Performance Trade-off for Integrated Communication and Data-Assisted Positioning in MIMO-OFDM System

Lincong Han,Rongke Liu,2,*,Zijie Wang,Qirui Liu,Qian Zhu,John S.Thompson

1 School of Electronic and Information Engineering,Beihang University,Beijing 100191,China

2 Shenzhen Institution of Beihang University,Shenzhen 518063,China

3 Institute for Digital Communications,School of Engineering,University of Edinburgh,King’s Buildings,Edinburgh,EH9 3JL,U.K.

Abstract: Communication and positioning,the two pillars of mobile communication systems,are currently being integrated together.The development of communication technologies is the driving force of the positioning progress.In turn,the location information provided by positioning improves the communication performance in various ways.However,the competition of these two functions in terms of resource allocation is a critical issue hindering their integration.In this article,we investigate the trade-off for the integrated communication and data-assisted positioning in multiple-input multiple-output orthogonal frequency division multiplexing systems.A data-assisted positioning method is designed first,which uses both positioning reference signals(PRSs)and data signals for positioning.The positioning and communication performance are theoretically evaluated respectively,then combined to obtain an integrated performance metric.The trade-off is analyzed and the integrated performance is optimized considering the priority of different functions.Numerical simulations show that the data-assisted positioning can not only improve the positioning accuracy,but also reduce the PRS overhead.And the established integrated performance metric can identify the optimal performance and the corresponding resource allocation schemes.

Keywords: integrated communication and positioning;MIMO;OFDM;non-data aided;CRLB;MMSE

I.INTRODUCTION

With the global promotion and commercialization of the fifth generation(5G)wireless communication system,the development of beyond 5G and future sixth generation(6G)is inexorable[1].Abundant use cases have sprung up,which require improvements in the performance of various network functions.Among them,communication and positioning are two essential ones [2].From the first generation to 5G,wireless positioning embedded in communication networks continues to develop relying on the the progress of communication technologies [3].The capability of positioning in turn rewards the favor of communication by providing accurate directions to assist the beam alignment,pilot contamination avoidance,etc.[4,5].Communication and positioning are forming a virtuous circle of mutual benefit,with a continuous trend towards integrated communication and positioning.Multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM)play an important role in this process as they can not only be beneficial to promote communication capacity and mitigate multipath fading,but also have positive effects on positioning [6].The large antenna arrays of MIMO provide high angular resolution,thus improving the estimation accuracy of angle-of-departure(AoD) and angle-of-arrival (AoA) [7].The OFDM waveform permits a relatively simple synchronization procedure[8].These advantages make MIMO-OFDM system an appropriate technology for integrated communication and positioning.

However,despite of the synergetic effect of positioning and communication,there exists competition between them in wireless resource consumption (involving various domains,such as time,frequency,power,and space).Several researches have concentrated on the performance trade-off between communication and positioning w.r.t.the resource allocations.The authors in [9]study the trade-off between datarate and positioning efficiency by proposing a power allocation strategy in 5G millimeter-wave (mmWave)small cell networks.R.Koiralaet al.investigate the trade-off between positioning accuracy and throughput in multi-user multi-carrier mmWave MIMO systems [10].In [11],the effect of node selection on the trade-off between energy efficiency and positioning accuracy is studied.The time resource allocation is optimized in a single-user scenario[12]and a multiuser scenario [13],respectively.Although the contributions above mitigate the impact of resource competition,there remains two deficiencies.On the one hand,they fail to consider the assistance of communication to positioning.The relationship of them is assumed to be pure competition.On the other hand,the performance metrics of these two functions are separated,so the comparison of their performance is unable to be operated under a unified metric framework.

To consider the assistance of communication to positioning,an optional method initially for channel estimation can be used for positioning,which is called the non-data aided (NDA) approach.NDA is capable of extracting channel and positioning information from unknown communication data signals [14,15].This method is termed data-based positioning in this paper.This is different from current PRS-based positioning which uses dedicated PRSs.In this way,positioning can be realized without extra PRS overhead and the communication quality can be guaranteed in the meantime.S.Monfaredet al.apply data-based positioning in IoT sensor networks and show that it outperforms PRS-based positioning considering a much larger volume of communication signals than preambles [16].However,this research only considers the AoA estimation and the system is Bluetooth Low Energy.Besides,communication analysis is not covered.The more important thing is that the data-based positioning can be combined with the PRS-based positioning,which is termed data-assisted positioning,so that all the signal resource can be used.To the best of our knowledge,the data-assisted positioning requires further research.

As for the lack of unified performance metric for trade-off,recently,some researchers have tried to overcome this,which can be categorized into three kinds [17].First,converting the positioning performance into the equivalent information rate.Hence the trade-off can be examined using the communication evaluation systems [18].Second,the communication performance metrics such as mutual information and spectrum efficiency,are equated to the minimum mean squared error (MMSE).So the trade-off can be studied under the estimation-theoretic framework[19,20].The third category regards the positioning metric,distortion,as a constraint on the communication metric,capacity[21].There remains some questions.For the first category,practically,the number of positioning performance metrics (e.g.the rang/direction/orientation/velocity of single/multiple user equipments(UEs)and base stations(BSs))is much larger than the number of metrics used for communication.The attempts of the second kind are preliminary since the channel model is scalar,which is not suitable for MIMOOFDM systems.The third kind also has the shortage of failing to cover many important scenarios.

As a result,although the trade-off is significant to integrated communication and positioning,the assistance of communication to positioning,as well as the unified performance metrics in MIMO-OFDM systems have remained absent so far.

In this article,we establish the integrated communication and data-assisted positioning system in a MIMO-OFDM system.A data-assisted positioning method which combines PRS-based positioning and data-based positioning is proposed.The comparison of these three kinds is conducted in terms of position error bound(PEB)and rotation error bound(REB)to show the superior performance of the data-assisted positioning.The communication performance is quantified by mutual information,and is further converted to the MMSE to obtain the integrated performance metric.Finally,we investigate the performance trade-off,and find the optimal integrated performance as well as the corresponding resource allocation schemes under different modulation patterns.To cover heterogeneous scenarios,different priorities are also considered.

The remainder of this article is organized as follows.The system model is introduced in Section II.Theoretical analysis of PEBs and REBs using PRS-based positioning,data-based positioning and data-assisted positioning approaches are derived in Section III.Communication performance is analyzed in Section IV.Section V gives the integrated performance metrics and the optimization problems.Through numerical results,comparisons of the three positioning methods’performance are demonstrated in Section VI.The optimal integrated performance and the corresponding resource allocation schemes under different weight cases are also discussed.Conclusions are drawn in Section VII.

Notations:A is a matrix,whereas AT,AH,A−1is its transpose,conjugate transpose and inverse,respectively.a is a vector,andais a scalar.〈a,b〉denotes the scalar product of vector a and b.∥A∥Fis the Frobenius norm of A.∥a∥is the norm of a.Ixdenotes the identity matrix of sizex×x.Besides,E[·]denotes the expectation operation,ℜ{·}refers to the real-part operator and vec([x1...xN])=[xT1...xTN]T.The tracing operation is denoted as tr{·}and[A]i,imeans selecting thei-th diagonal element of A.AB means that the matrix A−B is positive semi-definite.

II.SYSTEM MODEL

We consider a MIMO-OFDM system.There is one BS employing a closely spaced uniform linear array(ULA)ofNTco-located antennas transmits downlink signals to one UE,on whichNRULA antennas are mounted.The distance of each antenna element isd.Besides,the UE’s antenna array has an unknown rotation angleγrelative to BS’s.In a two dimensional Cartesian coordinate system,as shown in Figure 1,the BS is located at the origin,whose position is denoted by pT=[0,0]T,and UE’s position is pR=[pR,x,pR,y]T∈R2,which is unknown.The signal waveform is OFDM,with central carrier frequencyfc(corresponding to the wavelengthλc=c/fc,withcthe speed of light)and bandwidthW.

2.1 Transmission Model

We assume that data signals and PRSs are transmitted sequentially,which means each kind of signal uses all the frequency-domain resources but shares timedomain resources,as is shown in Figure 21.Here,we do not distinguish the kind of signals when building the transmission model.

The transmitted signal resource grid containsI ×Jresource elements(REs)withIthe number of subcarriers andJthe number of symbols.The RE occupying thei-th subcarrier and thej-th symbol has an index of(i,j)withi=0,...,I−1 andj=1,...,J.Within each RE,the beamforming is conducted according to the codebookF(NT),which denotes a set of vectors withNTentries.The transmitted signal vector in the(i,j)-th RE can be expressed as:

The normalized average power isDirectional beamforming is adopted,withMTthe number of beams.The beamforming matrix can be expressed as F[i,j]=[f1[i,j],f2[i,j],...fMT[i,j]].Each column of F[i,j],fmt[i,j]∈F(NT),has the following form:

wheremt=1,...,MTandψmt[i,j]is the direction of themt-th beam in the(i,j)-th RE.It is noted thatȷis the square root of−1,whilejis an integer variable.

2.2 Channel Model

We assume that for signal propagation,there are overallB+1 paths between the BS and the UE,the first of which (b=0) is line-of-sight (LOS) path and the rest (b=1,...,B) are non-LOS (NLOS) paths.All the NLOS paths are assumed to be single-bounce and generated by scattering or reflection.As shown in Figure 1,the position of the scatterer or reflector in thebth NLOS path,which is unknown,is denoted by pb=[pb,x,pb,y]T,and different paths have different AoAs and AoDs [22].Assuming that the channel remains constant within the time duration of one resource gird,the channel matrix for thei-th subcarrier can be written as H[i]=where Hb[i]denotes the channel matrix of theb-th path(b=0,...,B)and can be expressed as

where Λb=aR(θR,b)aHT(θT,b)denotes the frequency response matrix of the channel caused by the antenna arrays [23,24].Ts=1/Wis the sampling duration.And for theb-th(b=0,...,B)path,hb=hR,b+ȷhI,bis the complex channel gain,ρbis the path loss andτbis the propagation duration.Besides,aT(θT,b)∈CNT×1and aR(θR,b)∈CNR×1are the antenna steering and response vectors,withθT,bthe AoD at the BS side andθR,bthe AoA at the UE side.Notice that whenW ≪fc,the wavelength of thei-th subcarrierso the transmit steering vector can be expressed as

and the response vector aR(θR,b)is similar to Eq.(4).

2.3 Received Model

Based on the above assumptions,the received signal for the (i,j)-th RE after downsampling,matched filtering and the Fast Fourier Transform is given by:

wherePis the transmission power,and n[i,j]is the noise vector forming the circularly-symmetric complex normal distribution,that is,n[i,j]∼CN(0,Σn),with Σn=σ2nINRthe covariance matrix,whereinσ2n=N0/2 is the noise variance.Hence the transmitted SNR is denoted as snr=P/(N0W).

Ultimately,the set of all received signals within the whole resource grid can be expressed as

with x[i,j],y[i,j],n[i,j]located in thei-th row,j-th column of X,Y and N respectively.

III.POSITIONING PERFORMANCE ANALYSIS

In this section,we theoretically analyze the performance of the PRS-based positioning,which utilizes PRSs,the data-based positioning,which utilizes data signals and the data-assisted positioning,which is the combination of the above two methods through PEBs and REBs.

The positioning approach for these three kinds of method is the same.Since the MIMO system has the feature of high angular resolution,not only the time delay could be estimated(under the assumption of perfect synchronization between the BS and the UE),but also the estimation of AoAs and AoDs could be realized.Therefore,the angle and delay estimation is first adopted in this paper.After that,we can further obtain the estimation of UE’s location and orientation.The above approach is called a two-stage estimation approach [25].Correspondingly,we will first derive the Fisher information matrix(FIM)of the channel estimation,which contains the estimation of angles and delays.Then the FIM of channel parameter estimation is converted to the FIM of positioning parameters.Finally,the Cramr Rao lower bounds (CRLBs) of the position and orientation estimation are evaluated.

Letζ ∈R5(B+1)denote the channel parameter vector of interest,it can be written as

where forb=0,...,B,ζb=[τb,θTb,hTb]T,withθb=[θT,b,θR,b]Tand hb=[hR,b,hI,b]T.

where EY;ζ[·]denotes the conditional expectation parameterized by the unknown parametersζand Oζ ∈R5(B+1)×5(B+1)is the FIM of channel parameters defined as[26]

wherep(y[i,j];ζ) denotes the likelihood function of y[i,j].

In the following subsections,we will further derive the specific expressions of Eq.(9) for the three positioning methods,respectively.

3.1 FIM of Channel Parameters: PRS-Based Positioning Case

When transmitting the PRS for positioning,the signal is known to both transmitter and receiver,and we assume that it is independent with channel coefficients and noise.To evaluate Eq.(9),we have to first determine every element of Oζ,PRS[i,j],which is expressed as[26]

where s[i,j]=andζk,ζlrepresent thek-th andl-th(k,l=1,...,5(B+1))element ofζ.To determine Eq.(10),the first-order derivatives of s[i,j]byζb’s elements,which can be expressed as the gradient of s[i,j]w.r.t.ζb,denoted as∇sb[i,j],are obtained

where q[i,j]=F[i,j]x[i,j],ηb=βi=−ȷ2πi/(ITs),DT=ȷ2π(d/λc)cosθT,bdiag[0,...,NT−1],and DRhas similar form to DT.Applying the results of Eq.(11)to Eq.(10),every element of Oζ,PRS[i,j]can be revealed.Then applying Oζ,PRS[i,j]to Eq.(9),the FIM of channel parameter vector in condition of PRS positioning can be obtained finally as

3.2 FIM of Channel Parameters: Data-Based Positioning Case

When using data signals for positioning,the received symbols are unknown to UE.The most challenging thing is to extract the channel parameters from the random unknown data signals.To eliminate the uncertainty of data signals,a feasible way called NDA is utilized here,which multiplies the likelihood function by the probability distribution function (PDF) of the data symbols.In this way,the data dependency of the channel parameter estimation is removed [27].Several NDA channel estimation algorithms like the maximum search/error feedback algorithm for synchronization and time delay estimation,the spectrum analysis/phase increment estimation method for frequency estimation and the estimating signal parameter via rotational invariance techniques (ESPRIT) for angle estimation can be adopted [27,28].In the following part,we focus on the analysis of general performance bounds without specifying any particular estimation algorithm.

It is assumed that each point of x[i,j]comes from a digital modulation constellation such as phase shift keying (PSK) or quadrature amplitude modulation(QAM),and the modulation scheme is known to the receiver.Therefore,the PDF of each symbol can be obtained.Suppose that the set of constellation points is Ω,then for x[i,j]∈CMT×1,the number of all possible symbol sequences isM=ΩMT.We assume that every constellation point appears equiprobable and independently,then the possibility of the transmitted symbol sequence xm[i,j]isp(x[i,j]=xm[i,j])=1/M,withm=1,...,M[29].Under the above assumptions,the likelihood function is expressed as

whereϕm[n]=∥y[i,j]−sm[i,j]∥2with sm[i,j]=As such,the logarithm likelihood function can be derived

The FIM ofζwhen the received signal is data signal,for thei-th subcarrier,j-th symbol can be expressed as Oζ,data[i,j].Thek-th row,l-th column of Oζ,data[i,j]is[26]

with the first-order derivative equals to

where[26]

Recalling that for the PRS-based positioning,Eq.(11)has been obtained,so the result of∂sm[i,j]/∂ζkin Eq.(17)can be directly given by adding the subscript“m”.Then,Eq.(17) and Eq.(16) can be acquired successively.In this way,we have

3.3 FIM of Channel Parameters: Data-Assisted Positioning Case

It should be noted that the FIM of channel parameters for PRS-based positioning or data-based positioning analyzed above is under the condition of allocating all symbols to the PRS or data signal,for the sake of convenient demonstration.To further aggregate their abilities and analyze the performance of the dataassisted positioning (i.e.the mixed positioning),we should first distribute the total time-domain resource between PRSs and data signals.Assuming that within one resource grid,the number of symbols allocated to the PRS is denoted byJPRS,and the remaining symbols(Jdata=J−JPRS)are for the data signal,as is shown in Figure 2.Then the time-domain allocation fraction for PRS isαp=JPRS/Jand data signal’s resource fraction isαd=1−αp.Under the above assumption,the FIM of channel parameters Oζ,mixfor data-assisted positioning can be computed as

3.4 Error Bounds Calculation

In this subsection,we will first convert the FIM of channel parameters to the FIM of the UE’s position parameters,and finally obtain the CRLBs.The vector of positioning parameters,denoted as∈R(4B+5),can be expressed as=[,...,]T,where

From Figure 1,the geometric relationships betweenandζare shown as follows:

whered0=∥pR−pT∥denotes the distance between the BS and the UE.For theb-th NLOS path,the distance from the BS to the scatterer/reflector isdb,1=∥pb−pT∥,and the distance from the scatterer/reflector to the UE isdb,2=∥pR−pb∥.

Thus,by means of a bijective transformation,the FIM of position parameters can be obtained from the FIM of channel parameters.It is noted that for PRSbased,data-based and data-assisted positioning,the transformation methodology is similar,so we make Oζthe common expression of Oζ,PRS,Oζ,dataor Oζ,mixand the FIM of position parametersthe common expression of,or.The transformation can be written as

where U∈R(4B+5)×5(B+1)is the transformation matrix whose block-matrix form is shown as follows

where U(b,b′)=∂ζTb /.Whenb′=0,the entries of U(b,0)are shown as follows

and forb′≠0,U(b,b′)can be expressed as

The entries of Eq.(27) and Eq.(28) are shown as follows

Forb=0,...,B,∂hTb/∂hTb′=I2and∂θR,b/∂γ=−1.The rest elements equal to 0.

IV.COMMUNICATION PERFORMANCE ANALYSIS

The task of communication is to transmit the message through the channel as reliably as possible.To evaluate this,mutual information,which is one of the core concepts of the information theory,can be adopted as a performance metric.As has been proved in[30],for the complex Gaussian vector channel,with the input signal assumed to be zero-mean and having covariance E[x[i,j]x[i,j]H]=Σx=IMT,the mutual information reaches maximum when x is circularly symmetric complex Gaussian,i.e.x[i,j]∼CN(0,Σx).Thus,considering such x[i,j],the mutual information can be expressed as

Our final purpose is to investigate the performance trade-off between communication and positioning,but the mutual information derived above seems to have no direct relationship with PEBs and REBs in Section III.Therefore,we need to further process the mutual information to make it comparable.Fortunately,as shown in[31],the mutual information can be converted to the MMSE of estimating the transmitted signal from the received signal.This is consistent with the idea of estimating the channel H[i]from y[i,j],which is one of the steps of the PEB/REB evaluation.In this way,the performance trade-off can be conducted under comparable metrics.The relationship between the mutual information and MMSE is

where mmse[i,j](snr) is the MMSE of estimating[i,j],and can be denoted as

Furthermore,to obtain the MMSE of the whole resource grid,we give the vector-form system model

where y=vec(Y)∈CKNR×1,x=vec(X)∈CKMT×1,n=vec(N)∈CKNR×1,and=diag[,...,]∈CKNR×KMT,withK=IJ.Then the system’s MMSE matrix is expressed as

where Σx=IKMT.

V.PERFORMANCE TRADE-OFF AND OPTIMIZATION PROBLEM

In this section,we first establish an integrated communication and positioning performance metric by combining the PEB/REB analyzed in Section III and the MMSE evaluated in Section IV.Then the optimization problem is proposed on the trade-off between dataassisted positioning and communication w.r.t.the resource allocation scheme through distributing diverse weights to different metrics to better portray different demands and scenarios.

5.1 Integrated Performance Metrics

As has been analyzed in Section III,the PEB and REB reveal the lower bounds of the MSE of position and rotation estimation.And from Section IV,we have obtained the MMSE ofestimation.Thus,for the purpose of unification,we letφc=mmse denote the communication metric.And for data-assisted positioning,we letφp,mix=PEBmixdenote the PEB metric andφr,mix=REBmixdenote the REB metric.To conduct the trade-off between communication and positioning in terms of resource allocation,we firstly need to find the relationship between metrics and resource allocation factors (αpandαd).Using the results of Section 3.3,the equivalent positioning metrics of data-assisted positioning can be expressed as

And the equivalent communication metric is

with

5.2 Performance Trade-Off and Optimization Problem

In this subsection,to satisfy the heterogeneous demands of communication and positioning,we propose an optimization problem for the integrated performance w.r.t.the signal resource allocation scheme.Different priorities are allocated to positioning and communication,which reflects on different weights being assigned to the data-assisted positioning performance,in terms ofφp,mix,φr,mix,and the communication performance,in terms ofφc.We formulate a multi-objective optimization problem,which aims to optimize the overall equivalent MSE consisting of the MMSE of communication and MSE bounds of data-assisted positioning by finding the optimal timedomain resource allocation fraction for these two functions.The optimization problem can be formulated as

whereωp,ωrandωcare the normalized weights ofφp,mix,φr,mixandφc.The weights are set to be different values for different scenarios.The larger the weight,the higher the priority of the corresponding demand.For example,when the UE is a car passing through a crossroads,ωpandωrshould be high.While for a person staying at home conducting a video meeting on the mobile phone,ωcshould be higher instead.The change of weights will affect the optimization results ofαpandαd.It should be noted that constraint(47b)is based on the feature of data-assisted positioning.It is possible thatαpequals to zero,because pure data signals are able to provide some positioning information.By contrast,a zero-value ofαdis impractical.

From the above,we can observe the impact of timedomain resource allocation on communication and positioning performance.With the increase of data signal’s time duration,i.e.the increase ofαd,the equivalent MMSE increases,and the mutual information becomes larger,which is desirable.At the same time,positioning accuracy using data signals also increases.However,increasingαdmeans reducingαp,which results in the decrease of PRS positioning accuracy.Thus,there is a tension between the communication MMSE and the positioning error bounds.Changing the time-domain resource allocation has two opposite effects on positioning,which needs to be quantified before solving the optimization problem.

In this paper,we traverse the value ofαdthusαpto solve Eq.(47),which will be demonstrated in Section VI.We must admit that traversal is a direct and plain method,which may lack efficiency.But since our work is an initial attempt to establish an integrated communication and data-assisted positioning system and evaluate the integrated performance,the mathematical methods are beyond the scope of this paper.Here we give a basic idea and recommend some optional methods to the readers and ourselves for future researches and applications.For the optimization problem in Eq.(47),the communication metric termedφcis linear w.r.t the optimization variableαd,which can be discovered easily from Eq.(46).However,the positioning metric terms,i.e.φpandφr,can be non-convex,as has been proved in [20].Therefore,the integrated metricφi=ωpφp,mix(αp)+ωrφr,mix(αp)−ωcφc(αd)can be non-convex and we can adopt some methods to solve it,like finding the Pareto optimal point ofφi’s feasible non-convex value region [32,Ch.4]and converting the optimization problem of PEB/REB to the optimization problem of FIM,which is a convex semidefinite program (SDP)and can be solved using standard convex optimization tools[33].

VI.SIMULATION RESULTS

In this section,we first compare the performance of PRS-based,data-based and data-assisted positioning and then evaluate the trade-off between communication and positioning using unified performance metrics considering different time-domain resource allocation fractions and weights through simulations.

6.1 Simulation Setup

We consider a MIMO-OFDM system where the number of antennas for the BS and UE are 64 and 4 respectively.The antennas’rotation angle is 0 rad at the BS side and 10 rad at the UE side.The location of the BS is taken as the origin of the established twodimensional coordinate system.There are two beams whose directions are [ψ1,ψ2]=[π/6,π/3].The UE is located 10 m away from the BS,and the direction of the LOS path is set to beπ/4.In this way,the UE is located between the two beams,and the positioning capability can be implemented.The number of NLOS paths isB=2,with the scatterer and reflector located at p1=[8,4]Tand p2=[2,11]T,respectively.The speed of lightcis 0.3 m/ns,and the noise power spectral density per dimension isN0=−174 dBm/Hz.The positioning error bounds of data-based positioning is obtained using the Monte Carlo method with 1000 realizations.

The signal is transmitted through a mmWave channel,since its huge bandwidth can provide higher temporal diversity for positioning,making the time-ofarrival(ToA)estimation more accurate[34].The carrier frequencyfcis set to be 60 GHz,with bandwidthW=800 MHz,so that the time resolution can reach 1.25 ns.For OFDM signals,the number of subcarriers isI=52 [35].And we setJ=50.The channel complex gains for one LOS and two NLOS paths are set to be equivalent tohb=(1+ȷ)/(b=0,1,2).The path loss model is geometry-based according to[36],which is decided by the free space path loss FSPL(db),atmosphere attenuationµ(db) and reflection lossξ(db)over the distancedb=db,1+db,2.For NLOS paths,i.e.b≠0,the path lossρbcan be denoted as

where FSPL(db)=andξ2(db)=ξ20(εdb,2)2e−εdb,2.The atmosphere attenuation coefficientδ(fc)for 60 GHz is 16 dB/Km according to the measurement results in[37],the average reflection loss isξ20=10 dB,and the Poisson distributed reflector density isε=1/20[36].For the LOS path,the path loss model simplifies to

6.2 Performance Comparison of Different Positioning Methods

The proposed integrated communication and dataassisted positioning system is different from current integrated systems in that the positioning capability is implemented with the aid of data signals,instead of only processing PRSs.Therefore,our first task is to show the advantage of the data-assisted positioning(i.e.the mixed positioning)by comparing it with traditional PRS-based positioning and data-based positioning methods,in terms of positioning error bounds,under the change of received SNR and PRS overhead.

1) Positioning Performance Comparison versus SNR:Based on the above assumptions,we first investigate the positioning performance of the three positioning methods,with the change of the received SNR at the UE side.The received SNR can be denoted as SNR=10log10(snr∥HF∥F).The resource allocation fraction is set to beαp/αd=1/5,according to the 3GPP protocol [38].Simulations are carried out for BPSK,QPSK,8PSK and 16QAM,and can be easily expanded to modulation schemes with higher dimension and complexity.The SNR ranges from 0 dB to 30 dB.As is shown in Figure 3,for data-based positioning,PEBs and REBs increase when the modulation order gets higher,which is due to the introduction of larger signal sequence uncertainty,thus producing higher challenge for processing data signals to obtain positioning information.However,all these four modulation methods can achieve mm-level positioning accuracy,which is comparable to PRS-based positioning.Besides,the REBs are also below 0.01 degree.Furthermore,we can see that BPSK and QPSK data signals even have better performance than PRS-based positioning.Thus,exploiting the potential of data signals to resolve the positioning information can provide satisfactory positioning performance for widely used modulation methods in mmWave MIMO-OFDM systems.What is the most important to notice is that the data-assisted positioning has the best performance,since we make full use of signal resources for positioning.Specifically,for these four kinds of modulation patterns,the position estimation accuracy can be improved by 53.66%,32.27%,13.22%and 3.85%respectively,and the orientation estimation accuracy can be improved by 53.09%,32.22%,12.84%and 3.83%respectively,w.r.t.the PRS-based positioning.

2)Positioning Performance Comparison versus Resource Allocation Fractions:As has been analyzed in Section 5.2,the change of time-domain resource allocation fractions,i.e.αpandαd,has a dual effort on the data-assisted positioning.In Figure 4,we quantify this effect and compare the data-assisted positioning with the PRS-based and data-based positioning.The received SNR is fixed to 10 dB.The resource allocated to PRS is also regarded as signal overhead.Generally speaking,with the increase of PRS overhead,the performance of PRS-based positioning increases while data-based positioning’s performance decreases because the amount of data signals reduces.Specifically,data-based positioning with BPSK modulation can always achieve a lower PEB and REB than PRSbased positioning,when the PRS overhead is constrained to below 42.3%,which is already very high in current signal allocation schemes.In other words,up to 42.3%time resource can be saved if we utilize data signals for positioning with BPSK.This phenomenon verifies the value of data-based positioning in that it can not only achieve better performance than PRSbased positioning,but also save resources.However,we should also notice the different results for different modulation schemes.For QPSK and 8PSK,the threshold below which data-based positioning can outperform PRS is around 19.0%and 6.0%,respectively.By contrast,for 16QAM,even when there is only 0.1%time resource for PRS but 99.9% for data signal,the performance of data-based positioning is still worse than PRS.The reason for these results is that the decrease of positioning accuracy between data-based positioning and PRS-based positioning gets larger with the increase of modulation order,which ultimately cannot be compensated by occupying more resources.However,if we combine these two positioning methods,i.e.using the data-assisted positioning,we can see that the positioning accuracy can always be improved over the range of PRS overhead.For BPSK,QPSK,8PSK and 16QAM,the maximum gains of position estimation accuracy are 96.31%,93.54%,87.67%and 76.01%.respectively.And the maximum gains of orientation estimation accuracy for these four modulation patterns are 98.14%,96.71%,93.75%and 87.88%,respectively.What is more,it can be discovered that the change of positioning accuracy w.r.t.PRS overhead becomes more gentle by applying data-assisted positioning,which indicates that the proposed dataassisted positioning method has better reliability than current PRS-based positioning.

6.3 Positioning and Communication Performance Trade-Off

Through investigating the performance of different positioning methods,we confirm the validity of dataassisted positioning.After that,in this subsection,we will study the trade-off between communication and data-assisted positioning using the integrated performance metrics.The impact of the PRS overhead,as well as the weights for different functions will be considered.

1) Trade-off under the Change of Allocation Fractions with Fixed Weights:We consider a scenario where the requirements of position and orientation estimation are the same and slightly higher than communication.Under this circumstances,the weights allocated toφc,φp,mixandφr,mixare set to be 1/4,3/8 and 3/8.The received SNR is set to be 10 dB.Figure 5a depicts the integrated performance metricφiwith the increase of PRS overhead.We can learn that the trends are different for different kinds of modulation patterns.For BPSK,the integrated performance monotonically increases with the increase of PRS overhead,while for QPSK and 8PSK,the integrated performance first decreases and then increases,resulting in a minimum value.What is more,the minimum value for the QPSK case appears earlier than the 8PSK case.Specifically,when PRS overhead is 80.7%,the integrated performance for QPSK reaches its minimum value,while for 8PSK,the corresponding PRS overhead is 97.7%.As for 16QAM,the integrated performance decreases over the change of the PRS overhead.The reason for this phenomenon is that the integrated performance metric can be regarded as a linear combination of three functions,i.e.φc,φp,mixandφr,mix,whose arguments are the same,i.e.the PRS overhead.On the one hand,we focus on the relationship between the PEB/REB andαp.According to Eq.(20) and Eq.(25),can be written as a function of PRS overhead,i.e.=(−)αp+.As demonstrated in Figure 4,for the sameαp,the PEBs and REBs of data-based positioning increases with the increase of modulation orders,which indicates a decrease of.Besides,is the same for the four modulation schemes.Therefore,the slope of(αp) increases with the increase of modulation orders.Considering thatφp,mixandφr,mixhave negative correlations with,we can draw the conclusion that the slopes ofφp,mix(αp)andφr,mix(αp)decrease with the increase of modulation orders.Since the PEB/REB decreases with the increase ofαp,the slopes’ values are negative.Let|sp,BPSK|,|sp,QPSK|,|sp,8PSK|,|sp,16QAM|and|sr,BPSK|,|sr,QPSK|,|sr,8PSK|,|sr,16QAM|be the absolute-valued slopes of different modulations’PEBs and REBs,they have the relationship of|sp,BPSK| <|sp,QPSK|<|sp,8PSK|<|sp,16QAM|and|sr,BPSK|<|sr,QPSK| < |sr,8PSK| < |sr,16QAM|.On the other hand,as can be inferred from Eq.(46),the MMSE decreases with the increase of PRS overhead.Thus,the slope ofφc(αp),denoted assc,is also of negative value.Based on the above discussion,we can see that the weights essentially influence the slope ofφc(αp),φp,mix(αp) andφr,mix(αp),and subsequently influence the trend of the integrated performance metricφi.Specifically,if the weighted absolute-valued slopes ofφp,mix(αp)plusφr,mix(αp)are larger than the weighted absolute-valued slope ofφc(αp),the curve will be decrease,otherwise it will be increase.The relationship of slopes when the weights are fixed to 1/4,3/8 and 3/8 are shown in Figure 5b.We can see that for 16QAM,it is reduced sinceωp|sp,16QAM|+ωr|sr,16QAM| > ωc|sc|always holds for the entire range of PRS overhead.For BPSK,it increases sinceωp|sp,BPSK|+ωr|sr,BPSK| < ωc|sc|always holds.For 8PSK and QPSK,due to the fact thatωp|sp,QPSK|+ωr|sr,QPSK| < ωp|sp,8PSK|+ωr|sr,8PSK|,the relationship of “weighted absolutevalued positioning slope is bigger than the weighted absolute-valued communication slope” holds longer for 8PSK than QPSK,with the increase ofαp.Thus the minimum value appears later,corresponding to a larger PRS overhead.

2) Optimizing Integrated Performance with the Change of Weights:To find the optimal integrated performanceφi,we first distribute different weights to positioning and communication.The communication weightωcchanges from 0.001 to 1,and the rest is divided into two equal parts for PEB and REB,i.e.ωp=ωr=(1−ωc)/2.Considering that in practical applications,when configuring the signal resources,the number of PRS symbolsJPRSinstead of the timedomain resource allocation fractionαpis more direct and realistic,we choose to show the optimalJPRSinstead ofαpin the following simulations to better guide future applications.Since we have set the number of symbols in a resource grid to beJ=50,all possible number of PRS symbols can then be determined.The number of symbols allocated to PRS can be 0,1,...,49,i.e.JPRS ∈{0,1,...,49}.

Figure 6a shows the optimal integrated performance under different weight allocations for different modulation schemes.With the increase of the communication weight,for every modulation scheme,the optimal integrated performance decreases since for every symbol allocation fraction,(ωcφc)becomes larger,while(ωpφp+ωrφr)decreases.For different modulation schemes,the optimal integrated performance increases with the increase of the modulation order.This can be easily understood since the PEBs and REBs of the data-assisted positioning get larger with the increase of modulation order,under the same weights,SNR or PRS overhead,as shown in Figure 3 and Figure 4.Besides,it is observed that the gap is smaller whenωc →0 andωc →1,which can be explained as follows.Whenωc →0,this means that we only need to consider the positioning performance.Under this situation,the optimal performance appears when all symbols are for PRS,since PRS-based positioning has higher accuracy than data-based positioning under the same resource consumption.In this way,all the modulation schemes will have the same optimal integrated performance,which results in the overlap of these four modulations’ curves whenωc →0.While forωc →1,it means that the communication performance has the absolute priority,then all symbols need to be allocated for data signals,which results in the convergence of BPSK,QPSK,8PSK and 16QAM’s curves.However,they are just“converging”but not “overlapping”,because the data-assisted positioning converts to data-based positioning when all symbols are for data signals,and the higher the modulation order,the larger the PEBs and REBs.So there still exists the relationship thatφi,BPSK <φi,QPSK <φi,8PSK <φi,16QAM.

In Figure 6b,the optimal number of PRS symbols decreases with the increase of communication weights,which is because higher communication requirement needs more data signals,thus reducing the number of PRS symbols.The optimal number of PRS symbols w.r.t.the optimal integrated performance is quite different for different modulation methods.For a certain weight allocation,the optimal number of PRS symbols gets bigger with the increase of modulation order.It is similar to the discussion for Figure 5,which shows that with the increase of modulation order,the optimal PRS overhead comes later (when increasing PRS overhead) to reach the minimum point of integrated performance.Besides,we can see that whenωcis smaller than 0.082,the optimalJPRSequals to 49 for all the four modulation schemes,which corresponds to the overlap region of Figure 6a.It is worth emphasizing that the communication weights corresponding to the case when the optimalJPRSequals to zero are of practical significance.For BPSK,QPSK,8PSK and 16QAM,when the communication weights are bigger than 0.129,0.685,0.942 and 0.989,only transmitting data signals is adequate to achieve the optimal performance.This result means that by applying the proposed integrated communication and dataassisted positioning system,PRS will not be a forced choice when the positioning priority is lower than 0.871,which is capable of covering many scenarios.

3) The Influence of PEBs and REBs’ Weight Allocation to the Optimal Integrated Performance:Previously,while changing the weights,we assume that the weights of PEBs and REBs are the same,which may not be suitable in some cases.We take the road traffic as an example.When a car is passing through an intersection,its rotation estimation will be of higher priority than position estimation,since its direction changes quickly.On the contrary,if a car is driving on the highway,the priority of position estimation will be higher than rotation estimation.Considering the above practical scenarios,the weights of PEB and REB need to be properly chosen.We set the range of the communication weight to be from 0.001 to 1,then divide the remaining weight,(1−ωc),into five parts.PEB occupies some of this and the rest are for REB.Then all possible proportions ofωpandωcare 0:5,1:4,2:3,3:2,4:1 and 5:0.Figure 7 and Figure 8 show the optimal integrated performance and the corresponding number of PRS symbols under different modulation cases.From Figure 7,we find that when the communication weight is fixed,the larger proportion of the remaining weight allocated to PEB,the higher optimal integrated performance.And whenωr=0,the optimal integrated performance is maximized,while whenωp=0,it is minimized.The reason is that from Figure 3 and Figure 4,we can see that PEB has a larger value than REB,under the same modulation scheme,SNR or PRS overhead.Therefore,although we just simulate six PEB and REB weight allocation cases,we can draw a conclusion that the curves of optimal integrated performance for other PEB and REB weight allocations will appear between the curve ofωr/ωp=0 and the curve ofωp/ωr=0.Besides,the gap of different optimal integrated performance for differentωp/ωrbecomes smaller with the increase ofωc,which is because largerωccorresponds to smaller(ωr+ωp),which weakens the effect of different proportions on the optimal integrated performance.

In Figure 8,the optimal number of PRS symbols under different modulation schemes with the change of PEB and REB’s weight allocation are depicted.We can see that no matter what modulation scheme is utilized,under a fixed communication weight,to obtain an optimal integrated performance,more PRS symbols should be allocated with the increase ofωp/ωr.This can be explained by taking the slopes ofφp,mix(αp),φr,mix(αp)andφc(αd)into account.As has been discussed on Figure 5,with the increase of PRS overhead,the minimum point of the integrated performance’s curve appears whenωp|sp,BPSK|+ωr|sr,BPSK| > ωc|sc|starts to hold.And the absolute-valued slope ofφr,mix(αp)is bigger than forφp,mix(αp).Consequently,allocating a larger proportion of weight to REB will result in a smaller number of PRS symbols.A similar conclusion with Figure 7 can be drawn,that is,although we are unable to traverse all possible proportions of PEB and REB’s weights,we can infer that the curve of optimalJPRSwill appear between the curve ofωr/ωp=0 and the curve ofωp/ωr=0 in Figure 8.

VII.CONCLUSION

In this paper,we propose an integrated communication and data-assisted positioning system in MIMOOFDM system.The data-assisted positioning method which utilizes both PRSs and data signals is first developed.The PEB and REB of such method are evaluated theoretically.The communication performance is analyzed through the mutual information,and is further transformed to the equivalent MMSE.The integrated performance metric is derived,considering the priority of different functions.Through simulations provided for a mmWave scenario,for different modulation schemes,the trade-off for communication and positioning is conducted,and the optimal integrated performance as well as the corresponding resource allocation schemes are figured out.To the best of our knowledge,this work is the first to propose a dataassisted positioning method,which has a dual effect of improving positioning accuracy and reducing PRS overhead.Besides,we believe the methodology of optimizing the performance of the integrated communication and data-assisted positioning system through a unified performance measurement framework can support future researches and applications in the field of integrated communication and positioning.

NOTES

1Although Figure 2 is not comb structure as standardized in the Third Generation Partnership Project(3GPP)TS 38.211[39],3GPP allows further promotions on PRS configurations.For example,Intel and Qualcomm design and utilize a PRS pattern where each PRS symbol uses all subcarriers of a resource block[40,41],which is similar to Figure 2.Besides,Figure 2 only shows the quantitative relationship of PRS and data symbols,but not the specific pattern of signal transmission.