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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
8. Bandpass Modulation and DemodulationTechniques
Y. Yoganandam, Runa Kumari, and S. R. Zinka
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
October 21 – 30, 2015
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
1 Introduction
2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
1 Introduction
2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Symbols Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols Symbols Symbols
Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols Symbols Symbols
Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols Symbols Symbols
Symbols Symbols Symbols Symbols Symbols SymbolsSymbols Symbols Symbols Symbols Symbols
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Analog Modulation Techniques
Carrier Signal: Ac cos (ωct + θ)
Amplitude Modulation: AAM = f (m (t))
Frequency Modulation:ωFM = g (m (t))
Phase Modulation:θPM = h (m (t))
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Digital Modulation Techniques
The main difference between analog and digital modulation techniques ischaracterized by the message signal. In analog case m (t) is an analog signal,
whereas in digital case m (t) is a digital signal .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
d h h f ( ) ff l ( ) h f ( )
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
A Slight Modied Representation of Carrier Signal
A sinusoidal signal S (t) = Acos ω t can be represented in terms of it’s poweras
S (t) = √ 2P cos ω t (1) because P = A2/2.
The above equation can be further re-written as
S (t) = 2EsT S cos ω t (2) because P watts can be replaced by E
s joules/ T
S seconds .
As we have seen in the previous chapter, energy of a received signal is thekey parameter in determining the error performance of the detection process.
That is the reason why we are using the notation √ 2Es/ T S in this chapter.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
I t d ti Ph Shift K i (PSK) Diff ti l PSK (DPSK) F Shift K i (FSK) ASK & APK S
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
So, Digital Modulation Techniques are ...
Carrier Signal:
2Es/ T S cos (ωct + φ)Phase Shift Keying:
φPSK
= φi (t)
Frequency Shift Keying:ωFSK = ωi (t)
Amplitude Shift Keying:EASK = Ei (t)
ASK + PSK:EAPK = Ei (t) & φAPK = φi (t)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Digital Modulation Techniques – Examples
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Digital Modulation Techniques – Examples
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Digital Modulation Techniques – Examples
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Digital Modulation Techniques – Examples
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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y g ( ) ( ) q y y g ( ) y
Bits vs Symbols
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Bits vs Symbols
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Bits vs Symbols
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Bits vs Symbols
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Why Digital Modulation?
Digital modulation is a process of translating the symbols into waveforms .
In baseband modulation, the waveforms are shaped pulses .
We can not send baseband signals over wireless. We need to translate thesignals to higher frequencies for ease of transmission .
Higher frequencies give us the benet of multiplexing multiple channelsaround the same carrier.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Symbol Energy vs bit Energy
Es = nEb (3)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of ASK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of ASK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of ASK
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Spectral Properties of ASK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of ASK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of PSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of FSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of FSK
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Spectral Properties of FSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of FSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of FSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Spectral Properties of FSK
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Outline
1 Introduction
2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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Phase Shift Keying (MPSK)If a digital signal can be completely represented by M different levels , then
those M levels can be converted into M symbols (or alphabets ). Each of these M symbols can be associated with a unique phase φi, where i = 1,2,· · · , M.Since 0 ≤φ ≤2π , if we distribute these phases uniformly ,
φi = 2π i M
, i = 1, 2,· · · , M. (4)So, the modulated PSK signal is given by
Si (t) = 2EsT S sin ω0t + 2π i M , i = 1, 2,· · · , M= 2EsT S sin (ω0t) cos 2π i M + cos (ω0t) sin 2π i M= √ Es cos 2π i M ψ1 (t) + sin
2π i M
ψ2 (t) , (5)
where ψ1 (t) = √ 2/ T S sin ω0t and ψ2 (t) = √ 2/ T S cos ω0t.8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Modulation Mechanism
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Signal Space Representation of Si (t)
Si (t) = √ Es cos 2π i M ψ1 (t) + sin2π i M
ψ2 (t)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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MPSK – Constellation Diagram
Si (t) = √ Es cos 2π i M ψ1 (t) + sin2π i M
ψ2 (t)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
( )
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Binary PSK (BPSK/2PSK)
Si (t) = √ Es cos 2π i M ψ1 (t) + sin2π i M
ψ2 (t) , M = 2 for BPSK
S1 (t) = −√ Esψ1 (t) = − 2Es/ T S sin ω0t (6)S2 (t) = + √ Esψ1 (t) = + 2Es/ T S sin ω0t (7)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Q d i PSK (QPSK)
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Quadri PSK (QPSK)
Si (t) = √ Es cos 2π i M ψ1 (t) + sin2π i M
ψ2 (t) , M = 4 for QPSK (8)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
8PSK
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8PSK
The constellations become denser as M increases.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK C h t D d l ti
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MPSK – Coherent Demodulation
The demodulator is expected to give back the symbol .
Since the Symbol has been encoded into phase of the carrier, we need toextract the phase of the received carrier, during a particular symbol duration
and drop the carrier.
Since phase extraction is involved , the process has to be a coherent one .
Further, the received signal is noisy :
r (t) = √ Es cos 2π i M ψ1 (t) + sin2π i M
ψ2 (t) + n (t) (9)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK C h t D d l ti
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MPSK – Coherent Demodulation
Apply minimum distance criterion with respect to the pre determined set.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK Coherent Demodulation
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MPSK – Coherent Demodulation
Apply minimum distance criterion with respect to the pre determined set.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK Coherent Demodulation
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MPSK – Coherent Demodulation
Apply minimum distance criterion with respect to the pre determined set.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK Coherent Demodulation
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MPSK – Coherent Demodulation
Apply minimum distance criterion with respect to the pre-determined set .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK Coherent Demodulation
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MPSK – Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK Coherent Demodulation
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MPSK – Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Coherent Demodulation
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MPSK – Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Coherent Demodulation
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MPSK Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Coherent Demodulation
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MPSK Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Coherent Demodulation
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MPSK Coherent Demodulation
φ̂ = tan −1 YX
(10)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BPSK – Coherent Demodulation
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BPSK Coherent Demodulation
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BPSK – Coherent Demodulation
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BPSK – Coherent Demodulation
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S1 (t) = −√ Esψ1 (t) = − 2Es/ T S sin ω0tS2 (t) = + √ Esψ1 (t) = + 2Es/ T S sin ω0t
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BPSK – Coherent Demodulation
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BPSK – Probability of Symbol (Bit) Error
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y y ( )
The threshold γ 0 is 0, and decision rule is to declare S1 or S2 based on thethreshold crossing . This is similar to NRZ binary baseband problem.
So, for AWGN with one sided spectral density of N 0/2 Watts/Hz, probabilityof symbol error is given as
PBPSKS = Q 2EsN 0 . (11)8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
QPSK – Probability of Symbol Error
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y y
Probability of symbol error is given (proof will be provided later) as
PQPSKS = 2Q EsN 0 − Q EsN 02
≈2Q EsN 0 , for large SNR.8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Probability of Symbol Error
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For MPSK, probability of symbol error is given as
PMPSKS ≈2Q dmin√ 2N 0 = 2Q 2EsN 0 sin π M , for large SNR.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Symbol Error vs Bit Error
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An error in phase might cause symbol error ... and one symbol error cancause atmost n bit errors .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Symbol Mapping using Gray Code
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An error in phase might cause symbol error ... and Gray coding makes surethat symbols corresponding to adjacent phases change only one bit at a time .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
PS vs PB using Gray Code
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PB ≈ PS
k = PS
log2 M (for PS 1) (12)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of Gray Code
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generation of QPSK using BPSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Bit & Symbol Error Rates – BPSK vs QPSK
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Although QPSK can be viewed as a quaternary modulation, it is easier to seeit as two independently modulated quadrature carriers . So, BPSK demod-ulation can be applied on both the carriers independantly . As a result, theprobability of bit-error for QPSK is the same as for BPSK :
PBPSK/QPSKB = Q 2EbN 0 . (13)Since we know the probability of bit-error, we can calculate probability of sym- bol error as
PQPSKS = 1− 1 −PBPSKB2
= 2Q 2EbN 0 − Q 2EbN 02
≈ 2Q 2EbN 0 = 2Q 2EbN 0 . (14)8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK - PS and PB
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8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Bandwidth & Bandwidth Efciency of MPSKF MPSK th b b d PSD i i b
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For MPSK, the baseband PSD is given by
S base− bandMPSK ( f ) = 2Ebk sin π fkT b
π fkT b
2. (15)
From the above equation it is clear that null-to-null bandwidth correspondingto M ary PSK is given by
Bnull −to−nullT = 2kT b= 2Rb
k . (16)
However, if we take 3 dB bandwidth as the criteria, then the corresponding bandwidth is given by
B3 dBT = 1
kT b= Rb
k . (17)
So, bandwidth efciency is dened as
Bandwidth efciency = RbB3 dBT
= k . (18)
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
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1 Introduction
2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Coherence Requirement for MPSK
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In MPSK, since the information is in the phase of the transmitted waveform,coherence between Tx& Rx is a must .
For BPSK, if RF phase changes by angle θ, it can be shown that the probabilityof bit error changes to
PB = Q cos θ 2EbN 0 . (19)In order to make PSK amenable to non coherent detection , Differential PSK(DPSK) is used.
In DPSK, phase of the current symbol is not transmitted, but the phase differ-ence between current and previous symbols is transmitted. This avoids thenecessity of a coherent carrier at the receiver.
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Differential Phase Shift Keying (D8PSK)
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Symbol ∆φ
000 0001 π /4
011 2π /4010 3π /4110 4π /4111 5π /4101 6π /4
100 7π /4
Modulation ref
Symbol 110 001 110 010∆ φk π π /4 π 3π /4
φk = φk −1 +∆
φk 0 π 5π /4 π /4 π
Demodulation ref
φk = φk −1 + ∆ φk 0 π 5π /4 π /4 π ∆ φk = φk
−φk
−1 π π /4 π 3π /4
Recovered symbol 110 001 110 010
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Binary Differential Phase Shift Keying (DBPSK)
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Symbol ∆φ
1 00 π
Modulation ref
Symbol / Bit 1 0 1 1 0 0∆ φk 0 π 0 0 π π
φk =
φk −1 + ∆
φk 0 0 π π π 0 π
Demodulation
φk = φk −1 + ∆ φk 0 0 π π π 0 π ∆ φk = φk
−φk
−1 0 π 0 0 π π
Recovered Symbol / Bit 1 0 1 1 0 0
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Binary Differential Phase Shift Keying (DBPSK)
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Modulation ref
Message ak 1 0 1 1 0 0 0 1 1Encoding dk = ak ⊕dk −1 1 1 0 0 0 1 0 1 1 1
Signal phase φ 0 0 π π π 0 π 0 0 0
Transmitted NRZ-L signal 1 1 -1 -1 -1 1 -1 1 1 1
Demodulation
Sk (t) 1 1 -1 -1 -1 1 -1 1 1 1
1Eb ´ (k + 1)T
SkT S Sk (t) Sk −1 (t) dt 1 -1 1 1 -1 -1 -1 1 1Demodulator output âk 1 0 1 1 0 0 0 1 1
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSKModulation & Demodulation
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dk = ak ⊕dk −1
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 Bandpass Modulation and Demodulation Techniques Communication Systems Dept of EEE BITS Hyderabad Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 B d M d l ti d D d l ti T h iq C i ti S t D t f EEE BITS H d b d Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 B d M d l ti d D d l ti T h i C i ti S t D t f EEE BITS H d b d Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK Modulation & Demodulation
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dk = ak ⊕dk −1
8 B d M d l ti d D d l ti T h i C i ti S t D t f EEE BITS H d b d Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Two Different Types of DBPSK Demodulators
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8 B d M d l i d D d l i T h i C i i S D f EEE BITS H d b d Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Two Different Types of DBPSK Demodulators
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8 B d M d l i d D d l i T h i C i i S D f EEE BITS H d b d Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
DBPSK – Probability of Errors
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
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1 Introduction
2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
A Simple Introduction to FSK (BFSK)
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Generating BFSK on Emona Kit
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Coherent vs Non-Coherent FSK
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In its most general form, the binary FSK scheme uses two signals with differ-ent frequencies to represent binary 1 and 0 .
S1 (t) = 2EST S cos (2π f 1t + Φ 1) , kT b ≤t ≤ (k + 1) T S, for 1S2 (t) = 2EST S cos (2π f 2t + Φ 2) , kT b ≤t ≤ (k + 1) T S, for 0
where Φ 1 and Φ 2 are initial phases at t = 0, and T S is the symbol period of thedigital data.
When Φ 1 = Φ 2, this form of FSK is called coherent FSK .When Φ 1 = Φ 2, this form of FSK is called noncoherent or discontinuous FSK.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Condition for Orthogonality – Noncoherent FSK
If signals S1 (t) and S2 (t) are orthogonal
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If signals S1 (t) and S2 (t) are orthogonal
ˆ T S
0S1 (t) S2 (t) dt = 0
⇒ˆ T S
0cos (2π f 1t + Φ 1) cos (2π f 2t + Φ 2) dt = 0
⇓sin [2π ( f 1 + f 2) T S]2π ( f 1 + f 2)
cos (Φ 1 + Φ 2) + sin [2π ( f 1 − f 2) T S]
2π ( f 1 − f 2) cos (Φ 1 −Φ 2)
+ cos [2π ( f 1 + f 2) T S]−1
2π ( f 1 + f 2) sin (Φ 1 + Φ 2) +
cos [2π ( f 1 − f 2) T S]−12π ( f 1 − f 2)
sin (Φ 1 −Φ 2) = 0
Both sin x = 0 and cos x = 1 occur simultaneously when x = 2mπ . So, f 1 + f 2 = m/ T S. Similarly it can be proved that f 1 − f 2 = n/ T S.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Condition for Orthogonality – Coherent FSK
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For coherent FSK, Φ 1 = Φ 2 = Φ . So, the equation given in the previous slide becomes
⇓
sin [2π ( f 1 + f 2) T S]2π ( f 1 + f 2) cos2
Φ + sin [2π ( f 1
− f 2) T S]
2π ( f 1 − f 2)+ cos [2π ( f 1
+ f 2) T S]−12π ( f 1 + f 2)
sin2Φ = 0
Both sin x = 0 and cos x = 1 occur simultaneously when x = 2mπ . So, f 1 + f 2 = m/ T S. Similarly it can be proved that f 1 − f 2 = n/2 T S.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
So, Conditions for Orthogonality are
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Non-Coherent FSK:
f 1 + f 2 = m/ T S f 1
− f 2= n/ T S
Coherent FSK:
f 1 + f 2 = m/ T S f 1 − f 2= n/2 T S
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BFSK vs 4FSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
BFSK vs 4FSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MFSK Generation
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Coherent MFSK Detection
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Coherent MFSK Detection – PS & PB
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The symbol error probability for a coherently detected MFSK system has anupper bound , given as
PS ≤( M −1) Q ESN 0 . (20)Can you visualize the above equation geometrically?
In MFSK, the ratio of the bit error probability to the symbol error probabilityis
PBPS =
M/2 M −1 . (21)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Non-Coherent MFSK Detection
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Non-Coherent MFSK Detection
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In no noise case, assuming that the lters preserve the shape of the envelope
of the input signal waveforms, the output is of the type
z (T ) = 2ES/ T S. (22)8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Non-Coherent MFSK Detection – PS & PB
In the case of coherent detection, the pdf of the (signal + noise) , at the input
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of the decision stage, remained Gaussian .
In the case of non coherent detection, the pdf of the envelops of (signal +noise) , at the input of the decision stage, do not remain Gaussian .
So, rst, we need the knowledge of pdf of (signal + noise) at the decisionstage to evaluate the symbol / bit error probabilities.
The symbol error probability for a non coherently detected MFSK system isgiven as
PS = 1 M
exp −ESN 0
M∑
j= 2(−1) j
M j exp
ES jN 0
, where M j = M!
j! ( M − j)!
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Spectrum of MFSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Bandwidth & Bandwidth Efciency of MFSK
Bandwidth
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Non-Coherent MFSK: BT = M/ T S
Coherent MFSK: BT = M/2 T S
Bit rate Rb = 1/ T b = log2 M/ T S = k / T S
Bandwidth Efciency
(R/ W )NCMFSK = Rb/ BT = (1/ M) log2 M
(R/ W )CMFSK = Rb/ BT = (2/ M) log2 M
So, (R/ W )NCMFSK is better than (R/ W )NCMFSK .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Probability of Bit Errors for Various BinaryModulations
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
1 Introduction
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2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Amplitude Shift Keying (MASK)
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M-ary ASK waveform is given as
SMASKi (t) = Ai 2EsT S sin (ω0t + φ) , i = 1, 2,· · · , M (23)where √ ES is the energy of the nominal carrier in a symbol duration T S.For unipolar binary ASK , it is called on-off keying (OOK) . Binary 1 and 0 arerepresented by √ ES and 0, respectively, in the signal space.
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MASK – PS & PBIt can be shown that the symbol error probability for bipolar MASK is
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PS = 2 ( M −1) M Q 6Eavg( M2 −1) N 0 . (24)Similarly, the symbol error probability for unipolar MASK is
PS = 2 ( M
−1)
M Q 3Eavg
(2 M2 −3 M + 1) N 0 . (25)Eavg (average symbol energy ) can be written in terms of average bit energy,Eb, as
Eavg = (log2 M) Eb = kEb. (26)
At high signal-to-noise ratios, the most likely errors are the adjacent symbols(when we use Gray code ). So in this case
Pb ≈ PSlog2 M
= PSk
. (27)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MASK – Bandwidth & Bandwidth Efciency
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Power spectral density of MASK will have the same shape as that of MPSK .So, transmission bandwidth is given as
BT = 1kT
b
= Rbk
. (28)
So, bandwidth efciency is for MASK is
Bandwidth efciency = RbBT
= k = log2 M. (29)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Why ASK is Bad?
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From the above gure, it clear that MASK is usually not preferred due to itspoor power efciency .
We also know that MPSK constellation diagram gets crowded as M increases.
So, we need to come up with a modulation technique which shares features of both MPSK and MASK .
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
ASK + PSK = APK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MAPK (Quadrature Amplitude Modulation)
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For MAPK,
SMAPKi (t) = Ai 2EsT S sin (ω0t + φi) , i = 1, 2,· · · , M. (30)To get x and y coordinates corresponding to the signal in the constellationdiagram, the above equation can be re-written as
SMAPKi (t) = Ai√ Es cos φi
xi
ψ1 (t) + Ai√ Es sin φi
yi
ψ2 (t) . (31)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
16 QAM
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
8 QAM
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
QAM – Modulation & Demodulation
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
QAM – Modulation & Demodulation
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MQAM – PS & PB
It can be shown that the symbol error probability for bipolar MQAM is giveninterms of symbol average energy E as
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interms of symbol average energy Eavg as
PS ≤4Q 3kEb( M −1) N 0 , (32)where Eavg = (log2 M) Eb = kEb.
At high signal-to-noise ratios, the most likely errors are the adjacent symbols(when we use Gray code). So in this case
Pb
≈ PS
log2 M = PS
k . (33)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MQAM – Bandwidth & Bandwidth Efciency
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Power spectral density of MQAM will have the same shape as that of MPSK/ MASK. So, transmission bandwidth is given as
BT = 1kT b
= Rbk
. (34)
So, bandwidth efciency is for MQAM is
Bandwidth efciency = RbBT
= k = log2 M. (35)
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Comparison of MPSK, MQAM, and MFSK
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8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
Outline
1 Introduction
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2 Phase Shift Keying (PSK)
3 Differential PSK (DPSK)
4 Frequency Shift Keying (FSK)
5 ASK & APK
6 Summary
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
Introduction Phase Shift Keying (PSK) Differential PSK (DPSK) Frequency Shift Keying (FSK) ASK & APK Summary
MPSK – Summary
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SMPSKi (t) = 2EsT S sin ω0t + 2π i M , i = 1, 2,· · · , MPMPSKS ≈2Q
dmin√ 2N 0 = 2Q 2EsN 0 sin π M , for large SNRPMPSKB ≈
PSlog2 M
(for PS 1 and Gray coding )
Bandwidth efciency MPSK = RbBT
= log2 M
8. Bandpass Modulation and Demodulation Techniques Communication Systems, Dept. of EEE, BITS Hyderabad
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