Cognitive Waveform Design for Radar-Communication

Research ArticleCognitive Waveform Design for Radar-CommunicationTransceiver Networks

Yu Yao 1 and Lenan Wu2

1School of Information Engineering East China Jiaotong University Nanchang 330031 China2School of Information Science and Engineering Southeast University Nanjing 210096 China

Correspondence should be addressed to Yu Yao 1057604987qqcom

Received 4 December 2017 Revised 1 March 2018 Accepted 20 March 2018 Published 24 April 2018

Academic Editor Nandana Rajatheva

Copyright copy 2018 Yu Yao and Lenan Wu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The system architecture for cognitive radar-communication (CRC) transceiver is proposed A cognitive waveforms designapproach which is suitable for simultaneously performing both data communication and target detection is presented Thisapproach aims at estimating target scattering coefficient (TSC) from the radar scene and facilitating high data rate communicationsIn order to minimize the mean square error (MSE) of the TSC a convex cost function is established The peak to average powerratio- (PAPR-) constrained optimal solution is achieved by applying the Kalman filtering-based strategy to design the set of ultra-wideband (UWB) transmission pulses and embed into them the information data with the M-ary position phase shift keyingmodulation technique In addition to theoretical considerations the simulation results show an improvement in target scatteringcoefficient (TSC) estimation and target detection probability as the number of iterations increases while still transmitting data ratesin the range of several Mbps with low bit error rates between CRC transceivers

1 Introduction

The integration of multiple functions such as radar tasks andcommunication applications has attracted substantial interestin recent years and sparked a number of research initiatives[1ndash4] It is studied in [5] that the intelligent transportation sys-tem (ITS) employs communications device to convey trafficinformation and utilizes the radar device to sense the trafficcircumstance The demand of ITS is the motive to developradar-communication integration system

11 Background The objective of the joint design is to in-crease both energy efficiency and spectrum efficiency and toreduce manufacturing cost The design of integrated wave-form can be classified into two main categories One isbased on themultiplexing technique including space divisionmultiplexing (SDM) [6] time division multiplexing (TDM)[7] and frequency divisionmultiplexing (FDM) [8] and codedivision multiplexing (CDM) [9] However such a class hasthe same drawback that radar and communication cannotoperate in some domain simultaneously For instance the

radar and communication cannot operate at the same timeslot for the methods based on the TDM technique The otheris based on waveform sharing and has two types One is thatthe communication information is hidden in the conven-tional radar waveforms [10] the other is that the commu-nication waveforms generally employed are either slightlychanged or not [11]

The conventional orthogonal frequency division multi-plexing (OFDM) waveform in communication is continuousin general [12ndash14] In contrast it is noncontinuous for pulseradar Moreover most of the employed OFDM waveformsin radar consist of OFDM pulse train which is indispensablefor communication and one pulse only contains one OFDMsymbol If the integrated radar and communication systememploys the continuous OFDM waveform the transmit andreceive antennas need to be well separated which is difficultto realize in practice especially in those cases when eithertransmit or receive antennas are close to each other If theintegrated OFDM waveform is impulse the transmit andreceive antennas can be shared and the number of antennaswill be reduced to half Furthermore the problem of isolation

HindawiJournal of Advanced TransportationVolume 2018 Article ID 4182927 11 pageshttpsdoiorg10115520184182927

2 Journal of Advanced Transportation

between transmit and receive antennas can be perfectly set-tled For the communication applications however the datarate will decrease because the radar duty ratio is 10 in somecases that is the operation time of communication becomes10 of what it was

These works have adopted OFDM techniques fused withultra-wideband (UWB) technologies to realize the communi-cation-radar integration However these designs create otherimplementation issues such as excessive demand of signalprocessing power high-speed analog-to-digital circuitry andagile radio frequency front end for multimode operationFurthermore systems employing UWB-OFDM for localiza-tion [13 14] utilize the same waveform family for design-ing joint communication-radar signals Consequently thesemethods share a common drawback due to the fact that theautocorrelation of UWB-OFDM signals depend on both thelocation of the notch and the OFDM signal bandwidthHence although the radar target range estimation is unaf-fected by the presence of anOFDMsignal its range resolutiondepends on the notch bandwidth into which the OFDM sig-nal is embedded Literature [15] presents the system employ-ing UWB pulse position modulation (PPM) for designingjoint communication-radar signals Compared to the con-ventional OFDM system the system bit error rate (BER) per-formance is poor relatively [16 17]

Cognitive radar (CR) system can adjust its transmit wave-form and receive filter adaptively based on the prior knowl-edge of targets and the environment and thus has great poten-tial in enhancing the detection and recognition performancefor extended targets [18] In CR [19] cognition plays a criticalrole in the feedback loop which includes long-termmemoryfor example geographicmap and elevationmodel and short-term memory developed by the receiver online By usingprior information the work mode transmit waveform andsignal processing approach of CR can be optimized to yieldbetter performance

Thewideband cognitive radar is not sensitive to active andpassive interference [20] It is very important in intelligenttransmitting In the wideband cognitive radar system theextended target has a complex target impulse response (TIR)[21] which is the target scattering coefficient (TSC) in thefrequency domain [22]The estimation of TSC has gotten lotsof attention in the recent research of radar system [23ndash25]Literature [23] models the extended target as TIR functionunchanged in the waveform design Reference [26] modelsthe extended target as a wide sense stationary-uncorrelatedscattering TIR model considering the change of target viewangle and the strong correlation of TSC during the plusesinterval The interference might be comprised of clutter andnoise Clutter such as unwanted ground returns and environ-ment clutter is assumed to be signal dependent and noise issignal independent too [27] The radar reflection character-istics of the surrounding environment are regarded as timeinvariant

Constant-envelope in cognitive waveform design is dis-cussed to get high power efficiency Literature [28] presentsOFDM optimization waveform design method under theconstant-envelope constraint But constant-envelope condi-tion is too strict in OFDM waveform design Peak to average

power ratio (PAPR) is presented as relaxation form and theOFDM radar system under the PAPR constraint has beensufficiently studied [12] If transmitted signal power is verysmall the estimation precision may degrade violently andthe power spectral density (PSD) of the target TIR cannot beestimated This is the primary reason why the algorithms in[29] cannot be used directly in CR waveform design In orderto solve this problem the performance of the TSC estimationshould be considered in the CR transmission waveformA new CR waveform design algorithm for both estimationand detection is studied In a relative long time the priorknowledge of the clutter is presented inwaveformdesign [30]In a pulse duration time it can be approximately regarded astime invariant in [31] However the TIR varies gradually inpractice TSC is varying with the relative motion between theradar and the target So the TSC estimation update is neededas a feedback

An iteration approach based on the Kalman filtering (KF)is proposed by Dai et al in [32] to estimate the TIR for singletarget And the transmitted waveform is optimized in orderto improve the estimation performances [33] However thedirect optimization problem of waveform design in the tem-poral correlated cognitive radar system (CRS) is nonconvexand cannot be solved efficiently Considering multiple targetscenarios [34 35] presented a multiple-waveform designalgorithm that is based on maximizing a weighted sum ofmutual information measures corresponding to the activetargets and radar waveforms employed The related work ondesigning estimation waveforms for multiple input multipleoutput (MIMO) radar systems is proposed in [36ndash38] whichdiscuss the equivalence between maximizing mutual infor-mation and minimizing the mean square estimation error(MSE) Therefore to our best knowledge only an indirectapproach based on the water-filling method is expressed tooptimize the PSD of transmitted waveform for single target[13] No existing work has considered the direct waveformoptimization for multiple extended targets in the temporalcorrelation CRS

12 Contributions In this paper we combine the temporalcorrelated cognitive algorithm presented in [22] and M-ary position phase shift keying (MPPSK) technique [26] toobtain an optimizationwaveformwhich offers superior radarperformance and high data rate communication capabilitybetween cognitive radar-communication (CRC) transceiversWith this method the radar and communication signalscan coexist by sharing the same frequency band Hencethe target parameter estimation is not affected by the com-munication signal design parameters The UWB-MPPSKwaveforms would not only benefit from a KF approach fortarget estimation and detection but also establish ad hoccommunication links The main contributions of this paperare summarized as follows

(1) We present a novelMPPSK-based radar-communica-tion waveform design scheme

(2) We propose a cognitive radar probing strategy basedon Kalman filtering between successive backscatterpulses for TSC estimation

Journal of Advanced Transportation 3

(3) We provide performance analysis of the CRCnetworkin terms of the TSC estimation and communicationBER between CRC transceivers

The organization of this paper is as follows In Section 2the CRC transceiver network and the node system architec-ture are described In Section 3 we analyze the performanceof the communication link achieved through the MPPSK-based waveformThe Kalman filtering-based cognitive wave-form optimization approaches are presented in Section 4The simulation results illustrating the proposed methods areprovided in Section 5 and conclusions are given in Section 6

Throughout this paper the following notations will beused Vectors are denoted by boldface lowercase letters andmatrices by boldface uppercase letters 119867 and Re( ) denotetranspose conjugate operation and the real part of a variablerespectively The 1198972 norm is denoted as 2 linear convolu-tion operator as lowast expectation operator as 119864 and varianceoperator as Varsdot2 Channel Model

21 Target Channel Model The received echo can be rep-resented as the convolution of the TIR 119902(119905) with the trans-mission waveform 119891(119905) the additive white Gaussian noise(AWGN) 119899(119905) which can be written as

119903 (119905) = 119902 (119905) lowast 119891 (119905) + 119899 (119905) (1)

A model in radar transmission waveform optimization isshown in Figure 1

During the 119896th pulse the TIR between the transmitantennas and the receive antenna is defined as q119896 We denotethe cognitive radar waveform that will be emitted from thetransmitter as f119896 ≜ [119891119896(1) 119891119896(2) 119891119896(119873)]119879 where 119873 isthe sample number of cognitive radar waveform The totaltransmission energy is (1119873)sum119873119899=1 |119891119896(119899)|2 = 119864119891 A denoteschannel attenuation factor Let n sim C119873(0R119873) represent theAWGNR119873 denotes the covariancematrix of noise If a targetexists the received scattered signal can be described as

r119896 = A diag q119896 f119896 + n

= AQ119896f119896 + n (2)

It is difficult to optimize the transmitted waveform with theconvolution operation in the time domainThe complexity ofwaveformdesign is increased and cannot be solved efficientlyThe echo waveforms in the CRS will be processed in thefrequency domain The received signal vector y119896 can berepresented as

y119896 ≜ Γr119896 (3)

where Γ is the matrix of the Fourier transform The echowaveform in the frequency domain can be described as

y119896 = AZ119896g119896 + w (4)

The transmitted waveform is given by a diagonal matrixZ119896 ≜ diagz119896 and the waveform in the frequency domain

is z119896 ≜ Γf119896 g119879119896 ≜ Γh119879119896 denotes the TSC g119896 sim C119873(0R119879)w119896 sim C119873(0R119873) denotes AWGN R119879 and R119873 denote thecovariance matrix of target and noise respectively

Multiple-pulse samples for the TIR estimation are takeninto consideration From the literature if these fluctuationsare temporally correlated during the pulse repetition interval(PRI) this type of the extended target is closely related tothe target radar cross section (RCS) and can be describedby a wide sense stationary-uncorrelated scattering (WSSUS)model The TIR during the kth pulse sample is

q119896 = 119890minus119879120591q119896minus1 + u119896minus1 (5)

where u119896minus1 sim N0 (1 minus 1198902119879120591)R119873 is the zero mean Gaussianvector 119896 is the index of radar pulses 119879 denotes the radarpulses interval and 120591 describes the temporal correlationof TIR during the pulses interval The frequency domaincharacterization of the extended target can be derived bythe Wiener-Khintchine theorem [27] TSC model can beexpressed in the frequency domain

g119896 = 119890minus119879120591g119896minus1 + k119896minus1 (6)

where k119896minus1 sim N0 (1 minus 1198902119879120591)R119873 is the zero mean Gaussianvector

3 Waveform Design

31 UWB-MPPSK Waveforms Each normalized secondderivative Gaussian UWB waveform can be represented as

119906 (119905) = 119868sum119894=1

119886119894 [1 minus 4120587(119905 minus 120572119894119879119879119901 )2]

sdot expminus2120587(119905 minus 120572119894119879119879119875 )2 cos (120579119894) (7)

where 119868 is the number of second derivative Gaussian mono-cycles within the UWB waveform and 119879119875 is the pulse widthof the single UWB pulse and is assumed to be 02 ns whichis a value commonly used in UWB ranging applications 120572119894represents the normalized amplitude of the 119894th monocyclewhich is uniformly distributed 120572119894119879 is the uniformly dis-tributed random pulse repetition time between [0 119879] and 120579119894represents the phase of the 119894th pulseThe phase 120579119894 is chosen as0 or 120587 in accordance with a pseudorandom binary sequenceMPPSK modulated waveforms are defined as follows

1198920 (119905) = sin 2120587119891119888119905 0 le 119905 lt 119873119879119888

1198921 (119905) =

sin (2120587119891119888119905) 0 le 119905 le (119896 minus 1)119870119879119888minus sin (2120587119891119888119905) (119896 minus 1)119870119879119888 lt 119905 lt 119896119870119879119888sin (2120587119891119888119905) 119870119879119888 le 119905 lt 119873119879119888

1 le 119896 le 119872 minus 1

(8)

with 1198920(119905) and 1198921(119905) being modulation waveforms of symbolldquo0rdquo and ldquo119898(119898 gt 0)rdquo and 119891119888 and 119879119888 represent the carrier


Target (TIR) + KalmanFiltering

The MSE of theestimated TSC

The transmittedpower

PAPR

Target detectionperformance

The EstimatedTSC

constraint condition

Optimizationwaveform

f(t) r(t)

n(t)

Figure 1 The system model of the temporal correlated cognitive transceiver

frequency and the carrier period respectively 119870 and 119873stand for the number of the carrier period in each timeslot and the number of the carrier period in each symbolrespectively 119873119870 means the slot number in each symbol119898 (119898 = 0 1 119872 minus 1) is M-ary (119872 ge 2) source symbolHence increased 119872 leads to higher data rate as more timeslots are utilized The waveforms of 4-PPSK modulation areillustrated as in Figure 2 The coefficient for the 119909-axis is theindex of a certain sample point Set119872 = 4 119870 = 2119873 = 20

Themodulation waveform for symbol ldquo0rdquo is sinusoidal asshown in Figure 2(a) Figure 2(b) illustrates the modulationwaveform for symbol ldquo1rdquo with the phase hopping during thefirst two carrier period (from 0 to 20) the next (from 20 to40) is for symbol ldquo2rdquo in Figure 2(c) and last (from 40 to 60)is for symbol ldquo3rdquo in Figure 2(d)

The MPPSK modulated signal has the capability of highprecise ranging measurement The time hopping scheme forMPPSK waveform has been analyzed in the literature [39]The UWB-MPPSK pulse waveforms are defined by

1198910 (119905) = 1198920 (119905) 119906 (119905) 0 le 119905 lt 119873119879 0 le 119905 le (119898 minus 1)119870119879119888

1198911 (119905) = 1198921 (119905) 119906 (119905) (119898 minus 1)119870119879119888 lt 119905 lt 119898119870119879119888 119870119879119888 le 119905 lt 119873119879119888

1 le 119898 le 119872 minus 1

(9)

with 1198910(119905) and1198911(119905) being modulation waveforms of symbolsldquo0rdquo and ldquo1rdquo UWB-MPPSK waveform communications offerhigh data rates for communications and good immunityagainst multipath fading over short ranges According to theliterature [39] the BER for such a UWB-MPPSK waveform isgiven as

119875119890 = 12 [1 + 1198761 (1198600120575 119906119879120575 ) minus 1198762 ((1 + 119896)1198600120575 119906119879120575 )] (10)

where 1198600 denotes the amplitude of transmitted signal1198761(119886 119887) is Marcumrsquos function which can be defined as fol-lows

1198761 (119886 119887) = 119890minus(1198862+1198872)2 infinsum119896=0

(119886119887)119896119868119896 (119886119887) (11)

32 System Architecture and CRC Waveform Design Wedesign the CRC waveforms by introducing UWB-MPPSKwaveform for communication and radar functionalities inthis paper The proposed phase-coded waveform is transmit-ted to detect target and send the data to other receivers Thereceived signal includes the radar echoes reflected from targetand the communication information from other receiversThe received signal is passed on to a matched filter bankCommunication data is extracted by MPPSK demodulationAnd the radar echo is sent to the target parameter estimationfor target detection The system architecture of the CRCtransceiver is described in Figure 3

UWB-MPPSK waveform design feedback loop is shownin Figure 4

The waveform ensemble consists of individual MPPSK-based UWB waveforms in which the PRI amplitude andphase are dictated by uniformly distributed randomvariablesIt is also assumed that the receiver has full knowledge ofthe transmitted waveform A generalized likelihood ratio test(GLRT) is adopted to detect the presence of the target in aparticular range-Doppler bin The TSC estimation in the fre-quency domain based on the KF is proposed to exploit thistemporal correlation at the receiver The waveform optimiza-tion is modeled to minimize the MSE at the transmitter

The proposed cognitive waveform design feedback loopis summarized as follows

(1) TheCRC transceiver updates TSCby successivemeas-urements of the radar scene


0

20 40 60 80 100 120 140 160 180 2000minus1

01

(a)20 40 60 80 100 120 140 160 180 2000

1

minus101

(b)

20 40 60 80 100 120 140 160 180 2000

2

minus101

(c)20 40 60 80 100 120 140 160 180 2000

3

minus101

(d)

Figure 2 4PPSK modulated waveforms

UWB-MPPSK

CommunicationData

WaveformOptimization Transmitter

Target(TSC)

Kalmanfilter

The MSE ofestimated

TSC

Data Output MPPSKdemodulation

MatchedFilterBank

Targetparameters

Transmittedpower

Targetdetection

performationPAPR

Feedback

CognitiveComposite

SignalConstraintcondition

Receiver

Transmitter

Figure 3 The system architecture of the CRC transceiver

UWB-MPPSKWaveform

ReceiverMatched filter

Range-DopplerProcessing

CR WaveformDesign Loop

Kalmanfilter

TSCestimation

DetectionTransmit

Waveform

Figure 4 Cognitive waveform design feedback loop

(2) The CRC transceiver adapts its UWB-MPPSK wave-form and selects a suitable UWB-MPPSK waveformin the next time instant

(3) The cognitive waveform design feedback loop fromthe receiver to the transmitter allows the delivery ofTSC to the transmitter Transmitter utilizes theTSC to

select the optimal waveform based on Kalman filter-ing for transmission

(4) The process is repeated iteratively

4 KF-Based Waveform Optimization

41 TSC Estimation Based on MAP Criterion In the wide-band cognitive radar system the extended target has acomplex target impulse response (TIR) which is the targetscattering coefficient (TSC) in the frequency domain Ref-erence [13 14] model the extended target as a wide sensestationary-uncorrelated scattering TIR model consideringthe change of target view angle and the strong correlationof TSC during the pluses interval The target scattering ismodeled as a linear system By the Bayesian rule the TSCestimation algorithm based onmaximum a posteriori (MAP)in AWGN channel can be written as

g119896 = argmaxg119896

119901 (g119896 | y119896) = argmaxg119896

119901 (y119896 | g119896) 119901 (g119896)119901 (y119896) (12)


where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612

sdot exp (minus12 (y119896 minus A119896Z119896g119896)119867Rminus1119873 (y119896 minus A119896Z119896g119896))

119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus

12 (g119896)119867Rminus1119879 g119896) 119901 (y119896) = int119901 (y119896 | g119896) 119901 (g119896) 119889g119896

(13)

We can obtain the posterior probability

119901 (g119896 | y119896) = 119901 (y119896 | g119896) 119901 (g119896)119901 (y119896)= exp ((11205902119899) (A119896Z119896g119896)119879 y119896 minus (121205902119899) (A119896Z119896g119896)119879A119896Z119896g119896 minus (12) (g119896)119879Rminus1119879 (g119896))exp((12) ((A119896Z119896)119879 y1198961205902119899)119879 ((11205902119899) (A119896Z119896)119879A119896Z119896 + Rminus1119879 )minus119879 ((A119896Z119896)119879 y1198961205902119899))radic10038161003816100381610038161003816100381610038162120587 ((11205902119899) (A119896Z119896)119879A119896Z119896 + Rminus1119879 )minus11003816100381610038161003816100381610038161003816

(14)

The receivedwaveform y119896 followsGaussian distribution giveny119896 | g119896 sim C119873(A119896Z119896g119896R119873) and 119901(g119896 | y119896) is the probabilitydistribution of TSC during the 119896th pulse So the estimation ofTSC in the frequency domain with MAP estimation is

g119896 = argmaxg119896

minus12g119879119896 ( 11205902119899 (A119896Z119896)119879A119896Z119896 + Rminus1119873) g119896

+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)

The receiver filter can be denoted as the matrix form Q119896

Q119896 = ((A119896Z119896)119879A119896Z119896 + 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 (16)

We have g119896 = Q119896y119896 Now let the transmitted waveforms beS119896 = A119896Z119896 Thus the mean square error (MSE) of MAPestimation can be obtained by

119890119896 = 119864 1003817100381710038171003817g119896 minus g119896100381710038171003817100381722 = E (Q119896y119896 minus g119896) (Q119896y119896 minus g119896)119867

= Q119896 (S119896R119879S119867119896 + R119873)Q119867119896 minusQ119896S119896R119879 minus R119879S119867119896 Q119867119896

+ R119879(17)

42 Waveform Optimization Since the time correlation ofthe TSC a KF-based estimation method is proposed toestimate TSC when the GLRT detection shows the presenceof target in this paper The TSC estimation performancecan be improved by taking the advantage of prediction andestimation at the same timeThe iteration process is describedin Appendix (Algorithm 1)

Considering transmitted power 119864119891 PAPR 120590 and targetdetection probability 120576 constraints the multiple-pulse sam-ples of wideband radar waveform based on Kalman filteringare designed by minimizing the MSE of estimation TSCThe

optimization waveform design problem can be preliminarydescribed as follows

f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)

The objective function is the MSE of estimation TSC basedon Kalman filtering which can be simplified as follows

P119896|119896 = ((P119896|119896minus1)minus1

+ (Q119896A119896Z119896)119867 (Q119896R119873 (Q119896)119867)minus1Q119896A119896Z119896)minus1

= ((P119896|119896minus1)minus1 + (A119896Z119896)119867 (R119873)minus1 A119896Z119896)minus1 (19)

From literature (18) (19) can be rewritten as

z = argminztr(((P119896|119896minus1)minus1 + (A119896Z119896)119867Rminus1119873A119896Z119896)minus1)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0z119867z le 119864119891radic120590119864119891I minus diag f ge 0radic120590119864119891I + diag f ge 0z119867Q119896

119867Rminus1119873 Q119896z ge 1205761015840

(20)

Thefixed value is obtained if z is the eigenvector of Q119896119867Rminus1119873 Q119896

with themaximum eigenvalue [28]Thenwe havemax119901(z) =120582max119864119891 120582max is the maximum eigenvalue of Q119896

119867Rminus1119873 Q119896


Step 1 Set iteration index as 119896 = 1 and the initial MSE matrix of estimation TSCStep 2 Utilizing the temporal correlation of TSC we can get the prediction of TSC

g119896|119896minus1 = 119890minus119879120591g119896minus1|119896minus1Step 3 According to the prediction of TSC the estimation MSE matrix is

P119896|119896minus1 = 119890minus2119879120591P119896minus1|119896minus1 + (1 minus 119890minus2119879120591)R119879Step 4 Define the Kalman gain matrix as

Φ119896 = P119896|119896minus1(Q119896A119896Z119896)119867[(Q119896A119896Z119896)P119896|119896minus1(Q119896A119896Z119896)119867 +Q119896R119873(Q119896)119867]minus1Step 5 The estimation of TSC is

g119896|119896 = g119896|119896minus1 +Φ119896(g119896 minusQ119896A119896Z119896g119896|119896minus1)g119896 = Q119896y119896

where g119896 is the estimated values based on the MAP estimationStep 6 The MSE matrix is

P119896|119896 = P119896|119896minus1 minusΦ119896Q119896A119896Z119896P119896|119896minus1If 119896 = 119870max end Otherwise iterate Step 2 to Step 6

Algorithm 1 Kalman filtering for TSC estimation in CRC system

This optimization problem is convex satisfying the condition120582max119864119891 ge 1205761015840 If rank(ff119867) = 1 f0 is the optimal radar wave-form According to [30] the optimal signal waveform withrank(ff119867) gt 1 can be obtained viaCVX toolbox In each itera-tion determining whether the feasible set is empty can beevaluated by solving a feasibility problem using the CVXtoolbox

The MPPSK modulated CR waveform design algorithmcan be summarized as follows

(1) The MPPSK modulated CR waveform embedded thecommunication data is transmitted

(2) The radar echoes y119896 are used to estimate the MSEmatrix of the TSC P119896|119896 which are updated using thecurrent radar echoes and are relayed back to the Kal-man filtering

(3) The received communication signals are passedthrough a matched filter bank which demodulatesMPPSK modulated waveform

5 Simulation Results and Discussion

Firstly we set theMPPSKmodulation parameter119872 le 3119873 =10 119870 = 5 make sure that the cross-correlation coefficientbetween the transmission waveforms Δ le 04 In this waywe can obtain an acceptable BER for communications [39]As described in the previous sections the orthogonalitybetween CRC transmission waveforms is maintained forradar waveform optimization purposes

Next the received signal is matched filtered to estimatethe propagation delay The communication data are demod-ulated and the radar signal processing is carried out by theTSC estimation module separately The MSE matrix of theTSC is estimated by using Kalman filtering in the subsequenttime interval We use the normalized MSE to defining theestimation performance

119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)

Table 1 Simulation parameters 2

119864119904 Transmitted power 1ASNR Average signal noise ratio 8 dB120591 Temporal correlation 01 s119872119905 Pulse interval 1ms119901fa False alarm probability 005119901119889 Detection probability 095PAPR Peak to average power ratio 3 dB119891119904 The sampling frequency 10GHz119891119888 Center frequency of UWB 3GHz

where g and g denote the estimation TSC and the real mea-surement data respectively The simulation parameters areshown in Table 1

Figure 5 shows the detection probability based on theNeyman-Pearson criterion for false alarm probability 119901fa =5 For a stationary radar scene 800 simulations have beenrun for each SNRThe next CRC waveform is chosen accord-ing to the Kalman filtering algorithm and the process isrepeated for 20 iterations As seen from Figure 4 the pro-posed algorithm converges after 10 iterations yielding adetection probability of 09 at SNR = 6 dB as compared toSNR= 15 dB at the first iterationHowever the detection prob-ability does not show further improvement after 15 iterations

In Figure 6 we compare the detection probability foroptimization waveforms selected by the proposed algorithmto the probability for waveform based on MI minimizationand compare this result with the random waveform inmultipath environments As the proposed algorithm utilizesthe temporal correlation of TIR during the pulses interval theCRC transceiver adapts its radar signal better than waveformbased MI minimization to the fluctuating target RCS On theother hand random waveform is unable to match the time-varying TSC after multiple iterations Hence the detectionprobability is suboptimal in this case

In Figure 7 under the constraint of transmitted powerand ASNR we compare the TSC estimation performance


0

01

02

03

04

05

06

07

08

09

1

Pd

0 5 10 15minus5SNR (dB)

Iteration 20Iteration 15Iteration 10

Iteration 5Iteration 1

Figure 5 Detection probability for various iterations of the Kalmanfiltering approach

Mutual-information approachKalman filtering approachStatic assignment

0 105 15minus10minus15 minus5SNR (dB)

0

01

02

03

04

05

06

07

08

09

1

Pd

Figure 6 Detection probability for optimization waveforms basedon Kalman filtering approach and random waveform

based on the Kalman filtering algorithm andMAP estimationcriterion in multipath environments As seen from Figure 7the normalizedMSE of TSC estimation based on the Kalmanfiltering algorithm is smaller than that using the MAPcriterion Similarly the normalized MSE of TSC estimationregarding clutter based on Kalman filtering is smaller thanthat regardless clutter In Figure 8 under the constraints oftransmitted power PAPR ASNR and detection probabilitywe also compare the normalized MSE of TSC estimationbased on the Kalman filtering algorithm andMAP estimationcriterion The TSC estimation performances of optimization

Random signal based on MAP estimationRandom signal based on Kalman FilteringOptimal signal regardless clutter based on Kalman filteringOptimal signal regarding clutter based on Kalman filtering

10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE

0 10 155Iteration Index

Figure 7 The MSE of TSC estimation under power and SNR

Random signal based on MAP estimationOptimal signal regardless clutter based on Kalman filteringRandom signal based on Kalman FilteringOptimal signal regarding clutter based on Kalman filtering

0 10 15 205Iteration Index

05

1

15

2N

orm

lized

MSE

Figure 8 The MSE of TSC estimation under power SNR PAPRand detection constraint

waveform and random waveform are compared to verify theefficiency of optimizing waveform at each Kalman filteringiteration step

We discuss the performance of the UWB-MPPSK wave-form from a communications perspective in this subsectionFigure 9 illustrates the BER for the UWB-MPPSK waveformsand UWB-OFDM waveforms

As seen from Figure 9 the SNR performance of BinaryUWB-MPPSK signal may be improved by approximately1 dB 4 dB and 8 dB as compared with Binary UWB-PPM4-ary UWB-MPPSK and 16-ary UWB-MPPSK respectivelyOFDM signals offer better bit error performance Howeverthe MPPSK design performs comparably to OFDM schemeswhen no data redundancy bit for error control is added

From (9) the data rate ofMPPSK signal is proportional tocarrier frequency andmodulation parameter119872 but inversely


0 93 6 82 5 101 4 7SNR (dB)

UWB-OFDMBinary UWB-MPPSKBinary UWB-PPM

4-ary UWB-MPPSK16-ary UWB-MPPSK

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER

Figure 9 Comparative SER results of UWB-OFDM Binary UWB-MPPSK 4-ary UWB-MPPSK and 16-ary UWB-MPPSK

proportional to modulation parameter 119873 Setting modula-tion parameter 119873 = 10119872 = 4 down-conversion IF =100MHz and duty cycle of the pulse signal 119879 = 110 pulsewidth is 120591 = 20 120583sWe can obtain burst transmission data rate2 lowast 10010 lowast 110 = 2Mbps

Figure 10 presents the throughput result for the proposedwaveform as compared to OFDM waveform 4-ary PPSKwaveform offers a burst transmission data rate of about18Mbps at a distance of 15mwhich is better than that offeredby the four-carrier OFDM UWB communications achievehigh data rate over short distances as the distance betweenthe transceivers increases the throughput falls According tothe relational expression

Data volume of a beam

= Bit rate times Pulse width times Pulse number (22)

Since the MPPSK-based CRC transceiver transmits 20pulses within a radar beam we can obtain burst transmissiondata volume 20 lowast 400010 = 8 kB However as modulationparameter119872 is increased the sidelobes in the autocorrelationplot become more prominent This distorts the orthogonal-ity of the MPPSK waveform and in turn may deterioratethe target detection performance So we choose reasonableMPPSK modulation parameters results in a tradeoff betweencommunication and radar signal design requirements

6 Conclusion

In this paper a waveform design concept for a CRC tran-sceiver system has been studied that allow for simultane-ous wireless communications and radar operation A newUWB-MPPSKmodulation scheme is proposed for integrated

30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)

4-ary PPSKBinary PPSKOFDM

Figure 10 Comparative throughput performance of UWB-OFDMBinary UWB-MPPSK and 4-ary UWB-MPPSK

waveformdesignTheKalmanfiltering-basedwaveformopti-mization approach is addressed for improving the target esti-mation performance The proposed approach is based uponlearning about the detection environment and adjusting thetransmission waveform characteristics to suit the dynamictarget scene The implementation has been shown to offermany advantages regarding the performance of the radarapplication in particular better TSC estimation performanceand independence from the transmitted user data Theproposed method also facilitates high data rate performancefor the communications applicationThe discussedwaveformdesign concepts offer interesting perspectives for the real-ization of future sensor devices in intelligent transportationsystem

Appendix

Kalman Filtering for TSC Estimation inCRC System

The KF-based TSC estimation in the frequency domain hasbeen discussed The estimation performance is improved byexploiting the temporal correlation of TSC Compared withthe convolution operation in the time domain the complexityof waveform design for TSC estimation in the frequency isreduced (see Algorithm 1)

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (61761019)


References

[1] D W Bliss ldquoCooperative radar and communications signalingthe estimation and information theory odd couplerdquo in Proceed-ings of the 2014 IEEE Radar Conference RadarCon 2014 pp 50ndash55 Cincinnatim Ohio USA 2014

[2] J R Guerci R M Guerci A Lackpour and D MoskowitzldquoJoint design and operation of shared spectrum access for radarand communicationsrdquo in Proceedings of the 2015 IEEE Inter-national Radar Conference RadarCon 2015 pp 761ndash766 USAMay 2015

[3] A R Chiriyath B Paul G M Jacyna and D W Bliss ldquoInnerbounds on performance of radar and communications co-existencerdquo IEEE Transactions on Signal Processing vol 64 no2 pp 464ndash474 2016

[4] A R Chiriyath B Paul and DW Bliss ldquoJoint radar-communi-cations information bounds with clutter The phase noise me-nacerdquo in Proceedings of the 2016 IEEE Radar ConferenceRadarConf 2016 USA May 2016

[5] J S Kwak and J H Lee ldquoInfrared Transmission for Intervehi-cle Ranging and Vehicle-to-roadside Communication SystemsUsing Spread-SpectrumTechniquerdquo IEEETransactions on Intel-ligent Transportation Systems vol 5 no 1 pp 12ndash19 2004

[6] A Hassanien M G Amin Y D Zhang and F Ahmad ldquoDual-function radar-communications information embedding usingsidelobe control and waveform diversityrdquo IEEE Transactions onSignal Processing vol 64 no 8 pp 2168ndash2181 2016

[7] L Han and K Wu ldquo24-GHz integrated radio and radar systemcapable of time-agile wireless communication and sensingrdquoIEEETransactions onMicrowaveTheory and Techniques vol 60no 3 pp 619ndash631 2012

[8] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challenges andopportunitiesrdquo IEEE Journal on Selected Areas in Communica-tions vol 32 no 9 pp 1637ndash1652 2014

[9] H Takase and M Shinriki ldquoA dual-use radar and communi-cation systemwith complete complementary codesrdquo inProceed-ings of the 2014 15th International Radar Symposium IRS 2014Poland June 2014

[10] D Ciuonzo A De Maio G Foglia and M Piezzo ldquoIntrapulseradar-embedded communications via multiobjective optimiza-tionrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 51 no 4 pp 2960ndash2974 2015

[11] Y L Sit and T Zwick ldquoMIMO OFDM radar with communica-tion and interference cancellation featuresrdquo in Proceedings of the2014 IEEERadarConference RadarCon 2014 pp 265ndash268USAMay 2014

[12] C Sturm T Zwick and W Wiesbeck ldquoAn OFDM system con-cept for joint radar and communications operationsrdquo in Pro-ceedings of the VTC Spring 2009 - IEEE 69th Vehicular Technol-ogy Conference 2009

[13] S Sen ldquoPAPR-constrained pareto-optimal waveform designfor OFDM-STAP Radarrdquo IEEE Transactions on Geoscience andRemote Sensing vol 52 no 6 pp 3658ndash3669 2014

[14] A Cailean B Cagneau L Chassagne S Topsu Y Alayli andJ-M Blosseville ldquoVisible light communications Application tocooperation between vehicles and road infrastructuresrdquo inProceedings of the 2012 IEEE Intelligent Vehicles Symposium IV2012 pp 1055ndash1059 Spain June 2012

[15] Y Nijsure Y Chen S Boussakta C Yuen Y H Chew andZ Ding ldquoNovel system architecture and waveform design for

cognitive radar radio networksrdquo IEEE Transactions onVehicularTechnology vol 61 no 8 pp 3630ndash3642 2012

[16] Y-S Shen F-B Ueng J-D Chen and S-T Huang ldquoA perfor-mance analysis of the high-capacity TH multiple access UWBsystem using PPMrdquo in Proceedings of the 2009 IEEE 20th Per-sonal Indoor and Mobile Radio Communications SymposiumPIMRC 2009 Japan September 2009

[17] N V Kokkalis P T Mathiopoulos G K Karagiannidis and CS Koukourlis ldquoPerformance analysis of M-ary PPM TH-UWBsystems in the presence of MUI and timing jitterrdquo IEEE Journalon Selected Areas in Communications vol 24 no 4 I pp 822ndash828 2006

[18] X Gong H Meng Y Wei and X Wang ldquoPhase-modulatedwaveform design for extended target detection in the presenceof clutterrdquo Sensors vol 11 no 7 pp 7162ndash7177 2011

[19] S Haykin ldquoCognitive radarrdquo IEEE Signal Processing Magazinevol 23 no 1 pp 30ndash40 2006

[20] Y Chen and P Rapajic ldquoUltra-wideband cognitive interrogatornetwork Adaptive illumination with active sensors for targetlocalisationrdquo IET Communications vol 4 no 5 pp 573ndash5842010

[21] X Deng C Qiu Z Cao M Morelande and B Moran ldquoWave-formdesign for enhanced detection of extended target in signal-dependent interferencerdquo IET Radar Sonar amp Navigation vol 6no 1 pp 30ndash38 2012

[22] P Chen and L Wu ldquoWaveform design for multiple extendedtargets in temporally correlated cognitive radar systemrdquo IETRadar Sonar amp Navigation vol 10 no 2 pp 398ndash410 2016

[23] S Sen and C W Glover ldquoOptimal multicarrier phase-codedwaveform design for detection of extended targetsrdquo in Proceed-ings of the IEEE Radar Conference pp 1ndash6 Ottawa CanadaApril-May 2013

[24] X Zhang and C Cui ldquoRange-spread target detecting for cogni-tive radar based on track-before-detectrdquo International Journalof Electronics vol 101 no 1 pp 74ndash87 2014

[25] L K Patton S W Frost and B D Rigling ldquoEfficient design ofradarwaveforms for optimised detection in colourednoiserdquo IETRadar Sonar amp Navigation vol 6 no 1 pp 21ndash29 2012

[26] S Sen ldquoCharacterizations of PAPR-constrained radar wave-forms for optimal target detectionrdquo IEEE Sensors Journal vol14 no 5 pp 1647ndash1654 2014

[27] R A Romero andNAGoodman ldquoWaveformdesign in signal-dependent interference and application to target recognitionwith multiple transmissionsrdquo IET Radar Sonar amp Navigationvol 3 no 4 pp 328ndash340 2009

[28] S CThompson and J P Stralka ldquoConstant envelope OFDM forpower-efficient radar and data communicationsrdquo in Proceedingsof the 2009 International Waveform Diversity and Design Con-ference WDD 2009 pp 291ndash295 USA February 2009

[29] Y Nijsure Y Chen P Rapajic C Yuen Y H Chew and TF Qin ldquoInformation-theoretic algorithm for waveform opti-mization within ultra wideband cognitive radar networkrdquo inProceedings of the 2010 IEEE International Conference on Ultra-Wideband ICUWB2010 pp 595ndash598 China September 2010

[30] N A Goodman P R Venkata and M A Neifeld ldquoAdaptivewaveform design and sequential hypothesis testing for targetrecognition with active sensorsrdquo IEEE Journal of Selected Topicsin Signal Processing vol 1 no 1 pp 105ndash113 2007

[31] M Fan D Liao X Ding and X Li ldquoWaveform design for targetrecognition on the background of clutterrdquo in Proceedings of the8th European Radar Conference EuRAD 2011 Held as Part of the


14th European Microwave Week 2011 EuMW 2011 pp 329ndash332gbr October 2011

[32] F Z Dai H W Liu P H Wang and S Z Xia ldquoAdaptive wave-form design for range-spread target trackingrdquo IEEE ElectronicsLetters vol 46 no 11 pp 793-794 2010

[33] B Jiu H Liu L Zhang YWang and T Luo ldquoWideband cogni-tive radar waveform optimization for joint target radar sig-nature estimation and target detectionrdquo IEEE Transactions onAerospace and Electronic Systems vol 51 no 2 pp 1530ndash15462015

[34] A Leshem O Naparstek and A Nehorai ldquoInformation the-oretic adaptive radar waveform design for multiple extendedtargetsrdquo IEEE Journal of Selected Topics in Signal Processing vol1 no 1 pp 42ndash55 2007

[35] X Zhang C Cui and J Yu ldquoMultiple extended targets trackingfor cognitive radar in the presence of signal-dependent clutterrdquoJournal of Circuits and Systems vol 18 no 2 pp 492ndash499 2013

[36] S Sen and A Nehorai ldquoOFDM-MIMO Radar With Mutual-Information Waveform Design for Low-Grazing Angle Track-ingrdquo IEEE Transactions on Signal Processing vol 58 no 6 pp3152ndash3162 2010

[37] T Huang and T Zhao ldquoLow PMEPR OFDM radar waveformdesign using the iterative least squares algorithmrdquo IEEE SignalProcessing Letters vol 22 no 11 pp 1975ndash1979 2015

[38] B Li andA Petropulu ldquoMIMOradar and communication spec-trum sharing with clutter mitigationrdquo in Proceedings of the 2016IEEE Radar Conference RadarConf 2016 USA May 2016

[39] C Lu L Wu P Chen J Wang and H Liu ldquoM-ary phase posi-tion shift keying with orthogonal signallingrdquo IET Communica-tions vol 9 no 13 pp 1627ndash1634 2015

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Submit your manuscripts atwwwhindawicom


between transmit and receive antennas can be perfectly set-tled For the communication applications however the datarate will decrease because the radar duty ratio is 10 in somecases that is the operation time of communication becomes10 of what it was

These works have adopted OFDM techniques fused withultra-wideband (UWB) technologies to realize the communi-cation-radar integration However these designs create otherimplementation issues such as excessive demand of signalprocessing power high-speed analog-to-digital circuitry andagile radio frequency front end for multimode operationFurthermore systems employing UWB-OFDM for localiza-tion [13 14] utilize the same waveform family for design-ing joint communication-radar signals Consequently thesemethods share a common drawback due to the fact that theautocorrelation of UWB-OFDM signals depend on both thelocation of the notch and the OFDM signal bandwidthHence although the radar target range estimation is unaf-fected by the presence of anOFDMsignal its range resolutiondepends on the notch bandwidth into which the OFDM sig-nal is embedded Literature [15] presents the system employ-ing UWB pulse position modulation (PPM) for designingjoint communication-radar signals Compared to the con-ventional OFDM system the system bit error rate (BER) per-formance is poor relatively [16 17]

Cognitive radar (CR) system can adjust its transmit wave-form and receive filter adaptively based on the prior knowl-edge of targets and the environment and thus has great poten-tial in enhancing the detection and recognition performancefor extended targets [18] In CR [19] cognition plays a criticalrole in the feedback loop which includes long-termmemoryfor example geographicmap and elevationmodel and short-term memory developed by the receiver online By usingprior information the work mode transmit waveform andsignal processing approach of CR can be optimized to yieldbetter performance

Thewideband cognitive radar is not sensitive to active andpassive interference [20] It is very important in intelligenttransmitting In the wideband cognitive radar system theextended target has a complex target impulse response (TIR)[21] which is the target scattering coefficient (TSC) in thefrequency domain [22]The estimation of TSC has gotten lotsof attention in the recent research of radar system [23ndash25]Literature [23] models the extended target as TIR functionunchanged in the waveform design Reference [26] modelsthe extended target as a wide sense stationary-uncorrelatedscattering TIR model considering the change of target viewangle and the strong correlation of TSC during the plusesinterval The interference might be comprised of clutter andnoise Clutter such as unwanted ground returns and environ-ment clutter is assumed to be signal dependent and noise issignal independent too [27] The radar reflection character-istics of the surrounding environment are regarded as timeinvariant

Constant-envelope in cognitive waveform design is dis-cussed to get high power efficiency Literature [28] presentsOFDM optimization waveform design method under theconstant-envelope constraint But constant-envelope condi-tion is too strict in OFDM waveform design Peak to average

power ratio (PAPR) is presented as relaxation form and theOFDM radar system under the PAPR constraint has beensufficiently studied [12] If transmitted signal power is verysmall the estimation precision may degrade violently andthe power spectral density (PSD) of the target TIR cannot beestimated This is the primary reason why the algorithms in[29] cannot be used directly in CR waveform design In orderto solve this problem the performance of the TSC estimationshould be considered in the CR transmission waveformA new CR waveform design algorithm for both estimationand detection is studied In a relative long time the priorknowledge of the clutter is presented inwaveformdesign [30]In a pulse duration time it can be approximately regarded astime invariant in [31] However the TIR varies gradually inpractice TSC is varying with the relative motion between theradar and the target So the TSC estimation update is neededas a feedback

An iteration approach based on the Kalman filtering (KF)is proposed by Dai et al in [32] to estimate the TIR for singletarget And the transmitted waveform is optimized in orderto improve the estimation performances [33] However thedirect optimization problem of waveform design in the tem-poral correlated cognitive radar system (CRS) is nonconvexand cannot be solved efficiently Considering multiple targetscenarios [34 35] presented a multiple-waveform designalgorithm that is based on maximizing a weighted sum ofmutual information measures corresponding to the activetargets and radar waveforms employed The related work ondesigning estimation waveforms for multiple input multipleoutput (MIMO) radar systems is proposed in [36ndash38] whichdiscuss the equivalence between maximizing mutual infor-mation and minimizing the mean square estimation error(MSE) Therefore to our best knowledge only an indirectapproach based on the water-filling method is expressed tooptimize the PSD of transmitted waveform for single target[13] No existing work has considered the direct waveformoptimization for multiple extended targets in the temporalcorrelation CRS

12 Contributions In this paper we combine the temporalcorrelated cognitive algorithm presented in [22] and M-ary position phase shift keying (MPPSK) technique [26] toobtain an optimizationwaveformwhich offers superior radarperformance and high data rate communication capabilitybetween cognitive radar-communication (CRC) transceiversWith this method the radar and communication signalscan coexist by sharing the same frequency band Hencethe target parameter estimation is not affected by the com-munication signal design parameters The UWB-MPPSKwaveforms would not only benefit from a KF approach fortarget estimation and detection but also establish ad hoccommunication links The main contributions of this paperare summarized as follows

(1) We present a novelMPPSK-based radar-communica-tion waveform design scheme

(2) We propose a cognitive radar probing strategy basedon Kalman filtering between successive backscatterpulses for TSC estimation






119903 (119905) = 119902 (119905) lowast 119891 (119905) + 119899 (119905) (1)



r119896 = A diag q119896 f119896 + n

= AQ119896f119896 + n (2)


y119896 ≜ Γr119896 (3)


y119896 = AZ119896g119896 + w (4)








3 Waveform Design


119906 (119905) = 119868sum119894=1

119886119894 [1 minus 4120587(119905 minus 120572119894119879119879119901 )2]



1198920 (119905) = sin 2120587119891119888119905 0 le 119905 lt 119873119879119888

1198921 (119905) =


1 le 119896 le 119872 minus 1

(8)






PAPR


The EstimatedTSC



f(t) r(t)

n(t)





1198910 (119905) = 1198920 (119905) 119906 (119905) 0 le 119905 lt 119873119879 0 le 119905 le (119898 minus 1)119870119879119888

1198911 (119905) = 1198921 (119905) 119906 (119905) (119898 minus 1)119870119879119888 lt 119905 lt 119898119870119879119888 119870119879119888 le 119905 lt 119873119879119888

1 le 119898 le 119872 minus 1

(9)


119875119890 = 12 [1 + 1198761 (1198600120575 119906119879120575 ) minus 1198762 ((1 + 119896)1198600120575 119906119879120575 )] (10)


1198761 (119886 119887) = 119890minus(1198862+1198872)2 infinsum119896=0

(119886119887)119896119868119896 (119886119887) (11)







0

20 40 60 80 100 120 140 160 180 2000minus1

01

(a)20 40 60 80 100 120 140 160 180 2000

1

minus101

(b)

20 40 60 80 100 120 140 160 180 2000

2

minus101

(c)20 40 60 80 100 120 140 160 180 2000

3

minus101

(d)


UWB-MPPSK

CommunicationData


Target(TSC)

Kalmanfilter

The MSE ofestimated

TSC


MatchedFilterBank

Targetparameters

Transmittedpower

Targetdetection

performationPAPR

Feedback

CognitiveComposite


Receiver

Transmitter


UWB-MPPSKWaveform




Kalmanfilter

TSCestimation

DetectionTransmit

Waveform








g119896 = argmaxg119896

119901 (g119896 | y119896) = argmaxg119896

119901 (y119896 | g119896) 119901 (g119896)119901 (y119896) (12)


where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612


119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus


(13)



(14)


g119896 = argmaxg119896


+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)






+ R119879(17)




f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)


P119896|119896 = ((P119896|119896minus1)minus1





st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1


119867Rminus1119873 Q119896z ge 1205761015840

(20)



119867Rminus1119873 Q119896


















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







119903 (119905) = 119902 (119905) lowast 119891 (119905) + 119899 (119905) (1)



r119896 = A diag q119896 f119896 + n

= AQ119896f119896 + n (2)


y119896 ≜ Γr119896 (3)


y119896 = AZ119896g119896 + w (4)








3 Waveform Design


119906 (119905) = 119868sum119894=1

119886119894 [1 minus 4120587(119905 minus 120572119894119879119879119901 )2]



1198920 (119905) = sin 2120587119891119888119905 0 le 119905 lt 119873119879119888

1198921 (119905) =


1 le 119896 le 119872 minus 1

(8)






PAPR


The EstimatedTSC



f(t) r(t)

n(t)





1198910 (119905) = 1198920 (119905) 119906 (119905) 0 le 119905 lt 119873119879 0 le 119905 le (119898 minus 1)119870119879119888

1198911 (119905) = 1198921 (119905) 119906 (119905) (119898 minus 1)119870119879119888 lt 119905 lt 119898119870119879119888 119870119879119888 le 119905 lt 119873119879119888

1 le 119898 le 119872 minus 1

(9)


119875119890 = 12 [1 + 1198761 (1198600120575 119906119879120575 ) minus 1198762 ((1 + 119896)1198600120575 119906119879120575 )] (10)


1198761 (119886 119887) = 119890minus(1198862+1198872)2 infinsum119896=0

(119886119887)119896119868119896 (119886119887) (11)







0

20 40 60 80 100 120 140 160 180 2000minus1

01

(a)20 40 60 80 100 120 140 160 180 2000

1

minus101

(b)

20 40 60 80 100 120 140 160 180 2000

2

minus101

(c)20 40 60 80 100 120 140 160 180 2000

3

minus101

(d)


UWB-MPPSK

CommunicationData


Target(TSC)

Kalmanfilter

The MSE ofestimated

TSC


MatchedFilterBank

Targetparameters

Transmittedpower

Targetdetection

performationPAPR

Feedback

CognitiveComposite


Receiver

Transmitter


UWB-MPPSKWaveform




Kalmanfilter

TSCestimation

DetectionTransmit

Waveform








g119896 = argmaxg119896

119901 (g119896 | y119896) = argmaxg119896

119901 (y119896 | g119896) 119901 (g119896)119901 (y119896) (12)


where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612


119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus


(13)



(14)


g119896 = argmaxg119896


+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)






+ R119879(17)




f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)


P119896|119896 = ((P119896|119896minus1)minus1





st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1


119867Rminus1119873 Q119896z ge 1205761015840

(20)



119867Rminus1119873 Q119896


















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






PAPR


The EstimatedTSC



f(t) r(t)

n(t)





1198910 (119905) = 1198920 (119905) 119906 (119905) 0 le 119905 lt 119873119879 0 le 119905 le (119898 minus 1)119870119879119888

1198911 (119905) = 1198921 (119905) 119906 (119905) (119898 minus 1)119870119879119888 lt 119905 lt 119898119870119879119888 119870119879119888 le 119905 lt 119873119879119888

1 le 119898 le 119872 minus 1

(9)


119875119890 = 12 [1 + 1198761 (1198600120575 119906119879120575 ) minus 1198762 ((1 + 119896)1198600120575 119906119879120575 )] (10)


1198761 (119886 119887) = 119890minus(1198862+1198872)2 infinsum119896=0

(119886119887)119896119868119896 (119886119887) (11)







0

20 40 60 80 100 120 140 160 180 2000minus1

01

(a)20 40 60 80 100 120 140 160 180 2000

1

minus101

(b)

20 40 60 80 100 120 140 160 180 2000

2

minus101

(c)20 40 60 80 100 120 140 160 180 2000

3

minus101

(d)


UWB-MPPSK

CommunicationData


Target(TSC)

Kalmanfilter

The MSE ofestimated

TSC


MatchedFilterBank

Targetparameters

Transmittedpower

Targetdetection

performationPAPR

Feedback

CognitiveComposite


Receiver

Transmitter


UWB-MPPSKWaveform




Kalmanfilter

TSCestimation

DetectionTransmit

Waveform








g119896 = argmaxg119896

119901 (g119896 | y119896) = argmaxg119896

119901 (y119896 | g119896) 119901 (g119896)119901 (y119896) (12)


where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612


119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus


(13)



(14)


g119896 = argmaxg119896


+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)






+ R119879(17)




f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)


P119896|119896 = ((P119896|119896minus1)minus1





st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1


119867Rminus1119873 Q119896z ge 1205761015840

(20)



119867Rminus1119873 Q119896


















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

20 40 60 80 100 120 140 160 180 2000minus1

01

(a)20 40 60 80 100 120 140 160 180 2000

1

minus101

(b)

20 40 60 80 100 120 140 160 180 2000

2

minus101

(c)20 40 60 80 100 120 140 160 180 2000

3

minus101

(d)


UWB-MPPSK

CommunicationData


Target(TSC)

Kalmanfilter

The MSE ofestimated

TSC


MatchedFilterBank

Targetparameters

Transmittedpower

Targetdetection

performationPAPR

Feedback

CognitiveComposite


Receiver

Transmitter


UWB-MPPSKWaveform




Kalmanfilter

TSCestimation

DetectionTransmit

Waveform








g119896 = argmaxg119896

119901 (g119896 | y119896) = argmaxg119896

119901 (y119896 | g119896) 119901 (g119896)119901 (y119896) (12)


where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612


119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus


(13)



(14)


g119896 = argmaxg119896


+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)






+ R119879(17)




f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)


P119896|119896 = ((P119896|119896minus1)minus1





st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1


119867Rminus1119873 Q119896z ge 1205761015840

(20)



119867Rminus1119873 Q119896


















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



where

119901 (y119896 | g119896) = 1(2120587)1198722 1003816100381610038161003816R119873100381610038161003816100381612


119901 (g119896) = 1(2120587)1198722 1003816100381610038161003816R119879100381610038161003816100381612 exp (minus


(13)



(14)


g119896 = argmaxg119896


+ 11205902119899 (A119896Z119896g119896)119879 y119896 = ((A119896Z119896)119879A119896Z119896

+ 1205902119899Rminus1119873 )minus1 (A119896Z119896)119879 y119896

(15)






+ R119879(17)




f = argminftr (P119896|119896)

st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1

119875119899 (120596119896) ge 0f119867f le 119864119891PAPR le 120577119875119863 ge 120576

(18)


P119896|119896 = ((P119896|119896minus1)minus1





st119870sum119896=1

119875119902 (120596119896) 119875119891 (120596119896) minus 119870sum119896=1


119867Rminus1119873 Q119896z ge 1205761015840

(20)



119867Rminus1119873 Q119896


















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















119899MSE = 1003817100381710038171003817g minus g1003817100381710038171003817221003817100381710038171003817g100381710038171003817100381722 (21)








0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

01

02

03

04

05

06

07

08

09

1

Pd







0

01

02

03

04

05

06

07

08

09

1

Pd




10minus3

10minus2

10minus1

100

Nor

mliz

ed M

SE





05

1

15

2N

orm

lized

MSE







0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 93 6 82 5 101 4 7SNR (dB)



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

BER







6 Conclusion


30 600 5010 20 40Distance (m)

002040608

112141618

2

Thro

ughp

ut (M

bps)




Appendix





Acknowledgments



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Cognitive Waveform Design for Radar-Communication