Collaborative Covert Communication Design Based on Lattice...

Research ArticleCollaborative Covert Communication Design Based onLattice Reduction Aided Multiple User Detection Method

Baoguo Yu12 Yachuan Bao12 Haitao Wei12 Xin Huang3 and Yuquan Shu12

1State Key Laboratory of Satellite Navigation System and Equipment Technology Shijiazhuang China2The 54th Research Institute of CETC Shijiazhuang China3Northwestern Polytechnical University Xirsquoan China

Correspondence should be addressed to Yachuan Bao baoyachuan126com

Received 13 April 2017 Accepted 28 June 2017 Published 6 August 2017

Academic Editor Xiaoqiang Ma

Copyright copy 2017 Baoguo Yu et al This 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

Spread spectrum communication is a typical scheme for covert communication because of its low detectability and antijamcharacteristic However the associated design concerns multiple factors such as cochannel multiple access interference (MAI) andspread spectrum gain In this paper the lattice reduction theory is applied toMAI cancellation of spread spectrum communicationand a novel lattice reduction aidedmultiple user detectionmethod is proposedThenearmaximum likelihood (ML) performance ofMAI resistance is verified by simulation and theoretical analysisThe superiority of detection performance in strongMAI scenariosis especially addressed Based on the algorithm a collaborative covert communication systemdesign is proposed Low-power covertsignals can be transmitted at a higher bit ratewith the same coverage asmore high-power cochannel signalsThe covert transmissionperformance can be improved significantly compared to traditional designs

1 Introduction

For the purposes of information transmission securitycovert communication is applied in many special scenariosincluding military and national security applications Thedevelopment of covert communication systems shows a trendfor diversity where different designs are tailored to differentapplications Covert communication systems can be dividedinto two main groups covert information transmission andcovert signal transmission The covert transmission of infor-mation can be satisfied by securing both the informationsource and the communication protocol encryption A typ-ical schema includes information transmission with imageand video compression [1] and covert P2P channels over theInternet [2] among othersThe covert transmission of signalsis realized by signal or transmitter-receiver mode design withlow detectability Typical schemes include designs based ondirect antenna modulation (DAM) [3] and spread spectrum(SS) communication

The most common method for covert communicationdesign based on SS involves reducing the signal power to

hide it in noise or transmit the covert signal covered byseveral high-power signals An improved method involvingfrequency and code hopping is proposed in this paper withan improvement in anticapture performance [4] SS signalsare also designed to transmit coupled with satellite televisionsignals and broadcast signals to achieve covert communica-tion [5]

Transmitting low-power covert signals coupled withhigh-power signals is an effective way to reduce thedetectability of a signal However the designwill be restrictedby multiple access interference (MAI) and wireless linkresources To achieve high imperceptibility signal power andinformation rates will be limited

Research on covert communication based on SS is dis-cussed in this paper Lattice reduction (LR) is applied tomultiple user detection (MUD) of SS communication andan LR-MUD algorithm is also proposed Near maximumlikelihood (ML) performance of lower power signals isachieved with low complexity in serious MAI scenariosBased on the LR-MUD algorithm a novel design of collabo-rative SS covert communication is proposed Covert signals

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 8949430 8 pageshttpsdoiorg10115520178949430

2 Wireless Communications and Mobile Computing

can be transmitted with the coverage of a greater numberof high-power signals Thus the transmission concealmentand robustness of covert communication will be improvedsignificantly

The remainder of the paper is organized as followsSection 2 gives the covert communication model based onSS communication while the traditional MUD method isanalyzed in Section 3 The lattice theory and lattice aidedMUD algorithm is given in Section 4 followed by simulationexperiments of the algorithm in Section 5 The design of asystem based on LR-MUD is given in Section 6 Finally theconclusions are provided in Section 7

2 Covert Communication Model Based onSpread Spectrum

Consider a covert SS communication system consisting ofone low-power covert signal and 119873 minus 1 high-power signalsThe received signal at the receiver is

119903 (119905) = 119873sum119896=1

119860119896 (119905) 119887119896 (119905)PN119896 (119905) + 119899 (119905) (1)

where119860 is the signal amplitude 119887 is the information bit whichtakes values in the interval minus1 +1 and PN is the pseudonoise code used for spread spectrum modulation

Suppose signal 119896 is the desired signal Then the output ofthe matched filter for signal 119896 is as follows

119910119896 = int1198791198870

119903 (119905)PN119896 (119905) 119889119905= int1198791198870

[ 119873sum119896=1

119860119896119887119896PN119896 (119905) + 119899 (119905)]PN119896 (119905) 119889119905= 119860119896119887119896 + 119873sum

119895=1119895 =119896

119860119895119887119895120588119895119896 + 119899119896(2)

where 120588119895119896 = int1198791198870

PN119896(119905)PN119895(119905)119889119905 119899119896 = int1198791198870

119899(119905)PN119896(119905)119889119905 and119879119887 is the time length of the information bitThe first item is the expected signal whereas the second

item is the correlation sum of the spread spectrum code andother signals which is the MAIThe third item is the channelnoise

The output of a matched filter of119873 signals is given below

Y = [1199101 1199102 119910119873]119879

Y =[[[[[[[

12058811 12058812 sdot sdot sdot 120588111987312058821 12058822 sdot sdot sdot 1205882119873 1205881198731 1205881198732 sdot sdot sdot 120588119873119873

]]]]]]]

[[[[[[

1198601 1198602d

119860119873

]]]]]]

[[[[[[[

11988711198872119887119873

]]]]]]]

+[[[[[[[

11989911198992119899119873

]]]]]]]= RAb + n

(3)

Definite H = RA and formula (3) can be written asfollows

Y = Hb + n (4)

In traditional detection the output of amatched filter willbe sampled at every bit interval and the bit will be decided onthe basis of the decision threshold

b = dec (Y) = dec (Hb + n) (5)

where dec( ) represents the decision value of the bit Gettingthe bit directly with the decision of the matched filer outputcritical errors could possibly be caused byMAI especially forthe covert low-power signal

3 Multiple User Detection Method for SpreadSpectrum Communication

As an effective method to improve the capacity of aspread spectrum communication system a MAI suppressionmethod has been developed in depth [6 7] The typicalmethod includes two types multiple user detection (MUD)and an interference cancellation method The foundation ofthe MUD method is the calculation of correlation betweensignals and the interference is suppressed by the decorrela-tion process The traditional MUDmethod includes the zeroforcing (ZF) method and the minimum mean square error(MMSE)method amongmany other newmethods proposedover the years

Here aMUDmethod aided by aHopfield neural networkis proposed [8] With the method detection performancecan be improved but the improvement will decrease with anincrease in signal number A weighted orthogonal matchedfilter method based on quantum signal processing is pro-posed [9] With this method the estimation of noise poweris not necessary but the detection performance is reducedcompared to the MMSE method A blind MUD methodbased on Schmidt-orthogonalization and subspace-trackingKalman filtering is also presented and with this methodthe complexity of the blind MUD method is reduced [10]There are two types of interference cancellation methodsserial interference cancellation (SIC) and parallel interferencecancellation (PIC) Based on the correlation computation ofsignals the signal interference influence of other signals canbe cancelled by the serial or parallel mode The performanceof this kind ofmethod is suboptimal comparedwith theMUDmethod Its performance is limited by the initial detectionaccuracy of multiple signals When multiple interferenceis serious the platform effect will emerge early and thedetection performance will not be ideal [11 12] In practicalapplications the detection performance can be improvedwith usage combined with high-gain error correction codingThe benefit from the low computation complexity and flexibleprocessing architecture leads to this interference cancellationmethod being applied in some satellite communication sys-tem designs

The article is focused on theMUDmethodThe basic ideaof the MUD method is to cancel MAI between signals with

Wireless Communications and Mobile Computing 3

the calculation and transformation of a correlation matrixMaximum likelihood (ML) ZF and MMSE methods aretypical algorithms applied

The ML algorithm is the theoretical optimum MUDalgorithm Its principle is shown as follows Generate atransmit signal traversal set and complete the followingoperation

b = argmin (Y minusHb) b isin b (6)

The main process of ZF algorithm involves calculatingthe inverse matrix G of the correlation matrix H and thencalculating the dot product of G and the output of thematched filter group After that estimation of transmittersignals can be obtained with the following decision [13]

G = (H119867H)minus1H119867b = dec (G (Hb + n)) = b + n1015840 (7)

n1015840 is the noise component after ZF conversion and bitdecision

The calculation complexity of the ZF method is relativelylow and scales with the number of signals

The estimation error covariance matrix is as follows

120593MMSE = 119864 (b minus b) (b minus b)119867 = 1205902 (H119867H)minus1 (8)

1205902 is the variance of noise The influence of noise is alwaysincreased with the ZF method which is why ZF performspoorly with a low signal noise ratio (SNR) scenario (H119867H)minus1can be defined as the demodulation error coefficient for ZFwhich measures how the influence of noise is enlarged by theZF method

The basic idea of MMSE is to minimize the mean squareerror between transmit signal and estimation result Unlikethe ZF method MMSE takes noise suppression into accountand thus the estimation performance is improved to someextent The process of MMSE is as follows

G1015840 = (H119867H + 1205902I)minus1H119867b = dec (G1015840 (Hb + n)) = b + n10158401015840 (9)

n10158401015840 is the noise component after MMSE conversion andbit decision

The estimation error covariance matrix of MMSE is

120593MMSE = 119864 (b minus b) (b minus b)119867= 1205902 (H119867H + 1205902I)minus1 (10)

Based on formal analysis it can be shown that theperformance of MUD is influenced by noise and the orthog-onality of the correlation matrix If the correlation matrix isorthogonal the detection performance of MUD will equalthat of the performance of a single signal without MAI Inaddition for special users it is possible to suppress noise withthe transformation of the correlation matrix Searching for amethod which can improve the orthogonality of the matrixis an important pathway to fulfill enhancedMAI cancellation

Squarelattice

Rhombiclattice

Hexagonlattice

B = 1 0

0 1 B =

1

21 2

0 1 B =

1

22 1

0 3

Figure 1 Several typical lattices

4 Multiple User Detection Methods Based onLattice Reduction

41 LatticeTheory A lattice is a congregation of scatter pointsarranged with scheduled rule [14ndash16] Any lattice can begenerated by a group of linear unrelated vectors Figure 1shows several typical types of lattice

Suppose a group of 119899 dimensional vectors is definedby B = (b1 b2 b119898) isin 119877119899 The number of vectors is119898 and the vectors are linearly independent The integratedlinear combination of the vectors can form an119898-dimensionallattice It can be written as follows

119871 (b1 b2 b119898) = 119898sum119894=1

119905119894119887119894 119905119894 isin 119885 (11)

Vector B = (b1 b2 b119898) is one foundation of thelattice and t = [1199051 1199052 119905119899]119879 is the coefficient vectorcomposed of integers It can be written in matrix mode

119871 = l = Bt (12)

The three different lattices are generated from the basisbelow the figures The dimensionality is decided by thenumber of base vectorsThe dimensionality of the base vectoris called the rank of the generated lattice

The basis of a lattice is diversified A lattice can be denotedby different bases An119898-dimensional space can be generatedby any group of 119898 linearly independent vectors but not anygroup of119898 linearly independent vectors can form a lattice

There is a fixed relation between the different base vectorsof one lattice For the lattice 119871(B) generated by vector groupB = (b1 b2 b119898) all of the vectors transformed fromB by an elementary column transfer from the base vectorsof the lattice The product of several elementary columntransfer matrices equals one unimodular transfer matrix TThe elements of T are complex integers and the determinantof T equals plusmn1 As long asT is a unimodularmatrix the samelattice can be generated by B and BT

119871 (B) = 119871 (BT) (13)

The shortest base vector that is the base vector of shortestlength is a common research object for a lattice If theshortest base vector cannot be reached the nearest shortbase vector is always desired The basis of a lattice has the


InputQ RReduction processInitialization Q1015840 = Q R1015840 = R 119896 = 2While 119896 le 119899for 119897 = 119896 minus 1 1119887 = R1015840(119897 119896)R1015840(119897 119897) 119887 rounded to complex integer 120583if (120583 = 0)

R1015840(1 119897 119896) = R1015840(1 119897 119896) minus 120583R1015840(1 119897 119897)P( 119896) = P( 119896) minus 120583P( 119897)

endendif (120575R1015840(119896 minus 1 119896 minus 1)2 gt R1015840(119896 119896)2 + R1015840(119896 minus 1 119896)2)

Interchange column 119896 minus 1 and column 119896 of matrix R1015840and PCalculate the Givens rotation matrix 120579 to make R1015840(119896 119896 minus 1) = 0

R1015840 (119896 minus 1 119896 119896 minus 1 119873119905) = 120579R1015840 (119896 minus 1 119896 119896 minus 1 119873119905)Q1015840 ( 119896 minus 1 119896) = Q1015840 ( 119896 minus 1 119896) 120579119867(120579 = [ c s

minuss c] c = R1015840 (119896 minus 1 119896 minus 1)R1015840 (119896 minus 1 119896 119896 minus 1) s = R1015840 (119896 119896 minus 1)R1015840 (119896 minus 1 119896 119896 minus 1))119896 = max 119896 minus 1 2

else119896 = 119896 + 1end

If 119896 gt 119899 export R1015840 Q1015840 and transfer matrix PReduction completed

Algorithm 1 Algorithm LLL

feature that a shorter basis will be more orthometric Latticereduction is the process by which the nearest short basevector is found while the orthogonality of the base vector isimproved

42 Lattice Reduction Algorithms Lattice reduction is aprocess to obtain the nearest short base vector while theorthogonality of the base vector is improved Common latticereduction algorithms include the LenstrandashLenstrandashLovasz(LLL) reduction [17] and the Seysen reduction [18 19]

To measure the orthogonality of a lattice basis the degreeof orthogonality defect is defined Suppose (b1 b2 b119898) isone group of base vectors of lattice L and the base vectormatrix isHThe degree of orthogonality defect ofH is definedas

Δ (H) = prod119872119898=1 1003817100381710038171003817h11989810038171003817100381710038172det (H119867H) (14)

In the formula 119872 is the column number of H h119898 is thecolumn 119898 of H and det( ) is the determinant operatorΔ(H) ge 1 and only whenH is an orthogonal matrix Δ(H) =1

SupposeH1015840 is the matrix generated by an LLL reduction

H1015840 = HP P is a unimodular matrix (15)

If R1015840 is found via a QR decomposition of H1015840 it satisfiesthe following two conditions

10038171003817100381710038171003817119903101584011989711989610038171003817100381710038171003817 le 12 10038171003817100381710038171003817119903101584011989711989710038171003817100381710038171003817 1 le 119897 le 119896 le 119899120575 100381710038171003817100381710038171199031015840119896minus1119896minus110038171003817100381710038171003817 le 10038171003817100381710038171003817119903101584011989611989610038171003817100381710038171003817 + 100381710038171003817100381710038171199031015840119896minus111989610038171003817100381710038171003817 119896 = 2 119899

(16)

ThenH1015840 is the matrix processed by LLL reductionThe basic procedure of LLL [20ndash22] is

shown in Algorithm 1Compared with the LLL reduction themain difference in

the Seysen reduction is a different definition of the degree oforthogonality defect

119878 (H) = 119872sum119898=1

1003817100381710038171003817h11989810038171003817100381710038172 10038171003817100381710038171003817h119898100381710038171003817100381710038172 (17)

In the formula H has 119872 columns h119898 is the 119898 columnof H and h119898 is the 119898 column of the dual matrix H =((H119867H)minus1H119867)119867 [12 13]

WhenH is an orthogonal matrix

119878 (H)min = 119872 (18)

The Seysen algorithm takes both the raw matrix anddual matrix into account as a result a better reductionperformance can be achieved


1 Estimation of signals Y is calculated by matched filtersSignal power relative delay and carrier phase difference of signals are estimated2 A correlation matrix between signalsH is calculated3 ProcessH with lattice reduction algorithm (LLL or Seysen)

Conversion matrix P and optimized matrixH1015840 = HP is obtained4 The ZF or MMSE method is implementedZLLL_ZF = (H1015840119867H1015840)minus1H1015840119867YZLLL_MMSE = (H1015840119867H1015840 + 1205902P119867P)minus1H1015840119867Y5 The modified quantization in improved lattice space is takenZ = 119886 (lceil1119886 Zminus 12Pminus1Irfloor + 12Pminus1I) 119886 is the power normalization parameter and lceil rfloor is the roundness of real value6 Final detection result X is calculated

X = PZ

Algorithm 2 Algorithm LR-MUD

Matchedfilter

Correlationmatrix

calculationLattice

reduction MUD Modifiedquantization

Figure 2 Process of the LR-MUD algorithm

43 Lattice Reduction Aided Multiple User Detection (LR-MUD) With lattice reduction the correlation matrix H canbe transformed to matrixH1015840 which has better orthogonalityThe analysis of theMUDmethod in Section 2 shows that witha correlationmatrixwith better orthogonality the influence ofnoise can be better suppressed

The process of lattice reduction aided multiple userdetection algorithm is shown in Algorithm 2

The basic process of the algorithm is shown in Figure 2The signal power and signal delay estimation accuracy isimportant to the performance of the algorithm To estimatethe signal power in the MAI scene a synchronization-headcan be used to improve the estimation accuracy The signaldelay and carrier phase information can be given by the signaltracking loop The measurement accuracy can be improvedby extending integration time and by using a large correlatordesign Related research shows that week spread spectrumsignals like GPS can be tracked stably when SNR is lower thanminus4 dB

The complexity of ML is 119874(119873119904119872) where 119873119904 is the mod-ulation order and 119872 is the signal number The complexityof ML increases with 119873119904 exponentially The complexity ofZF and MMSE is relatively low given as 119874(1198723) The maincomputation of the MUD method is in the inversion of thecorrelation matrix The lattice reduction process is addedbased on the MUD in the LR-MUD method The increasedcomputation includes QR decomposition and inversion ofmatrix P The increase in complexity is linear and thus thecomplexity is still119874(1198723) Compared with ML LR-MUD hassuperior performance in regard to complexity

10minus3

10minus2

10minus1

100BE

R

minus6 20 4 6minus2minus4

SNR (dB)

Matched filterZFZF-LLLZF-Seysen

MMSEMMSE-LLLMMSE-SeysenML

Figure 3 BER of LR-MUD with different SNR scenarios

5 Simulation and Analysis

In this section simulations of the LR-MUD method ofSS communication are presented The signal modulation isQPSK and the spread code sequence is a group of gold codes

Figure 3 shows a demodulation BER in different SNRscenarios The signal number is 6 and the spread ratio is 16Signal power is distributed randomly in the range of 0ndash6 dBand the BER of all signals is counted MAI can be cancelledeffectively by the ZF or MMSE method The BER of thetwo algorithms is lower than the BER of the basic matchedfilter method but the performance is much weaker than thatof the ML method In the figure ZF-LLL and ZF-Seysenare the tested LR-MUD methods based on a combinationof the ZF method using a lattice reduction by LLL andSeysen Likewise MMSE-LLL and MMSE-Seysen are thetested LR-MUDmethods based on the MMSE method usinga lattice reduction by LLL and SeysenTheBER of LR-MUD is


10minus3

10minus2

10minus1

100

BER

3 4 5 6 7 82Signal number



Figure 4 BER of desired signal with different signal numbers

Matrix processed by lattice reductionInitial correlation matrix

0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect


Figure 5Degree of orthogonality defect of a correlationmatrixwithdifferent signal numbers

reduced significantly compared with theMUDmethods andits performance approachesML with an increase of SNRThealgorithm gain compared to MUD is more than 4 dB

Figure 4 shows the demodulation BER of a desired signalwith different numbers of interference signals Here thespread ratio is 16 and the SNR of the covert signal is 0 dBThe power of the other signals is randomly distributed in the0ndash20 dB range compared to the desired signalThe BER of thetraditional MUDmethod increases with an increase in signalnumber Performance near ML is achieved by LR-MUD andremains steady even with an increase in signal number LR-MUD shows superiority when subjected to a greater numberof interference signals With the same BER requirements thenumber of interfering high-power signals is 7 for LR-MUDcompared to 2 for the traditional MUDmethod

Figure 5 shows the variation in the orthogonality of thecorrelationmatrix Along with the increase of signal numberthe degree of orthogonality defect for the initial correlationmatrix increases which results in the demodulation dete-rioration in the traditional MUD method In contrast the

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER

2 4 6 8 10 12 14 16 18 200Interference to desired signal power ratio (dB)



Figure 6 BERof a desired signalwith different interference to signalpower ratios

degree of orthogonality defect of the matrix processed by LRincreases only slightly Furthermore this is the explanationfor why LR-MUD performs better than the traditional MUDmethod

Figure 6 shows the simulation result with different signalpower ratios The spread ratio is 32 and the signal number is6 SNR of covert signal is 0 dBThe power of the covert signaland noise remain stable while the power of 5 interferencesignals increases gradually The BER of the desired signalis counted The BER of the MUD method does not changewith the increase in power a fixed gap remains between MLand MUD method The BER of LR-MUD decreases withthe power increase of interference signals and finally nearML performance is achieved when the interference to signalpower ratio is larger than 10 dBThis shows the effect of latticereduction When the correlation between signals is goodthe algorithm gain of the LR is relatively limited When thecorrelation between signals is poor the algorithm gain of LRwill increaseTherefore LR-MUD is suitable to use in intensenear-far scenarios

Figure 7 shows the variation of the degree of orthog-onality defect for a correlation matrix with an increase ofinterference to signal power ratio The orthogonality defectof the correlation matrix does not change With a latticereduction the orthogonality of the correlation matrix isimproved and the effect improves further with an increasein interference power

Figure 8 shows the variation of demodulation errorcoefficient for a desired signal with an increase of interferenceto signal power ratio The change of the demodulation errorcoefficient is consistent with the BER change shown inFigure 6 With additional increase of interference to signalpower ratio the amplification of noise decreases with theLR-MUD method This is the main reason why LR-MUDperforms better than traditional the MUDmethod


Initial correlation matrixMatrix processed by lattice reduction

123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect


Figure 7The degree of orthogonality defect for a correlationmatrixwith different interference to signal power ratios

LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t


Figure 8Demodulation error coefficient with different interferenceto signal power ratios

6 Design of a Covert Communications SystemBased on LR-MUD

Because of the excellent performance gain in intense near-far scenarios LR-MUD is appropriate for implementationin covert communication systems based on SS principles Ablock diagram for a covert communications system design isgiven in Figure 9

The system includes a covert signal transmitter covertsignal receiver and common signal transmitter High-powersignals can be transmitted by the covert transmitter as well asa number of common signal transmitters The covert signaland at least one high-power signal should be transmittedby a covert transmitter synchronously At the receiver thecapture and tracking of covert signals should be performedusing the synchronous high-power signal All signals will bedemodulated with the LR-MUDmethod

Figure 10 is the simulation result of the covert trans-mission performance with different spread ratios SNR ofcovert signal is 0 dB and coverage signal number is 5 With

Coverttransmitter

Signal captureand track

LR-MUD

SS signaltransmitter


covertsignal

High-powersignal

High-power signal

High-power signal

Estimation ofcovert signal

Covert signal receiver

Figure 9 Systemdiagramof a covert communications systembasedon LR-MUD

10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio



Figure 10 BER of a covert signal with different spread ratios

the increase of spread ratio BER decreases with the cost ofinformation rateThe same BER can be achieved by LR-MUDwith a lower spread ratio compared to the common MUDmethod Higher information rates can be realized by LR-MUD with the same wireless link resource and concealmentrequirements

7 Summary and Conclusions

In this paper lattice reduction theory and related algorithmsare applied to the MUD of a spread spectrum communi-cations system and an algorithm called LR-MUD is pre-sented Theoretical analyses and simulation results on theLR-MUD method are carried out showing excellent near-far effect suppression performance Based on the LR-MUDmethod a design of a covert communications system canbe feasibly realized The covert signal can be transmitted ata higher information rate with the coverage of more high-power cochannel signalsThus higher transmission rates andconcealment performance are achieved using the same linkresources

Conflicts of Interest

The authors declare that they have no conflicts of interest


Acknowledgments

The authors acknowledge the National Natural ScienceFoundation of China (Grant 91638203) and the NationalKey Research and Development Program of China (Grant2016YFB0502102)

References

[1] Y Cao H Zhang X Zhao and H Yu ldquoCovert communicationby compressed videos exploiting the uncertainty of motionestimationrdquo IEEE Communications Letters vol 19 no 2 pp203ndash206 2015

[2] M Cunche M-A Kaafar and R Boreli ldquoAsynchronous covertcommunication using bittorrent trackersrdquo in Proceedings ofthe 16th IEEE International Conference on High PerformanceComputing and Communications HPCC 2014 11th IEEE Inter-national Conference on Embedded Software and Systems ICESS2014 and 6th International Symposium on Cyberspace Safety andSecurity CSS 2014 pp 827ndash830 fra August 2014

[3] H Shi and A Tennant ldquoCovert communication using a directlymodulated array transmitterrdquo in Proceedings of the 8th EuropeanConference on Antennas and Propagation EuCAP 2014 pp 352ndash354 nld April 2014

[4] L Li J Zheng and L Zheng ldquoThe Chaotic Code-hoppingSpread Spectrum Communication System[J]rdquo Science Technol-ogy and Engineering vol 13 no 30 pp 176ndash180 2014

[5] X Zhao X Ma and W Qu ldquoAnalysis of the parasitic smallsignal coupling with RDSS RF signal [J]rdquo TelecommunicationEngineering vol 49 no 8 pp 40ndash44 2009

[6] Y Hou M Li X Yuan Y T Hou and W Lou ldquoCooperativeInterference Mitigation for Heterogeneous Multi-HopWirelessNetworks Coexistencerdquo IEEE Transactions onWireless Commu-nications vol 15 no 8 pp 5328ndash5340 2016

[7] Q Zhou and X Ma ldquoReceiver designs for differential UWBsystemswithmultiple access interferencerdquo IEEETransactions onCommunications vol 62 no 1 pp 126ndash134 2014

[8] G I Kechriotis and E S Manolakos ldquoHopfield neural networkimplementation of the optimal CDMA multiuser detectorrdquoIEEE Transactions on Neural Networks vol 7 no 1 pp 131ndash1411996

[9] S-N Shi Y Shang and Q-L Liang ldquoA novel linear multi-userdetectorrdquo Acta Electronica Sinica vol 35 no 3 pp 426ndash4292007

[10] Y Yu J Li Z Wang S Wang and H Zhang ldquoBlind multiuserdetection in MC-CDMA Schmidt-orthogonalization and sub-space tracking Kalman filteringrdquo in Proceedings of the 20113rd International Conference on Communications and MobileComputing CMC 2011 pp 375ndash380 chn April 2011

[11] Z Xie R T Short and C K Rushforth ldquoA Family of Sub-optimum Detectors for Coherent Multiuser CommunicationsrdquoIEEE Journal on Selected Areas in Communications vol 8 no 4pp 683ndash690 1990

[12] W Zheng J Li Y Luo J Chen and J Wu ldquoMulti-userinterference pre-cancellation for downlink signals of multi-beam satellite systemrdquo in Proceedings of the 2013 3rd Inter-national Conference on Consumer Electronics Communicationsand Networks CECNet 2013 pp 415ndash418 chn November 2013

[13] Y Bao and B Yu ldquoA MAI cancellation algorithm with nearML performancerdquo in Proceedings of the IEEE InternationalConference on Communication Software and Networks ICCSN2015 pp 196ndash200 chn June 2015

[14] M R Bremner Lattice Basis Reduction An introduction to theLLL algorithm and its applications vol 300 CRC Press IncBoca Raton FL USA 2012

[15] S M Dias and N J Vieira ldquoConcept lattices reductionDefinition analysis and classificationrdquo Expert Systems withApplications vol 42 no 20 pp 7084ndash7097 2015

[16] B A Lamacchia Basis reduction algorithms and subset sumproblems [D] [Masterrsquos dissertation] Massachusetts Inst Tech-nol 1991

[17] A K Lenstra J Lenstra and L Lovasz ldquoFactoring polynomialswith rational coefficientsrdquoMathematische Annalen vol 261 no4 pp 515ndash534 1982

[18] P Q Nguyen and J Stern ldquoLattice reduction in cryptology anupdaterdquo in Algorithmic number theory (Leiden 2000) vol 1838of Lecture Notes in Comput Sci pp 85ndash112 Springer Berlin2000

[19] C-P Schnorr and M Euchner ldquoLattice basis reductionimproved practical algorithms and solving subset sum prob-lemsrdquoMathematical Programming vol 66 no 2 Ser A pp 181ndash199 1994

[20] P Q Nguyen and J Stern ldquoLattice Reduction in Cryptology AnUpdate [C]rdquo Lecture Notes in Computer Science no 4 pp 85ndash112 1838

[21] XMa andW Zhang ldquoPerformance analysis forMIMO systemswith lattice-reduction aided linear equalizationrdquo IEEE Transac-tions on Communications vol 56 no 2 pp 309ndash318 2008

[22] L G Barbero T Ratnarajah and C Cowan ldquoA comparison ofcomplex lattice reduction algorithms for MIMO detectionrdquo inProceedings of the 2008 IEEE International Conference on Acous-tics Speech and Signal Processing ICASSP pp 2705ndash2708 usaApril 2008

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

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can be transmitted with the coverage of a greater numberof high-power signals Thus the transmission concealmentand robustness of covert communication will be improvedsignificantly

The remainder of the paper is organized as followsSection 2 gives the covert communication model based onSS communication while the traditional MUD method isanalyzed in Section 3 The lattice theory and lattice aidedMUD algorithm is given in Section 4 followed by simulationexperiments of the algorithm in Section 5 The design of asystem based on LR-MUD is given in Section 6 Finally theconclusions are provided in Section 7

2 Covert Communication Model Based onSpread Spectrum

Consider a covert SS communication system consisting ofone low-power covert signal and 119873 minus 1 high-power signalsThe received signal at the receiver is

119903 (119905) = 119873sum119896=1

119860119896 (119905) 119887119896 (119905)PN119896 (119905) + 119899 (119905) (1)

where119860 is the signal amplitude 119887 is the information bit whichtakes values in the interval minus1 +1 and PN is the pseudonoise code used for spread spectrum modulation

Suppose signal 119896 is the desired signal Then the output ofthe matched filter for signal 119896 is as follows

119910119896 = int1198791198870

119903 (119905)PN119896 (119905) 119889119905= int1198791198870

[ 119873sum119896=1

119860119896119887119896PN119896 (119905) + 119899 (119905)]PN119896 (119905) 119889119905= 119860119896119887119896 + 119873sum

119895=1119895 =119896

119860119895119887119895120588119895119896 + 119899119896(2)

where 120588119895119896 = int1198791198870

PN119896(119905)PN119895(119905)119889119905 119899119896 = int1198791198870

119899(119905)PN119896(119905)119889119905 and119879119887 is the time length of the information bitThe first item is the expected signal whereas the second

item is the correlation sum of the spread spectrum code andother signals which is the MAIThe third item is the channelnoise

The output of a matched filter of119873 signals is given below

Y = [1199101 1199102 119910119873]119879

Y =[[[[[[[

12058811 12058812 sdot sdot sdot 120588111987312058821 12058822 sdot sdot sdot 1205882119873 1205881198731 1205881198732 sdot sdot sdot 120588119873119873

]]]]]]]

[[[[[[

1198601 1198602d

119860119873

]]]]]]

[[[[[[[

11988711198872119887119873

]]]]]]]

+[[[[[[[

11989911198992119899119873

]]]]]]]= RAb + n

(3)

Definite H = RA and formula (3) can be written asfollows

Y = Hb + n (4)

In traditional detection the output of amatched filter willbe sampled at every bit interval and the bit will be decided onthe basis of the decision threshold

b = dec (Y) = dec (Hb + n) (5)

where dec( ) represents the decision value of the bit Gettingthe bit directly with the decision of the matched filer outputcritical errors could possibly be caused byMAI especially forthe covert low-power signal

3 Multiple User Detection Method for SpreadSpectrum Communication

As an effective method to improve the capacity of aspread spectrum communication system a MAI suppressionmethod has been developed in depth [6 7] The typicalmethod includes two types multiple user detection (MUD)and an interference cancellation method The foundation ofthe MUD method is the calculation of correlation betweensignals and the interference is suppressed by the decorrela-tion process The traditional MUDmethod includes the zeroforcing (ZF) method and the minimum mean square error(MMSE)method amongmany other newmethods proposedover the years

Here aMUDmethod aided by aHopfield neural networkis proposed [8] With the method detection performancecan be improved but the improvement will decrease with anincrease in signal number A weighted orthogonal matchedfilter method based on quantum signal processing is pro-posed [9] With this method the estimation of noise poweris not necessary but the detection performance is reducedcompared to the MMSE method A blind MUD methodbased on Schmidt-orthogonalization and subspace-trackingKalman filtering is also presented and with this methodthe complexity of the blind MUD method is reduced [10]There are two types of interference cancellation methodsserial interference cancellation (SIC) and parallel interferencecancellation (PIC) Based on the correlation computation ofsignals the signal interference influence of other signals canbe cancelled by the serial or parallel mode The performanceof this kind ofmethod is suboptimal comparedwith theMUDmethod Its performance is limited by the initial detectionaccuracy of multiple signals When multiple interferenceis serious the platform effect will emerge early and thedetection performance will not be ideal [11 12] In practicalapplications the detection performance can be improvedwith usage combined with high-gain error correction codingThe benefit from the low computation complexity and flexibleprocessing architecture leads to this interference cancellationmethod being applied in some satellite communication sys-tem designs

The article is focused on theMUDmethodThe basic ideaof the MUD method is to cancel MAI between signals with


















Squarelattice

Rhombiclattice

Hexagonlattice

B = 1 0

0 1 B =

1

21 2

0 1 B =

1

22 1

0 3





119871 (b1 b2 b119898) = 119898sum119894=1

119905119894119887119894 119905119894 isin 119885 (11)


119871 = l = Bt (12)




119871 (B) = 119871 (BT) (13)









else119896 = 119896 + 1end






Δ (H) = prod119872119898=1 1003817100381710038171003817h11989810038171003817100381710038172det (H119867H) (14)






(16)




119878 (H) = 119872sum119898=1

1003817100381710038171003817h11989810038171003817100381710038172 10038171003817100381710038171003817h119898100381710038171003817100381710038172 (17)



119878 (H)min = 119872 (18)





X = PZ


Matchedfilter

Correlationmatrix

calculationLattice







10minus3

10minus2

10minus1

100BE

R


SNR (dB)








10minus3

10minus2

10minus1

100

BER






0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect






10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























Squarelattice

Rhombiclattice

Hexagonlattice

B = 1 0

0 1 B =

1

21 2

0 1 B =

1

22 1

0 3





119871 (b1 b2 b119898) = 119898sum119894=1

119905119894119887119894 119905119894 isin 119885 (11)


119871 = l = Bt (12)




119871 (B) = 119871 (BT) (13)









else119896 = 119896 + 1end






Δ (H) = prod119872119898=1 1003817100381710038171003817h11989810038171003817100381710038172det (H119867H) (14)






(16)




119878 (H) = 119872sum119898=1

1003817100381710038171003817h11989810038171003817100381710038172 10038171003817100381710038171003817h119898100381710038171003817100381710038172 (17)



119878 (H)min = 119872 (18)





X = PZ


Matchedfilter

Correlationmatrix

calculationLattice







10minus3

10minus2

10minus1

100BE

R


SNR (dB)








10minus3

10minus2

10minus1

100

BER






0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect






10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















else119896 = 119896 + 1end






Δ (H) = prod119872119898=1 1003817100381710038171003817h11989810038171003817100381710038172det (H119867H) (14)






(16)




119878 (H) = 119872sum119898=1

1003817100381710038171003817h11989810038171003817100381710038172 10038171003817100381710038171003817h119898100381710038171003817100381710038172 (17)



119878 (H)min = 119872 (18)





X = PZ


Matchedfilter

Correlationmatrix

calculationLattice







10minus3

10minus2

10minus1

100BE

R


SNR (dB)








10minus3

10minus2

10minus1

100

BER






0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect






10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












X = PZ


Matchedfilter

Correlationmatrix

calculationLattice







10minus3

10minus2

10minus1

100BE

R


SNR (dB)








10minus3

10minus2

10minus1

100

BER






0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect






10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10minus3

10minus2

10minus1

100

BER






0102030405060708090

100

Deg

ree o

f ort

hogo

nalit

y de

fect






10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











123456789

1011

Deg

ree o

f ort

hogo

nalit

y de

fect



LR-MUDZF

times10minus3

08

1

12

14

16

18

2

Dem

odul

atio

n er

ror c

oeffi

cien

t







Coverttransmitter


LR-MUD



covertsignal

High-powersignal

High-power signal

High-power signal




10minus4

10minus3

10minus2

10minus1

100

BER

14 16 18 20 22 24 26 2812Spread ratio










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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