The document discusses various modulation techniques in communication, including hybrid amplitude/phase modulation, coherent frequency-shift keying (FSK), and differential phase-shift keying (DPSK). It explores their error probabilities, signal detection methods, and performance comparisons under different conditions. The conclusion highlights the efficiency and applications of these modulation schemes.

1. RadioTechnology Lab
Seoul National University
[ ]Passband Data Transmission
김창회
| 전파 및 무선통신 연구소 |

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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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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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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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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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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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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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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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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2014-07-07 13
 BFSK transmitter
BFSK Receiver

14. RadioTechnology Lab
Seoul National University
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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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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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2014-07-07 16
 In-phase & Quadrature components of MSK
 In-phase
 Quadrature
In-phase Quadrature

17. RadioTechnology Lab
Seoul National University
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2014-07-07 17
 Signal-Space Diagram

18. RadioTechnology Lab
Seoul National University
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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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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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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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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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 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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 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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 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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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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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

33. RadioTechnology Lab
Seoul National University
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Comparison of Modulation Schemes

34. RadioTechnology Lab
Seoul National University
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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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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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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