introduce the basic modulation tech (PSK, FSK, QAM etc)
and comparison between them.
ref : Communication System (4ed, Haykin)
this ppt is for my seminar
2. INDEX
1. Hybrid Amp/Phase Modulation
2. Coherent FSK
3. Detection of Signals with Unknown Phase
4. Differential PSK
5. Comparison of Modulation Schemes
6. Conclusion
RadioTechnology Lab
Seoul National University
3. RadioTechnology Lab
Seoul National University
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2014-07-07 3
Hybrid Amp/Phase Modulation
• QAM
• Carrierless Amp/Phase Modulation (CAP)
4. RadioTechnology Lab
Seoul National University
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aboratory1. Hybrid Amp/Phase Modulation
2014-07-07 4
M-ary QAM
Two-dimensional generalization of M-ary PAM
The transmitted M-ary QAM signal
5. RadioTechnology Lab
Seoul National University
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aboratory1. Hybrid Amp/Phase Modulation
2014-07-07 5
QAM Square Constellation
Product of L-ary PAM constellation (L= 𝑀)
Error Probability
(correct detection of QAM)
(symbol error prob of L-ary PAM)
Average value of transmit Energy
Symbol에 따라 transmit Energy가 바뀜 평균 에너지 이용
6. RadioTechnology Lab
Seoul National University
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2014-07-07 6
QAM Cross Constellation
QAM with odd number of bits cross constellation
Error Probability
7. RadioTechnology Lab
Seoul National University
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aboratory1. Hybrid Amp/Phase Modulation
2014-07-07 7
Carrierless Amp/Phase Modulation (CAP)
Appears to be carrierless
M-ary QAM signal Equation [g(t)=pulse shaping function]
Represent the QAM Signal
8. RadioTechnology Lab
Seoul National University
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aboratory1. Hybrid Amp/Phase Modulation
2014-07-07 8
new formulation of the transmit signal
S(t) appears to be carrierless
Hybridized amplitude/phase modulation
Orthogonal Set
after passed LTI channel, orthogonal property holds
9. RadioTechnology Lab
Seoul National University
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aboratory1. Hybrid Amp/Phase Modulation
2014-07-07 9
Basic Structure of the CAP system
CAP transmitter
CAP receiver
• X(t) = s(t) * h(t) + w(t)
10. RadioTechnology Lab
Seoul National University
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2014-07-07 10
Coherent FSK
• BFSK
• MSK (Minimum-shift Keying)
• GMSK (Gaussian-filtered MSK)
• M-ary FSK
11. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 11
Binary FSK
Continuous-phase signal
Continuous-phase frequency-shift keying (CPFSK)
Orthogonal basis set
12. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 12
Error Probability
New Gaussian R.V (y=x1-x2)
P(BPSK Error) =
1
2
erfc
𝐸 𝑏
𝑁 𝑜
P(BFSK Error) =
1
2
erfc
𝐸 𝑏
2𝑁 𝑜
13. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 13
BFSK transmitter
BFSK Receiver
14. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 14
Minimum Shift Keying (MSK)
Minimum frequency spacing allowing two FSK signals to be
coherently orthogonal
h=0.5 MSK
15. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 15
Phase Trellis
𝜃 𝑇𝑏 − 𝜃 0 =
𝜋
2
𝑠𝑦𝑚𝑏𝑜𝑙 1 , −
𝜋
2
(𝑠𝑦𝑚𝑏𝑜𝑙 0)
16. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 16
In-phase & Quadrature components of MSK
In-phase
Quadrature
In-phase Quadrature
18. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 18
GMSK (Gaussian-filtered MSK)
Frequency response with narrow BW & sharp cutoff
Impulse response with low overshoot
The spectral efficiency of MSK is further enhanced by filtering the
baseband signal with a Gaussian filter
19. RadioTechnology Lab
Seoul National University
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2014-07-07 19
ISI vs compactness
WT의 값에 따라 GMSK의 성능 달라짐
Compactness를 높이면 error probability
높아짐
20. RadioTechnology Lab
Seoul National University
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aboratory2. Coherent FSK
2014-07-07 20
M-ary FSK
M-dimensional signal-space
Orthogonality
Error Probability
Bandwidth Efficiency
• 𝐵 =
𝑀
2𝑇
=
𝑅 𝑏 𝑀
2 log2 𝑀
(𝑇 = 𝑇𝑏 ∗ log2 𝑀 , 𝑅 𝑏 =
1
𝑇 𝑏
)
• 𝜌 =
𝑅 𝑏
𝐵
=
2 log2 𝑀
𝑀
(bits/s/Hz) M의 크기가 커짐에 따라 매우 비효율
21. RadioTechnology Lab
Seoul National University
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2014-07-07 21
Detection of Signals with Unknown
Phase
• Detection algorithm (case of BFSK)
• Error Probablity of noncoherent modulation
22. RadioTechnology Lab
Seoul National University
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aboratory3. Detection of Signals with Unknown Phase
2014-07-07 22
Unknown Phase
실제로 phase 정보는 큰 random성을 가지고 있음
전송거리, 전송경로 등이 매우 다양함에 따라 received signal의
phase가 매우 빠르게 변화할 수 있음
Phase 정보를 모를 때, 신호를 detect하는 방법의 필요
noncoherent receiver
Optimum Quadratic Receiver
BFSK signal
Take the expectation with respect to all possible θ
phase independent
23. RadioTechnology Lab
Seoul National University
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2014-07-07 23
Given the carrier phase θ,
Conditional likelihood function of symbol 𝑠𝑖
Integrating equation over all possible θ
24. RadioTechnology Lab
Seoul National University
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2014-07-07 24
Likelihood function
Signal detection
Bessel function
Signal detection (𝑆1, 𝑆2)
Modified Bessel function of zero order
Modified Bessel function
25. RadioTechnology Lab
Seoul National University
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aboratory3. Detection of Signals with Unknown Phase
2014-07-07 25
Error Probability of noncoherent receiver
Noncoherent receiver diagram
• 𝑆1 𝑡 가 전송되었을 때,
𝑆2(𝑡)로 인식할 확률
• 𝑆1 𝑡 , 𝑆2(𝑡)는 orthogonal이므로
𝑙2는 오로지 w(t)에 의한 것
In-phase & quadrature components of Matched filter output
26. RadioTechnology Lab
Seoul National University
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aboratory3. Detection of Signals with Unknown Phase
2014-07-07 26
Rayleigh-distribution of envelop
R.V 𝑋𝐼2, 𝑋 𝑄2 are Gaussian-distributed (zero mean and variance
𝑁0
2
)
Because of AWGN
Probability density function
Conditional Probability
27. RadioTechnology Lab
Seoul National University
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aboratory3. Detection of Signals with Unknown Phase
2014-07-07 27
probability density of 𝑋𝐼1, 𝑋 𝑄1
𝑋𝐼1 is signal + noise, 𝑋 𝑄1 is only noise
Error Probability of noncoherent Receiver
대입
28. RadioTechnology Lab
Seoul National University
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2014-07-07 28
Differential Phase-Shift Keying
• Signal generation of DPSK
• Signal Detection
29. RadioTechnology Lab
Seoul National University
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aboratory4. Differential Phase-Shift Keying
2014-07-07 29
DPSK
The noncoherent version of PSK
Eliminates the need for a coherent reference signal
Differential encoding + Phase-shift Keying
Define the signals
When symbol 1 leaves, the carrier phase is unchanged over the
interval 0 ≤ 𝑡 ≤ 2𝑇𝑏
When symbol 0 leaves, the carrier phase is changed
30. RadioTechnology Lab
Seoul National University
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2014-07-07 30
Error Probability of DPSK
DPSK is a special case of noncoherent orthogonal modulation
T=2𝑇𝑏
𝑆1 𝑡 , 𝑆2(𝑡)는 orthogonal
Signal generation
31. RadioTechnology Lab
Seoul National University
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2014-07-07 31
DPSK transmitter
DPSK receiver
The signal points are (𝐴 cos 𝜃 , 𝐴 sin 𝜃), (−𝐴 cos 𝜃 , −𝐴 sin 𝜃)
𝑥0 = 𝑥𝐼0, 𝑥 𝑄0 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 = 𝑇𝑏
𝑥1 = 𝑥𝐼1, 𝑥 𝑄1 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 = 2𝑇𝑏
Two signals map to the same point or different point inner product
32. RadioTechnology Lab
Seoul National University
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2014-07-07 32
DPSK receiver
Inner product x0, x1
𝑥0 𝑥𝐼0, 𝑥 𝑄0 가 𝑥1 𝑥𝐼1, 𝑥 𝑄1 과 그것의 대칭인 −𝑥𝐼1, −𝑥 𝑄1 중 어느 것에
가까운 지 검사하는 것과 같다
𝑄1
34. RadioTechnology Lab
Seoul National University
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aboratory5. Comparison of Modulation Schemes
2014-07-07 34
Bit Error Rate of modulation
BFSK <-> BPSK,QPSK,MSK (3dB)
At high values of SNR, DPSK and
noncoherent BFSK perform as well as
coherent BPSK and coherent BFSK,
respectively
35. RadioTechnology Lab
Seoul National University
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aboratory5. Comparison of Modulation Schemes
2014-07-07 35
Comparison of power-bandwidth requirements
M-ary PSK with BPSK (symbol error prob = 10−4)
Signal constellation
• Distance between the message points is short
when M is large
36. RadioTechnology Lab
Seoul National University
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aboratory6. Conclusion
2014-07-07 36
• QAM • Carrierless Amp/Phase Modulation(CAP)
Hybrid Amp/Phase Modulation
• FSK • MSK • GMSK
Coherent
• BFSK • Error probability • DPSK
Noncoherent
• BER comparison • Power-bandwidth comparison
Comparison of modulations