Modulation and Multiplexing Joe Montana IT 488 - Fall 2003

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3. 3 Modulation

4. 4 Why Modulate Signals? If we transmit signal through electromagnetic waves, we need antennas to recover them at a remote point. At low frequencies (baseband), the wavelengths are very large. Ex. Voice, at approx. 4 kHz, has a wavelength of 75 Km!! If we “move” those signals to higher frequencies, we can get more manageable antennas. After receiving the signal, we need to “move” them back to the original frequency band (baseband) through demodulation. Therefore, you can see the modulation task as “giving wings” to the information message.

5. 5 Modulation – Basic Principles Modulation is achieved by varying the amplitude, phase or frequency of a high frequency sinusoid. The initial high frequency sinusoid that will have a parameter modified is called the “Carrier”. The original message signal (baseband) is called the “Modulating” signal. The resulting bandpass signal is the “Modulated” signal, which is a combination of the carrier and the original message.

6. 6 Modulation – Basic Principles

7. 7 MODULATION AND MULTIPLEXING - 1 MODULATION THIS IS THE WAY INFORMATION IS ENCAPSULATED FOR TRANSMISSION MULTIPLEXING THIS IS THE WAY MORE THAN ONE LINK CAN BE CARRIED OVER A SINGLE COMMUNICATIONS CHANNEL

8. 8 MODULATION AND MULTIPLEXING - 2

9. 9 MODULATION AND MULTIPLEXING - 3 KEY POINTS You have to multiplex before modulating on the transmit side (that is, you have to get all of the output signals together prior to modulating onto a carrier) You have to demodulate before demultiplexing on the receive side (that is, before you can separate - i.e. demultiplex - the incoming signals, you have to demodulate the carrier to obtain the transmitted information)

10. 10 Analog Communications

11. 11 ANALOG TELEPHONY - 1 Baseband voice signal 300 - 3400 Hz (CCITT, now called ITU-T) 300 - 3100 Hz (Bell)We will use the ITU-T definition

12. 12 ANALOG TELEPHONY - 2 KEY POINT THE NUMBER OF VOICE CHANNELS A SATELLITE TRANSPONDER CAN CARRY VARIES INVERSELY WITH THE AVERAGE POWER LEVEL PER CHANNEL

13. 13 CHANNEL LOADING EXAMPLE - 1

14. 14 SATELLITE ANALOG Satellite transponders are bandwidth limited A flexible scheme is therefore required for loading analog voice channels earth stations may transmit in multiples of 12 voice channels (from 12 to 1872)

15. 15 FREQUENCY MODULATION - 1 DEFINITION“Frequency modulation results when the deviation, ?f, of the instantaneous frequency, f, from the carrier frequency fc is directly proportional to the instantaneous amplitude of the modulating voltage”.

16. 16 FREQUENCY MODULATION - 1

17. 17 FREQUENCY MODULATION - 2

18. 18 FREQUENCY MODULATION - 3

19. 19 CARSON’S RULE - 1

20. 20 CARSON’S RULE - 2

21. 21 FM IMPROVEMENT FM modulation is relatively inefficient with the use of transmission spectrum A small baseband bandwidth is converted into a large RF bandwidth FM demodulation and detection converts the wide RF bandwidth occupied into a small baseband bandwidth occupied Ratio of RF to baseband bandwidths gives an improvement in signal to noise ratio which leads to the so-called FM IMPROVEMENT

22. 22 Digital Communications

23. 23 DIGITAL COMMUNICATIONS -1 Many signals originate in digital form data from computers data from digital fixed and mobile systems digitized information (e.g. voice) World-wide network is moving towards all-digital system Computers can only handle digital signals

24. 24 Why Digital Transmission? Robustness Generally less susceptible to degradations But...when it does degrade tends to fail quickly Adaptiveness Can easily combine a mix of signal information Data, voice, video, multiple user signals Compatibility - with digital storage, etc. Security - not easily received except by recipient

25. 25 DIGITAL COMMUNICATIONS -2 At baseband, send ? V (volts) to represent a logical 1 and 0 At RF - digitally modulate the carrier ASK Amplitude Shift Keying FSK Frequency Shift Keying PSK Phase Shift Keying Binary forms of these areOOK, BFSK, and BPSK, respectively

26. 26 DIGITAL COMMUNICATIONS -3

27. 27 DIGITAL COMMUNICATIONS - 4

28. 28 DIGITAL COMMUNICATIONS - 5

29. 29 DIGITAL COMMUNICATIONS - 5 Analog-to-Digital recap; we have: Sampled at 2 times highest frequency Stored the sampled value Compared stored value with a quantized level Selected the nearest quantized level Turned the selected quantized level into a digital value using the selected number of bits We now need to generate a line code

30. 30 LINE CODES - 1

31. 31 LINE CODES - 2 SELECTION OF LINE CODE BASED ON NEED TO HAVE SYNCHRONIZATION (OR OTHERWISE) NEED TO HAVE A NET ZERO VOLTAGE (OR OTHERWISE) NEED TO PREVENT STRING OF SAME VOLTAGE LEVEL SIGNALS SPECTRAL EFFICIENCY

32. 32 TYPICAL SPECTRA

33. 33 PULSE SPECTRA

34. 34 EFFECT OF FILTERING - 1

35. 35 EFFECT OF FILTERING - 2 Rectangular pulses (i.e. infinite rise and fall times of the pulse edges) need an infinite bandwidth to retain the rectangular shape Communications systems are always band-limited, so send a SHAPED PULSE Attempt to MATCH the filter to the spectrum of the energy transmitted

36. 36 INTER-SYMBOL INTERFERENCE Sending pulses through a band-limited channel causes “smearing” of the pulse in time “Smearing” causes the tail of one pulse to extend into the next (later) pulse period Parts of two pulses existing in the same pulse period causes Inter-Symbol Interference (ISI) ISI reduces the amplitude of the wanted pulse and reduces noise immunity

37. 37 ISI - contd. - 1

38. 38 ISI - contd. - 2 To avoid ISI, you can SHAPE the pulse so that there is zero energy in adjacent pulses Use NRZ; pulse lasts the full bit period Use Polar Signaling (+V & -V); average value is zero if equal number of 1’s and 0’s Communications links are usually AC coupled so you should avoid a DC voltage component Then use a NYQUIST filter

39. 39 NYQUIST FILTER - 1 Bit Period is Tb Sampling of the signal is usually at intervals of Tb Thus, if we could generate pulses that are at a one-time maximum at t = Tb and zero at each succeeding interval of Tb (i.e. t = 2Tb, 3Tb, ….. , NTb then we would have no ISI This is called a NYQUIST filter

40. 40 NYQUIST FILTER - 2

41. 41 NYQUIST FILTER - 3

42. 42 NYQUIST FILTER - 4 Arranging to sample at EXACTLY the right instant is the “Zero ISI” technique, first proposed by Nyquist in 1928 Networks which produce the required time waveforms are called “Nyquist Filters”. None exist in practice, but you can get reasonably close

43. 43 NYQUIST FILTER - 5 Noise into receiver must be held to a minimum Place half of Nyquist filter at transmit end of link, half at receive end, so that the individual filter transfer function H(f) is given by Vr(f)NYQUIST = H(f) ? H(f)Filter is a “Square Root Raised Cosine Filter”

44. 44 MATCHED FILTER - 1

45. 45 MATCHED FILTER - 2 A Raised Cosine Filter gives a Matched Filter response The “Roll-Off Factor”, ?, determines bandwidth of Raised Cosine Low Pass Filter (LPF) Gives zero ISI when the output is sampled at correct time, with sampling rate of Rb (i.e. at a sampling interval of Tb)

46. 46 BANDWIDTH REQUIRED - 1 Bandwidth required depends on whether the signal is at BASEBAND or at PASSBAND Bandwidth needed to send baseband digital signal using a Nyquist LPF isBandwidth = (1/2)Rb(1 + ?) Bandwidth needed to send passband digital signal using a Nyquist Bandpass filter isbandwidth = Rb(1 + ?)

47. 47 BANDWIDTH REQUIRED - 2 SYMBOL RATE is the number of digital symbols sent per second BIT RATE is the number of digital bits sent per second Different modulation schemes will “pack” different numbers of Bits in a single Symbol BPSK has 1 bit per symbol QPSK has 2 bits per symbol

48. 48 BANDWIDTH REQUIRED - 3 OCCUPIED BANDWIDTH, B, for a signal is given by B = Rs ( 1 + ? ) where Rs is the symbol rate and ? is the filter roll-off factor NOISE BANDWIDTH, BN, for a channel will not be affected by the roll-off factor of filter. Thus BN = Rs

49. 49 BANDWIDTH EXAMPLE - 1 GIVEN: Bit rate 512 kbit/s QPSK modulation Filter roll-off, ?, is ? = 0.3 FIND: Occupied Bandwidth, B, and Noise Bandwidth, BN SOLUTION: Symbol Rate = Rs = (1/2) ? (512 ? 103) = 256 ? 103

50. 50 BANDWIDTH EXAMPLE - 2 Occupied Bandwidth, B, is B = Rs (1 + ? ) = 256 ? 103 ( 1 + 0.3) = 332.8 kHz Noise Bandwidth, BN, is BN = Rs = 256 kHz Now what happens if you have FEC?

51. 51 BANDWIDTH EXAMPLE - 3 SAME Example, but 1/2-rate FEC is now used SOLUTION Symbol Rate, Rs = (1/2) ? (2) ? (512 ? 103) = 512 ? 103 symbols/sOccupied Bandwidth, B, is B = Rs ( 1 + ? ) = 665.6 kHz

52. 52 BANDWIDTH EXAMPLE - 3 Noise Bandwidth, BN, is BN = Rs = 512 ? 103 = 512 kHz Summary: High Modulation Index ? More Bandwidth Efficient FEC (Block or Convolutional) ? Increases bandwidth required

53. 53 Digital Modulations

54. 54 Digital Modulations In digital communications, the modulating signal is a binary or M-ary data. The carrier is usually a sinusoidal wave. Change in Amplitude: Amplitude-Shift-Keying (ASK) Change in Frequency: Frequency-Shift-Keying (FSK) Change in Phase: Phase-Shift-Keying (PSK) Hybrid changes (more than one parameter). Ex. Phase and Amplitude change: Quadrature Amplitude Modulation (QAM)

55. 55 Binary Modulations – Basic Types

56. 56 Coherent and Non-coherent Detection Coherent Detection (most PSK, some FSK): Exact replicas of the possible arriving signals are available at the receiver. This means knowledge of the phase reference (phased-locked). Detection by cross-correlating the received signal with each one of the replicas, and then making a decision based on comparisons with pre-selected thresholds. Non-coherent Detection (some FSK, DPSK): Knowledge of the carrier’s wave phase not required. Less complexity. Inferior error performance.

57. 57 Design Trade-offs Primary resources: Transmitted Power. Channel Bandwidth. Design goals: Maximum data rate. Minimum probability of symbol error. Minimum transmitted power. Minimum channel bandiwdth. Maximum resistance to interfering signals. Minimum circuit complexity.

58. 58 Coherent Binary PSK (BPSK) Two signals, one representing 0, the other 1. Each of the two signals represents a single bit of information. Each signal persists for a single bit period (T) and then may be replaced by either state. Signal energy (ES) = Bit Energy (Eb), given by:

59. 59 Orthonormal basis representation Gram-Schmidt Orthogonalization: basis of signals that are both ortogornal between them and normalized to have unit energy. Allows representation of M energy signals {si(t)} as linear combinations of N orthonormal basis functions, where N<=M. Ex.: N=2

60. 60 BPSK representation Let’s consider the unidimensional base (N=1) where: Let’s also rewrite the signal amplitudes as a function of their energy:

61. 61 BPSK representation Therefore, we can write the signals s1(t) and s2(t) in terms of ?1(t):

62. 62 BPSK Physical Implementation

63. 63 Detection of BPSK Actual BPSK signal isreceived with noise We assume AWGN inthis class Other noise properties are possible AWGN is a good approximation Other noise models are more complex Constellation becomes a distribution because of noise variations to signal

64. 64 Recall Gaussian Distribution

65. 65 Calculating Error Probability

66. 66 Bit Error Rate (BER) for BPSK BER is therefore given by

67. 67 Ambiguity Resolution We haven’t discussed yet how to tell which signal state is a 1 and which a 0 Because of variations in the signal path, its impossible to tell a priori Two common approaches resolutions: Unique Word Differential Encoding

68. 68 Unique Word Ambiguity Resolution A specific, known unique word is sent The unique word is sent at a known time in the data The correct signal state is chosen as 1 to correctly decode the unique word Usually implemented with two detectors - the output of the correct one is simply used Could lead to problems until a new UW is RX if a phase slip occurs All bits after slip will be received wrong!

69. 69 Differential Encoding Ambiguity Resolution Data is not transmitted directly Each bit is represented by: 0 => phase shift of p radians 1 => no phase shift in the carrier This results in ~ doubling the BER since any error will tend to corrupt 2 bits BER is then

70. 70 Coherent Quaternary PSK (QPSK) Four signals are used to convey information This leads to a constellation of:when shown as a phasorreferenced to the signal phase, q Each of the two states representsa two bits of information

71. 71 QPSK Constellation Representation In this case we use the following orthonormal basis: Which gives, after application of some trigonometric identities, the following constellation representation:

72. 72 QPSK Constellation

73. 73 QPSK Waveform

74. 74 QPSK Physical Implementation

75. 75 Bit Error Rate (BER) for QPSK The BER is still the probability of choosing the wrong signal state (symbol now) Because the signal is Gray coded (00 is next to 01 and 10 for instance but not 11) the BER for QPSK is that for BPSK: BER (after a lot of derivation) is given by:

76. 76 Frequency Shift Keying Two signals are used to convey information In principle, the transmitted signal appears as 2 sinx/x functions at carrier frequencies Each of the two states representsa single bit of information Each state persists for a single bit period and then may be replaced either state BER is: 2x BPSK BER for coherent for non-coherent

77. 77 Frequency Shift Keying

78. 78 Other Modulations (cont.) M-ary PSK PSK with 2n states where n>2 Incr. spectral eff. - (More bits per Hertz) Degraded BER compared to BPSK or QPSK QAM - Quadrature Amplitude Modulation Not constant envelope Allows higher spectral eff. Degraded BER compared to BPSK or QPSK

79. 79 M-ary PSK

80. 80 M-ary QAM

81. 81 Other Modulations OQPSK QPSK One of the bit streams delayed by Tb/2 Same BER performance as QPSK MSK QPSK - also constant envelope, continuous phase FSK 1/2-cycle sine symbol rather than rectangular Same BER performance as QPSK

82. 82 Shannon Bound 1948 Shannon demonstrated that, with proper coding a channel capacity of

83. 83 Modulation Schemes Error Performance

84. 84 M-ary PSK Error Performance

85. 85 Operation Point Comparison

86. 86 Error Detection and Correction

87. 87 Coding position on a transmission system

88. 88 Error Protection Coding Three types to discuss Parity Bits (error detection only, really a subset of BC) Block Coding (eg. Reed-Solomon) Convolutional Coding (eg. Viterbi or Turbo) All impose an overhead on channel Additional information must be transmitted This additional information is the redundant information of the error coding Block codes develop less coding gain but are (much) easier to process (esp. at high data rates) Often advantageous to use both together Gain depends on BER - must be careful here Coding ~ necessary for non-lin. ch.s (discuss BER flare)

89. 89 Parity Bits The data is parsed into uniform k-bit words 7 bits is a common data length An extra bit is added to this to make an k+1 bit transmission word The value of the k+1th bit is determined by: Even parity: Odd parity: Doesn’t correct errors just detects, and only an odd number of errors (discuss why)

90. 90 Block Codes - 1 The data is parsed into uniform k-bit blocks Coder adds n-k unique redundant bits An n-bit block is transmitted Coder is memoryless - only this block used Transmitted data rate is then: Redundant bits used to correct errors

91. 91 Block Codes - 2 Hamming, Golay, BCH, Reed-Solomon, maximal-length are different types of block codes Important for this class Depending on amount of redundancy added, block codes may be used to detect only or to actually correct bit errors. Block codes correct burst errors (ie. adjacent errors) as well as they do random errors. Not as powerful as convolutional

92. 92 Ciclic Codes (block codes)

93. 93 Convolutional Codes - 1 Process as sliding window of data Use constraint length of k (window length) Transmit at rate of where r is rate Fairly high coding gain Turbo codes are even higher (but harder) Do not handle burst errors well

94. 94 Convolutional Codes - 2

95. 95 Trellis Coding - 1

96. 96 Trellis Coding - 2

97. 97 Interleaving and Code on Code Problem: Noise often happens in bursts Can use interleaving - spreading adjacent bits of convolutional code over time to avoid having adjacent bits corrupted But, we still have a quandary: Block codes are robust against bursts Convolutional codes provide more gain Solution: use both inner convolutional and outer block codes to get both effects

98. 98 Summary of Useful Formulas

99. 99 Summary of Digital Communications -1

100. 100 Summary of Digital Communications - 2

101. 101 Summary of Digital Communications - 3

102. 102 Summary of Digital Communications - 4

103. 103 BER Calculation as a Function of Modulation Scheme and Eb/No Available

104. 104 BER Calculation as a Function of Modulation Scheme and Eb/No Available - 2