Automatic Modulation Classificationfor Rapid Radio Deployment

Adolfo RecioDepartment of Electrical and

Computer EngineeringVirginia Tech

Blacksburg, VA 24061Email: recio@vt.edu

Jorge A. Surı́sOak Ridge National Laboratory

Oak Ridge, TN 37831Email: surisja@ornl.gov

Peter AthanasDepartment of Electrical and

Computer EngineeringVirginia Tech

Blacksburg, VA 24061Email: athanas@vt.edu

Abstract—Cognitive Radio and signal intelligence (SIGINT)applications require radios to perform situation-awareness func-tions, as spectrum sensing to detect the spectral occupation.In more advanced systems, for SIGINT and for interferencecancellation purposes, a radio receiver may need to classify anotherwise unknown signal without prior information about itsmodulation type, and rapidly synthesize, prototype, and deploya suitable demodulator.

The Rapid Radio framework uses a signal analysis stage to ob-tain the parameters of the signal of interest, to quickly prototypea suitable radio demodulator using the reconfiguration featuresand processing capabilities of FPGAs. This paper presentsthe techniques devised to perform the Automatic ModulationClassification stage of the framework, considering its interactionwith the parameter estimation and signal synchronization stages,and presents performance results obtained under simulationconditions as well as in over-the-air transmissions.

I. INTRODUCTION

Automatic Modulation Classification (AMC) is an importantstage of the Rapid Radio prototyping framework, allowinga receiver to be constructed by analysis of an otherwiseunknown signal. While traditional approaches for radio designare focused on area and power efficiency, in applications asSIGINT and Cognitive Radio, a tradeoff between efficiencyand speed of development may be desired. Today’s largeFPGA platforms make this tradeoff worthy of considerationeven for more traditional applications.

While there are many proposed AMC techniques, fewconsider the problem of lack of synchronization at the symboland the carrier levels, as well as the capability to classifyan arbitrary set of modulation types. This paper focuses onthe description of the AMC strategy adopted for the class oflinear modulations, as well as its interactions with the synchro-nization stages and with the general flow of the prototypingsystem.

This paper is organized as follows: Section II presents anoverview of AMC techniques. The approach chosen for themodulation classification stage is explained in Section III.The parameter estimation and signal conditioning stage ispresented in Section IV. Section VI shows the format of theXML constellation descriptors used to feed constellation typesto the classifier. The classification features are explained inSection VII, while the Bayesian network classifier is discussed

in Section VIII. Section IX is an introduction to the prototypeconstruction. The results are presented in Section X. Finally,conclusions are drawn in Section XI.

II. PREVIOUS WORK

The literature about Automatic Modulation Classification(AMC) covers several techniques directed toward classifyinga signal using diverse features or performing likelihood tests.Many of these techniques rely on assumptions about the stageof processing of the signal (i.e.: a baseband representation isavailable, or sampling is synchronous to the symbol epochs),or about the modulation being restricted to a limited set. Acomprehensive summary of the literature in AMC can be foundin [1]. The author classifies the algorithms as either likelihood-based (LB) or Feature-based (FB).

Likelihood-based algorithms perform hypotheses testing di-rectly over a baseband representation of the signal. Simplifi-cations of the exact likelihood function lead to the generalizedlikelihood ratio test (GLRT), the average likelihood ratio test(ALRT), and the hybrid likelihood ratio rest (HLRT). Detailedexplanations of each of the methods can be found in [2].The work [3] proposes the quasi-log-likelihood ratio qLLR toapproximate the likelihood function of BPSK/QPSK signals,assuming that the carrier frequency and symbol timing areknown. [4] presents a suboptimal implementation of a HLRTthat provides independence of the noise parameters for theM-PSK class of modulations. [5] develops asymptotic resultson the performance of maximum likelihood classifiers in theI-Q domain for linear modulations. A drawback of this familyof methods is their capability to differentiate only among aparticular set of constellations, given that other constellationsget “nested”, that is, when a set of constellations generate thesame value of the test statistic.

Most of the already mentioned authors use the quasi-baseband signal obtained after downconversion, which isknown the signal space approach. The signal space approachhas the advantage that it is readily available as an intermediatesignal in a receiver, after the symbol timing recovery.

Alternative analysis of the constellation in the signal spaceusing pattern recognition techniques such as clustering have

also been proposed in [6], and [7]. However, clustering intro-duces additional degrees of freedom to the problem, which arenot required as linear digital modulation constellations havehighly regular shapes. Modulation classification techniquesbased on fuzzy logic [8], and artificial neural networks [9],[10], [11] are also proposed in the literature.

Feature based algorithms include the wide family of cyclo-stationarity based classifiers [12], as those based in spectralcoherence and spectral correlation [13], [14], [15], and [9];cyclic cumulants [16], [17], [18]; and higher order statistics[19]. Other features explored in the literature are: moment ma-trices [20], the standard deviation of the normalized-centeredinstantaneous amplitude and kurtosis [21], and Hellinger dis-tance [22].

“Holistic” approaches that acknowledge the requirement togather the basic parameters of the signal and consider the inter-actions between modulation recognition and synchronizationare presented in [23], [24], [25], [26], and [27].

III. PROPOSED APPROACH

The problem of developing a Rapid Radio receiver prototypefits the holistic models considering, first, that an importantportion of the signal processing used for recognition purposescan be re-used in the implemented receiver and second, thatthe synchronization and re-sampling tasks must be solvedbefore running the modulation classification algorithms. Onlythe family of linear modulations is considered at this time.

The technique implemented for AMC is based in theanalysis of four features: amplitude, differential phase, andI-Q plane histograms, as well as the symbol transition matrix.Symbol synchronization is a condition to obtain the amplitudeand differential phase profiles. Carrier synchronization is re-quired to obtain the I-Q plane histogram and the symbol tran-sition matrix. The generation of a baseline probability densityfunction (pdf) for histogram matching with each hypothesizedconstellation type requires accurate constellation descriptions.SNR estimates are also needed for the construction of thebaseline pdfs. A Bayesian network is used for the integrationof the metrics and for the calculation of total scores used toreach a classification result.

IV. PARAMETER ESTIMATION AND SIGNAL

CONDITIONING

The first step for the classification of the signal is theisolation of the frequency band where the carrier of interestresides, the implementation of a downconverter, and the coarseestimation of the parameters of the signal, including carrierfrequency offset (CFO), symbol rate, roll-off factor, and signalto noise ratio, as described in [28]. The complex basebandsignal 𝑥(𝑛) signal is conditioned according to the systempresented Figure 1 by using the estimates of the symbol rateand the roll-off factor to produce a matched filter followed byan arbitrary frequency re-sampler to obtain a filtered signal𝑦(𝑚) with a nominal sampling frequency of four samples persymbol, value assumed at the succeeding symbol synchroniza-tion stage [29].

Fig. 1: Signal parameter estimation and pre-conditioning

Fig. 2: Symbol synchronizer architecture

V. SYNCHRONIZATION AND AMPLITUDE NORMALIZATION

Symbol timing recovery is a baseband adaptation of theGodard synchronizer [30] at four samples per symbol, whichuses a non-linearity to generate a spectral line at the symbolrate, aided by a half-symbol delay in one of its branches, asproposed in [31], followed by a PLL to filter out the phasenoise. Figure 2 presents a block diagram of the synchronizer.

This symbol synchronization approach is constellation ag-nostic, and can be performed without any previous assump-tions on the hypothesized constellation.

The value of the signal 𝑠(𝑘) at the optimum sampling instantis found using a Lagrange polynomial interpolator controlledby the PLL time base.

A. Carrier Frequency Offset Synchronization Ambiguity

Two of the modulation classification features presentedbelow, the differential phase profile and the amplitude profile,can be applied to the signal without the need of carrierfrequency offset (CFO) synchronization, and a low-tier classi-fication can be performed using the symbol synchronizer andthe aforementioned features. A high-tier classification systemrequires the implementation of a CFO synchronizer, whichallows testing two additional features: the two dimensionalprobability density function (pdf) and the symbol differentialmatrix.

The CFO synchronizer must be fed the parameters of thehypothesized constellation to obtain hard decisions used tomeasure the phase error, and therefore is not constellationagnostic. This approach produces constellation nesting. Forinstance, an 8-PSK CFO synchronizer applied to a QPSKsignal may produce what looks like a 8-PSK constellation, byintroducing an additional 𝜋/4 phase rotation between consecu-tive symbols. Similarly, a 𝜋/4-DQPSK modulated signal fed toa 8-PSK hypothesis will produce a valid two-dimensional pdf.The differential matrix comes handy at resolving the rotationambiguities introduced by a CFO synchronizer running underdifferent hypotheses.

Fig. 3: XML description of a QPSK constellation

VI. CONSTELLATION XML DESCRIPTORS

To avoid the burden of modifying the classification algo-rithms, the Rapid Radio framework uses a “Plug-in” approach:a new constellation can be added to the set of hypotheses justby creating an XML constellation description file and addingit to the working directory.

Figure 3 presents a sample XML description file. In it,the Constellation element has associated a Name and BPS,attributes, used to identify the constellation type and to indicatethe number of bits per symbol respectively, a child elementsFactor, with a Value attribute containing a normalizing factorto obtain unit power, and Symbol elements with attributes I,Q, and Value, containing the coordinates and index for eachpoint of the constellation which defines the modulation type.

VII. CLASSIFICATION FEATURES

A. Amplitude Profile Test

If the channel noise is assumed to be AWGN, the theoreticalamplitude probability density function at the proper samplinginstants can be described as a mixture of Ricean-distributedrandom variables calculated according to (1).

𝑓𝑎𝑝∣𝑐(𝑥) =𝑁−1∑𝑖=0

𝑝𝑖𝑓(𝑥, 𝜈𝑖) (1)

where the value 𝜈𝑖 represents the magnitude of the 𝑖𝑡ℎ elementof the constellation under test, 𝑁 is the number of elementsin the constellation, and 𝑝𝑖 is the probability of a constellationelement. All of these values are obtained from the XMLconstellation description assuming equiprobable symbols. Thefunction 𝑓(𝑥, 𝜈) is the pdf of the Ricean distribution given by(2).

𝑓(𝑥, 𝜈) =𝑥

𝜎2exp

(𝑥2 + 𝜈2

2𝜎2

)𝐼0

(𝑥𝜈𝜎2

)(2)

where 𝐼0(𝑥) is a Bessel function of the first kind.To obtain the proper constellation points, the amplitude

of the signal is normalized according to (3), in order toachieve unit power. The parameter 𝜎2 can then be calculatedas according to (4).

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

2

2.5Amplitude profile under 16QAM − Band Edge Sync

x

f(x)

Empirical pdfHypothesized pdf

Fig. 4: Amplitude profiles of a 16-QAM constellation with 18dB SNR

𝑠(𝑘) =𝑠(𝑘)√𝑃 𝛾−1

𝛾

(3)

where 𝑃 = 𝐸[𝑠2(𝑘)] is the mean square value of the receivedsymbol sequence 𝑠𝑖 assuming 𝐸[𝑠(𝑘)] = 0, and 𝛾 is themeasured carrier plus noise to noise ratio obtained at theparameter estimator.

𝜎2 =1

2

1

𝛾 − 1(4)

A histogram of the received signal amplitudes is obtainedwith 𝐿 bins of size 𝛿, chosen according to Scott’s rule [32].This histogram is scaled to form the empirical pdf of thereceived data set. A similarity metric between the hypothesizedpdf and the empirical pdf is obtained using the Hellingerdistance (5), presented in [22]. The factor 𝛿/2 is added toproduce results in the interval [0, 1].

𝑑𝐻(𝑓1, 𝑓2) =𝛿

2

𝐿∑𝑖=1

(√𝑓1(𝑥𝑖)−

√𝑓2(𝑥𝑖)

)2

(5)

B. Differential Phase Profile Test

The amplitude profile test is useful to classify amplitude-modulated signals. However, it does not permit a classificationamong phase-modulated signals, such as BPSK, QPSK, 8-PSK, and 𝜋/4-DQPSK. The differential profile is obtainedby forming the histogram of the phase difference betweenconsecutive symbols. Contrary to the amplitude profile, itis not independent of the CFO: the obtained profile will bephase-shifted by an amount of 2𝜋Δ𝑓𝑇𝑠𝑦𝑚𝑏, where Δ𝑓 is theCFO, and 𝑇𝑠𝑦𝑚𝑏 is a symbol duration. The hypothesized phaseprofile is obtained as a mixture distribution from the XMLconstellation description and the estimated SNR value usingthe expression for the pdf of the angle between two vectorscontaminated by AWGN [33], presented in (6).

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8Hellinger Distance of phase difference under QPSK − Band Edge Sync

Lag (bins)

−4 −3 −2 −1 0 1 2 3 40

0.2

0.4

0.6

0.8

Differential angle

Empirical pdfHypothesized pdf

Fig. 5: Differential phase profile under QPSK with 12 dB SNR

𝑓(𝜓) =1

2𝜋

∫ 𝜋/2

0

exp (−𝜌(1− cos𝜓 cos 𝜃))

× (1 + 𝜌+ 𝜌 cos𝜓 cos 𝜃) cos 𝜃 d𝜃 (6)

where 𝜌 = 1/𝜎2, and 𝜓 = 𝜃(𝑛) − 𝜃(𝑛 − 1) represents thephase difference between consecutive symbols.

The integral is solved numerically for each angle underevaluation. In order to overcome the offset introduced by theCFO, an exhaustive search is performed over all the phaseshifts allowed by the discrete histogram bins, looking forthe smallest Hellinger distance. The minimum distance isused as the metric for this classification feature. An exampledifferential phase profile is presented in Figure 5. The top partof the figure presents the results of the minimum search, whilethe bottom part presents the matched pdfs.

C. Two-dimensional pdf Test

The two-dimensional pdf is one of the features that can beobtained after the CFO tracking loop. As the CFO trackingsystem requires knowledge of the hypothesized constellation,this measurement is sometimes meaningless when used underincorrect hypotheses, being usually out-of-lock. However, un-der the correct hypothesis, the tracking loop will be locked,producing a small distance metric when the empirical and thehypothesized pfds are compared.

The hypothesized pdfs are build as two-dimensional gaus-sian mixtures, with centers given by the constellation points,and variance 𝜎2 obtained from the SNR estimate. An examplefor the case of QPSK modulation is presented in Figure 6.

D. Transition matrix test

The transition matrix test is added to solve constellationnesting problems presented in 8-PSK vs. 𝜋/4-DQPSK orQPSK vs. 𝜋/4-DQPSK. When a signal is demodulated undercertain hypothesis, a transition matrix is calculated. Thisfeature provides insight into the differential structure of themodulation scheme, allowing, for example, the classificationof a 𝜋/4-DQPSK signal, that would obtain the same metric

−20

2

−20

20

1

2

I

Hypothesized pdf under QPSK − Band Edge Sync

Q −20

2

−20

20

1

2

I

Empirical pdf

Q

I

Q

Hypothesized pdf under QPSK − Band Edge Sync

−2 −1 0 1 2

−1

0

1

I

Q

Empirical pdf

−2 −1 0 1 2

−1

0

1

Fig. 6: Two-dimensional pdf under QPSK with 12 dB SNR

as 8-PSK under the two-dimensional pdf test, and the samemetric as QPSK under the differential phase test.

VIII. BAYESIAN NETWORK CLASSIFIER

Several approaches to signal classification make use ofdecision trees and class spaces. To support the “plug-in”capabilities of the signal classifier, a Bayesian Network waschosen to form the classifier. The Bayesian approach offersseveral advantages, among them:

1) Different sets of prior probabilities can be used accord-ing to the environment and previous experience.

2) There is no need to revise a decision tree if a newconstellation type is added to the set under consideration.

3) The classifications are soft: instead of a yes/no answer,the posterior probabilities can be sorted and used as alikelihood measurement. A human can then participatein a decision in the case of similarly-ranked top results.

To apply a Bayesian approach to the metrics discussedabove, the conditional probabilities of an empirical pdf givenhypothesis ℎ𝑖 is assigned according to (7).

𝑃 (𝑎𝑝∣ℎ𝑖) = 1− 𝑑𝐻(𝑓𝑎𝑝, 𝑓𝑎𝑝∣𝑐𝑖) Amplitude profile

𝑃 (𝑝𝑝∣ℎ𝑖) = 1− 𝑑𝐻(𝑓𝑝𝑝, 𝑓𝑝𝑝∣𝑐𝑖) Differential phase profile

𝑃 (𝑠𝑑∣ℎ𝑖) = 1− 𝑑𝐻(𝑓𝑠𝑑, 𝑓𝑠𝑑∣𝑐𝑖) 2-D distribution

𝑃 (𝑡𝑚∣ℎ𝑖) = 1− 𝑑𝐻(𝑓𝑡𝑚, 𝑓𝑡𝑚∣𝑐𝑖) Transition matrix (7)

where the set of functions 𝑓𝑥 represent the empirical dis-tribution for the feature 𝑥, and the functions 𝑓𝑥∣𝑐𝑖 representthe theoretical pdf of such feature given the hypothesizedconstellation 𝑐𝑖.

The posterior probabilities are calculated according to Bayesrule, as presented in (8).

𝑃 (ℎ𝑖∣𝑎𝑝, 𝑝𝑝, 𝑠𝑑, 𝑡𝑚) =𝑃 (𝑎𝑝, 𝑝𝑝, 𝑠𝑑, 𝑡𝑚∣ℎ𝑖)𝑃 (ℎ𝑖)∑𝑁−1

𝑖=0 [𝑃 (𝑎𝑝, 𝑝𝑝, 𝑠𝑑, 𝑡𝑚∣ℎ𝑖)𝑃 (ℎ𝑖)](8)

TABLE I: Set of metrics for a BPSK signal

Hypothesis AP PP SD TM Posteriors

BPSK 99.40% 99.59% 97.68% 100.00% 66.06%

QPSK 99.40% 69.26% 68.97% 50.76% 16.47%

8PSK 99.40% 48.71% 49.27% 28.71% 4.68%

16QAM 80.78% 46.72% 62.35% 28.57% 4.59%

64QAM 75.84% 44.09% 61.02% 27.49% 3.83%

32QAM 70.43% 43.62% 49.27% 30.09% 3.11%

PI4DQPSK 99.40% 69.15% 49.27% 2.72% 0.63%

8QAM 42.02% 48.71% 9.00% 28.46% 0.36%

STAR16 29.72% 48.71% 11.18% 24.92% 0.28%

where the set of prior probabilities 𝑃 (ℎ𝑖) can be chosenaccording to an experience-based criteria. Conditional inde-pendence is assumed for the set of conditional probabilities.Therefore:

𝑃 (𝑎𝑝, 𝑝𝑝, 𝑠𝑑, 𝑡𝑚∣ℎ𝑖) = 𝑃 (𝑎𝑝∣ℎ𝑖)𝑃 (𝑝𝑝∣ℎ𝑖)𝑃 (𝑠𝑑∣ℎ𝑖)𝑃 (𝑡𝑚∣ℎ𝑖)(9)

IX. RADIO PROTOTYPE CONSTRUCTION

The results of the analysis stage are written into an XMLplatform-independent radio description file (RDF), which com-bined with a platform specific description file performs thetasks of generating the required modules using a creation scriptthat automatically invokes Matlab and Coregen, in the case ofXilinx FPGAs, to generate modules that are instantiated in aplatform specific top-level file [34]. A radio prototype can becreated this way with minimum user intervention. The detailedflow of the radio creation process is presented in Figure 7.

X. RESULTS

The results of the AMC system implemented are affecteddoubly when the signal to noise radio is low. A low SNRaffects the synchronization stages, specially for highly denseconstellations, as 64-QAM. Therefore, the rate of correctclassification is much lower to the one obtained under idealsynchronization conditions.

Tables I to IX present results of the individual metricsand the Bayesian network output for the classification ofsignals of different modulation types under a SNR of 18 dB.4096 symbols are used to obtain this result. An importantaspect that requires further development is the fact that thetransition matrix is only being helpful in the case of a QPSKconstellation being masked as 𝜋/4-DQPSK. In other cases,as in 64-QAM, presented in Table IX, it even produces aclassification error that could have been otherwise avoidedby using only the remaining three features, which are clearwinners against the set of false hypotheses.

XI. CONCLUSION

A system for rapid prototyping of radio receivers waspresented, with an emphasis in the automatic modulationclassification stage. The use of a holistic approach to mod-ulation classification that considers the effect of symbol and

TABLE II: Set of metrics for a QPSK signal

Hypothesis AP PP SD TM Posteriors

QPSK 99.62% 99.18% 96.95% 99.89% 48.24%

BPSK 99.62% 70.09% 45.20% 99.99% 15.91%

8PSK 99.62% 70.92% 68.94% 55.70% 13.68%

16QAM 78.71% 68.06% 68.43% 41.22% 7.62%

64QAM 74.07% 64.24% 62.20% 37.29% 5.56%

32QAM 68.72% 63.60% 54.19% 45.06% 5.38%

PI4DQPSK 99.62% 99.06% 68.94% 4.73% 1.62%

8QAM 39.92% 70.92% 14.48% 66.84% 1.38%

STAR16 26.28% 70.92% 13.42% 48.62% 0.61%

TABLE III: Set of metrics for an 8-PSK signal

Hypothesis AP PP SD TM Posteriors

8PSK 99.60% 98.75% 95.71% 99.79% 33.22%

PI4DQPSK 99.60% 69.87% 95.71% 71.15% 16.76%

QPSK 99.60% 69.89% 54.53% 99.93% 13.42%

16QAM 82.61% 85.68% 64.11% 62.11% 9.97%

32QAM 71.45% 86.64% 53.52% 68.06% 7.98%

64QAM 76.41% 86.66% 62.75% 48.93% 7.19%

BPSK 99.60% 49.10% 34.43% 99.98% 5.95%

8QAM 43.99% 98.75% 23.82% 99.84% 3.65%

STAR16 33.32% 98.75% 17.73% 89.85% 1.85%

TABLE IV: Set of metrics for a 𝜋/4-DQPSK signal

Hypothesis AP PP SD TM Posteriors

PI4DQPSK 99.45% 99.05% 95.10% 99.40% 42.68%

8PSK 99.45% 71.66% 95.10% 75.51% 23.46%

16QAM 84.39% 70.44% 62.15% 52.18% 8.84%

32QAM 73.17% 66.37% 53.47% 55.94% 6.66%

BPSK 99.45% 70.10% 19.65% 100.00% 6.28%

64QAM 77.88% 67.04% 63.23% 38.98% 5.90%

8QAM 45.69% 71.66% 24.04% 77.84% 2.81%

QPSK 99.45% 98.91% 4.28% 99.97% 1.93%

STAR16 35.92% 71.66% 18.56% 66.44% 1.45%

TABLE V: Set of metrics for an 8-QAM signal

Hypothesis AP PP SD TM Posteriors

8QAM 99.35% 98.11% 94.25% 99.83% 35.34%

STAR16 89.97% 98.11% 82.42% 77.25% 21.66%

32QAM 88.66% 92.86% 73.32% 67.19% 15.63%

64QAM 84.96% 92.83% 70.71% 55.10% 11.84%

16QAM 70.23% 91.63% 35.94% 84.86% 7.56%

8PSK 35.44% 98.11% 28.65% 99.85% 3.83%

PI4DQPSK 35.44% 69.26% 28.65% 70.63% 1.91%

QPSK 35.44% 69.22% 16.44% 99.96% 1.55%

BPSK 35.44% 48.63% 9.81% 99.98% 0.65%

carrier synchronization is presented. A set of extracted featuresconducts to successful classifications under non-ideal synchro-nization conditions.

The symbol transition feature prevents the nesting of the

Fig. 7: System for rapid assembly of a prototype radio

TABLE VI: Set of metrics for a 16-QAM signal

Hypothesis AP PP SD TM Posteriors

16QAM 99.64% 98.85% 91.40% 99.27% 27.45%

32QAM 88.73% 98.72% 70.41% 92.97% 17.61%

64QAM 92.26% 98.64% 77.38% 69.73% 15.08%

STAR16 75.57% 86.16% 52.56% 97.45% 10.24%

8PSK 73.09% 86.16% 53.01% 99.63% 10.21%

8QAM 70.19% 86.16% 34.60% 99.11% 6.37%

PI4DQPSK 73.09% 67.12% 53.01% 67.18% 5.36%

QPSK 73.09% 67.13% 32.63% 99.91% 4.91%

BPSK 73.09% 46.85% 26.20% 100.00% 2.76%

TABLE VII: Set of metrics for a STAR-16 signal

Hypothesis AP PP SD TM Posteriors

STAR16 99.56% 96.64% 91.77% 99.28% 37.24%

8QAM 90.59% 96.64% 54.41% 96.10% 19.44%

32QAM 79.15% 95.05% 62.42% 84.08% 16.77%

16QAM 74.47% 93.60% 43.87% 93.75% 12.18%

64QAM 78.92% 95.07% 63.49% 58.66% 11.87%

8PSK 20.56% 96.64% 14.15% 99.87% 1.19%

PI4DQPSK 20.56% 68.86% 14.15% 70.20% 0.60%

QPSK 20.56% 68.90% 8.29% 99.97% 0.50%

BPSK 20.56% 47.90% 4.92% 100.00% 0.21%

𝜋/4-DQPSK modulation for QPSK classification, but presentsproblems under other modulation types.

Future work in this project can include the classificationof single-carrier modulation families, as FSK and MSK, aswell as multi-carrier modulations, along with their prototypegeneration flow.

ACKNOWLEDGMENT

The authors would like to thank the Harris Corporation,Government Communications Division, for supporting thisresearch.

TABLE VIII: Set of metrics for a 32-QAM signal

Hypothesis AP PP SD TM Posteriors

32QAM 99.74% 99.00% 88.08% 96.53% 26.07%

64QAM 97.43% 99.01% 84.55% 74.84% 18.96%

16QAM 88.14% 97.24% 59.87% 97.99% 15.62%

STAR16 77.51% 86.76% 55.80% 99.00% 11.54%

8QAM 86.47% 86.76% 45.61% 98.33% 10.45%

8PSK 63.89% 86.76% 44.62% 99.83% 7.67%

PI4DQPSK 63.89% 62.48% 44.62% 71.01% 3.93%

QPSK 63.89% 62.48% 31.45% 99.97% 3.90%

BPSK 63.89% 43.80% 21.49% 100.00% 1.87%

TABLE IX: Set of metrics for a 64-QAM signal

Hypothesis AP PP SD TM Posteriors

32QAM 96.22% 99.25% 77.83% 96.16% 22.36%

64QAM 99.79% 99.27% 87.63% 76.73% 20.84%

16QAM 90.92% 97.59% 60.12% 97.87% 16.33%

STAR16 75.65% 87.39% 53.87% 99.11% 11.04%

8QAM 81.24% 87.39% 42.46% 98.66% 9.30%

8PSK 67.40% 87.39% 47.69% 99.79% 8.77%

QPSK 67.40% 63.69% 34.33% 99.97% 4.61%

PI4DQPSK 67.40% 63.69% 47.69% 69.27% 4.44%

BPSK 67.40% 44.50% 24.65% 99.97% 2.31%

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