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