteristics• Signal spread over a wide bandwidth >> minimum bandwidth necessary to transmit information• Spreading by means of a code independent of the data• Data recovered by de-spreading the signal with a synchronous replica of the reference code – TR: transmitted reference (separate data-channel and reference-channel, correlation detector) – SR: stored reference (independent generation at T & R pseudo-random identical waveforms, synchronization by signal received, correlation detector) – Other (MT: T-signal generated by pulsing a matched filter having long, pseudo-randomly controlled impulse response. Signal detection at R by identical filter & correlation computation)28/01/2003 39
31. 31. DS SS: transmitter Modulator X Antenna [A(t), (t)] [g1(t)] Information Carrier Modulated signal Spread signal cos( 0t) S1(t) = A(t) cos( 0t + (t)) g1(t)S1(t) band Bm Hz band Bc Hz Bc >> Bmgi(t): pseudo-random noise (PN) spreading functions that spreads the energy of S1(t) over a bandwidth considerably wider than that of S1(t): ideally gi(t) gj(t) = 1 if i = j and gi(t) gj(t) = 0 if i j 28/01/2003 40
32. 32. DS SS-receiver To demodulator Correlator & antenna X bandpass filter Linear combination g1(t) g1(t)S1(t) g1(t)S1(t) Spreading g (t) g (t)S (t) 1 2 2 g2(t)S2(t) function ……. S1(t) ……. [g1(t)] g (t) g (t)S (t) 1 n n gn(t)Sn(t) g1(t) N(t) N(t) (noise) g1(t) S’(t) S’(t)28/01/2003 41
33. 33. SS-receiver’s Input W/Hz Unwanted signals SS s.: g2(t)S2(t); …; gn(t)Sn(t) Other s. : S’(t) Wanted (spread) signal: g1(t)S1(t) Noise: N(t) Hz Bc Signal-to-interference ratio (S/ I)in = S/ [I( )*Bc] Bc = Input correlator bandwidth I( ) = Average spectral power density of unwanted signals in Bc S= Power of the wanted signal28/01/2003 42
34. 34. SS-correlator/ filter outputWanted (correlated) signal: de-spread to its original bandwidth as g1(t) g1(t)S1(t) = S1(t) with g1(t) g1(t) = 1 Bm Uncorrelated (unwanted) signals spread & rejected by correlator + noise g1(t) S’(t); g1(t) N(t); g1(t) gj(t)Sj(t) = 0 as gi(t) gj(t) = 0 for i j Signal-to-interference ratio (S/ I)out = S/ [I( )*Bm] Bc = Input correlator bandwidth Bm = Output filter bandwidth I( ) = Average spectral power density of unwanted signals & noise in Bm Bc S = power of the wanted signal at the correlator output Spreading = reducing spectral power density 28/01/2003 43
35. 35. SS Processing Gain = = [(S/ I)in/ (S/ I)out ] = ~Bc/ Bm Example: GPS signal RF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz Processing gain ~20’000 (+43 dB) Input S/N = -20 dB (signal power = 1% of noise power) Output S/N = +23 dB (signal power = 200 x noise power) (GPS = Global Positioning System)28/01/2003 44
36. 36. SS systems attributes (1) • Low spectral density of the signal – LPI: low probability of intercept – LPPF: low probability of position fix – LPSE: low probability of signal exploitation – Privacy – Covert operations capabilities – Low interference potential28/01/2003 45
37. 37. SS systems attributes (2)• AJ: anti-jamming/ anti-interference capability• Security• Natural cryptographic capabilities• Multiple-user random access communications with selective addressing (CDMA)• High time resolution (~1/B; multi-path suppression)28/01/2003 46
38. 38. Summary• To illustrtae the nature of the multiple access techniques consider a number of guests at a cocktail party. The aim is for all the guests to hold an intelligible conversation. In this case the resource available is the house itself• FDMA: each guest has a separate room to talk to their partner• TDMA: everyone is in a common room and has a limited time slot to hold the conversation• FH-CDMA: the guests run from room to room to talk• DS-CDMA: everyone is in a common room talkim at the same time, but each pair talks in a different language28/01/2003 47
39. 39. Access Control to Radio Resources• Distributed wireless networks (e.g. packet radio, ad hoc networks) have no central control.• Centralized wireless networks (e.g. WLAN, Cellular) control the use of radio channel; various approaches exist• Slotted systems (e.g. TDMA) require wide network synchronization for use of discrete time slots28/01/2003 48
40. 40. Packet Radio Protocols28/01/2003 49
41. 41. Packet Radio• In packet radio access techniques, many user attempt to access a single channel, which may led to collisions.• Protocols aim at limiting collisions• ALOHA is the oldest, classic protocol, developed in 1970 in Hawaii as an extension of TDMA and FDMA28/01/2003 50
42. 42. ALOHA• If 2 or more users transmit at the same time so that receiver receives more than one packet, the receiver is unable to separate the packets since they are not orthogonal in time (like in TDMA) or in frequency (like in FDMA).• The vulnerable period is the time interval during which the packets are susceptible to collisions with transmissions from other users Transmitter 1 Packet B Packet C Transmitter 2 Packet A t1 T1+228/01/2003 51
43. 43. • In pure ALOHA, the vulnerable period is 2 packet durations. A user transmits whenever it has a packet to deliver. If no acknowledgment (ACK) is received, the user waits a random time and retransmit the packet. The throughput is T = Re-2R, R being the normalized channel traffic in Erlangs (Tmax = 0.184 at R = 0.5)• In slotted ALOHA, time is divided into equal time slots of length greater than the packet duration. The users have synchronized clocks and transmit messages only at the beginning of a new time slot. This prevent partial collisions where one packet collides with a portion of another. The vulnerable period is only one packet duration. The throughput is T = Re-R (Tmax = 0.368 at R = 1)• ALOHA protocols do not listen to the channel before transmission, and do not exploit information about the other users.28/01/2003 52
44. 44. • Carrier Sense Multiple Access (CSMA) protocols base on monitoring the channel. If the channel is idle (no carrier is detected), then the user is allowed to transmit. Important are detection delay and propagation delay.• Reservation protocols – certain packet slots are assigned with priority28/01/2003 53
45. 45. References• Coreira LM, “Wireless Flexible Personalized Communications”, J Wiley• Dunlop J, Smith DG, “Telecommunication Engineering”, Chapman & Hall• Reed JH, “Software Radio”, Prentice Hall• Taub H, Shilling DL, “Principles of Communication Systems”, McGraw Hill28/01/2003 54