Feng Zheng ＊, Yijian Chen , Qian Zhan , Jie Zhang

1 Beijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, Beijing, China

2 ZTE Corporation, Shenzhen 518055, China

3 Beijing University of Posts and Telecommunications, Beijing 100876, China

4 Department of Electronic and Electrical Engineering, The University of Sheffield, Western Bank, Sheffield S102TN, UK

* The corresponding author, email: zhengfeng@bupt.edu.cn

I. INTRODUCTION

The demand for wireless data traffic almost doubles every year and this trend is very likely to continue in the years to come [1]. To meet the envisioned capacity demand, massive MIMO with a large number of antenna elements is viewed as a crucial component of future wireless systems [2][3]. Large numbers of antenna can be utilized for beamforming in which radio transmission from multiple antenna elements is combined to form narrow beams to reduce interference and improve system capacity. In addition, spatial multiplexing gain can also be achieved by massive MIMO to transmit multiple data streams to one or more UEs(user equipment) simultaneously.

Both beamforming and spatial multiplexing have already been adopted in 4G LTE systems,but their potentials remain to be unleashed with a much larger number of antenna elements in massive MIMO. In principle, beamforming gain and the number of supported data layers in a MIMO system depend on the scale of antenna and the accuracy of CSI information. More antenna elements usually bring more performance gain but it also needs larger installation size for avoiding tight coupling.This makes the deployment of large antenna array difficult due to physical constraints, especially in urban environment. A promising solution is to deploy two antennas with different polarization directions at the same spot.Dual-polarized antennas also enable more degrees of freedom for spatial multiplexing as antennas with different polarization directions are usually uncorrelated. Therefore, dual-polarized antennas become the primary choice of massive MIMO deployment [21].

This paper proposes LMPIF scheme for achieving higher spectrum efficiency for dual-polarized antenna system with low feedback overhead in dual-polarized MIMO Systems.

The benefit of large antenna array can be fully explored only when the transmitter side acquires precise CSI. Inaccurate CSI will result in loss in the beamforming gain and interference among data layers and users.The problem of CSI acquisition is especially prominent in FDD systems as it is hard to acquire CSI by using channel reciprocity like the case in TDD systems. the UE usually needs to quantize and feedback downlink CSI to the base station, which means the tradeoff between the feedback overhead and the CSI accuracy related performance gain must be considered.

Limited feedback (LB) techniques are proposed for FDD MIMO systems (e.g. [4]–[8])in LTE, in which The eNodeB acquires CSI using the PMI (Precoding Matrix Indicator)which is fed back by UE to perform precoding. The eNodeB and UE maintain a common codebook, UE picks the best codeword in the codebook based on the measured channel matrix and feeds back its index to the eNodeB.The performance of LB is highly dependent on the codebook design, which is the focus of numerous articles [9]-[18]. A widely accepted methodology is to base the codebook design on the analytical characteristics of channels.For example, DFT codebook in LTE uses Discrete Fourier transformation (DFT) vectors to match the phase variation among different antennas with the same polarization direction.This is suitable for highly correlated channels(e.g. LOS channels) with uniform linear array for LTE eNodeBs. Antenna polarization plays an important role in channel characteristics[21] and the feature of the polarized channel is analyzed in [22]. To match the eigenvector of dual-polarized channel, a codeword model with the same beam direction for each polarized direction and data layer is also derived.However, the performances of both DFT vector based codebooks and the codeword model in [22] degrade severely when the angular spread is large [36]. To improve performance in partial correlated channel, the well-known rotated codebook [19] transforms the codewords in codebook by channel correlation matrix. It has been proved that rotated codebook is asymptotically optimal in quantizing any spatially correlated channels [37]. However,the performance relies heavily on accurate channel spatial correlation matrix can be obtained by the eNodeB. An initial analysis is presented on the feature of eigenvector of dual-polarized medium and low correlated channel in [23]. But the relevance of different beams is ignored as different beams are considered for different layers.

Existing researches mainly focus on the design of codeword model to match the various characteristics of MIMO channel. In generally,MIMO channel characteristics are determined by the distribution of delay and power, the direction and phase of multi-path components and antenna topology. In this paper, the essential characteristics of MIMO channel are analyzed for dual-polarized antenna. On this basis,we propose a feedback and precoding scheme named layered Multi-paths Information based CSI Feedback (LMPIF). LMPIF only needs to feedback a limited amount of basic multipath information to construct precoder at the transmitter. In practical channel, multipath direction and amplitude usually hold static for a long period while channel phase changes much more rapidly. In LMPIF, the long term component and short term component are fed back by using different time granularities, thus feedback overhead can be reduced. The main contributions of this paper are as follows:

a) The mathematical relationship between the eigenvector of channel matrix and the multi-paths parameters of dual polarized MIMO channel is derived in the closed form. The results reveal the essential characteristics of MIMO channel, which provide guidance for the feedback and precoder design.

b) A novel feedback and precoding scheme named LMPIF is proposed, which reduces feedback overhead considerably for large scale massive MIMO systems.

c) The performance of LMPIF is verified using system level simulations. A significant performance gain is observed, compared to the performance achieved by the DFT based codebook design in LTE.

The remainder of the paper is organized as follows. The system model is introduced in Section II. Section III presents the relationship between multi-path parameters and channel eigenvectors. Based on the derived relationship,the LMPIF feedback scheme is elaborated in Section IV. Section V provides the simulation results and Section VI concludes this paper.

Notation: a lowercase letterindicate a vector, an uppercase letterdenotes a matrix,denotes the conjugate transpose of a matrixdenotes the kronecker product,denotes the matrix Frobenious norm,denotes the vector 1-norm.denotes the conjugate transpose of a vector

Fig. 1 Block diagram of an Nr ×Nt dual-polarized channel MIMO system

II. SYSTEM MODEL

Consider a massive MIMO system withtransmit antennas andreceive antennas. As dual-polarized deployment is assumed,andare both even numbers. In each polarization direction, the antennas are arranged intorows andcolumns at the transmitter,rows andcolumns at receiver. Thus we have. The antenna configuration is shown in Fig. 1. The two polarization directions of the eNodeB antennas are denoted asandrespectively while the polarization directions of UE antennas areand. Usually the angle betweenandis 90 degrees, i.e. the two polarization directions are orthogonal, which also holds forand.

Under flat fading assumption, the channel matrix can be modeled by an input-output relation withto,to,to, andtopolarized waves. The typical polarization configuration at the eNodeB isanddegree polarization directions. For UE, vertical and horizontal polarization is more representative,

ent and identically distributed (i.i.d.)entries following normal distributionrepresents the transmitted symbol whose energy isis the signal to noise ratio (SNR). The channelis a dual-polarized MIMO channel parameter. The literature[32] formulates the fast fading part of. This method is widely used since it can accurately reflect the characteristics of the fast fading part of actual channel, including correlation in frequency, time and space domain. What’s more,it also models the characteristic of polarization. There is a further discussion in 3GPP about channel coefficient (time domain) in fast fading part between 3D transmission side and antenna pairon the reception side. Enhance the 2D model to 3D, the expression ofcan be shown in equation (2.2) shown in the bottom at this page and related angle parameters are illustrated in Fig 2, wheredenotes the index of clusters anddenotes the index of rays.anddenote the horizontal and vertical arrival angle of rayin cluster.anddenote the horizontal and vertical departure angle of rayin clusterandare the antenna gain in the two polarization directions respectively.andare the uniform distancesbetween transmitter antenna elements and receiver antenna elements,is the cross polarization power ratio in linear scale andλ0is the wavelength of the carrier frequency.anddenote the random phase of each ray in two polarization directions, whereasanddenote the random phase of polarization leak.vectorsanddenote the distance of transmit and receive antennas.andare the vector forms of the Angle of Arrival (AOA) and Angle of depart (AoD).denotes the power of the ray.is the moving velocity which can be computed as (2.3) shown in the bottom at this page.

Assuming maximal-ratio combiner (MRC)is used at the receiver, which is aimed to maximize SNR. The MRC weight can be represented asand the resultant SNR is

III. CHANNEL CHARACTERISTIC ANALYSIS

In this section, we give some analyses on channel characteristic in frequency domain,which reveal the relationship between eigenvectors and multipath parameters of a dual-polarized MIMO channel.

3.1 Channel Matrix in Frequency Domain

Fig. 2 Angle parameters of rays in radio channel

Based on the channel model in time domain,the channel matrix in the frequency domain can be expressed as (3.1) shown in the bottom at this page, whereis the frequency of subcarrier, andis the delay of each ray. Since the delay is same for each ray in a cluster, we can replacewithdenotes the fast fading channel response between transmit antennaand receive antennaof Rayin(3.1), we ignore the impact of delay inside a ray among different antennas on the frequency channel since this impact is small for narrow bands channel. Based on (3.1), we can analyze the channel feature with the following assumptions for (2.2).

a) The polarization leak is usually small,which meansandare approximately 0.

b) The Amplitude response of each path isincluding theantenna gain andantenna gain andDifferentandcorrespond to differentIfantennas are omnidirectional, the difference of antenna gain is caused byantennas.

d) Massive MIMO transmission usually occurs at low speed, thusis assumed so as to simplify the analysis, which corresponds tois further considered in the subsequent feedback design.

Based on the above assumptions, substituting (2.2) to (3.1) we have

According to the assumption above, it can be simplified as

Considering typical configuration I[11]:antennas andantennas are-degree polarized.

Considering typical configuration II[38]:transmit antennas are-degree polarized, andantennas are-degree polarized.

3.2 Channel eigenvector analysis for polarization configuration I

When configuration I is adopted,can be represented as (3.11) shown in the bottom at this page.

According to (3.13), the two eigenvectors ofsatisfies

Hence it can be observed from (3.13) that

Thus we have

In above analysis for a channel with two important components, we can assumeand it is a function of the direc-tion vectors, amplitudes and phases of the two paths. Extensions to more general assumptions for a partial correlated channel with more path components, based on the similar analysis method, the two eigenvectors can be expressed as (3.20),(3.21) shown in the bottom at this page.

We have the similar observation that the two eigenvectors of a rich scattering channel can be described based on a function of multipaths information.

3.3 Channel eigenvector analysis for polarization configuration II

First, we also consider a partial correlated channel with two main components. For antenna configuration II,can be expressed as (3.11) and (3.12) too.

Note that (3.12) can be further written as(3.22) under polarization configuration I

Based on (3.22), the eigenvectors ofcan be expressed as follows

Moreover, assuming the following relationship：

The following is to prove (3.24) is true and obtain the parametersIt is known thatcan also be expressed as:

Furthermore, considering the above equations and expressions in Appendix B, we have

By analyzing the above relationships, we have

The difference between the phases ofandisand the difference between the phases ofandisConstrainingas normalized eigenvectors, we can obtain the amplitudes ofIn fact, the difference betweenfalls in the phase gaps betweenandWhenis very large, the impact of the phase gap is small. But whentends to 1,the impact of the phase gap on the eigenvectors is large.can be calculated based on (3.28), thus we can obtain the final expression ofwhich can be expressed by a function of the direction vector, amplitudes and phases of the two paths.Extending to more general assumption for a partial correlated channel with more path components, based on the similar analysis method, the two eigenvectors can be expressed as(3.29),(3.30) shown in the bottom at this page

We have the similar observation that the two eigenvectors of a rich scattering channel can be described based on a function of multipaths information.

IV. LAYERED MULTI-PATHS INFORMATION BASED FEEDBACK

4.1 LMPIF design

According to previous analysis on channel feature, the channel eigenvectors are functions of multi-path parameters. In practical channel,some features, such as multi-path amplitudes and directions, do not change for a long term.The only parameter that changes rapidly in time and frequency domain is the phase in multi-path combination, which depends onIf UE moving velocity is considered, it is also affected by the termHence the explicit feedback can be classified into two classes: Long term/wideband information and short term/subBand information.

The explicit CSI reporting type for different polarization configurations are listed in Tables I and Table II seperately.

Based on the above feedback and the expressions of the eigenvectors given in the previous section, the channel eigenvectors and precodercan be constructed by this information based on (3.20), (3.21) and (3.29), (3.30).

4.2 CSI overhead analysis

The direction and amplitude information for each path is long-term/wideband reported, a same set of these information can be used for each layer and each polarization, thus, only a small amount of bits are needed. The Short-term/Subband reporting types,andfor each pathi. Considering QPSK or 8PSK for quantization, which only need total 4 or 6 bits, and it is meaningful that the total number of bit will not increase obviously with the increase of antenna number, thus CSI feedback overhead is obviously reduced especially in a massive MIMO system.

Table I CSI reporting types description, for polarization configuration I

Table II CSI reporting types description, for polarization configuration II

V. PERFORMANCE EVALUATION

In this section, link level and system level simulation results are presented to validate the proposed LMPIF feedback scheme. For comparison, the performances of LTE DFT codebook based feedback and ideal feedback are evaluated. Two kinds of MIMO channels are considered, i.e. two paths channel and three paths channel. In the link level simulation,SU-MIMO is assumed and one user can have one or two data layers. In the system level simulation, SU/MU-MIMO dynamic switching and adaptive selection of the number of transmission layers are adopted. More specific parameters and details of the simulation can be found in APPENDIX A.

5.1 Link level performance evaluation

Fig. 3 Link level simulation results of various feedback schemes, 16(8 columns, dual-polarized), Rank1 (a) and Rank2 (b), Uma

Fig. 4 Link level simulation results of various feedback schemes, 64(4 columns,8 rows, dual-polarized), Rank1 (a) and Rank2 (b), Uma

The link level performances of the three feedback schemes are shown in Fig.3 to Fig.5 under a variety of antenna setting and transmission schemes. LMPIF outperforms DFT based codebook under all scenarios, which clearly demonstrates the effectiveness of the proposed scheme. The more multipath components LMPIF feeds back, the performance loss compared to ideal feedback narrows down.This feature provides system designer with the flexibility to tradeoff between performance and feedback overhead. Moreover, the performance gain over DFT based codebook is more prominent under 2-layer data transmission.

The performance gap among the three schemes widens under Umi(Urban micro)channel with richer scattering. This proves again that DFT based codebook works poorly in practice due to its single path assumption.On the contrary, LMPIF can narrow down this performance gap by feeding back more multipath components. The influence of quantization errors on the performance of LMPIF is plotted in Fig. 6. It can be observed that the performance of 2 or 3-bits quantization is very close to the ideal case. This means that LMPIF is insensitive to quantization errors and a low feedback overhead can be achieved with only a few feedback bits.

5.2 System Level performance evaluation

The system level simulation results are listed in Table 3. Compared to DFT based codebook,a 22%～32% gain is observed for mean UPT while a 86%～113% gain is achieved for cell edge UEs. Overall, the performance gain of LMPIF over DFT based codebook is significant. In addition, the proposed LMPIF is able to boost the performance of cell edge UEs,which can help to provide consistent user experience.

VI. CONCLUSIONS

Fig. 5 Link level simulation results of various feedback schemes, 64(4 columns,8 rows, dual-polarized), Rank1, Umi

Fig. 6 Link level simulation results of LMPIF scheme with different phase precision,64(4 columns,8 rows, dual-polarized), Rank1, Uma

Table III System simulation results of various feedback schemes,643D-UMi

Table III System simulation results of various feedback schemes,643D-UMi

This paper proposes LMPIF scheme for achieving higher spectrum efficiency for dual-polarized antenna system with low feedback overhead in dual-polarized MIMO Systems,which outperforms current DFT codebook based feedback. In this paper we reveal the relationship between some of the multipath parameters and the final form of channel characteristic vectors, and takes into account some feedback based on this. For the feedback methods that we consider in this paper, most of their parameters are semi-static, long-period, full bandwidth, only a few phase parame-ters are dynamic feedback. Compared with the situation of single polarization, dual-polarized feedback only adds a dynamic phase parameter. Basing on these parameters information,the base station can reconstruct channel characteristic vectors more accurately.

ACKNOWLEDGEMENTS

This work was supported by the National High-Tech R&D Program (863 Program 2015AA01A705).

Appendix A

Table A.1 Simulation parameters for Macro cell Scenario

APPENDIX B

In the above equations,

In the above equations,

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