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)
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, 2001. 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 2(20)
Amplitude Shift Keying (ASK) Switch on-off the carrier: L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001. 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)
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001. 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 4(20)
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, 2001. 22-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. 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)
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, 2001. 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 7(20)
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)
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, 2001. Not popular (spectral noise + PLL problems) 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 9(20)
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, 2001. 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems S. Loyka 10(20)
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)
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)
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)
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)
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)
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)
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)
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)
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 2 2 2 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)
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)