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Blind Digital Modulation Classification based onM th-Power Nonlinear Transformation
Vincent Gouldieff1,2, Jacques Palicot1, Steredenn Daumont2
1CentraleSupelec/IETR, Rennes, France2Zodiac Data Systems/Zodiac Aerospace, Caen, France
December 9, 2016
Motivation
Cognitive Radio Context
Cognitive Node
Senses its environmentDecision: C ∈ C
Cognitive Terminal
Blind estimation of CNo prior knowledgeLow complexity
Motivation 2 / 19
Motivation
Cognitive Radio Context
Cognitive Node
Senses its environmentDecision: C ∈ C
Cognitive Terminal
Blind estimation of CNo prior knowledgeLow complexity
Motivation 2 / 19
Motivation
Cognitive Radio Context
Cognitive Node
Senses its environmentDecision: C ∈ C
Cognitive Terminal
Blind estimation of CNo prior knowledgeLow complexity
Motivation 2 / 19
Motivation
Is the “M th-Power Nonlinear Transformation”a good candidate for the estimation of C?
Motivation 3 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 4 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 5 / 19
AMC: a short Review
Automatic Modulation Classification
Likelihood-based Feature-based
ALRT GLRT HLRT
MPT
Statistics Mom.-Cumul. CMs-CCs
[1]
[1] O. A. Dobre et al., Survey of AMC Techniques: Classical Approaches and New Trends, IET Communications, 2007
[2] [3]
[2] W. Wei and J. M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations, IEEE Trans. Commun., 2000
[3] A. Hazza et al., An Overview of Feature-Based Methods for Digital Modulation Classification, in Proc. ICCSPA, 2013
[4] [5]
[4] A. Swami and B. M. Sadler, Hierarchical Digital Modulation Classification using Cumulants, IEEE Trans. Commun., 2000
[5] O. A. Dobre et al., Cyclostationarity-based Blind Classification of Analog and Digital Modulations, in Proc. MILCOM, 2006
[6]
[6] C. W Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in Proc. ICC, 2012
AMC: a short Review General Overview 6 / 19
AMC: a short Review
Automatic Modulation Classification
Likelihood-based Feature-based
ALRT GLRT HLRT
MPT
Statistics Mom.-Cumul. CMs-CCs
[1]
[1] O. A. Dobre et al., Survey of AMC Techniques: Classical Approaches and New Trends, IET Communications, 2007
[2] [3]
[2] W. Wei and J. M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations, IEEE Trans. Commun., 2000
[3] A. Hazza et al., An Overview of Feature-Based Methods for Digital Modulation Classification, in Proc. ICCSPA, 2013
[4] [5]
[4] A. Swami and B. M. Sadler, Hierarchical Digital Modulation Classification using Cumulants, IEEE Trans. Commun., 2000
[5] O. A. Dobre et al., Cyclostationarity-based Blind Classification of Analog and Digital Modulations, in Proc. MILCOM, 2006
[6]
[6] C. W Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in Proc. ICC, 2012
AMC: a short Review General Overview 6 / 19
AMC: a short Review
Automatic Modulation Classification
Likelihood-based Feature-based
ALRT GLRT HLRT
MPT
Statistics Mom.-Cumul. CMs-CCs
[1]
[1] O. A. Dobre et al., Survey of AMC Techniques: Classical Approaches and New Trends, IET Communications, 2007
[2] [3]
[2] W. Wei and J. M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations, IEEE Trans. Commun., 2000
[3] A. Hazza et al., An Overview of Feature-Based Methods for Digital Modulation Classification, in Proc. ICCSPA, 2013
[4] [5]
[4] A. Swami and B. M. Sadler, Hierarchical Digital Modulation Classification using Cumulants, IEEE Trans. Commun., 2000
[5] O. A. Dobre et al., Cyclostationarity-based Blind Classification of Analog and Digital Modulations, in Proc. MILCOM, 2006
[6]
[6] C. W Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in Proc. ICC, 2012
AMC: a short Review General Overview 6 / 19
AMC: a short Review
Automatic Modulation Classification
Likelihood-based Feature-based
ALRT GLRT HLRT
MPT
Statistics Mom.-Cumul. CMs-CCs
[1]
[1] O. A. Dobre et al., Survey of AMC Techniques: Classical Approaches and New Trends, IET Communications, 2007
[2] [3]
[2] W. Wei and J. M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations, IEEE Trans. Commun., 2000
[3] A. Hazza et al., An Overview of Feature-Based Methods for Digital Modulation Classification, in Proc. ICCSPA, 2013
[4] [5]
[4] A. Swami and B. M. Sadler, Hierarchical Digital Modulation Classification using Cumulants, IEEE Trans. Commun., 2000
[5] O. A. Dobre et al., Cyclostationarity-based Blind Classification of Analog and Digital Modulations, in Proc. MILCOM, 2006
[6]
[6] C. W Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in Proc. ICC, 2012
AMC: a short Review General Overview 6 / 19
AMC: a short Review
Automatic Modulation Classification
Likelihood-based Feature-based
ALRT GLRT HLRT
MPT
Statistics Mom.-Cumul. CMs-CCs
[1]
[1] O. A. Dobre et al., Survey of AMC Techniques: Classical Approaches and New Trends, IET Communications, 2007
[2] [3]
[2] W. Wei and J. M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations, IEEE Trans. Commun., 2000
[3] A. Hazza et al., An Overview of Feature-Based Methods for Digital Modulation Classification, in Proc. ICCSPA, 2013
[4] [5]
[4] A. Swami and B. M. Sadler, Hierarchical Digital Modulation Classification using Cumulants, IEEE Trans. Commun., 2000
[5] O. A. Dobre et al., Cyclostationarity-based Blind Classification of Analog and Digital Modulations, in Proc. MILCOM, 2006
[6]
[6] C. W Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in Proc. ICC, 2012
AMC: a short Review General Overview 6 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 7 / 19
System Model
Scheme of Feature-based AMC
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Single-carrier digital signal in AWGN
x(n) = a · ei·(2πfr·n+φ) ·∑k
s(k) · h(nTe − kT − τ) + ω(n)
No synchronization/demodulation
No prior knowledge
→ Blind & Robust AMC method
System Model 8 / 19
System Model
Scheme of Feature-based AMC
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Single-carrier digital signal in AWGN
x(n) = a · ei·(2πfr·n+φ) ·∑k
s(k) · h(nTe − kT − τ) + ω(n)
No synchronization/demodulation
No prior knowledge
→ Blind & Robust AMC method
System Model 8 / 19
System Model
Scheme of Feature-based AMC
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Single-carrier digital signal in AWGN
x(n) = a · ei·(2πfr·n+φ) ·∑k
s(k) · h(nTe − kT − τ) + ω(n)
No synchronization/demodulation
No prior knowledge
→ Blind & Robust AMC method
System Model 8 / 19
System Model
Scheme of Feature-based AMC
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Single-carrier digital signal in AWGN
x(n) = a · ei·(2πfr·n+φ) ·∑k
s(k) · h(nTe − kT − τ) + ω(n)
No synchronization/demodulation
No prior knowledge
→ Blind & Robust AMC method
System Model 8 / 19
System Model
Scheme of Feature-based AMC
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Single-carrier digital signal in AWGN
x(n) = a · ei·(2πfr·n+φ) ·∑k
s(k) · h(nTe − kT − τ) + ω(n)
No synchronization/demodulation
No prior knowledge
→ Blind & Robust AMC method
System Model 8 / 19
System Model
Preprocessing Unit: some details
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Based on 1PT (classical PSD):
Normalization step: y(n) has unit useful power (a = 1)
Spectral centering: fr ≈ 0
Output parameters: η = {σ2ω, ρ, β, ...}
System Model 9 / 19
System Model
Preprocessing Unit: some details
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Based on 1PT (classical PSD):
Normalization step: y(n) has unit useful power (a = 1)
Spectral centering: fr ≈ 0
Output parameters: η = {σ2ω, ρ, β, ...}
System Model 9 / 19
System Model
Preprocessing Unit: some details
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Based on 1PT (classical PSD):
Normalization step: y(n) has unit useful power (a = 1)
Spectral centering: fr ≈ 0
Output parameters: η = {σ2ω, ρ, β, ...}
System Model 9 / 19
System Model
Preprocessing Unit: some details
x(n)Preprocessing
Unit
Feature
Computation
Decision
AlgorithmCy(n)
ηRecognition Algorithm
Automatic Modulation Classifier
Based on 1PT (classical PSD):
Normalization step: y(n) has unit useful power (a = 1)
Spectral centering: fr ≈ 0
Output parameters: η = {σ2ω, ρ, β, ...}
System Model 9 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 10 / 19
Basics on MPT
MPT function:
MPTy(f) =
∣∣∣∣∣ 1
Ns·Ne−1∑n=0
yM (n) · e−2iπnf
∣∣∣∣∣2M
= M
√Γn [yM ] (f)
CMn,p,τy (f) =
1
Ns·Ne−1∑n=0
n∏i=1
y(∗)i(n+ τi) · e−2iπnf
Behavior:
−1 −0.5 0 0.5 1
x 104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
MP
Ty
2PT4PT
→ Minimum Distance Classification
Basics on MPT 11 / 19
Basics on MPT
MPT function:
MPTy(f) =
∣∣∣∣∣ 1
Ns·Ne−1∑n=0
yM (n) · e−2iπnf
∣∣∣∣∣2M
= M
√Γn [yM ] (f)
CMn,p,τy (f) =
1
Ns·Ne−1∑n=0
n∏i=1
y(∗)i(n+ τi) · e−2iπnf
Behavior:
−1 −0.5 0 0.5 1
x 104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
MP
Ty
2PT4PT
→ Minimum Distance Classification
Basics on MPT 11 / 19
Basics on MPT
MPT function:
MPTy(f) =
∣∣∣∣∣ 1
Ns·Ne−1∑n=0
yM (n) · e−2iπnf
∣∣∣∣∣2M
= M
√Γn [yM ] (f)
CMn,p,τy (f) =
1
Ns·Ne−1∑n=0
n∏i=1
y(∗)i(n+ τi) · e−2iπnf
Behavior:
−1 −0.5 0 0.5 1
x 104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
MP
Ty
2PT4PT
→ Minimum Distance Classification
Basics on MPT 11 / 19
Basics on MPT
MPT function:
MPTy(f) =
∣∣∣∣∣ 1
Ns·Ne−1∑n=0
yM (n) · e−2iπnf
∣∣∣∣∣2M
= M
√Γn [yM ] (f)
CMn,p,τy (f) =
1
Ns·Ne−1∑n=0
n∏i=1
y(∗)i(n+ τi) · e−2iπnf
Behavior:
−1 −0.5 0 0.5 1
x 104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
MP
Ty
2PT4PT
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
2PTy(2fr)
4PT y(4
f r) 8AMPM
R8QAM
BPSKC8QAM
QPSK
16QAM
8PSK
→ Minimum Distance Classification
Basics on MPT 11 / 19
Basics on MPT
MPT function:
MPTy(f) =
∣∣∣∣∣ 1
Ns·Ne−1∑n=0
yM (n) · e−2iπnf
∣∣∣∣∣2M
= M
√Γn [yM ] (f)
CMn,p,τy (f) =
1
Ns·Ne−1∑n=0
n∏i=1
y(∗)i(n+ τi) · e−2iπnf
Behavior:
−1 −0.5 0 0.5 1
x 104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
MP
Ty
2PT4PT
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
2PTy(2fr)
4PT y(4
f r) 8AMPM
R8QAM
BPSKC8QAM
QPSK
16QAM
8PSK
→ Minimum Distance Classification
Basics on MPT 11 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 12 / 19
References
Asymptotic: Poisson Summation Formula [7]
+∞∑n=−∞
g(t+ na) =1
a
+∞∑m=−∞
G(ma
)· ei2πf
mat
Theory for M = 2:2PTCth =
∣∣E[s2]H2(0)∣∣
Theory for M = 4:
4PTCth =
∣∣∣∣∣ 1
T
(E[s4]H4(0) + 6
(E[s2]
)2∑k>0
H(k)22 (0)
)∣∣∣∣∣12
Distributions for accurate references (or corrective terms)
[7] J. E. Mazo, Jitter Comparison of Tones Generated by Squaring and by Fourth-Power Circuits, Bell System Journal, 1978
References Asymptotic behavior 13 / 19
References
Asymptotic: Poisson Summation Formula [7]
+∞∑n=−∞
g(t+ na) =1
a
+∞∑m=−∞
G(ma
)· ei2πf
mat
Theory for M = 2:2PTCth =
∣∣E[s2]H2(0)∣∣
Theory for M = 4:
4PTCth =
∣∣∣∣∣ 1
T
(E[s4]H4(0) + 6
(E[s2]
)2∑k>0
H(k)22 (0)
)∣∣∣∣∣12
Distributions for accurate references (or corrective terms)
[7] J. E. Mazo, Jitter Comparison of Tones Generated by Squaring and by Fourth-Power Circuits, Bell System Journal, 1978
References Asymptotic behavior 13 / 19
References
Asymptotic: Poisson Summation Formula [7]
+∞∑n=−∞
g(t+ na) =1
a
+∞∑m=−∞
G(ma
)· ei2πf
mat
Theory for M = 2:2PTCth =
∣∣E[s2]H2(0)∣∣
Theory for M = 4:
4PTCth =
∣∣∣∣∣ 1
T
(E[s4]H4(0) + 6
(E[s2]
)2∑k>0
H(k)22 (0)
)∣∣∣∣∣12
Distributions for accurate references (or corrective terms)
[7] J. E. Mazo, Jitter Comparison of Tones Generated by Squaring and by Fourth-Power Circuits, Bell System Journal, 1978
References Asymptotic behavior 13 / 19
References
Asymptotic: Poisson Summation Formula [7]
+∞∑n=−∞
g(t+ na) =1
a
+∞∑m=−∞
G(ma
)· ei2πf
mat
Theory for M = 2:2PTCth =
∣∣E[s2]H2(0)∣∣
Theory for M = 4:
4PTCth =
∣∣∣∣∣ 1
T
(E[s4]H4(0) + 6
(E[s2]
)2∑k>0
H(k)22 (0)
)∣∣∣∣∣12
Distributions for accurate references (or corrective terms)
[7] J. E. Mazo, Jitter Comparison of Tones Generated by Squaring and by Fourth-Power Circuits, Bell System Journal, 1978
References Asymptotic behavior 13 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 14 / 19
Performance and Complexity
Theory and Simulation results
Distance Matrix Correct Classification Rate (CCR)
Constellation
BPSK QPSK 8PSK 8AMPM R8QAM C8QAM 16QAM
BPSK 0 1.004 1.419 0.905 0.564 0.988 1.055
Con
stel
latio
n
QPSK 0 0.761 0.219 0.656 0.068 0.159
8PSK 0 0.639 0.861 0.829 0.602
8AMPM 0 0.468 0.268 0.161
R8QAM 0 0.677 0.629
C8QAM 0 0.227
16QAM 0
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
Cor
rect
Cla
ssif
icat
ion
Rat
e
BPSKQPSK
8PSK
8AMPM
R8QAM
C8QAM16QAM
PSK/QAM/PAM35% Root-Raised-Cosine
1024 symbolsρ = 235% Root-Raised-Cosine
Performance and Complexity Simulation results 15 / 19
Performance and Complexity
Theory and Simulation results
Distance Matrix Correct Classification Rate (CCR)
Constellation
BPSK QPSK 8PSK 8AMPM R8QAM C8QAM 16QAM
BPSK 0 1.004 1.419 0.905 0.564 0.988 1.055
Con
stel
latio
n
QPSK 0 0.761 0.219 0.656 0.068 0.159
8PSK 0 0.639 0.861 0.829 0.602
8AMPM 0 0.468 0.268 0.161
R8QAM 0 0.677 0.629
C8QAM 0 0.227
16QAM 0
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)C
orre
ct C
lass
ific
atio
n R
ate
BPSKQPSK
8PSK
8AMPM
R8QAM
C8QAM16QAM
PSK/QAM/PAM35% Root-Raised-Cosine
1024 symbolsρ = 235% Root-Raised-Cosine
Performance and Complexity Simulation results 15 / 19
Performance and Complexity
Comparison between MPT and Cumulant-based classification
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
Mea
n C
orre
ct C
lass
ifica
tion
Rat
e
Swami’s C40
− Blind
Swami’s C40
− Non−Blind
AMPT − Blind
AMPT − Non−Blind
Advantages
No need for pre-demodulationMore robustness to noise/uncertaintyLow complexity (FFTs)
Performance and Complexity Simulation results 16 / 19
Performance and Complexity
Comparison between MPT and Cumulant-based classification
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
Mea
n C
orre
ct C
lass
ifica
tion
Rat
e
Swami’s C40
− Blind
Swami’s C40
− Non−Blind
AMPT − Blind
AMPT − Non−Blind
Advantages
No need for pre-demodulationMore robustness to noise/uncertaintyLow complexity (FFTs)
Performance and Complexity Simulation results 16 / 19
Agenda
AMC: a short Review
System Model & Assumptions
Basics on M th-Power Transform (MPT)
Computation of the References
Performance and Complexity
Conclusion and Perspectives
Agenda 17 / 19
Conclusion and Perspectives
This work:
MPT = great tool for AMC (but not only!)
Basic theory
Blind performance
Future work:
Distributions & theoretical CCR
Other contexts (channel, interference,...)
Conclusion 18 / 19
Conclusion and Perspectives
This work:
MPT = great tool for AMC (but not only!)
Basic theory
Blind performance
Future work:
Distributions & theoretical CCR
Other contexts (channel, interference,...)
Conclusion 18 / 19
Thank you!
Conclusion 19 / 19