psk, qam, fsk different modulation

RadioTechnology LabSeoul National University

[ ]Passband Data Transmission

김창회| 전파 및 무선통신 연구소 |

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

04/13/2023 3RadioTechnology Lab


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Hybrid Amp/Phase Modulation

• QAM

• Carrierless Amp/Phase Modulation (CAP)



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adioechnologyaboratory1. Hybrid Amp/Phase Modulation

M-ary QAM Two-dimensional generalization of M-ary PAM

The transmitted M-ary QAM signal



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QAM Square Constellation Product of L-ary PAM constellation (L=)

Error Probability (correct detection of QAM)

(symbol error prob of L-ary PAM)

Average value of transmit Energy Symbol 에 따라 transmit Energy 가 바뀜 평균 에너지 이용



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QAM Cross Constellation QAM with odd number of bits cross constellation

Error Probability



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Carrierless Amp/Phase Modulation (CAP) Appears to be carrierless M-ary QAM signal Equation [g(t)=pulse shaping function]

Represent the QAM Signal



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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



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Basic Structure of the CAP system CAP transmitter

CAP receiver• X(t) = s(t) * h(t) + w(t)



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Coherent FSK

• BFSK

• MSK (Minimum-shift Keying)

• GMSK (Gaussian-filtered MSK)

• M-ary FSK



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adioechnologyaboratory2. Coherent FSK

Binary FSK

Continuous-phase signal Continuous-phase frequency-shift keying (CPFSK) Orthogonal basis set



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Error Probability New Gaussian R.V (y=x1-x2)

P(BPSK Error) = P(BFSK Error) =



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BFSK transmitter

BFSK Receiver



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Minimum Shift Keying (MSK) Minimum frequency spacing allowing two FSK signals to be co-

herently orthogonal

h=0.5 MSK



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Phase Trellis



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In-phase & Quadrature components of MSK

In-phase

Quadrature

In-phase Quadrature



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Signal-Space Diagram



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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



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ISI vs compactness WT 의 값에 따라 GMSK 의 성능 달라짐 Compactness 를 높이면 error probability 높아짐



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M-ary FSK M-dimensional signal-space

Orthogonality

Error Probability

Bandwidth Efficiency

• (bits/s/Hz) M 의 크기가 커짐에 따라 매우 비효율



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Detection of Signals with Unknown Phase

• Detection algorithm (case of BFSK)

• Error Probablity of noncoherent modulation



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adioechnologyaboratory3. Detection of Signals with Unknown Phase

Unknown Phase 실제로 phase 정보는 큰 random 성을 가지고 있음 전송거리 , 전송경로 등이 매우 다양함에 따라 received signal 의

phase 가 매우 빠르게 변화할 수 있음 Phase 정보를 모를 때 , 신호를 detect 하는 방법의 필요 noncoherent receiver

Optimum Quadratic Receiver BFSK signal

Take the expectation with respect to all possible θ phase independent



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Given the carrier phase θ, Conditional likelihood function of symbol

Integrating equation over all possible θ



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Likelihood function

Signal detection Bessel function

Signal detection ()

Modified Bessel function of zero order

Modified Bessel function



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Error Probability of noncoherent receiver

Noncoherent receiver diagram• 가 전송되었을 때 , 로 인식할 확률• 는 orthogonal 이므로 는 오로지 w(t) 에 의한 것

In-phase & quadrature components of Matched filter output



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Rayleigh-distribution of envelop R.V are Gaussian-distributed (zero mean and variance ) Because of AWGN

Probability density function

Conditional Probability



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probability density of is signal + noise, is only noise

Error Probability of noncoherent Receiver

대입



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Differential Phase-Shift Keying

• Signal generation of DPSK

• Signal Detection



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adioechnologyaboratory4. Differential Phase-Shift Keying

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 in-

terval When symbol 0 leaves, the carrier phase is changed



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Error Probability of DPSK DPSK is a special case of noncoherent orthogonal modulation T= 는 orthogonal

Signal generation



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DPSK transmitter

DPSK receiver The signal points are

Two signals map to the same point or different point inner product



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DPSK receiver Inner product x0, x1

과 그것의 대칭인 중 어느 것에 가까운 지 검사하는 것과 같다

𝑄1



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Comparison of Modulation Schemes



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adioechnologyaboratory5. Comparison of Modulation Schemes

Bit Error Rate of modulation

BFSK <-> BPSK,QPSK,MSK (3dB)

At high values of SNR, DPSK andnoncoherent BFSK perform as well ascoherent BPSK and coherent BFSK,respectively



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adioechnologyaboratory5. Comparison of Modulation Schemes

Comparison of power-bandwidth requirements M-ary PSK with BPSK (symbol error prob = )

Signal constellation• Distance between the message points is shortwhen M is large



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adioechnologyaboratory6. Conclusion

• 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

psk, qam, fsk different modulation

Engineering

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adio echnology aboratory1

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signal phase phase

fsk signals

unknown phase phase

carrier phase

phase trellis