Modulation and Multiplexing Joe Montana IT 488 Fall

Modulation and Multiplexing Joe Montana IT 488 - Fall 2003 1

Agenda • Modulation Concept • Analog Communication • Digital Modulation Schemes • Error Detection and Correction 2

Modulation 3

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 k. Hz, 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. 4

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. 5

Modulation – Basic Principles Modulating Signal V(t), at baseband(f. B) Action on carrier’s amplitude, frequency or phase Modulated Signal carrying the information of V(t), bandpass (f. C) Carrier (f. C) f. C 6

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 WE WILL BE LOOKING AT MODULATION INITIALLY, BUT WHERE DO MODULATION AND MULTIPLEXING FIT INTO A SYSTEM? 7

MODULATION AND MULTIPLEXING - 2 Fig. 5. 1 in text: (A) At uplink earth station (B) At downlink earth station 8

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) 9

Analog Communications 10

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 11

ANALOG TELEPHONY - 2 KEY POINT THE NUMBER OF VOICE CHANNELS A SATELLITE TRANSPONDER CAN CARRY VARIES INVERSELY WITH THE AVERAGE POWER LEVEL PER CHANNEL Simple Example NOTE: A pessimistic choice (power level set too high) will lower capacity estimate; An optimistic choice (power level set too low) can reduce quality of signals 12

CHANNEL LOADING EXAMPLE - 1 A 25 W transponder is designed to carry 250 two-way telephone channels (giving 500 channels at RF). Q 1. How much power is available for each telephone channel? Answer: Power per channel = (25) / (500) = 50 m. W Q 2. If the amplifier requires to be backed off 3 d. B to preserve linearity, what is the power available per telephone channel now? Answer: Power per channel = (25/2) / (500) = 25 m. W Q 2. What is the power per channel in the second case if 1000 RF channels are carried? Answer: Power per channel = (25 m. W) / 2 = 12. 5 m. W 13

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) NOTE: There is very little analog (FM) voice traffic over satellites now. The bulk of the high capacity traffic is carried over optical fibers. The majority of voice capacity is in small digital carriers called IDR (Intermediate Digital Rate) 14

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”. LET’S LOOK AT THIS PICTORIALLY 15

FREQUENCY MODULATION - 1 Input voltage Transfer characteristic Vmax Range of Input Voltage, v(t) Instantaneous Input Voltage Vmin f NOTE: In this example, fmin = the carrier frequency, fc Instantaneous Output Frequency Range of Output Frequency f min f max 16

FREQUENCY MODULATION - 2 Schematic representation of a sinusoidal modulating signal, vp, on a carrier signal, frequency fc NOTE: instantaneous frequency increases with increase in modulating voltage, and vice versa 17

FREQUENCY MODULATION - 3 The Frequency Modulated output signal, follows: c = 2 fc = carrier radian frequency , will be as Maximum angular frequency deviation of the modulator (5. 2) Maximum value of input modulating radian frequency 18

CARSON’S RULE - 1 Carson’s rule states that the transmission bandwidth, BT, is given by: Where B is the bandwidth of the modulating signal which, for a sinusoidal modulating signal, is the highest modulating frequency, fmod. 19

CARSON’S RULE - 2 A. Single-frequency sinusoid: Approximate value for required bandwidth B: (5. 5) Maximum frequency deviation Modulating frequency B. Real signal (practical case): Approximate value for required bandwidth B: (5. 6) Maximum modulating frequency 20

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

Digital Communications 22

DIGITAL COMMUNICATIONS -1 § 5. 4 in Chapter 5 + updated material 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 23

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 24

DIGITAL COMMUNICATIONS -2 At baseband, send V (volts) to represent a logical 1 and 0 At RF - digitally modulate the carrier ASK FSK PSK Amplitude Shift Keying Frequency Shift Keying Phase Shift Keying Binary forms of these are OOK, BFSK, and BPSK, respectively Let’s first look at basic Digital Communications from the book by COUCH (7 th. Edition) 25

DIGITAL COMMUNICATIONS -3 NOTE: from Couch 26

DIGITAL COMMUNICATIONS - 4 From Couch, Fig. 3 -15 27

DIGITAL COMMUNICATIONS - 5 From Couch, Fig. 3 -13 28

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 Line Codes are serial bit streams that are used to drive the digital modulator 29

LINE CODES - 1 Couch Fig. 3 -15 Usually used in digital circuits Always have net zero voltage 30

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 SOME TYPICAL SPECTRA 31

TYPICAL SPECTRA Couch Fig. 2 -6 32

PULSE SPECTRA A random train of ones and zeroes has a spectrum (power spectral density) of (5. 40) X = f. Tb, Tb = bit period, and f = frequency in Hz Max value of Tb at f = 0 G(f) extends to f = Filtering affects the pulse shape 33

EFFECT OF FILTERING - 1 Fig. 5. 8 in text 34

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 bandlimited, so send a SHAPED PULSE Attempt to MATCH the filter to the spectrum of the energy transmitted Before FILTERS, let’s look at Inter-Symbol Interference 35

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 Example of ISI 36

ISI - contd. - 1 Form Couch, Fig. 3 -23 37

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 Nyquist Filter? ? ? 38

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 = 2 Tb, 3 Tb, …. . , NTb then we would have no ISI This is called a NYQUIST filter 39

NYQUIST FILTER - 2 Sampling instant is CRITICAL Impulse at this point 0 Tb 2 Tb 3 Tb 4 Tb t 40

NYQUIST FILTER - 3 NOTE: At each sampling interval, there is only one pulse contribution - the others being at zero level Fig. 5. 9 in text 41

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 42

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) matches pulse characteristic, hence it is called a Filter is a “Square Root Raised Cosine“matched Filter” filter” Matched Filter 43

MATCHED FILTER - 1 f f Roll-off factor = = (f / f 0 ) 6 d. B where f 0 = 6 d. B bandwidth B = absolute bandwidth (here shown for = 0. 5) and f 1 f 0 B B = f + f 0 f 1 = start of ‘roll-off’ of the filter characteristic Fig. 5. 10 in text 44

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) BUT how much bandwidth is required for a given transmission rate? ? ? 45

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 is Bandwidth = (1/2)Rb(1 + ) Bandwidth needed to send passband digital signal using a Nyquist Bandpass filter is bandwidth = Rb(1 + ) NOTE: It is the Symbol Rate that is key to bandwidth, not the Bit Rate 46

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 47

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 rolloff factor of filter. Thus BN = Rs 48

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 2 bits per Number SOLUTION: symbol of bits/s Symbol Rate = Rs = (1/2) (512 103) = 256 103 49

BANDWIDTH EXAMPLE - 2 Occupied Bandwidth, B, is B = Rs (1 + ) = 256 103 ( 1 + 0. 3) = 332. 8 k. Hz Noise Bandwidth, BN, is BN = Rs = 256 k. Hz Now what happens if you have FEC? Example with FEC 50

BANDWIDTH EXAMPLE - 3 SAME Example, but 1/2 -rate FEC is now used 2 bits per symbol 1/2 -rate FEC used Number of bits/s SOLUTION Symbol Rate, Rs = (1/2) (512 103) = 512 103 symbols/s Occupied Bandwidth, B, is B = Rs ( 1 + ) = 665. 6 k. Hz 51

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

Digital Modulations 53

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) 54

Binary Modulations – Basic Types These two have constant envelope (important for amplitude sensitive channels) 55

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 (phasedlocked). 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. 56

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. 57

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: Therefore 58

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 59

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

BPSK representation Therefore, we can write the signals s 1(t) and s 2(t) in terms of 1(t): • Which can be graphically represented as: 61

BPSK Physical Implementation +A -A 62

Detection of BPSK Actual BPSK signal is received with noise We assume AWGN in this 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 63

Recall Gaussian Distribution Area to the right of this line represents Probability (x>x 0) m= mean =standard deviation Where: x 0 x Approximation for large positive values of y Both Q(. ) and erfc(. ) functions are integrals widely tabled and available as functions in Excel and calculators 64

Calculating Error Probability Noise Spectral Density = N 0 Noise Variance: BPSK error probability 65

Bit Error Rate (BER) for BPSK BER is therefore given by Approximation valid for Eb/No greater than ~4 d. B Eb/No (d. B) 0 2 4 6 8 10 10. 543 BER 0. 08 0. 04 0. 014 0. 0027 2*10 -4 4*10 -6 Note that these calculations are for synchronous detection 66

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 67

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! 68

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 Valid for BER<~0. 01 69

Coherent Quaternary PSK (QPSK) Four signals are used to convey information Constant Modulus => This leads to a constellation of: when shown as a phasor referenced to the signal phase, q Each of the two states represents a two bits of information 70

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

QPSK Constellation 72

QPSK Waveform 73

QPSK Physical Implementation Note that the QPSK signal can be seen to be two BPSK signals in phase quadrature 74

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: Approximation valid for Eb/No greater than ~4 d. B Note that Eb is here, not Es! 75

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

Frequency Shift Keying 77

Other Modulations (cont. ) M-ary PSK with 2 n 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 78

M-ary PSK 79

M-ary QAM 80

Other Modulations OQPSK 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 81

Shannon Bound 1948 Shannon demonstrated that, with proper coding a channel capacity of Required channel quality for error free communications =>we’re doing much worse 82

Modulation Schemes Error Performance 83

M-ary PSK Error Performance 84

Operation Point Comparison 85

Error Detection and Correction 86

Coding position on a transmission system 87

Error Protection Coding Three types to discuss Parity Bits (error detection only, really a subset of BC) Block Coding (eg. Reed-Solomon) Forward Error Convolutional Coding (eg. Viterbi or Turbo) Correction codes 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) 88

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+1 th bit is determined by: Even parity: Odd parity: Doesn’t correct errors just detects, and only an odd number of errors (discuss why) 89

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 90

Block Codes - 2 Hamming, Golay, BCH, Reed-Solomon, maximallength 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 91

Ciclic Codes (block codes) 92

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 Coding Gain (d. B) for various Viterbi codes 93

Convolutional Codes - 2 94

Trellis Coding - 1 95

Trellis Coding - 2 96

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 97

Summary of Useful Formulas 98

Summary of Digital Communications -1 Legend of variables mentioned in this section: M = modulation size. (Ex: 2, 4, 16, 64) Bw = Bandwidth in Hertz = Roll-off factor (from 0 to 1) Gc = Coding Gain (convert from d. B to linear to use in formulas) Ov = Channel Overhead (convert from % to fraction : 0 to 1) BER = Bit Error Rate 99

Summary of Digital Communications - 2 • Bits per Symbol: • Symbol Rate [symbol/second]: • Gross Bit Rate [bps]: • Net Data Rate [bps]: 100

Summary of Digital Communications - 3 • Required Eb/No (assuming no coding) [adimensional]: (function of modulation scheme and required bit error rate – see table later) • Required Eb/No (using coding gain) [adimensional]: • Required C/N [adimensional]: 101

Summary of Digital Communications - 4 • Required Signal Strength [Watts]: Where k = Boltzman constant = 1. 38 e-23 J/Hz TS = System Noise Temperature T 0 = ambient temperature (usually 290 K) F = System Noise figure in linear scale (not in d. B) 102

BER Calculation as a Function of Modulation Scheme and Eb/No Available • Equations given on next slide are used to calculate the bit error rate (BER) given the bit energy by spectral noise ratio (Eb/No) as input. • These functions are used in their direct form for the bit error rate calculations. Excel and some scientific calculators provide the solution for the “erfc” function. • The formulas provided can be inverted by numerical methods to obtain the Eb/No required as a function of the BER. • Also possible to draw the graphic and obtain the “inverse” by graphical inspection. 103

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