This paper discusses the multiuser beamforming in FDD massive MIMO systems. It first introduces the feature of FDD massive MIMO systems to implement multiuser beamforming schemes. After that, considering the realistic implementation of multiuser beamforming scheme in FDD massive MIMO systems, it introduces the knowledge of channel quantization. In the main part of the paper, we introduce two traditional multiuser beamforming schemes and analyse their merits and demerits. Based on these, we propose a novel multiuser beamforming scheme to flexibly combine the merits of the traditional beamforming schemes. In the final part of the paper, we give some simulation results to compare the beamforming schemes mentioned in the paper. These simulation results show the superiority of the proposed beamforming scheme.
As of the exponential increasing load of wireless communications networks, research on network architecture and quality of service has been done in various fields [
A large number of surveys on massive MIMO have been done by communication researchers [
Owing to the channel reciprocity in timedivision duplex (TDD) massive MIMO systems, it is feasible to obtain the instantaneous CSIT, while the CSIT acquisition is a great challenge in frequencydivision duplex (FDD) massive MIMO systems.
In FDD massive MIMO systems, the two largest problems are reference signal (RS) design and codebook design. A great deal of research has been done to solve the problems [
In order to fully exploit the potential of massive MIMO in FDD systems, a beamforming (BF) scheme exploiting the spatial correlation (SC) was proposed [
In this paper, we consider that the BSs feed back quantizedchannelcodebook index. Based on the quantized channel, we put forward a SC and interference suppression (SCIS) based MUBF scheme, to make it feasible for the BSs to simultaneously schedule tens of UEs in FDD massive MIMO systems. The proposed BF scheme only needs partial CSIT, which can be derived by transmitting some affordable RSs. Therefore, the RS overhead in FDD massive MIMO systems is flexible. With the partial CSIT, SCISBF can be transformed from SCBF by a transformation matrix and a rotation angle. The transformation matrix can be deduced through Householder rotation, and the rotation angle can be derived by transmitting a RS in the downlink. Moreover, based on the quantizedchannelcodebook and quantizedchannelselection approach given in this paper, we evaluate the performance of the proposed SCISBF scheme with different levels of feedback overhead, and numerical results indicate that SCISBF performs better than SCBF when UEs only feed back a few bits of quantizedchannelcodebook index.
The remainder of the paper is organized as follows. Section
As depicted in Figure
System model.
Transmission model.
In this part, we mainly introduce the antenna modeling of the 3D channel used in this paper [
3D antenna model.
In this paper, we select the 3GPP 3D channel as the reference channel [
In terms of 3D beamforming steering direction, the transmit correlation matrix can also be defined as
In (
In this part, we talk about the channel quantization. A simple way to design the quantizedchannel codebook is based on DFT. Suppose that the BSs select
To select the quantizedchannel vector from the abovementioned codebook, we firstly define
The criterion of quantizedchannelvector selection is to find
Suppose
Based on the aforementioned channel model, the received signal of user
In this section, we first review two conventional BF schemes, namely, ZFBF scheme and SCBF scheme. Then, a novel BF scheme exploiting both the SC matrix and partial channels is proposed to synthesize the merits of the two types of BF schemes.
The criterion of ZFBF is to eliminate the interferences among users. Define
As for SCBF, the criterion is to maximize the signal power of the desired user by exploiting the spatial correlation without considering the interference to other users. From [
Compared to ZFBF, SCBF only needs the quasistatic SC matrix, which can significantly simplify the BF process and release the dependence on the CSIT in LSMIMO systems. Nevertheless, the system performance degrades correspondingly.
Ignoring the subscript of user index, notice that
That is to say, the proposed SCISBF weight vector
Next, with the quantizedchannel vector fed back in the uplink, we will deduce transform matrix
There exists a unitary transformation matrix
Denote
In the unitary space
Assume
Here, we have to note that the ZFBF weight vector is calculated from reduceddimension channel matrix; thus, the calculation complexity is adjustable and depends on the antennaselection proportion. Moreover, it is easy to obtain the transformation matrix. As to SCSLBF, the SLBF weight vector is calculated from the wholedimension, no matter what the antennaselection proportion. Besides, the transformation matrix of SCSLBF needs many times of matrix multiplication [
The rotation angle in expression (
The calculation of the rotation angle
In order to maximize
Expression (
Although the BS is ignorant of the full channel vector
RS transmission model to get
To evaluate the proposed SCISBF scheme, we build a systemlevel simulation platform. In our simulation, the network model consists of 19 macrocells. Each cell contains 3 sectors, where each BS is located at the cell center with uniform planar array (UPA). The main simulation parameters are listed in Table
Parameters configuration.
Parameters  Settings 

Scenario  3DUma 
Carrier frequency  2 GHz 
Bandwidth  5 MHz 
User speed  3 km/h 
Channel model  3GPP 3D channel model 
eNB transmit power  43 dBm 
Antenna gain  8 dBi 
Antenna element pattern  BS: UPA (row × col: 12 × 10) user: single antenna 
Antenna element interval  0.5 
UE height  1.5 m 
UE distribution  30 UEs per sector, uniform in cell 
Noise density  −174 dBm/Hz 
Path loss/shadow fading/fast fading  See TR36.873 [ 
To evaluate the performance of SCISBF, we have to confirm the antenna index set firstly. From the above derivation, we can see that
For antennaselection approach (SCIS(
In this part, we evaluate the performance of SCISBF with different antennaselection proportion. Fixing the number of scheduled users as 10, we compare the performance of SC, MRT, ZF, SCIS
Figure
CDF versus SINR of SCISBF.
CDF versus throughput of SCISBF.
In this part, we evaluate the performance of SCISBF with perfect CSIT. With the antennaselection approach given above, the spectral efficiency (SE) versus scheduled user numbers of different BF schemes is shown in Figure
CDF versus SE of different BF schemes with perfect CSIT.
Considering practical FDD systems, the BS does not know the real channel but the quantizedchannel vector. Based on limited feedback, fixing the number of scheduled users as 10, we evaluate the system performance of SCISBF in this part.
Figure
Measurement of spectral efficiency.
Feedback overhead 





BF scheme  SCSL( 
SCIS( 
SCSL( 
SCIS( 
SCSL( 
SCIS( 


System SE (bit/s/Hz)  7.153  8.865  7.974  8.865  8.592  9.632 


System SE gain (compared to SC)  −9.73%  11.88%  0.63%  19.40%  8.43%  21.55% 
CDF versus SINR of SCSL and SCIS with imperfect CSIT.
CDF versus SE of SCSL and SCIS with imperfect CSIT.
Table
Feature of beamforming schemes.
BF scheme  Spatial correlation  CSIT  Performance  RS overhead  Feedback overhead  Calculation complexity 

SC  √ 

Normal  Low  None  Low 


SCSL  √  √  Poor dynamic balance  High  High  


SCIS  √  √  Good dynamic balance  Low  Flexible 
In this paper, we study the performance of different MUBF schemes in massive MIMO systems, where the BSs feed back quantizedchannelcodebook index, but not conventional precoding codebook index. Based on it, we put forward a novel SCISBF scheme in order to make it feasible for the BSs to simultaneously serve tens of UEs in the same timefrequency resources. In contrast to other conventional BF schemes, the calculation complexity of SCISBF is relatively low as it only requires the reduceddimension channel matrix, and the performance of it is quite well. Besides, it can effectively balance the system performance and overhead of RSs. Furthermore, it only needs a few feedback bits to implement SCISBF in practical FDD massive MIMO systems. In a word, SCISBF can make it feasible and flexible to implement massive MIMO in FDD systems.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Key Scientific Instrument and Equipment Development Project under Grant 2013YQ20060706, the High Technology Research and Development Program of China under Grant 2014AA01A705, and the China Natural Science Funding (NSF) under Grant 61171106.