Lecture 10. Digital Modulation

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1 Digital Modulation Lecture 10 On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary PSK (BPSK) Frequency shift keying Typical spectra Modulation/demodulation principles Main difference between digital and analog systems: goal of transmission. Advantages of digital modulation: More flexibility through DSP (processing, services, etc.) Noise/interference immunity; security Fits to computer/data communications 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 1(20)

2 Baseband Binary Modulation Binary data representation: 0 or 1. Unipolar modulation: high level (e.g., 5V) / zero, or 1/0 Bipolar modulation: +high level / -high level, or +1/-1 1 R = bit (data) rate, bit/s Tb NRZ L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 2(20)

3 Amplitude Shift Keying (ASK) Switch on-off the carrier: L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Signal representation: Is it similar to something? Signal spectrum? ( ) = ( ) cos ( 2π ) x t A m t f t binary ASK: c m( t ) = 1 or 0 general case: a fixed number of levels c 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 3(20)

4 L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 4(20)

5 Amplitude Shift Keying (ASK) Signal spectrum (FT): Square-wave message: Random message PSD: How to detect? S f A S f f S f f 2 c ( ) = ( ) + ( + ) x m c m c S ( f ) = c δ( f nf ), m + n= n π n j n sinc 2, 1 1 R cn = e f0 = = 2 2 2T 2 0 b L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 5(20)

Binary Phase Shift Keying L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001. BPSK signal representation: where m( t ) = ± 1 is bipolar message.

6 Binary Phase Shift Keying L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, BPSK signal representation: where m( t ) = ± 1 is bipolar message. Another form of the BPSK signal -> ( ) = cos ( ω + ϕ ( )) x t A t m t c c ( ) cos cos x t = A ϕ ω t c A sin ϕ m( t)sin ω t c c c 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 6(20)

7 Binary Phase Shift Keying Digital modulation index: 2 ϕ β d = π Important special case β = 1 (random message) d Compare with ASK! How to detect? PSD L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 7(20)

8 Same as analog PM Detection of BPSK Add a quantizer (sign(*) function) to improve performance (noise immunity) sign(.) out (+/-1) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 8(20)

9 Frequency Shift Keying Discontinuous FSK: x ( t) ( ω 1t + θ1 ) ( ω t + θ ) Ac cos, mark (1) = Ac cos 2 2, space (0) L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Not popular (spectral noise + PLL problems) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 9(20)

10 Continuous FSK: Frequency Shift Keying t x ( t) = Ac cos ω ct + Ω m( τ) dτ 0 L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 10(20)

11 Pulse-Amplitude Modulation (PAM) Baseband modulation (no carrier yet) Baseband signal represents digital data (e.g. binary) PAM: a conversion of an analog signal to a pulse-type signal in which the pulse amplitude carriers the analog information. This is the 1st step in converting an analog signal (waveform) to a digital signal. b... b A... A x( t) = A s( t kt ) { } { } 1 n 1 n k k= 1 n 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 11(20)

12 Pulse-Amplitude Modulation Based on the sampling theorem: analog band-limited (to F max ) signal can be represented by its samples taken at f 2F PAM provides pulse-like waveform that contains the same information as the original analog signal. Pulse rate [pulses/s] is the same as f s. Pulse shape can be any. Discuss rectangular pulse waveform first. Two types of sampling: natural sampling (gating) and instantaneous sampling (flat-top or sample-and-hold). s max 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 12(20)

13 Natural Sampling (Gating) The sampled (PAM) signal is x( t) x ( t) = s( t) x( t), s s( t) t kts = Π τ k= where f = 1/ T 2F s s max xs ( t ) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 13(20)

14 Natural Sampling (Gating): Spectrum Spectrum (FT) of the sampled (PAM) signal is [ ] ( ) Sx ( f ) = FT x ( ) sinc( ), s s t = d kd Sx f kfs k= where d = τ T is the duty cycle of s(t). / s Example: original signal spectrum sampled signal spectrum S f x ( ) d S x ( f ) Sx s ( f ) d sinc( kd) similar to ideal (delta-function) sampling? 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 14(20)

15 Start with Natural Sampling: Proof Find Fourier series of s(t): FT of s(t) is Finally, x ( t) = s( t) x( t) S ( f ) = S ( f )* S ( f ) This concludes the proof. s x x s How to recover (demodulate) the original signal? s jnω s( t) = c s ne, cn = d sinc( nd ) n= Ss( f ) = cnδ( f nfs ) n= Sx ( f ) = S ( )* ( ) ( ) s x f Ss f = cnsx f nfs n= t 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 15(20)

16 Instantaneous Sampling Also known as flat-top PAM or sample-and-hold. The sampled signal is t kt x ( ) ( ) s s t = x kts Π τ k= t = Π * x( kts ) δ( t kts ) τ k= x( t) xs ( t ) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 16(20)

17 Instantaneous Sampling: Spectrum The sampled signal spectrum (FT) is 1 Sx ( f ) = H ( f ) S ( ), ( ) sinc( ) s x f kfs H f = τ τf T s k= original signal spectrum sampled signal spectrum Sx ( f ) Example: ( ) d sinc( τf ) Sx f Sx s ( f ) d sinc( τf ) Proof homework. How to recover (demodulate) x(t)? 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 17(20)

18 Baseband PAM: Generic Case Basic pulse shape is not necessarily rectangular. The information is represented by the pulse amplitude A m. M-ary PAM signal waveform: x ( t) = A s( t), m = 1,2,... M, 0 t T m m s(t) signal waveform, T symbol interval, M the number of symbols. The information transmitted by one symbol: n = log M [bits] b 2 generic signal waveform s( t) Transmitted signal sequence xt ( t) = Ak s( t kt) k 0 T t 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 18(20)

19 PAM: Energy, Spectrum Baseband signal energy: Depends on m. Bandpass PAM signal: x ( t) = A s( t) cos ω t, m = 1, 2,... M, 0 t T Its spectrum (FT): m m c It is DSB-SC signal! The bandwidth is twice of that of baseband signal. T 2 2 A Bandpass signal energy: E ( ) m m = xm t dt = Es 2 Similar modulation formats: PPM, PWM. T T m = m = m s s = 0 0 E x ( t) dt A E, E s ( t) dt m Sx ( f ) = A S ( ) ( ) m s f fc + Ss f + fc 2 0 ( ) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 19(20)

20 Summary Basic digital modulation formats. Unipolar and bipolar NRZ baseband signals. ASK (OOK), PSK and FSK. Spectra and bandwidth. PAM. Instantaneous and flat-top sampling. Spectra of sampled signals. Recovery (demodulation) of the original signal. Generic form of a PAM signal. Homework: Reading: Couch, 3.1, 3.2, 5.9. Study carefully all the examples, make sure you understand and can solve them with the book closed. 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 20(20)

Digital Communication System

Digital Communication System Purpose: communicate information at certain rate between geographically separated locations reliably (quality) Important point: rate, quality spectral bandwidth requirement