Passband Digital Transmission Introduction Passband Transmission Model Coherent

Passband Digital Transmission • • • • Introduction Passband Transmission Model Coherent Phase-Shift Keying Hybrid Amplitude/Phase Modulation Schemes Coherent frequency-Shift Keying Detection of Signals with Unknown Phase Noncoherent Orthogonal Modulation Noncoherent Binary Frequency-Shift Keying Differential Phase-Shift Keying Comparison of Digital Modulation Schemes Using a Single Carrier Voiceband Modems Multichannel Modulation Discrete Multitone Synchronization 2

Introduction (1) • Amplitude Shift Keying • Phase Shift Keying • Frequency Shift Keying (with continuous phase) 3

Introduction (2) Digital Modulation Techniques: • Coherent • Non-coherent M-ary Signaling Schemes: • M-ary ASK • M-ary PSK • M-ary FSK • M-ary Amplitude-Phase Shift Keying (APK) (Special case: Quadrature Amplitude Modulation (QAM) 4

Introduction (3) Power Spectra: Passband Signal Baseband Signal (Complex) Power Spectral Density Bandwidth Efficiency: 5

Passband Transmission Model Two assumptions for Channel: • Channel is linear with wide enough bandwidth no distortion • Channel noise is zero-mean white Gaussian 6

Coherent Phase-Shift Keying (1) (BPSK: Constellation) 7

Coherent Phase-Shift Keying (2) (BPSK: Signal-Space Diagram) 8

Coherent Phase-Shift Keying (3) (BPSK: Error Probability) 9

Coherent Phase-Shift Keying (4) (BPSK: Generation and Coherent Detection) Binary PSK Transmitter Coherent Binary PSK Receiver 10

Coherent Phase-Shift Keying (5) (BPSK: Power Spectra) Pulse Shaping Function: Baseband Power Spectrum 11

Coherent Phase-Shift Keying (6) (QPSK: Constellation) 12

Coherent Phase-Shift Keying (7) (QPSK: Signal-Space Diagram) 13

Coherent Phase-Shift Keying (8) (QPSK: Example 6. 1) 14

Coherent Phase-Shift Keying (9) (QPSK: Error Probability) for each channel of QPSK 15

Coherent Phase-Shift Keying (10) (QPSK: Error Probability) another way nearest and 16

Coherent Phase-Shift Keying (11) (QPSK: Generation and Coherent Detection) QPSK Transmitter Coherent QPSK Receiver 17

Coherent Phase-Shift Keying (12) (QPSK: Power Spectra) Pulse Shaping Function: Baseband Power Spectrum 18

Coherent Phase-Shift Keying (13) (Offset QPSK) only ± 90° phase transitions but twice as frequently ± 180° & ± 90° phase transitions QPSK Offset QPSK Possible paths for switching between message points Basis Functions Same probability of error 19

Coherent Phase-Shift Keying (14) (π/4 Shifted QPSK) QPSK π/4 Shifted QPSK Possible paths for switching between message points 20

Coherent Phase-Shift Keying (15) (π/4 Shifted DQPSK) Noncoherent Detector 21

Coherent Phase-Shift Keying (16) (π/4 Shifted DQPSK: Example 6. 2) 22

Coherent Phase-Shift Keying (17) (M-ary PSK: Signal-Space Diagram) 23

Coherent Phase-Shift Keying (18) (M-ary PSK: Error Probability) (M-ary PSK: Power Spectra) Baseband Power Spectrum 24

Coherent Phase-Shift Keying (19) (M-ary PSK: Bandwidth Efficiency) 25

Hybrid Amplitude/Phase Modulation Schemes (1) M-ary QAM is a two-dimensional generalization of M-ary PAM. M-ary QAM Square Constellation: (M=L 2) Cartesian Product of L-ary PAM constellation PAM 26

Hybrid Amplitude/Phase Modulation Schemes (2) (M-ary QAM: Probability of Error) Probability of correct detection: (M=L 2) Probability of symbol error for L-ary PAM Probability of symbol error for M-ary QAM: 27

Hybrid Amplitude/Phase Modulation Schemes (3) (M-ary QAM: Cross Constellation) (for odd number of bits per symbol) 2 n-1 + 4 x(2 n-3) = 2 n 28

Hybrid Amplitude/Phase Modulation Schemes (4) (CAP: Carrierless Amplitude/Phase Modulation) 29

Hybrid Amplitude/Phase Modulation Schemes (5) (CAP: Presentation) • The transmitted signal s(t) appears to be carrierless. • The transmitted signal s(t) represents a symbol-time-invariant realization of hybrid amplitude and phase modulation. Ignoring rotation 30

Hybrid Amplitude/Phase Modulation Schemes (6) (CAP: Properties) 31

Hybrid Amplitude/Phase Modulation Schemes (7) (CAP: Example) 32

Hybrid Amplitude/Phase Modulation Schemes (8) (CAP: Basic Structure) 33

Hybrid Amplitude/Phase Modulation Schemes (9) (CAP: Basic Structure) 34

Hybrid Amplitude/Phase Modulation Schemes (10) (CAP: Digital Implementation of CAP Receiver) 35

Coherent frequency-Shift Keying (1) (BFSK: Constellation) (Continuous Phase FSK) 36

Coherent frequency-Shift Keying (2) (BFSK: Signal-Space Presentation) 37

Coherent frequency-Shift Keying (3) (BFSK: Probability of Error) Same for p 01 38

Coherent frequency-Shift Keying (4) (BFSK: Generation and Coherent Detection) Transmitter Coherent Receiver 39

Coherent frequency-Shift Keying (5) (BFSK: Power Spectra) Baseband Power Spectrum 40

Coherent frequency-Shift Keying (6) (MSK: Minimum Shift Keying) CPFSK Angle Modulated Signal Center Frequency Deviation Ratio 41

Coherent frequency-Shift Keying (7) (MSK: Phase Trellis) h=1 πh is same as –πh No memory (minimum value for orthogonal basis) h=0. 5 ±π/2 at odd multiples of Tb and 0 , π at even multiples of Tb Phase Trellis: Boldfaced path represents the sequence 1101000. Phase Tree h=0. 5 42

Coherent frequency-Shift Keying (8) (MSK: Signal-Space Diagram) Half Cycle Cosine Pulse: Half Cycle Sine Pulse: 43

Coherent frequency-Shift Keying (9) (MSK: Signal-Space Diagram) 44

Coherent frequency-Shift Keying (10) (MSK: Signal-Space Diagram) 45

Coherent frequency-Shift Keying (11) (MSK: Signal-Space Diagram) 46

Coherent frequency-Shift Keying (12) (MSK: Example) 47

Coherent frequency-Shift Keying (13) (MSK: Probability of Error) Same as BPSK and QPSK(BER) This good performance is the result of the detection of the MSK signal being performed in the receiver on the observation over 2 Tb interval. 48

Coherent frequency-Shift Keying (14) (MSK: Generation and Coherent Detection) Transmitter Coherent Receiver 49

Coherent frequency-Shift Keying (15) (MSK: Power Spectra) 3. In-phase and quadrature components are statistically independent. Hence the baseband power spectral density is given by: 50

Coherent frequency-Shift Keying (16) (Gaussian-Filtered MSK: Necessity) Desired specifications of MSK: • Constant envelope • Relatively narrow bandwidth • Coherent detection performance equivalent to that of QPSK Need to improve: Although the out-of-band spectral characteristics of MSK signals are good, but they do not satisfy the stringent requirements of certain applications such as wireless communications. 51

Coherent frequency-Shift Keying (17) (GMSK: Conditions ) Premodulation lowpass filter or baseband pulse-shaping filter: 1) Frequency response with narrow bandwidth and sharp cutoff characteristics. Is needed to suppress the high-frequency components of the transmitted signal. 2) Impulse response with relatively low overshoot. Avoids excessive deviation in the instantaneous frequency of the FM signal. 3) Evolution of a phase trellis where the carrier phase of the modulated signal assumes the two values ±π/2 at odd multiples of Tb and the two values 0 and π at even multiples of Tb as in MSK. Ensures that the modified FM signal can be coherently detected in the same way as the MSK signal, or it can be noncoherently detected as a simple binary FSK signal. 52

Coherent frequency-Shift Keying (18) (GMSK: Shaping Pulse) Frequency response Impulse response (W is the 3 d. B basebandwidth) 53

Coherent frequency-Shift Keying (19) (GMSK: Shaping Pulse) 54

Coherent frequency-Shift Keying (20) (GMSK: Probability of Error) (Empirical) 55

Coherent frequency-Shift Keying (21) (GMSK: Power Spectra) 56

Coherent frequency-Shift Keying (22) (GMSK: Example) 57

Coherent frequency-Shift Keying (23) (M-ary FSK) Constellation Probability of Error 58

Coherent frequency-Shift Keying (24) (M-ary FSK) Power Spectra Bandwidth Efficiency 59

Detection of Signals with Unknown Phase (1) (Optimum Quadratic Receiver) 60

Detection of Signals with Unknown Phase (2) (Optimum Quadratic Receiver) 61

Detection of Signals with Unknown Phase (3) (Optimum Quadratic Receiver) Binary Hypothesis Test 62

Detection of Signals with Unknown Phase (4) (Optimum Quadratic Receiver) Quadrature receiver using correlators Quadrature receiver using matched filters 63

Detection of Signals with Unknown Phase (5) (Optimum Quadratic Receiver) Noncoherent matched filter Output of matched filter for a rectangular RF wave 64

Noncoherent Orthogonal Modulation (1) Sent: s 1(t) and s 2(t) (two orthogonal signals with equal energy) Received: g 1(t) and g 2(t) (phase shifted versions of s 1(t) and s 2(t)) Generalized binary receiver for noncoherent orthogonal modulation 65

Noncoherent Orthogonal Modulation (2) (Scaled version of si(t)) Quadrature receiver equivalent to either one of the two matched filters 66

Noncoherent Binary Frequency-Shift Keying Transmitted FSK Signal Noncoherent receiver for the detection of binary FSK signal 67

Differential Phase-Shift Keying (1) Two basic operations: Differential encoding of input binary wave and Phase Shift Keying DPSK Transmitted for “ 1” Transmitted for “ 0” 68

Differential Phase-Shift Keying (2) DPSK Transmitter An example 69

Differential Phase-Shift Keying (3) DPSK Receiver 70

Comparison of Digital Modulation Schemes (1) 71

Comparison of Digital Modulation Schemes (2) 72

Comparison of Digital Modulation Schemes (3) 1) Increasing Eb/N 0 Decreasing BER 2) For any Eb/N 0 , PSK, QPSK and MSK have smaller BER 3) 3 d. B less Eb/N 0 requirement for PSK and DPSK than Coh. FSK and Noncoh. FSK to realize the same BER 4) At high Eb/N 0 , DPSK and Noncoh. FSK perform as Coh. FSK 5) In Coherent QPSK two orthogonal carriers are used. Thus two independent bit streams can be transmitted simultanuously and subsequently detected in the receiver. 6) In coherent MSK two orthogonal carriers are modulated by the two antipodal symbol shaping pulses, respectively, over 2 Tb intervals. The receiver uses a coherent phase decoding process over two successive bit intervals. 7) QPSK has not memory, but MSK has. 73

Comparison of Digital Modulation Schemes (4) 74

Voiceband Modems (1) Mo. Dem: Modulator-Demodulator PSTN: Public Switched Telephone Network ISP: Internet Service Provider Symmetric Configuration: data rate downstream = data rate upstream Asymmetric Configuration: data rate downstream > data rate upstream 75

Voiceband Modems (2) Signal constellation of V. 32 Modem using nonredundant coding 76

Voiceband Modems (3) Signal constellation of V. 32 Modem using trellis coding 77

Multichannel Modulation (1) (Capacity of AWGN Channel) Shannon’s information capacity theorem Signal to noise ratio gap Capacity of implementable system 78

Multichannel Modulation (2) (Continuous-Time Channel Partitioning) The need for complicated equalization of a wide-band channel is replaced by the need for multiplexing and de-multiplexing the transmission of the incoming data stream over a large number narrowband sub-channels that are contiguous and disjoint. 79

Multichannel Modulation (3) 80

Multichannel Modulation (4) (Properties of pass-band basis functions) 81

Multichannel Modulation (5) (Properties of pass-band basis functions) 82

Multichannel Modulation (6) (Geometric Signal to Noise Ratio) Assuming is high enough to ignore the two unity terms 83

Multichannel Modulation (7) (Loading of the Multichannel Transmission System) Channel Effect: Total bit rate: Constraint: Constrained optimization problem: Maximize the rate for the entire multichannel transmission system through an optimal sharing of the total transmit power P between the N sub-channels, subject to the constraint the P in maintained constant. 84

Multichannel Modulation (8) (Loading of the Multichannel Transmission System) Method of Lagrange Multipliers Differentiating J with respect to Pn 85

Multichannel Modulation (8) (Water-Filling Interpretation of the Optimization Problem) Set of equations to be solved: K always should to be positive. But some Ps may be negative. They should to be discarded and the new set of equations should to be solved again. 86

Multichannel Modulation (8) (Water-Filling Interpretation of the Optimization Problem) 87

Discrete Multitone (1) 88

Discrete Multitone (2) (Functional Blocks) Transmitter: 89

Discrete Multitone (3) (Functional Blocks) Receiver: 90

Discrete Multitone (4) (Applications) 91

Discrete Multitone (5) (Comparison of DSL and Voiceband Modem) Voiceband Modem (33. 6 Kbps Upstream & 56 Kbps downstream) ADSL/VDSL 160 Kbps/3 Mbps Upstream & 1. 54 Mbps /26 Mbps Downstream 92

Orthogonal Frequency-Division Multiplexing (1) Another closely related form of multichannel modulation is orthogonal frequency-division multiplexing (OFDM) that differs from DMT in areas of application and some aspects of its design. OFDM is used for data transmission over radio broadcast channels and wireless communication channels. Unlike DMT that uses loading for bit allocation, OFDM uses a fixed number of bits per subchannel. This restriction is made necessary by the fact that a broadcast channel involves oneway transmission, and in a wireless communications environment the channel is varying too rapidly. Accordingly, in both cases it is not feasible for the transmitter to know the channel and how to load it. 93

Orthogonal Frequency-Division Multiplexing (2) The block diagram of DMT applies equally to OFDM except for the signal constellation encoder does not include a loading algorithm for bit allocation. In addition, two other changes have to be made: Ø In the transmitter, an upconverter is included after the digital-to-analog converter to translate frequency, thereby facilitating the propagation of the transmitted signal over a radio channel. Ø In the receiver, a downconverter is included before the analog-to-digital converter to undo frequency translation that was performed by the upconverter in the transmitter. 94

Orthogonal Frequency-Division Multiplexing (3) Applications: Ø Wireless communications OFDM, combined with coding and interleaving, provides an effective technique to combat multipath fading that is a characteristic feature of wireless communication channels. Ø Digital audio broadcasting (DAB) OFDM has been adopted as the standard for digital audio broadcasting in Europe. Here again the system involves the combined use of coding and interleaving. 95

Synchronization (1) Ø When coherent detection is used, knowledge of both the frequency and phase of the carrier is necessary. The estimation of carrier phase and frequency is called carrier recovery or carrier synchronization. Ø To perform demodulation, the receiver has to know the instants of time at which the modulation can change its state. It has to know the starting and finishing times of the individual symbols. So it may determine when to sample and when to quench the product-integrators. The estimation of these times is called clock recovery or symbol synchronization. 96

Synchronization (2) Ø Data-aided Synchronization A preamble, which contains information about the carrier and symbol timing, is transmitted along with the data bearing signal in a time-multiplexed manner on a periodic basis. Its limitations are two-fold: 1) reduced data-throughput efficiency 2) reduced power efficiency Ø Nondata-aided Synchronization The use of a preamble is avoided, and the receiver has the task of establishing synchronization by extracting the necessary information from the modulated signal. Throughput and power efficiency are improved but at the expense of an increase in the time taken to establish synchronization. 97