Signal Modulation Identification Based on Deep Learning in

Research ArticleSignal Modulation Identification Based on Deep Learning inFBMCOQAM Systems

Jing Chen1 Jianzhong Guo2 Xin Shan1 and Dejin Kong 2

1Electronic Information School Wuhan University Wuhan 430072 China2School of Electronic and Electrical Engineering Wuhan Textile University Wuhan 430200 China

Correspondence should be addressed to Dejin Kong djkouwtueducn

Received 6 August 2021 Accepted 27 September 2021 Published 14 October 2021

Academic Editor Han Wang

Copyright copy 2021 Jing Chen et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Signal modulation identification (SMI) has always been one of hot issues in filter-bank multicarrier with offset quadratureamplitude modulation (FBMCOQAM) which is usually implemented by the machine learning-based feature extractionHowever it is difficult for conventional methods to extract the signal feature resulting in a limited probability of correctclassification (PCC) To tackle this problem we put forward a novel SMI method based on deep learning to identify FBMCOQAM signals in this paper It is noted that the block repetition is employed in the FBMCOQAM system to achieve theimaginary interference cancelation In the proposed deep learning-based SMI technique the in-phase and quadrature samples ofFBMCOQAM signals are trained by the convolutional neural network Subsequently the dropout layer is designed to preventoverfilling and improve the identification accuracy To evaluate the proposed scheme extensive experiments are conducted byemploying datasets with different modulations +e results show that the proposed method can achieve better accuracy thanconventional methods

1 Introduction

Filter-bank multicarrier with offset quadrature amplitudemodulation (FBMCOQAM) has been considered as one ofthe potential physical-layer techniques for future wirelesscommunications [1ndash4] Owing to the use of pulse shapingfilter with low spectrum sidelobe FBMCOQAM offers thehigh spectrum utilization and good ability of asynchronoustransmission [1 2] In addition the cyclic prefix is not re-quired in FBMCOQAM leading to a high spectral effi-ciency However in contrast to the classical orthogonalfrequency division multiplexing (OFDM) the orthogonalityof FBMCOQAMonly holds in the real-valued field Tomeetthe orthogonality condition FBMCOQAM systemstransmit real-valued symbols obtained by the real andimaginary parts of complex-valued QAM symbols and thereexist imaginary interferences among the transmitted real-valued symbols called the intrinsic imaginary interference[3] +e imaginary interference will make a major effect on

the algorithms about the parameter estimation which has tobe considered in the algorithm design

With the rapid development of wireless communica-tions noncooperative communications will be very com-mon in military and civilian areas In order to identifydifferent modulations of the received signals signal mod-ulation identification (SMI) is required in the noncooper-ation wireless communications [5 6] For instance diverseeavesdropping risks can be identified in wireless links by theSMI technique which ensure the system integrity [7] In theelectronic countermeasure the signal modulation type isfirst required to estimate from the intercepted electro-magnetic waves On this basis the intercepted signal couldbe decrypted further [8] +erefore SMI has been regardedas one of the most crucial techniques when we design anoncooperative communication system Developing theaccurate SMI method is necessary to identify FBMCOQAMsignals [9] since the SMI design is a big challenge to identifytypes of FBMCOQAM signals

HindawiMobile Information SystemsVolume 2021 Article ID 4809699 6 pageshttpsdoiorg10115520214809699

So far most existing modulation identification ap-proaches are based on feature extraction and machinelearning classification A lot of SMI schemes are developedby combining different machine learning-based classifiersand feature extraction strategies [10] However since con-ventional feature extraction schemes rely on statistics it isdifficult for these methods to extract the signal features ofdifferent modulation types As a result the classificationresult is vulnerable tomix up In addition machine learning-based SMI schemes will suffer performance bottleneck forthe problem associated with big data +at is to say theprobability of correct classification is not good enoughwhich indicates unpreferred in practical FBMCOQAMsystems To solve this issue deep learning (DL) has beendeemed to be one of effective techniques to deploy SMI [11]In [12] an enhanced identification scheme was presentedbased on deep neural network (DNN) In [13] the geneticprogramming (GP) was combined with the k-nearestneighbor (KNN) to identify four modulation typesaccurately

In this paper we propose a novel SMI technique basedon the convolutional neural network (CNN) to make anidentification on FBMCOQAM signals It is noted that theblock repetition is employed in the FBMCOQAM system toachieve the imaginary interference cancelation In theproposed scheme 3 fully connected layers and 2 convolu-tional layers are designed In addition the dropout layer isdesigned to lower the interaction neurons of the same layerTo evaluate the proposed scheme extensive experiments areconducted by employing datasets with different modula-tions +e results show that the proposed method canachieve better accuracy than conventional methods

+e rest of the paper is organized as follows +e systemmodel of FBMCOQAM with block repetition is introducedbriefly as well as the model of the deep learning in Section 2Subsequently the proposed SMI method is presented inSection 3 Section 4 gives experimental results followed bythe conclusion in Section 5

2 Model of FBMCOQAM

Figure 1 depicts the baseband FBMCOQAM system dia-gram with M subcarriers +e transmitted signal of eachFBMCOQAM subcarrier gets through a pulse shaping filterdmn is the transmitted symbol at the time frequency position(m n) Denote g[l] as the pulse shaping filter for all sub-carriers in FBMCOQAM which has the even and sym-metric coefficients and exhibits the extremely low spectrumsidelobe [2] According to Figure 1 the transmitted signal ofFBMCOQAM can be expressed as follows [3 14]

s[l] 1113944Mminus 1

m01113944nisinZ

dmng l minus nM

21113876 1113877e

((j2πml)M)e

((jπ(m+n))2)

(1)

Assume h[l] is the Rician fading channel +e trans-mitted signal s[l] passes through the channel h[l] and thereceived signal can be written as

r[l] h[l]lowast s[l] + η[l] (2)

where lowast represents the convolution operator and η[l]

stands for the additive white Gaussian noise [15]+en after FBMCOQAM demodulation at the receiver

it can obtain the following [16 17]

1113954dmn 1113944infin

lminus infinr[l]g l minus n

M

21113876 1113877e

minus (j2πmlM)e

minus (jπ(m+n)2)

Hmn dmn + 1113944

m0 n0( )ne(mn)

dm0 n0ζm0 n0

mn⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ + ηmn

Hmn dmn + jdcmn1113872 1113873 + ηmn

(3)

where ζm0 n0mn is the imaginary interference factor in FBMC

OQAM which is a pure imaginary value dcmn is the

imaginary interference to the symbol dmn [17] and ηmn isthe noise to the symbol dmn Note that although η[l] is whiteGaussian noise ηmn is not white due to the real-valuedorthogonality of FBMCOQAM systems Hmn is the channelfrequency response at the subcarrier m For the time-in-variant channels the value of Hmn is not relevant to the timeindex n

It has been demonstrated that the imaginary interferencefactor ζm0n0

mn is symmetrical [18] On this basis of symmetricthe block repetition is designed in FBMCOQAM to achievethe imaginary interference cancelation [18 19] As shown inFigure 2 the frame consists of two parts ie original blockand repeated block dmn m isin [0 M minus 1] n isin [0 N minus 1] arethe symbols in the original block which are obtained fromthe QAM constellation amn+N are the symbols in the re-peated block and it is noted that amn+N amNminus 1minus n

At the receiver the demodulations of original block andrepeated block are respectively written as

1113954dmn Hmn dmn + jdcmn1113872 1113873 + ηmn n 0 1 N minus 1

(4)

1113954dm2Nminus 1minus n Hm2Nminus 1minus n dm2Nminus 1minus n + jdcm2Nminus 1minus n1113872 1113873

+ ηm2Nminus 1minus n

Hmn dmn + jdcm2Nminus 1minus n1113872 1113873

+ ηm2Nminus 1minus n n 0 1 N minus 1

(5)

Note that the imaginary interferences of the originalblock and repeated block satisfy the following equation [18]ie

jdcmn + jd

cm2Nminus 1minus n 0 (6)

Subsequently the imaginary interferences can be re-moved by the following linear combination

1113954dmn + 1113954dm2Nminus 1minus n

2 Hmndmn +

ηmn + ηm2Nminus 1minus n

2 (7)

2 Mobile Information Systems

Let dmm (1113954dmn + 1113954dm2Nminus 1minus n)2 and ηmn (ηmn +

ηm2Nminus 1minus n)2 +en equation (7) can be rewritten as

dmm Hmndmn + ηmn (8)

Note that the noise ηmn satisfies the white Gaussiandistribution [18]

Suppose the Rician fading channel only consists of a lineof sight (LOS) between the receiver and the transmitter+en the probability of correct classification (PCC) of theRician distribution is written as

f[x] x

σ2e

minus x2+A22σ2( ) middot I0Ax

σ21113890 1113891 (9)

where σ2 stands for the power of the multipath signalcomponent A represents the amplitude peak of the mainsignal I0[middot] stands for the modified Bessel function of the 0-th order +e Rician channel model can be written as

h[l]

κ

κ + 1

1113970

σejθ

+

1

κ + 1

1113970

N 0 σ21113872 1113873 (10)

where the first part stands for the mirror path which has theuniform phase θ +e second part represents a majority ofscattering paths and reflection paths which are independentof θ κ is the Rician factor that indicates the Rician distri-bution +e Rician factor is defined as

κ Ax

σ2 (11)

When the factor κ goes to zero gradually the Riciandistribution will become a Rayleigh distribution

3 Proposed Deep Learning-Based SMI

31 CNN Algorithm After converting to IQ samples theFBMCOQAM signal can be used to train the CNN As acommonly used algorithm CNN is one of hot researchissues in the area of artificial intelligence+e CNN structuremainly includes input layers convolution layer poolinglayer fully connected layer and output layer +e mainfeatures of CNN are summarized as follows

(i) Local Connection For this connection each neuronis not required to connect the whole neurons fromthe upper layer but only a small part of neuronswhich can reduce the parameters significantly

(ii) Weight Sharing It not required that each connec-tion corresponds to one weight Instead one set ofconnections has the same weight which is alsobeneficial to reduce the number of parameters

(iii) Down Sampling +e number of samples for eachlayer can be reduced by the pooling layer which canenhance the model robustness

In the CNN structure the convolution layer is the mostimportant part which can be compared with the convolu-tion operation in calculus For instance the convolutionalsignal between a time-domain signal x[k] and a time-do-main signal w[k] can be written as

y[k] 1113944l

x[k minus l]w[l] (12)

For the two-dimension signals x[p q] and w[p q] theconvolutional signal can be written as

y[p q] 1113944k

1113944l

x[p minus k q minus l]w[k l] (13)

It is noteworthy that the convolution formula in theCNN algorithm has a difference slightly with the above-mentioned convolution definition For example the two-dimensional convolution in CNN is written as

Me

e

g[l] g[l]

g[l]

g[l]

g[l]

j2πlMe

j2πl

Mj2π (Mndash1)l

e Mj2π (Mndash1)l

g[l]

d0n

d1n

dMndash1n

2jπn

e 2jπn

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2M

2M

2M

2M

2M

2M

d0n

d1n

dMndash1n

(∙)

(∙)

(∙)

Figure 1 +e FBMCOQAM system diagram

Original block Repeated blockin reversed order

d00 d01 d02 d03 d04

d10 d11 d12 d13 d14

d20 d21 d22 d23 d24

d30 d31 d32 d33 d34

d40 d41 d42 d43 d44

d50 d51 d52 d53 d54

d04 d03 d02 d01 d00

d14 d13 d12 d11 d10

d24 d23 d22 d21 d20

d34 d33 d32 d31 d30

d44 d43 d42 d41 d40

d54 d53 d52 d51 d50

Figure 2 +e reversed-order block for FBMCOQAM

Mobile Information Systems 3

y[p q] 1113944k

1113944l

x[p + k q + l]w[k l] (14)

32 Deep Learning-Based SMI Method In this subsectionthe deep learning-based SMI method is proposed via theCNN algorithm in which 2 convolutional layers and 3 fullyconnected layers are included as shown in Figure 3 Spe-cifically the first one of convolutional layers consists of 128convolution kernels with the 1 times 16 dimension matrix forevery convolution kernel As for the second one of con-volutional layers there exist 64 convolution kernels with the2 times 8 dimension matrix for every convolution kernel +eneuron numbers of the 3 fully connected layers are 256 128and λ respectively Note that λ denotes the number of themodulation modes used in FBMCOQAM systems In ad-dition except the last one of 3 fully connected layers theactivation function of all layers is the parametric rectifiedlinear unit (PReLU) which can effectively reduce theproblem of the gradient disappearance during the operationof back-propagation As for the last one of 3 fully connectedlayers softmax is taken to acquire the probability distri-bution matrix

In addition the dropout layer is added in the first 4 layersin the proposed deep learning-based SMI structure to de-crease the overfitting effectively In a circle some neuronsare randomly selected in the neural layer and are hiddentemporarily Subsequently the training process of the CNNis carried out In the next circle some other neurons will behidden until the training ends Note that the proposedscheme can decrease the interaction among neurons whichmakes the technique more generalizable

33 Dataset To verify the proposed method two datasetsare created for the task of SMI+emodulations in dataset θ1consist of BPSK QPSK 8PSK and 16QAM and themodulations in dataset θ2 include BPSK QPSK 8PSK16QAM and 64QAM For the training and testing of CNN40000 data samples are created for each modulation Forexample for a certain signal-to-noise ratio (SNR) there are160000 data samples that are input into the neural networkNote that the samples for training take up 70 of the wholesamples and the samples for testing take up 30 of the wholesamples

(a) IQ Samples +rough the FBMCOQAMmodulationand the channel the i-th samples can be obtained as

Si s0 s1 sNs1113960 1113961 (15)

where Ns stands for the number of samples and sl isthe value of the l-th sample Since sl is a complex-valued number it can be rewritten as

sl R sl1113864 1113865 + jI sl1113864 1113865 (16)

where R middot and I middot represent the operations oftaking real and imaginary parts respectively R sl1113864 1113865

and I sl1113864 1113865 stand for the in-phase component andquadrature component of the signal

(b) AP Samples +e module and phase of sl can beobtained as

A

R sl1113864 11138652

+ I sl1113864 11138652

1113969

(17)

θ arctanI sl1113864 1113865

R sl1113864 1113865 (18)

(c) Manmade Features +e higher order cumulants(HOC) feature can be calculated and the manmadefeature can be constituted by combining the in-stantaneous feature of the signal

4 Experiment Results

In this section experiments are conducted to verify theperformance of the proposed deep learning-based SMItechnique in the noncooperative FBMCOQAM system Wealso give compare the identification accuracy with con-ventional methods In the experiments 256 subcarriers areconsidered in the FBMCOQAM system and only 16subcarriers are active In addition each subcarrier contains 8symbols As for the Rician channel the Rician factor is 20and the sampling frequency is 10 kHz suffering from aDoppler frequency offset 400Hz In the experiment 3existing classification schemes are used for the comparisonwhich are all machine learning-based methods ie CNNwith IQ samples CNN with AP samples and deep neuralnetwork (DNN) with manmade features extracted by logisticregressive

Figure 4 depicts the PCC comparison between theproposed scheme and the existing schemes in which datasetθ1 is used for training From the results the PCC of theproposed scheme is improving gradually while the existingmethods remain unchanged almost When SNR gt20 dB theaccuracy of modulation identification nearly achieves 100by the proposed deep learning-based SMI technique Inaddition the CNN with AP samples can achieve better PCCaccuracy than the DNN method with manmade featureswhich is because that CNN can extract the data featuresautomatically via the convolution kernel

As shown in Figure 5 the PCCs for different modulationmodes are depicted by the CNN with IQ samples From theresults the BPSK modulation can be always identifiedcorrectly at the whole range of the SNR while the other threemodulations suffer the accuracy degradation at the SNRrange below 15 dB When the SNR comes to the high SNRrange the PCCs of all modulations stabilize graduallyAbove all the proposed technique can achieve high PCCaccuracy for the signal modulation identification

In Figures 4 and 5 dataset θ1 is used for the signalidentification to evaluate the proposed SMI techniqueHowever the performance may be affected by the intro-duction of a newmodulation in practice To demonstrate therobustness of the proposed scheme dataset θ2 is used for thecausing the dataset mismatch Figure 6 shows the PCCs of


the proposed scheme under the dataset mismatch From theresult the curve trend of Figure 6 is similar to that ofFigure 4 and the PCC accuracy remains steady in theproposed scheme achieving the accuracy of above 90 +emismatch of the datasets has no damage on the signalmodulation identification

In the following experiments the sample points of thesignal are increased to verify the proposed deep learning-based SMI technique Figure 7 depicts the PCC comparisonof the proposed scheme under different sample points inwhich dataset θ1 is employed From the results the proposedscheme with 256 points can achieve higher PCC accuracythan the method with 128 sample points Especially theperformance difference is more obvious at low SNR +ereason is that as the sample points increase more features of

Convolutional Layer D

atas

et (I

Q sa

mpl

es)

PReL

U+D

ropo

ut

128 kernels1times16 matrix


256 128 λ

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

Softm

ax

Fully-connected Layer

Figure 3 +e structure of deep learning-based SMI

0 5 10 15 20 2502

04

06

08

1

SNR (dB)

PCC

Proposed deeping learningminusbased SMICNN + AP samplesLogistic + ManmadeFeatures

Figure 4 PCC comparison between the proposed scheme and theexisting schemes dataset θ1

0 5 10 15 20 25SNR (dB)

02

0

04

06

08

1

PCC

16QAM8PSK

QPSKBPSK

Figure 5 PCC comparison between different modulation typesdataset θ1

0 5 10 15 20 25SNR (dB)

01

02

04

03

06

05

08

09

07

1

PCC

CNN + IQ samplesCNN + AP samplesLogistic + ManmadeFeatures

Figure 6 PCC comparison of different methods dataset θ2

02

0

04

06

08

1

PCC

0 5 10 15 20 25SNR (dB)

16QAMminus256QPSKminus256


Figure 7 PCC comparison of the proposed scheme under differentsample points dataset θ1


the signal can be extracted by the CNN algorithm im-proving the identification accuracy effectively

5 Conclusions

In this paper a deep learning-based SMI technique waspresented to identify FBMCOQAM signals in a nonco-operative system To achieve the imaginary interferencecancelation the concept of block repetition was employed inthe FBMCOQAM system to generate signals In the pro-posed scheme 3 fully connected layers and 2 convolutionallayers were designed In addition the dropout layer wasdesigned to lower the interaction neurons of the same layerTo evaluate the proposed scheme extensive experimentswere conducted by employing datasets with differentmodulations +e results indicated that the proposed deeplearning-based SMI scheme exhibited high accuracy ofmodulation identification and strong robustness

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is work was financially supported in part by the ScientificResearch Fund of Wuhan Textile University under Grant20200828

References

[1] R Nissel S Schwarz and M Rupp ldquoFilter bank multicarriermodulation schemes for future mobile communicationsrdquoIEEE Journal on Selected Areas in Communications vol 35no 8 pp 1768ndash1782 2017

[2] P Siohan C Siclet and N Lacaille ldquoAnalysis and design ofOFDMOQAM systems based on filterbank theoryrdquo IEEETransactions on Signal Processing vol 50 no 5 pp 1170ndash1183 2002

[3] D Kong D Qu and T Jiang ldquoTime domain channel esti-mation for OQAM-OFDM systems algorithms and perfor-mance boundsrdquo IEEE Transactions on Signal Processingvol 62 no 2 pp 322ndash330 2014

[4] R Nissel and M Rupp ldquoPruned DFT-spread FBMC lowPAPR low latency high spectral efficiencyrdquo IEEE Transac-tions on Communications vol 66 no 10 pp 4811ndash4825 2018

[5] F Wen Z Zhang K Wang G Sheng and G Zhang ldquoAngleestimation and mutual coupling self-calibration for ULA-based bistatic MIMO radarrdquo Signal Processing vol 144 no 3pp 61ndash67 2018

[6] S Hong Y Zhang Y Wang H Gu G Gui and H SarildquoDeep learning-based signal modulation identification inOFDM systemsrdquo IEEE Access vol 7 pp 114631ndash114638 2019

[7] M Liu J Chen B Li and J Li ldquoFractional frequency offsetestimation for OFDM systems in non-cooperative

communicationrdquo China Communications vol 13 no 9pp 65ndash71 2016

[8] G Gui H Huang Y Song and H Sari ldquoDeep learning for aneffective nonorthogonal multiple access schemerdquo IEEETransactions on Vehicular Technology vol 67 no 9pp 8440ndash8450 2018

[9] W Li H Liu Y Wang Z Li Y Jia and G Gui ldquoDeeplearning-based classification methods for remote sensingimages in urban built-up areasrdquo IEEE Access vol 7pp 36274ndash36284 2019

[10] H Huang W Xia J Xiong J Yang G Zheng and X ZhuldquoUnsupervised learning based fast beamforming design fordownlink MIMOrdquo IEEE Access vol 7 no 1 pp 7599ndash76052018

[11] F Meng P Chen L Wu and X Wang ldquoAutomatic mod-ulation classification a deep learning enabled approachrdquo IEEETransactions on Vehicular Technology vol 67 no 11pp 10760ndash10772 2018

[12] W Xie S Hu C Yu P Zhu X Peng and J Ouyang ldquoDeeplearning in digital modulation recognition using high ordercumulantsrdquo IEEE Access vol 7 pp 63760ndash63766 2019

[13] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modu-lation classification using combination of genetic program-ming and KNNrdquo IEEE Transactions on WirelessCommunications vol 11 no 8 pp 2742ndash2750 2012

[14] H Wang L Xu Z Yan and T A Gulliver ldquoLow-complexityMIMO-FBMC sparse channel parameter estimation for in-dustrial big data communicationsrdquo IEEE Transactions onIndustrial Informatics vol 17 no 5 pp 3422ndash3430 2021

[15] D Kong X-G Xia P Liu and Q Zhu ldquoMMSE channelestimation for two-port demodulation reference signals innew radiordquo Science China Information Sciences vol 64pp 1693031ndash1693032 2021

[16] C Lele P Siohan and R Legouable ldquo2 dB better than CP-OFDM with OFDMOQAM for preamble-based channelestimationrdquo in Proceedings of the IEEE International Con-ference on Communication pp 1302ndash1306 Xiamen ChinaMay 2008

[17] C Lele J-P Javaudin R Legouable A Skrzypczak andP Siohan ldquoChannel estimation methods for preamble-basedOFDMOQAM modulationsrdquo in Proceedings of the EuropeanWireless Conference pp 59ndash64 Delft Netherlands March2007

[18] D Kong X Zheng Y Zhang and T Jiang ldquoFrame repetitiona solution to imaginary interference cancellation in FBMCOQAM systemsrdquo IEEE Transactions on Signal Processingvol 68 pp 1259ndash1273 2020

[19] D Kong J Li K Luo and T Jiang ldquoReducing pilot overheadchannel estimation with symbol repetition in MIMO-FBMCsystemsrdquo IEEE Transactions on Communications vol 68no 12 pp 7634ndash7646 2020


So far most existing modulation identification ap-proaches are based on feature extraction and machinelearning classification A lot of SMI schemes are developedby combining different machine learning-based classifiersand feature extraction strategies [10] However since con-ventional feature extraction schemes rely on statistics it isdifficult for these methods to extract the signal features ofdifferent modulation types As a result the classificationresult is vulnerable tomix up In addition machine learning-based SMI schemes will suffer performance bottleneck forthe problem associated with big data +at is to say theprobability of correct classification is not good enoughwhich indicates unpreferred in practical FBMCOQAMsystems To solve this issue deep learning (DL) has beendeemed to be one of effective techniques to deploy SMI [11]In [12] an enhanced identification scheme was presentedbased on deep neural network (DNN) In [13] the geneticprogramming (GP) was combined with the k-nearestneighbor (KNN) to identify four modulation typesaccurately

In this paper we propose a novel SMI technique basedon the convolutional neural network (CNN) to make anidentification on FBMCOQAM signals It is noted that theblock repetition is employed in the FBMCOQAM system toachieve the imaginary interference cancelation In theproposed scheme 3 fully connected layers and 2 convolu-tional layers are designed In addition the dropout layer isdesigned to lower the interaction neurons of the same layerTo evaluate the proposed scheme extensive experiments areconducted by employing datasets with different modula-tions +e results show that the proposed method canachieve better accuracy than conventional methods

+e rest of the paper is organized as follows +e systemmodel of FBMCOQAM with block repetition is introducedbriefly as well as the model of the deep learning in Section 2Subsequently the proposed SMI method is presented inSection 3 Section 4 gives experimental results followed bythe conclusion in Section 5

2 Model of FBMCOQAM

Figure 1 depicts the baseband FBMCOQAM system dia-gram with M subcarriers +e transmitted signal of eachFBMCOQAM subcarrier gets through a pulse shaping filterdmn is the transmitted symbol at the time frequency position(m n) Denote g[l] as the pulse shaping filter for all sub-carriers in FBMCOQAM which has the even and sym-metric coefficients and exhibits the extremely low spectrumsidelobe [2] According to Figure 1 the transmitted signal ofFBMCOQAM can be expressed as follows [3 14]

s[l] 1113944Mminus 1

m01113944nisinZ

dmng l minus nM

21113876 1113877e

((j2πml)M)e

((jπ(m+n))2)

(1)

Assume h[l] is the Rician fading channel +e trans-mitted signal s[l] passes through the channel h[l] and thereceived signal can be written as

r[l] h[l]lowast s[l] + η[l] (2)

where lowast represents the convolution operator and η[l]

stands for the additive white Gaussian noise [15]+en after FBMCOQAM demodulation at the receiver

it can obtain the following [16 17]

1113954dmn 1113944infin

lminus infinr[l]g l minus n

M

21113876 1113877e

minus (j2πmlM)e

minus (jπ(m+n)2)

Hmn dmn + 1113944

m0 n0( )ne(mn)

dm0 n0ζm0 n0

mn⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ + ηmn

Hmn dmn + jdcmn1113872 1113873 + ηmn

(3)

where ζm0 n0mn is the imaginary interference factor in FBMC

OQAM which is a pure imaginary value dcmn is the

imaginary interference to the symbol dmn [17] and ηmn isthe noise to the symbol dmn Note that although η[l] is whiteGaussian noise ηmn is not white due to the real-valuedorthogonality of FBMCOQAM systems Hmn is the channelfrequency response at the subcarrier m For the time-in-variant channels the value of Hmn is not relevant to the timeindex n

It has been demonstrated that the imaginary interferencefactor ζm0n0

mn is symmetrical [18] On this basis of symmetricthe block repetition is designed in FBMCOQAM to achievethe imaginary interference cancelation [18 19] As shown inFigure 2 the frame consists of two parts ie original blockand repeated block dmn m isin [0 M minus 1] n isin [0 N minus 1] arethe symbols in the original block which are obtained fromthe QAM constellation amn+N are the symbols in the re-peated block and it is noted that amn+N amNminus 1minus n

At the receiver the demodulations of original block andrepeated block are respectively written as

1113954dmn Hmn dmn + jdcmn1113872 1113873 + ηmn n 0 1 N minus 1

(4)

1113954dm2Nminus 1minus n Hm2Nminus 1minus n dm2Nminus 1minus n + jdcm2Nminus 1minus n1113872 1113873

+ ηm2Nminus 1minus n

Hmn dmn + jdcm2Nminus 1minus n1113872 1113873

+ ηm2Nminus 1minus n n 0 1 N minus 1

(5)

Note that the imaginary interferences of the originalblock and repeated block satisfy the following equation [18]ie

jdcmn + jd

cm2Nminus 1minus n 0 (6)

Subsequently the imaginary interferences can be re-moved by the following linear combination

1113954dmn + 1113954dm2Nminus 1minus n

2 Hmndmn +

ηmn + ηm2Nminus 1minus n

2 (7)







f[x] x

σ2e


σ21113890 1113891 (9)


h[l]

κ

κ + 1

1113970

σejθ

+

1

κ + 1

1113970

N 0 σ21113872 1113873 (10)


κ Ax

σ2 (11)








y[k] 1113944l



y[p q] 1113944k

1113944l



Me

e

g[l] g[l]

g[l]

g[l]

g[l]

j2πlMe

j2πl

Mj2π (Mndash1)l

e Mj2π (Mndash1)l

g[l]

d0n

d1n

dMndash1n

2jπn

e 2jπn

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2M

2M

2M

2M

2M

2M

d0n

d1n

dMndash1n

(∙)

(∙)

(∙)



d00 d01 d02 d03 d04

d10 d11 d12 d13 d14

d20 d21 d22 d23 d24

d30 d31 d32 d33 d34

d40 d41 d42 d43 d44

d50 d51 d52 d53 d54

d04 d03 d02 d01 d00

d14 d13 d12 d11 d10

d24 d23 d22 d21 d20

d34 d33 d32 d31 d30

d44 d43 d42 d41 d40

d54 d53 d52 d51 d50



y[p q] 1113944k

1113944l

x[p + k q + l]w[k l] (14)





Si s0 s1 sNs1113960 1113961 (15)


sl R sl1113864 1113865 + jI sl1113864 1113865 (16)




A

R sl1113864 11138652

+ I sl1113864 11138652

1113969

(17)

θ arctanI sl1113864 1113865

R sl1113864 1113865 (18)











atas

et (I

Q sa

mpl

es)

PReL

U+D

ropo

ut



256 128 λ

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

Softm

ax



0 5 10 15 20 2502

04

06

08

1

SNR (dB)

PCC



0 5 10 15 20 25SNR (dB)

02

0

04

06

08

1

PCC

16QAM8PSK

QPSKBPSK


0 5 10 15 20 25SNR (dB)

01

02

04

03

06

05

08

09

07

1

PCC



02

0

04

06

08

1

PCC

0 5 10 15 20 25SNR (dB)






5 Conclusions


Data Availability




Acknowledgments


References



























f[x] x

σ2e


σ21113890 1113891 (9)


h[l]

κ

κ + 1

1113970

σejθ

+

1

κ + 1

1113970

N 0 σ21113872 1113873 (10)


κ Ax

σ2 (11)








y[k] 1113944l



y[p q] 1113944k

1113944l



Me

e

g[l] g[l]

g[l]

g[l]

g[l]

j2πlMe

j2πl

Mj2π (Mndash1)l

e Mj2π (Mndash1)l

g[l]

d0n

d1n

dMndash1n

2jπn

e 2jπn

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2jπ (1+n)

e

2jπ (Mndash1+n)

e

2M

2M

2M

2M

2M

2M

d0n

d1n

dMndash1n

(∙)

(∙)

(∙)



d00 d01 d02 d03 d04

d10 d11 d12 d13 d14

d20 d21 d22 d23 d24

d30 d31 d32 d33 d34

d40 d41 d42 d43 d44

d50 d51 d52 d53 d54

d04 d03 d02 d01 d00

d14 d13 d12 d11 d10

d24 d23 d22 d21 d20

d34 d33 d32 d31 d30

d44 d43 d42 d41 d40

d54 d53 d52 d51 d50



y[p q] 1113944k

1113944l

x[p + k q + l]w[k l] (14)





Si s0 s1 sNs1113960 1113961 (15)


sl R sl1113864 1113865 + jI sl1113864 1113865 (16)




A

R sl1113864 11138652

+ I sl1113864 11138652

1113969

(17)

θ arctanI sl1113864 1113865

R sl1113864 1113865 (18)











atas

et (I

Q sa

mpl

es)

PReL

U+D

ropo

ut



256 128 λ

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

Softm

ax



0 5 10 15 20 2502

04

06

08

1

SNR (dB)

PCC



0 5 10 15 20 25SNR (dB)

02

0

04

06

08

1

PCC

16QAM8PSK

QPSKBPSK


0 5 10 15 20 25SNR (dB)

01

02

04

03

06

05

08

09

07

1

PCC



02

0

04

06

08

1

PCC

0 5 10 15 20 25SNR (dB)






5 Conclusions


Data Availability




Acknowledgments


References






















y[p q] 1113944k

1113944l

x[p + k q + l]w[k l] (14)





Si s0 s1 sNs1113960 1113961 (15)


sl R sl1113864 1113865 + jI sl1113864 1113865 (16)




A

R sl1113864 11138652

+ I sl1113864 11138652

1113969

(17)

θ arctanI sl1113864 1113865

R sl1113864 1113865 (18)











atas

et (I

Q sa

mpl

es)

PReL

U+D

ropo

ut



256 128 λ

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

Softm

ax



0 5 10 15 20 2502

04

06

08

1

SNR (dB)

PCC



0 5 10 15 20 25SNR (dB)

02

0

04

06

08

1

PCC

16QAM8PSK

QPSKBPSK


0 5 10 15 20 25SNR (dB)

01

02

04

03

06

05

08

09

07

1

PCC



02

0

04

06

08

1

PCC

0 5 10 15 20 25SNR (dB)






5 Conclusions


Data Availability




Acknowledgments


References

























atas

et (I

Q sa

mpl

es)

PReL

U+D

ropo

ut



256 128 λ

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

PReL

U+D

ropo

ut

Softm

ax



0 5 10 15 20 2502

04

06

08

1

SNR (dB)

PCC



0 5 10 15 20 25SNR (dB)

02

0

04

06

08

1

PCC

16QAM8PSK

QPSKBPSK


0 5 10 15 20 25SNR (dB)

01

02

04

03

06

05

08

09

07

1

PCC



02

0

04

06

08

1

PCC

0 5 10 15 20 25SNR (dB)






5 Conclusions


Data Availability




Acknowledgments


References























5 Conclusions


Data Availability




Acknowledgments


References






















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