Yanrong Zhao, Xiyu Wang, Gongpu Wang,＊, Ruisi He, Yulong Zou＊, Zhuyan Zhao

1 School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China

2 the State Key Laboratory of Rail Traf fi c Control and Safety, Beijing Jiaotong University, Beijing 100044, China

3 the Key Laboratory of Broadband Wireless Communication and Sensor Network Technology of Ministry of Education,Nanjing University of Posts and Telecommunications, Nanjing 210003, China

4 Nokia Bell Labs, Beijing, Beijing100044, China

I. INTRODUCTION

The fifth generation communication (5G) has entered the critical stage of development and standards. One goal of 5G communications is to provide each user equipment (UE) with peak data rate about 100 megabits per second(Mbps) everywhere [1], which is a challenge for future 5G communication systems on high speed railways (HSR).To meet this requirement, the 3rd Generation Partnership Project(3GPP) proposes two candidate system con figurations for wireless communication systems on HSR [2], [3]: (1) macro cell with carrier frequency of 4 GHz; (2) macro cell plus relay with carrier frequency of 30 GHz.

Currently, most existing studies about 5G on HSR only con- sider single scenario [4] and construct channels with unveri fi ed parameters[5] or rayleigh distribution [6]. These works do not take into consideration the practical various HSR situations such as viaduct, urban,tunnel, and cutting, and thus may fail to factually evaluate the throughput performance of the 5G wireless communication systems on HSR [7]-[9].

In addition, the traditional channel estimators[10], [11], widely utilized in the existing studies are based on linear regression, such as linear minimum mean square error (LMMSE) and least square (LS). However, these estimators may not be suitable for the fast time-varying wireless channel estimation on HSR due to the large Doppler shift resulted from the high speed.

One candidate method to effectively estimate the time-varying channel is the basis expansion model (BEM). BEM approximates the time-variant channel parameters by linearly combining the determined basis functions.Typical BEMs include complex exponentials BEM (CE-BEM) [12], polynomial BEM(P-BEM) [13] and discrete prolate sequence BEM (DPS- BEM) [14]. Selecting the proper basis function plays a crucial role in the estimation accuracy[15].

To evaluate the performance of the 5G wireless communication systems on HSR,we investigate three typical HSR scenarios:urban, viaduct, and cutting1Noting that the tunnel is also a typical scenario of HSR, and it requires special channel modeling method different from urban, viaduct, and cutting scenarios.. Each scenario is deployed with micro cell speci fi cation in technical implementation which uses the macro plus relay cell deployment for control plane transmission. The micro cell2The micro cell is of the maximum radius of 572 meter and works at 3.5GHz with 100MHz bandwidth.sends data to UE directly (instead of relay). We generate the channels with the tapped delay line (TDL)parameters which are emulated from the constructed compound scenario[16], [17]. In addition to LS and LMMSE, we also utilize a new estimator based on the historical information based basis expansion model (HiBEM) [18]-[21], and compare their estimation performance and calculate the corresponding system throughput.

The contributions of this paper are summarized as follows:

? We investigate three typical HSR scenarios:urban, cutting and viaduct, and generate the channel parameters of each scenario with TDL model from ray-tracing simulations that are in agreement with practical situations.

? We investigate the estimation performance of the three different channel estimators:LS, LMMSE and HiBEM.

? We evaluate the corresponding 5G system throughputs of each estimator in three typical HSR scenarios.

? We discuss the effect of the speeds on throughputs for each scenario.

The rest of paper is organized as follows.Section II introduces the three HSR scenarios,our system con fi guration, and detailed channel parameters. Section III describes three basic channel estimation models and three channel estimators. Simulation and comparison results are illustrated in section IV. Finally, conclusions are provided in section V.

In this paper, we evaluate the downlink throughput of 5G HSR communication systems on three typical scenarios including urban, cutting and viaduct with three different channel estimators.

II. SYSTEM MODEL AND PARAMETER CONFIGURATION

2.1 System model

Figure 1 depicts our system model. There are three micro cells deployed successively and the coverage areas are urban, cutting and viaduct environment, respectively.

Urban, cutting and viaduct are representative scenarios of HSR [4]. Urban scenario has the highest buildings density compared with other two scenarios. Cutting Scenario has two slopes as the main scatters at both sides.And the viaduct is a long, high bridge across uneven ground and there are barriers along the side for safety and noise reduction.

Table I summarizes the main parameters of our system. The inter site distance of the micro cell is 572 meters. Base transceiver stations (BTSs) are deployed 5 meters away from the rail. The height of BTS is 3 meters and TX power is 30 dBm. BTS is con figured with unidirectional beam antenna of which half power beam width (HPBW) is 65°and antenna gain is 7 dBi. The main antenna beam points to right direction and azimuth angle is 0 degree,which is along (in parallel) direction of the rail track. And UE utilize omni-directional antenna with 0 dBi gain.

We assume passengers directly access micro cell, and thus we add 20 dB outdoor to indoor penetration loss. The interval distance between two sample snapshots is 1 meter. There are totally 1732 snapshots for three micro cells.

2.2 Channel model and generation

Jakes Model [22] is a commonly used channel model which is not applicable to the three HSR scenarios. In this paper, the channel on HSR is modeled as a multi-path Rice fading channel using TDL model for link level simulation platform. The TDL parameters are extracted from the simulation results based on the 3 dimension (3D) study scenario described[23]. It is shown that such channel constructed with TDL parameters can effectively reflect the channel characters of practical scenarios.Table II lists the TDL parameters of different areas in the study scenarios. The Delay and Power of each tap are the absolute arrival time compared with tap 1, and Rician K-factor is the ratio between the power of line-of-sight(LOS) path and the power of non-line-ofsight (NLOS) paths. Area1 represents the area located within 87 meters away from BTS and the multipath components are relatively strong as it is closer to the BTS. Area2 represents the range of 87 to 572 meters where the power of

multipath is too small except the fi rst two taps and the NLOS taps are arrived at long time interval. Urban and cutting are both scenarios abound in scatters, and the power of NLOS taps are weaker in Area2. Compared with urban and cutting scenarios, the NLOS taps in viaduct are arriving in a longer time interval as the scenario has little scatters.

Assume thenth path of the channel h as [24]

wherefDrepresents maximum Doppler frequency,Kis the Rician K-factor andp(n)represents the power of path in Watts,δ(?) is the Dirac’s delta function,C(n)is the phase of each path uniformly between 0 and 2π,Sdenotes the number of symbols during a transmission time interval (TTI), andPfis the absolutely instantaneous sample time of channel.

2.3 Frame structure

We reuse parameter configuration of long term evolution (LTE). The transmission frame structure of a TTI is shown in figure 2. Cell reference signal (CRS) marked by yellow part is utilized for channel estimation. And the channel estimates indicate the downlink channel quality.

Fig. 1. System model with three scenarios: urban, cutting and viaduct.

The frame structure includes three resource blocks (RB) in each slot and the subcarrier space is 15kHz. Each column represents an orthogonal frequency division multiplexing(OFDM) symbol and each row is a subcarrier.

III. CHANNEL ESTIMATION

In this section, three basis channel estimation models, interpolation, BEMs, and AR Model are briefly introduced, and three pilot-aided channel estimators, LS, LMMSE and HiBEM,are presented to recover the channel matrix H shown infigure 2.

De fi nenandmas the subscript of frequency dimension (FD) and time dimension (TD)of channel matrix H,pandqas the subscript of CRS tones in FD and TD respectively, and the corresponding capital letters as the length of vector in different dimension. Denoteh(?)as the FD channel of the (?) th OFDM symbol,h{?} as the {?} thsubcarrier channel and hRSas the channel in the CRS position.

The received signal of an OFDM symbol can be expressed as

where theN×Ndiagonal matrix X(?) is the transmit signal of the (?) th OFDM symbol,and v(?) is theN×1 complex zero-mean Gaussian white noise vector.

3.1 Interpolation

Interpolation is a mathematical method that constructs a special function to predict new data points within the range of a discrete set of known data points. In traditional channel estimation, interpolation is used to recover the channel between two known channel estimates, which are given by LS based on the knowledge of CRSs.

Denote the positions of two adjacent CRSs asp1andp2, and the channel estimations corresponding to the two CRSs asrespectively. Since the difference betweenis negligible,we always employ the linear function as the special function. Thus, the channel estimation can be expressed as

Where

However, the interpolation method with linear function can not completely adapt to the time variant channel parameters on HSR.

Fig. 2. Frame structure with 3 resource blocks. The yellow part indicates CRSs.

Table I. Parameters of micro cells.

3.2 BEMs

BEM, a popular model for time-varying channel approximation in academics, describe the time variant channel response within a block by a linear combination of finite number ofbasis functions [10]. Leth(n;m) denote the channel of themth symbol atnth subcarrier.The general form of BEMs can be written as

Table II. Parameters of tdl extracted from measured data on hsr.

wherebq(n) is the basis function andλq(m)is the BEM coefficient. The candidate choices for the basis functioninclude polynomial, wavelet, complex exponential (Fourier)bases, and DPS sequences. For example, the basis function of CE-BEM

Theorem 1: The lower bound of the mean square error (MSE) for BEMs is given by

where Rh(m)is the correlation matrix of the channel h(m)and ukis the (k + 1)th eigenvector of the basis matrix B.

Proof:See Appendix A.

With BEMs, the estimator can first obtain the BEM coefficients and then reconstruct the whole time-varying channel parameters.According to (4), BEMs will transform the time varying channel estimation into a linear parameter estimation problem and decrease the complexity fromNtoQ.

3.3 AR model

Autoregressive model (AR model) is represented as stochastic difference equation for the output variable that depends linearly on its own previous values and noise[25]. The AR model of orderpis indicated asAR(p) and defined as

whereare parameters of AR model andu(n) is white noise.

3.4 LS estimator

With the knowledge of transmitted and received signals at CRS position, the channel at theqth symbol is estimated through LS method

According to the estimated channelthe channel in data position can be obtained by linear interpolation in both time and frequency dimensions.

3.5 LMMSE estimator

Channel of theqth symbol can be estimated[26]:

whereσ2is the variance of white noise v(m)and I1is theP×Pidentity matrix.[X(q)]Hdenotes the hermitian of matrix X(q),is the cross-correlation matrix of CRS channel and symbol channel,is the autocorrelation matrix of CRS channel.

Since the channel of all subcarriers inqth symbol has been recovered, we can express the channel in nth subcarrier as

where I2is theQ×Qidentity matrix,is the cross-correlation matrix, andis the autocorrelation matrix.

3.6 HiBEM estimator

Given the lower bound of BEMs in (5), the optimal basis matrix of BEM that can reach the lower bound is comprised by eigenvectors of channel covariance matrix. Because of the fixed railway tracks, the HSR channel has strong correlation with historical channel information. By excavating this specialty of HSR, HiBEM employs the first R eigenvectors of channel covariance matrix as its basis matrix.

The channel covariance matrices are calculated from the parameters of table 2. And UE performs the channel estimation by using a basis matrix of the area. In addition, the calculation of basis matrix could be omitted since the channels in one area remain the same.

Theorem 2: The estimator MSE lower bound for HiBEM is

whereγiis the eigenvalue ofRh(m).

Proof:See Appendix B.

Figure 3 plots both theoretical MSE and simulation MSE of the optimal BEM. For comparison, the theoretical lower bound (10)is also given. We assume that the receiver has the perfect channel covariance and the first Q + 1 eigenvectors of the channel covariance matrix are chosen as the basis. It is shown in figure 3 that the theoretical MSE and simulation MSE of the optimal BEM agree well. It can be seen that the optimal BEM can reach the lower bound of estimation MSE.

TD and FD channel covariance matrixes can be expressed asrespectively. Therefore, the basis function B{n}and B(m)can be obtained by taking the singular decomposition and extracting the fi rst R columns of eigenvectors. Furthermore, we can extract the corresponding rows in CRS position from the basis matrix Rh{n}and Rh(m)to estimate coef fi cients,denoted asrespectively.

Rewrite (2) as

Suppose the part of y(q)in the CRS position asIt can be readily decided that

Denoteand the coefficient is given by

Hence, theqth symbol channel can be estimated as

Fig. 3. Theoretical and simulation MSE of new BEM approximation to the time-varying channel h(m).

With the channel estimate of theqth symbol, we can utilizeto estimate the coefficient of each subcarrierand recover the channel of each subcarrier.

IV. SIMULATION RESULT

We employ a comprehensive link level simulator, based on MATLAB, focused on single-input single-output (SISO) downlink wireless communication of LTE system. Detailed link level simulation parameters are summarized in table 3.

Figure 4 describes the simulation steps. The real-time signal to noise ratios (SNR) is calculated according to the received signal power firstly. Then we construct the channel with the given TDL parameters in each area and estimate channel using exist and proposed estimators. The MSE of three channel estimators and their Throughput-vs-SNR are compared.For a given SNR in one snapshot, we map it into the Throughput-vs-SNR of particular area and calculate the throughput by linear interpolation to obtain real-time throughput of study area shown infigure 1.

Fig. 4. Simulation steps.

Table III. Link level simulation parameters.

According to LTE mechanism, user will report the most appropriate channel quality indicator (CQI) based on veracity of channel estimation to the BS. According to CQI, BS has a scheduling algorithm to match a modulation and coding scheme (MCS) so as to perform adaptive modulation and coding (AMC) and transmit as high bit rate as possible.

In the link level simulation, the Doppler shiftfDin (1) was modeled as a random bias of frequency between -100 Hz and +100 Hz,which is a typical bias value of Doppler frequency adjustment for UE at 300 km/h.

4.1 System level simulation result

The real-time SNR between BS and high speed train with respect to the required model is calculated by:

where P is received power measured via deterministic modeling approach on the study scenario [23]. And it is largescale power of which the small-scale fading is eliminated by averaging samples at interval 40 wavelengths[27]. NT is the thermal noise power under normal temperature which can be representedIt is associated with the system bandwidth W and -174 is the spectral noise power density for 1 Hz bandwidth (indBm/Hz) at room temperature. The noise figure NF is set as 7 dB.

We assume that the micro cell only perform transmission during train pass through its coverage area. Thus there is no interference in data channel between neighbor cells. At the same time, neighbor cell signal combination technologies, such as Signal Frequency Network (SFN), are not enabled.

Figure 5 plots the received SNR versus distance (left) and cumulative distribution function (CDF) of SNR (right). It can be seen in figure 5 that the SNR value peaks at each position of BS and declines when the train moves away from BS. This is because the BS antenna is unidirectional with its beam along the track.The CDF shows that SNR values range from-5 dB to 40 dB and more than 95% of SNRs exceed 5 dB because of the close distance be-tween BS and the train.

4.2 Link level simulation result

1)MSE Performance: figure 6 displays the MSEs result of three estimators versus SNR.It can be seen in figure 6 that, HiBEM based on historical information yields the best performance. LS estimator has the worst performance when SNR is less than 0 dB. We also observed that at low SNRs, HiBEM has substantially lower MSEs than LMMSE and has similar performance with LMMSE when the SNR is larger than 20 dB.

2)Throughput Performance: The bandwidth in our platform is 10 MHz according to the LTE standard and 3 RBs are allocated for one UE. In this paper, we assume that BS can allocate all RBs for single UE, and the 100 MHz bandwidth will be assigned to one UE in each TTI. Thus we magnifytimes the throughput result to accord with the situation of 100 MHz bandwidth on HSR scenario.

We take the TDL model of Area2 in BS2 shown in table 2 as an example and results in other areas are identically obtained from simulation in the platform. Figure 7 depicts the throughput-vs-SNR results of three estimators.The throughput upper bound of the ideal estimation that the channels are perfectly known at the receiver is also shown for reference. It can be seen that the HiBEM outperforms the LS and LMMSE at high SNR.

Figure 8 presents real-time throughputs of various channel estimators and that of ideal estimation. It is not surprising to see that the viaduct scenario generates the larger throughput than urban and cutting since viaduct has less scatters and obstructions.

Figure 9 displays the corresponding throughput CDF. We can see that the HiBEM estimator has 96% and 42% gain compared with LS and LMMSE at 80% CDF, respectively. It can be found that more than 95% snapshots of throughput exceed 100 Mbps utilizing HiBEM estimator and ideal estimator, which meet the demand of 5G.

Fig. 5. Real-time SNR value and its CDF on micro scenario.

Fig. 6. MSE comparison between estimators.

Fig. 7. Throughput-vs-SNR results in the Area2 of BS2.

Fig. 8. Throughput performance comparison among different channel estimators.

Finally, figure 10 illustrates the system throughputs corresponding to the HiBEM estimator when the speeds of HSR are 100 km/h,300 km/h and 500 km/h, respectively. It can be seen that the throughput performance witnesses a downward trend when increasing the speeds.

V. CONCLUSION

This work investigated channel model on three typical scenarios: urban, cutting and viaduct for 5G wireless communication system on HSR and evaluated the downlink throughput in the case of different channel estimators. For each scenario,rice channels were constructed by TDL parameters generated through ray tracing simulation. It is found that both the MSEs and the corresponding downlink throughput of proposed HiBEM estimator outperforms LS and LMMSE methods. Furthermore, 95% system throughputs in the case of HiBEM estimator exceed 100 Mbps,which showed that 5G throughput demand of the communication system can be fulfilled with the micro cell deployment.

Appendix A. Proof for the theorem 1

Denote the channel parameter at thelth OFDM symbol with N subcarriers asWith out loss of generality, we focus on the first tap, i.e.,h0. Suppose BEM coefficients asWe can then rewrite (4) as

In general, the priori knowledge of the BEM coefficients remains unknown, and the statistics of approximation error is unavailable. Thus the LS method is the natural choice to estimate the BEM coefficients and then we have

where U is aN×Nunitary matrix, V is a unitary matrix, and isN×(Q+1) matrix with theQ+1 diagonal entries as c and other entries as zero. Then substituting (A.4) into(A.3) will produce

The MSE of the approximation error can be obtained as

Appendix B. Proof for the theorem 2

Supposeγ0,…,γN?1are the eigenvalues of Rh0in a descending order, andψ0,...,ψN?1are the corresponding normalized eigenvectors. DefineIt can be readily checked that for eachists a N vector vkthat can satisfySubstitutinginto (A.10) yields.

Clearly, to minimize MSEv, we should chooseβias

Fig. 9. CDF-vs-throughput for different channel estimator.

Fig. 10. HiBEM Throughput at different speeds.

which implies that the optimal B is composed ofQ+1 eigenvectors of Rh0corresponding to the fi rst largestQ+1 eigenvalues. For example, one optimal B can be

And the lower bounds of new BEM can be yielded from (B.2) as

ACKNOWLEDGEMENT

This study was partially supported by the National Natural Science Foundation of China(Grant Nos. 61522109, 61671253, 61571037 and 91738201), the Fundamental Research Funds for the Central Universities (No.2016JBZ006), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20150040 and BK20171446), and the Key Project of Natural Science Research of Higher Education Institutions of Jiangsu Province (No.15KJA510003).

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