To implement highorder multiuser multiple input and multiple output (MUMIMO) for massive MIMO systems, there must be a feedback scheme that can warrant its performance with a limited signaling overhead. The interferencetonoise ratio can be a basis for a novel form of Codebook (CB)based MUMIMO feedback scheme. The objective of this paper is to verify such a scheme’s performance under a practical system configuration with a 3D channel model in various radio environments. We evaluate the performance of various CBbased feedback schemes with different types of overhead reduction approaches, providing an experimental ground with which to optimize a CBbased MUMIMO feedback scheme while identifying the design constraints for a massive MIMO system.
I. Introduction
A key technology in nextgeneration mobile communication systems is that of massive multiple input and multiple output (MIMO) or fulldimension (FD)MIMO, where a base station or an evolved Node B (eNB) with a very large number of antenna elements serves a large number of user equipments (UEs) simultaneously on the same timefrequency resource set
[1]
–
[3]
. For downlink transmissions in a massive MIMO system, an eNB requires downlink channel state information (CSI) to perform beamforming for multiple UEs and to effectively nullify interuser interference. When timedivision duplexing (TDD) is employed, downlink CSI can be extracted from uplink signals using the channel reciprocity. However, since frequencydivision duplexing (FDD) is used in most existing cellular systems, effective CSI feedback schemes need to be developed to minimize the feedback overhead while maintaining high system throughputs
[4]
–
[12]
.
To reduce feedback overhead, a massive MIMO system can use a finite set of precoding matrices, called a codebook (CB). When only one UE is served each time with a CBbased feedback scheme, a feedback of a single CB index is sufficient for beamforming. In a multiuser MIMO (MUMIMO) system in which multiple UEs are simultaneously scheduled on the same timefrequency resource, however, multiple CB indices that minimize the multiuser interference must be reported so as to avoid performance degradation due to interference. In
[13]
, a novel CBbased MUMIMO feedback scheme was proposed by employing a feedback of interferencetonoise ratio (INR) for a given codebook. This scheme, referred to as a multiuser interference indicator (MUI) feedback scheme in this paper, allows an eNB to perform highorder MUMIMO with flexible scheduling while reducing feedback overhead as well as dedicated pilot overhead. Some simulation results are also provided in
[13]
based on a onering channel model to show that highorder MUMIMO is feasible in FDDbased massive MIMO systems. Although the simulation results in
[13]
are very satisfactory, they are not acceptable for realistic cellular systems, since it is critical to evaluate the performance of such systems under a more detailed systemlevel simulation (SLS) setup, including cell structures, scheduling, and a practical 3D channel model to capture the channel features of a massive MIMO system. It would be possible to extract insights from the simulation results for performance improvement or overhead reduction only with the SLS results under realistic environments.
In this paper, we present system performance results for an MUI scheme with SLS. In the SLS, we consider FDMIMO scenarios with a 2Dactive antenna array system (AAS), which are described in the 3rd Generation Partnership Project (3GPP)
[14]
. The SLS, including the 3D channel model, is verified with calibration procedures specified in
[14]
and
[15]
. We also discuss the characteristics of highorder MUMIMO in massive MIMO systems using various SLS results with different antenna configurations — for example, antenna polarization; number of horizontal antenna elements; and different cellular environments — for example, urban macro (UMa) or urban micro (UMi).
The rest of this paper is organized as follows. Section II describes the system model considered in this paper, including antenna configurations, CBs, scheduling, and several MUMIMO feedback schemes, including MUI. The systemlevel evaluation results of the MUMIMO feedback schemes are given in Section III, and a further analysis based on the simulation results is provided in Section IV. Finally, conclusions are drawn in Section V.
II. System Model
 1. Massive MIMO System Model
A. Antenna Configuration
In this paper, a uniformly spaced 2D planar antenna array model is used. Its configuration is represented by (
M
,
N
,
P
), where
M
is the number of antenna elements with the same polarization in each column,
N
is the number of columns, and
P
is the number of polarization dimensions.
Figures 1(a)
and
1(b)
illustrate an antenna configuration for (
M
,
N
, 2) and (
M
,
N
, 1), respectively. We consider a UE antenna configuration of (1, 1, 2) with a cross polarization (Xpol) of 0° and 90°; eNB has various antenna configurations with either a uniform linear array (ULA) or Xpol of ±45°
[14]
,
[15]
. In the current evaluation, we consider a total of 64 antennas; for example,
M
= 8,
N
= 4, and
P
= 2 for the configuration in
Fig. 1(a)
, which is considered as a realizable case of massive MIMO in practice, as implied in
[14]
and
[15]
.
2D planar antenna structure with (a) Xpol and (b) ULA.
B. Codebook for MUMIMO
A rank1 CB, denoted by 𝒲 , is employed for MUMIMO, in which a single data layer is assigned to each UE
i
by a beamforming vector
w
_{i}
∈ 𝒲. Note that for a rank1 CB, we consider an oversampled discrete Fourier transform (DFT) beamforming vector, which is defined by an ordered pair (
i
_{1}
,
i
_{2}
) for UE
i
.
A baseline vector
c
_{ℓ}
defined as
(1) c ℓ = 1 N [ 1, e −j2π⋅ ℓ 2N , … , e −j2π⋅ (N−1)ℓ 2N ].
For
P
= 1, we have a ULAbased CB with beamforming vectors
w i = c 2 i 2 + i 1 T
(
i
_{1}
= 0, 1 and
i
_{2}
= 0, 1, … ,
N
− 1). For
P
= 2 (that is, Xpol), we consider a double CB (a subsampled version of beamforming vector
w
_{i}
), which is given as
w
_{i}
= [
c
_{i2}
a
_{i1}
c
_{i2}
]
^{T}
(
i
_{1}
= 0, 1 and
i
_{2}
= 0, 1, … , 2
N
− 1), where
a
_{i1}
∈ {1, −1}. Let 𝒞 denote a set of codebook indices; that is, 𝒞 = {1, 2, …, 𝒲}. Note that each beamforming vector has a dimension of
PN
; And there exist 2
PN
beamforming vectors (that is, 𝒲 2
PN
).
C. MUMIMO System Model
Each eNB employs a 2D AAS (
M
,
N
,
P
); that is, a total of
N
_{T}
=
M
×
N
×
P
transmit antennas. The antenna configuration of all UEs is (1, 1, 2); that is, a total of
N
_{R}
= 1×1×2 receive antennas. Meanwhile, a fixed tilting is considered in the vertical dimension for the 3D channel model
[16]
. Denoting an effective channel with all Tx/Rx antennas and vertical tilting by
H ˜
, the signal received by the UE for an MUMIMO scenario is given as
(2) y= H ˜ x+n,
where
x
is an input signal vector,
x
= [
x
_{1}
,
x
_{2}
,…,
x_{K}
]
^{T}
, of rank
K
, of the input covariance given by ∑ = E[
xx
^{H}
] , and
n
denotes Gaussian noise including othercell interference with an average power of
σ n 2
, in a multicell environment.
Let 𝒮 denote a set of UEs that are scheduled for MUMIMO transmission (that is, 𝒮=
K
). Furthermore, let
w
_{u}
∈ 𝒲 and
d_{u}
,
u
denotes a UE (
u
= 1, … ,
K
,
u
∈
𝒮
), denote a beamforming vector and a data symbol for a UE, respectively. We consider a single data stream per user. Assuming an equal power allocation to all users served by the given eNB with transmit power of
ρ
; that is, tr(∑) =
ρ
/
K
·
I
_{K}
, the received signal for a UE is given as
(3) y u = ρ/K ⋅( H ˜ u w u d u + ∑ j∈𝒮\u H ˜ u w j d j ) +n.
Furthermore, its signaltointerferenceplusnoise ratio (SINR) is represented as
(4) γ u =  g u H ˜ u w u  2 K σ u 2 + ‖ g u H ˜ u w −u ‖ F 2 ,
where
σ u 2 =  g u  2 σ u 2 /ρ
,
W
_{−u}
denotes a precoding matrix that excludes the
u
th precoding vector (that is,
W
_{−u}
= [
w
_{1}
, … ,
w
_{u−1}
,
w
_{u+1}
, … ,
w
_{K}
]) and
g
_{u}
is a minimum mean square errorinterference rejection combining (MMSEIRC) filter in the receiver, which is given as
(5) g u = ( H ˜ u w u ) H ( ρ K H ˜ u w u ( H ˜ u w u ) H + σ n 2 I N R ) −1 .
D. Scheduling
Based on the precoding matrix indicator (PMI) information and the channel quality information (CQI) from UEs, eNB determines a set of users that will be scheduled for MUMIMO transmission (see
Fig. 2
). The scheduling is performed every time slot
t
and the number of scheduled users, denoted as
K
, varies from 1 to
K
_{max}
; that is,
K
∈ {1, 2, …,
K
_{max}
}. Let 𝒮
_{K}
(
t
) denote a set of users that are scheduled when
K
users are selected as an MUMIMO transmission group at time slot
t
. The optimal UE group, denoted by 𝒮* (
t
), is determined by selecting a set of users that maximize the proportional fairness metric
[17]
as follows:
(6) 𝒮 * ( t )= arg max 𝒮 K ( t ),K∈{ 1,2, … , K max } ∑ u ∈ 𝒮 K ( t ) R u 𝒮 K ( t ) T u ( t ) ,
where
R
_{u𝒮K (t)}
denotes the bandwidth efficiency of the
u
th UE (that is,
R
_{u𝒮K (t)}
= log
_{2}
(1+
γ_{u}
)) ,
γ_{u}
is the SINR of the
u
∈ 𝒮
_{K}
(
t
), and
T_{u}
(
t
) denotes the average throughput of the
u
th UE at time slot
t
, which is updated for all UE as
(7) T u (t+1)={ (1−1/ t c ) T u (t)+ R u 𝒮 ∗ (t) / t c u∈ 𝒮 ∗ (t), (1−1/ t c ) T u (t) u∉ 𝒮 ∗ (t).
System model: SU/MUMIMO dynamic switching.
The parameter
t_{c}
in (7) defines time window in which we wish to achieve fairness. We consider dynamic switching between SUMIMO and MUMIMO as shown in
Fig. 2
. SUMIMO can be regarded as a special case of MUMIMO with
K
= 1.
 2. MUMIMO Feedback Schemes
In an SUMIMO, each UE selects its own best PMI, which is reported to the eNB along with the CQI corresponding to the selected PMI. In an MUMIMO system, similarly, UEs shall report some information to the eNB to select the best set of users. Depending on the type of feedback information in this paper, we consider two different feedback schemes for MUMIMO: a multiuser channel quality information (MUCQI) scheme
[18]
,
[19]
and an MUI scheme
[13]
.
A. MUCQI Feedback Scheme
In the MUCQI feedback scheme, UEs report the
best companion
PMIs that can be coscheduled to maximize the SINR in (4). One simple approach that can reduce the feedback overhead is to consider only 2user MUMIMO systems; which selects the best companion PMI (
q_{u}
,
c_{u}
) such that
(8) q u = arg max i=1, 2, … ,  𝒲  ‖ H ˜ u w i ‖ F 2
and
(9) c u = arg min i=1, 2, … ,  𝒲  ‖ H ˜ u w i ‖ F 2 .
Then, the MUCQI for a given UE
u
is given by
(10) γ u =  g u H ˜ u w q u  2 2 σ u 2 +  g u H ˜ u w c u  2 .
Then, UE
u
reports (
q_{u}
,
c_{u}
,
γ_{u}
) to the eNB, which will be used to determine the best companion PMIs
[18]
. With this scheme, the interUE interference can be effectively minimized. In this paper, we consider a more aggressive approach to investigate the best possible performance of an MUCQI scheme for
K
_{max}
= 2. More specially, each UE
u
reports the PMI
q_{u}
, determined by (8), along with a set of CQI for all other PMIs except
q_{u}
; that is, {(
q_{u}
,
c_{u}
,
γ_{u}
)}
_{cu ∈𝒞\qu}
. In this way, the eNB can consider all possible UEpairs for a 2user MUMIMO by (6). Furthermore, CQI for SUMIMO must be also reported to support the dynamic switching between SUMIMO and MUMIMO for the system model in
Fig. 2
. Along with PMI associated with the CB and CQI for the selected PMI, a rank indicator is required to enable a single layer or two layers for SUMIMO. For a 2user MUMIMO system (that is,
K
_{max}
= 2), therefore, a total number of feedback values include one for RI, one for SUMIMO PMI, one for SUMIMO CQI, one for MUMIMO PMI, and 𝒲 − 1 for MUMIMO CQI. As the amount of feedback overhead increases exponentially as
K
increases, the MUCQI scheme may not be realistic for
K
> 2.
B. MUI Feedback Scheme
To deal with the feedback overhead problem with the MUCQI scheme for
K
> 2,
[13]
considers the MUI feedback scheme, in which each UE
u
reports the PMI
q_{u}
with the best signaltonoise ratio (SNR), along with the INRs for all other PMIs except
q_{u}
, as follows:
(11) INR u, c u =  g u H ˜ u w c u  2 σ u 2 ( c u ∈𝒞\ q u ).
Let 𝒱 denote a set of PMIs that are reported by the UE in the scheduled user group 𝒮 ; that is, 𝒱 = {
q_{u}
}
_{u∈𝒮}
. Since all of the INR feedback information for each UE is known to the eNB, we can rewrite the SINR for UE
u
as
(12) γ u = SNR u, q u K+ ∑ i∈𝒱\ q u INR u,i (K∈{1, 2, ... , K max }),
where
SNR u, q u =  g u H ˜ u w q u  2 / σ u 2
. Since each UE
u
reports its own , SNR
_{u,qu}
along with a set of INRs, {INR
_{u,cu}

c_{u}
∈ 𝒞 \
q_{u}
} , the number of feedback values for the MUI scheme will be 𝒲 (one for SNR and 𝒲 − 1 for INR values). The total number of feedback values will be the same as in the MUCQI scheme (that is, one for RI, one for SUMIMO PMI, one for SUMIMO CQI, one for MUMIMO PMI, one for SNR, and 𝒲 − 1 for INR). Even with the same amount of feedback, however, the MUI feedback scheme allows for
K
user grouping as opposed to the MUCQI feedback scheme, in which only twouser grouping is considered due to its overhead.
Feedback overhead can be further reduced if partial MUI and 1bit MUI feedback schemes are considered
[13]
. The partial MUI feedback scheme reports INR for PMIs in one of two subsets defined by
i
_{1}
= 0 or 1, reducing the feedback overhead by 1/2. Meanwhile, a 1bit MUI feedback scheme can be implemented by employing a bit map to report the INR values. More specifically, the INR value is set to 1 if it is lower than a given threshold value, which is defined relative to SNR, and to 0 otherwise, significantly reducing its feedback overhead.
III. Simulation Results
This section presents the systemspecific simulation results of SUMIMO and MUMIMO systems. Our evaluation methodology is strictly based on the simulation scenarios and system model in the 3GPP standardization process. In particular, it implements the 3D channel model in
[14]
, which has been verified by conducting phase1 and phase2 channel parameter calibrations with and without a fastfading mode. Furthermore, the overall SLS has been verified by the baseline throughput calibration specified in
[14]
. The calibration is completed by referring to the cumulative distribution function (CDF) reported by multiple companies
[20]
.
We follow the simulation parameters for the SLS in
[14]
and
[15]
, which are summarized in
Table 1
. While SUMIMO simulations use nine subbands (PUSCH 31 format), MUMIMO (both MUCQI and MUI schemes) simulations employ wideband feedback to reduce the feedback overhead. For simplicity of the simulation, we use four bits per CQI instead of differential encoding. We assume that only one or two UEs can be supported simultaneously in MUCQI due to the feedback limit to
K
_{max}
= 2. On the contrary, MUI can simultaneously support a large number of UEs with the same amount of feedback overhead. The maximum number of UEs for MUMIMO with the MUI feedback scheme is limited to eight (that is,
K
_{max}
= 8) in this simulation. Only fixed tilting is applied to the vertical axis by following the method discussed in
[14]
and
[16]
, while adaptive beamforming is applied to the horizontal axis using the CB structure discussed in Section II1B.
Parameter  Value 
Channel model  3DUMa (ISD = 500 m), 3DUMi (ISD = 200 m) 
Channel bandwidth  10 MHz 
Carrier frequency  2 GHz 
Duplexing  FDD 
Network layout  Hexagonal grid, 19 cell sites, 3 sectors per site 
Wrapping method  Geographical distancebased 
Antenna configuration  Tx  (8, 4, 2), (4, 8, 2), (10, 2, 2) : ±45°(4, 16, 1) 
Rx  (1, 1, 2) : 0° and 90° 
Polarized antenna model  Model1 from 3GPP TR36.873 [14] 
UE distribution  3DUMi and 3DUMa scenarios [14] 
UE speed  3 km/h 
UE attachment  Based on RSRP [14] 
UE array orientation  Ω_{UT,α}  Uniformly distributed on (0, 360°) 
Ω_{UT,β}  90° 
Ω_{UT,γ}  0° 
UE antenna pattern  Isotropic antenna gain pattern A'(θ', ϕ') = 1 
# of UEs per cell  10 
Traffic model  Full buffer 
# of layers  SUMIMO  1 or 2 layers 
MUMIMO  Up to 8 layers for MUI 
Scheduler  Proportional fair scheduling per TTI allocation 
Feedback information  SUMIMO  4 Tx: Rel8 CB [21],8 Tx: Rel10 double CB [22],16 Tx: double CB for P = 2 & DFT CB for P = 1 
MUMIMO  Wideband PMI, CQI, MUI or MUCQIP = 1: oversampled DFTbased CBP = 2: subsampled double CB 
Feedback type  SUMIMO  Subband feedback 
MUMIMO  Wideband feedback 
Feedback period  5 ms 
Receiver  Ideal channel estimation MMSEIRC receiver 
Interference model  Ideal interference estimation from interference measurement resource 
Hybrid ARQ  Maximum of 4 transmissionsNo error on ACK/NACK8 ms delay between retransmissions 
Overhead  DL CCHs  3 symbols 
CRS  16 REs/PRB/subframe 
CSIRS  Every 5 ms for 4/8/16 port and 1RE/port/ PRB 
DMRS  12 REs/PRB/subframe 
 1. System Evaluation Results
In this section, system evaluation results are presented in terms of the spectral efficiency (SE).
Figure 3
shows the CDFs of the SE for MUMIMO in a UMi environment with antenna configurations of (8, 4, 2), (4, 8, 2), and (4, 16, 1). Note that the antenna configurations under consideration are feasible for implementation in real systems. In
Fig. 3
, there are noticeable gaps in the SE between the MUCQI (
K
_{max}
= 2) and MUI schemes (
K
_{max}
= 8). Comparing the performance of these schemes with SUMIMO, the corresponding SE performance improvements are 10.3% and 24.6%, respectively. It implies that highorder MUMIMO can substantially improve the system performance over the SUMIMO system.
CDF of MUMIMO throughput with various antenna configurations: UMi.
Table 2
shows the cell average, median, and lowest 5% SEs of SUMIMO, MUCQI, and MUI schemes for an antenna configuration of (8, 4, 2), respectively. Although wideband feedback is used for the MUMIMO schemes (both MUCQI and MUI), they outperform that of SUMIMO, which is based on feedback from nine subbands.
Evaluation results for (8, 4, 2).
Feedback schemes  Cell average throughput (bps/Hz)  Median UE throughput (bps/Hz)  5% UE throughput (bps/Hz) 
PUSCH 31 SUMIMO (baseline)  UMa  2.20 (0%)  0.169 (0%)  0.057 (0%) 
UMi  2.30 (0%)  0.178 (0%)  0.066 (0%) 
MUI  UMa  2.72 (24%)  0.230 (36%)  0.084 (48%) 
UMi  3.00 (29%)  0.246 (38%)  0.082 (25%) 
MUCQI (K = 2)  UMa  2.64 (20%)  0.225 (33%)  0.077 (36%) 
UMi  2.73 (19%)  0.232 (30%)  0.076 (15%) 
Table 3
shows the SEs for an antenna configuration of (4, 8, 2). Owing to the increased spatial separation in horizontal beamforming (recalling that fixed tilting is applied to the vertical axis), a larger performance gain has been achieved, especially for the MUMIMO schemes. Note that the MUI performance gap between UMi and UMa is larger than that of
Table 2
.
Table 4
shows the SEs for an antenna configuration of (4, 16, 1). Comparing the results against those for (4, 8, 2) in
Table 3
(both with the same number of antenna elements), we can see that much larger MUMIMO performance gain can be achieved with ULA.
Evaluation results for (4, 8, 2).
Feedback schemes  Cell average throughput (bps/Hz)  Median UE throughput (bps/Hz)  5% UE throughput (bps/Hz) 
PUSCH 31 SUMIMO (baseline)  UMa  2.37 (0%)  0.189 (0%)  0.066 (0%) 
UMi  2.54 (0%)  0.202 (0%)  0.073 (0%) 
MUI  UMa  3.42 (44%)  0.277 (46%)  0.098 (49%) 
UMi  3.70 (46%)  0.332 (64%)  0.103 (41%) 
MUCQI (K = 2)  UMa  2.76 (16%)  0.227 (20%)  0.078 (18%) 
UMi  3.21 (26%)  0.283 (40%)  0.094 (28%) 
Evaluation results for (4, 16, 1).
Feedback schemes  Cell average throughput (bps/Hz)  Median UE throughput (bps/Hz)  5% UE throughput (bps/Hz) 
PUSCH 31 SUMIMO (baseline)  UMa  2.19 (0%)  0.180 (0%)  0.069 (0%) 
UMi  2.45 (0%)  0.209 (0%)  0.079 (0%) 
MUI  UMa  3.75 (71%)  0.293 (63%)  0.091 (33%) 
UMi  4.61 (88%)  0.392 (88%)  0.106 (35%) 
MUCQI (K = 2)  UMa  3.13 (43%)  0.267 (48%)  0.088 (28%) 
UMi  3.54 (44%)  0.302 (44%)  0.100 (27%) 
 2. Feedback Overhead Reduction Schemes
Table 5
compares the amount of feedback overhead for various schemes. Although the MUI scheme achieves better performance as compared to the MUCQI scheme with the same amount of feedback overhead (for example, 81 bits), the additional overhead compared to SUMIMO is significant. For example, a corresponding gain over SUMIMO requires 2.6 times as many more feedback bits. The additional feedback overhead is not negligible and more practical methods need to be used in real systems. Compared to the MUI scheme, both the partial MUI scheme and the 1bit MUI scheme can reduce the feedback overhead by 40% (for example, 49 bits) and 56% (for example, 36 bits), respectively. Note that the 1bit MUI scheme incurs only 16% more feedback overhead than the SUMIMO. The INR threshold in the 1bit MUI scheme is a critical parameter for the system performance and must be carefully determined. To achieve an acceptable performance, the SNRbased adaptive threshold shown in
Fig. 4
is used for the simulations rather than using the fixed threshold in
[13]
.
Wideband MUMIMO feedback overhead comparison (T= 9,O= 15 coPMIs, offset levelB= 4).
Feedback schemes  RI  PMI  CQI  MUCQI  MUI  Total 
PUSCH 31 SUMIMO (baseline)  1  8 = 4(1st) + 4(2nd)  4 + 2T  N/A  N/A  31 bits 
MUI  1  8 + 4  4 + 4  N/A  B·O  81 bits 
Partial MUI  1  8 + 4  4 + 4  N/A  $\frac{B(O1)}{2}$  49 bits 
1bit MUI  1  8 + 4  4 + 4  N/A  O  36 bits 
MUCQI (K=2)  1  8 + 4  4 + 4  B·O  N/A  81 bits 
MUCQI (K=3)  1  8 + 4  4 + 4  $O{\displaystyle \sum _{j=1}^{K1}\left(\begin{array}{c}L\\ j\end{array}\right)}$  N/A  501 bits 
INR threshold for 1bit MUI scheme.
Table 6
shows the SEs of the partial MUI and 1bit MUI schemes as compared to the MUI scheme. Note that their performances do not significantly degrade (around 10% or less in most cases) while they substantially reduce the feedback overhead.
Performance attenuation with feedback reduction.
Feedback schemes  Cell average throughput (bps/Hz)  Median UE throughput (bps/Hz)  5% UE throughput (bps/Hz) 
(8, 4, 2)  MUI  UMa  2.72 (0%)  0.230 (0%)  0.084 (0%) 
UMi  3.00 (0%)  0.246 (0%)  0.082 (0%) 
Partial MUI  UMa  2.59 (−5%)  0.212 (−8%)  0.074 (−12%) 
UMi  2.80 (−6%)  0.223 (−9%)  0.072 (−13%) 
1bit MUI  UMa  2.56 (−6%)  0.216 (−6%)  0.074 (−11%) 
UMi  2.73 (−8%)  0.228 (−7%)  0.086 (5%) 
(4, 8, 2)  MUI  UMa  3.42 (0%)  0.277 (0%)  0.098 (0%) 
UMi  3.70 (0%)  0.332 (0%)  0.103 (0%) 
Partial MUI  UMa  3.08 (−10%)  0.251 (−9%)  0.086 (−13%) 
UMi  3.65 (−1%)  0.311 (−6%)  0.111 (8%) 
1bit MUI  UMa  2.97 (−13%)  0.247 (−11%)  0.082 (−17%) 
UMi  3.25 (−12%)  0.280 (−16%)  0.097 (−6%) 
(4, 16, 1)  MUI  UMa  3.75 (0%)  0.293 (0%)  0.091 (0%) 
UMi  4.61 (0%)  0.392 (0%)  0.106 (0%) 
Partial MUI  UMa  3.69 (−2%)  0.298 (2%)  0.092 (1%) 
UMi  4.18 (−10%)  0.361 (−8%)  0.103 (−2%) 
1bit MUI  UMa  3.43 (−9%)  0.287 (−2%)  0.095 (4%) 
UMi  3.66 (−21%)  0.317 (−19%)  0.101 (−5%) 
The 𝒲 values of CQI feedback are required for the MUI scheme (more specifically, 1 SNR value and 𝒲 − 1 INR values).
Figure 5
illustrates the CDFs for 31 values of INR, given by (10), for one specific (but typical) UE for the different oversampled values
i
_{1}
, where
i
_{1}
= 0 or 1 in this simulation. Depending on the value of
i
_{1}
, there exist two groups of INR values. While all INR values (32 values) need to be reported in the MUI scheme, only one group (16 values) is required for feedback in the partial MUI scheme. From
Fig. 5
, we can see that high and low INR values can be easily distinguished even in a single group. This implies that MUMIMO is feasible with the reduced feedback overhead schemes (for example, the partial MUI scheme or the 1bit MUI scheme). However, highorder MUMIMO is less probable with the partial MUI or 1bit MUI schemes, since the candidate UEs of simultaneous transmissions will be limited as compared to the MUI scheme.
Figure 6
shows the transmission layer probability in a UMi environment with an antenna configuration of (4, 16, 1). We can see that the performance is significantly degraded with the feedback reduction schemes, especially when the order of MUMIMO increases; for example,
K
≥ 6.
CDF of INR with CB: UMi and (4, 16, 1).
Probability of transmission schemes with different numbers of layers: UMi and (4, 16, 1).
IV. Further Analysis with Various System Configurations
In addition to the previous simulation results on the overall system performance, we provide additional results to analyze how SUMIMO and MUMIMO performances are respectively governed by the different antenna configurations and channel environments. The current analysis will provide an insightful basis for understanding the systemlevel performance. The same simulation parameters and scenarios as in Section III are considered for the further analysis.
 1. Antenna Configurations: Xpol vs. ULA
Figure 7
presents the 2D beam patterns for the different antenna configurations, (4, 16, 1) and (4, 8, 2), with the same number of antenna elements.
Figures 7(a)
and
7(b)
show the beam gain pattern for azimuth angle of 30°, beamformed with DFT codebook, and elevation beam pattern for 102° tilting, respectively. It is obvious that the different antenna arrangement induces the different beam pattern, even if the same number of antennas is employed. In particular, the beam pattern of (4, 16, 1) is narrower than that of (4, 8, 2). Our simulation results are also consistent with both the current observation and the field measurement data for FDMIMO in
[3]
. For the SUMIMO, meanwhile, it has been shown that the average throughput with (4, 8, 2) is higher than that with (4, 16, 1). This is attributed to the fact that more spatial multiplexing gain can be achieved with Xpol, which involves less correlation between polarization signals. However, a narrow beam pattern of the ULA might be more useful to highorder MUMIMO, as will be shown in
Figs. 8
and
9
.
Beam gain patterns with fixed azimuth angle (30°) and fixed vertical tilting angle (102°): (a) azimuth and (b) elevation.
The channel capacity is affected not only by the maximal singular value of the channel, denoted as
λ
_{max}
, but also by its minimal value, denoted as
λ
_{min}
. We can define their ratio as the
condition number
; that is,
λ
_{max}
/
λ
_{min}
. The lower the condition number (that is, a wellconditioned channel), the greater the capacity, since a low correlation is involved in providing higher spatial multiplexing gain
[23]
.
Figure 8
shows the condition numbers for the different antenna configurations, including the one for (10, 2, 2) reported by Phase2 calibration in
[14]
. Furthermore, a CDF of the baseline throughput is presented in
Fig. 9
. It is observed that Xpol (10, 2, 2) and (8, 4, 2) are wellconditioned as opposed to the ULA. In particular, 20% of users are illconditioned for the ULA. The advantage of Xpol antennas is attributed to the additional dimension obtained by cross polarization. Meanwhile,
λ
_{max}
increases with
N
, which improves a beam gain.
Singular values with various antenna configurations.
CDF of baseline throughput: UMi.
Note that the average cellSE is mainly governed by the spatial multiplexing gain, while the beamforming gain is attributed to the celledge SE. In fact, it is clear that the average cellSE of (4, 8, 2) is greater than that of (4, 16, 1), while 5% UE SE of (4, 16, 1) is greater than that of (4, 8, 2).
Figure 10
shows the probabilities of various transmission schemes with different numbers of transmission layers, where the SUMIMO and MUMIMO schemes are dynamically switched by scheduling. It is observed that a group of three or four users are selected for MUMMO mostly when the antenna configuration of (8, 4, 2) is used, while a group of four, five, or six users are selected frequently for (4, 16, 1) and (4, 8, 2), realizing the narrower beams. It is clear that ULA (4, 16, 1) is more useful to highorder MUMIMO than Xpol (4, 8, 2).
For the antenna configurations of (4, 16, 1) and (4, 8, 2), each UE will report one SNR value and 31 INR values to the eNB, in which the SINR can be computed by (11). Those INR values that are of a significant distance from the SNR will make goodcompanion PMIs.
Figure 11
shows a CDF for the number of INRs that corresponds to goodcompanion PMIs subject to the given SNRINR gap or better. It is obvious that the number of goodcompanion PMIs increases as the required SNRINR gap decreases. We find that the two antenna configurations (4, 16, 1) and (4, 8, 2) show a significant difference in the number of INRs that provide goodcompanion PMIs when the SNRINR gap is subject to 20 dB or better. This observation leads to a difference in group size of highorder MUMIMO, which is consistent with the results in
Fig. 10
. For example, since a greater number of candidate PMIs are available with ULA (4, 16, 1) than Xpol (4, 8, 2), ULA tends to achieve a higher SE.
Probabilities of transmission schemes with different numbers of layers: UMi.
CDF of number of INRs that satisfy given SNRINR gap: UMi.
 2. Environmental Scenarios: Indoor vs. Outdoor and LineofSight vs. NonlineofSight
We consider various channel characteristics in different environments: outdoor lineofsight (OLOS), outdoor nonlineofsight (ONLOS), indoor LOS (ILOS), and indoor NLOS (INLOS). We consider two different types of channel environments — UMa and UMi — each with different characteristics of LOS, as given by the distribution in
Fig. 12
. It is observed that LOS is more probable for the UMi environment in which the distance between a UE and the eNB is shorter than that in UMa.
Channel environments of UE.
We have demonstrated in Section III2 that higher throughput can be achieved in UMi than UMa as long as the same number of UEs is assumed in each cell; furthermore, the throughput gain for UMi becomes more significant for the MUMIMO. We first investigate the performance of the SU MIMO for different channel environments with varying antenna configurations. As shown in
Fig. 13
, there is not much difference in average cellSE with the different environments and furthermore, even with the various antenna configurations. This is attributed to the fact that the performance of the SUMIMO is mainly governed by the number of receive antennas and its performance is already saturated by the two receive antennas in the current system.
Average cell spectral efficiency: SUMIMO.
Figure 14
presents the performance of the MUMIMO. It is observed that more gain can be achieved in UMi than UMa, simply because UMi finds more LOS UEs, which provide more beam gain or narrow beam patterns, subsequently improving the MUMIMO gain.
Figure 15
confirms the fact that most of the highthroughput UEs belong to OLOS while many of the lowthroughput UEs belong to ONLOS. In particular, there is a significant gap between UMi and UMa with ULA (4, 16, 1), since LOS UEs in UMi are significantly improved by ULA narrow beam patterns.
Average cell spectral efficiency: MUMIMO.
Average UE spectral efficiency with LOS/NLOS.
V. Conclusion
In this paper, we have investigated the systemlevel performance of an INRbased MUMIMO feedback scheme (MUI) for a massive MIMO system, especially under the standard 3D channel model (specified by 3GPP TR36.873). Our SLS results have demonstrated that the MUI scheme is acceptable for supporting the highorder MUMIMO, as opposed to the existing MUCQI scheme, which is typically limited to twouser grouping only. Furthermore, it has been shown that the performance of the highorder MUMIMO can be improved with a ULA configuration, in which the beam patterns are very narrow compared to Xpol, and in a UMi environment, in which LOS UEs are dominant compared to a UMa environment. Meanwhile, we have investigated the possibility of reducing feedback overhead for an MUI without compromising the performance gain. In particular, the 1bit MUI schemes can reduce the feedback overhead by 50% while incurring only 10% performance degradation. However, the overall gain still varies with the antenna configurations and channel environments. In our future work, further optimization of a feedback scheme will be performed, and a more effective feedback overhead reduction scheme will be developed for highorder MUMIMO system.
This work was supported by the ICT R&D program of MSIP/IITP (1400004001, Development of 5G Mobile Communication Technologies for Hyperconnected Smart Services).
BIO
only1korea@korea.ac.kr
Yongin Choi received his BS degree in electrical engineering from Korea University, Seoul, Rep. of Korea, in 2010. Since then, he has been with the Department of Electrical Engineering, Korea University, partaking in a combined MS and PhD course. His research interests include radio resource management; multipleinput and multipleoutput communication systems; and crosslayer design for mobile radio communication systems and wireless networks.
lijrew@korea.ac.kr
Jaewon Lee received his BS degree in information and communication engineering from Chungbuk National University, Cheongju, Rep. of Korea, in 2014. Since then, he has been with the Department of Telecommunication System Technology, Korea University, Seoul, Rep. of Korea, partaking in a combined MS and PhD course. His research interests include massive MIMO and waveforms.
minjoong@dongguk.edu
Minjoong Rim received his BS degree in electronics engineering from Seoul National University, Rep. of Korea, in 1987 and his PhD degree in electrical and computer engineering from the University of Wisconsin, Madison, USA, in 1993. From 1993 to 2000, he worked for Samsung Electronics, Seoul, Rep. of Korea. Currently, he is a professor at Dongguk University, Seoul, Rep. of Korea. His research interests include mobile and wireless communications.
Corresponding Author ccgkang@korea.ac.kr
Chung Gu Kang received his BS degree in electrical engineering from the University of California, San Diego, USA, in 1987 and his MS and PhD degrees in electrical & computer engineering from the University of California, Irvine, USA, in 1989 and 1993, respectively. Since March 1994, he has been with both the Department of Radio Communication & Engineering and the Department of Electrical Engineering, Korea University, Seoul, Rep. of Korea, where he is currently a full professor. He is currently serving on the “5G Forum of Korea” — a private and public cooperative platform for globally leading and promoting 5G technologies — as a chair of the subcommittee for wireless technology. His research interests include broadband wireless transmission technologies; radio access technologies for massive connectivity and low latency in cellular IoT infrastructure; and crosslayer design for mobile systems.
jynam@etri.re.kr
Junyoung Nam received his BS degree in statistics from Inha University, Incheon, Rep. of Korea, in 1997 and his MS and PhD degrees in electrical engineering from KAIST, Daejeon, Rep. of Korea, in 2008 and 2015, respectively. He was with the Communications R&D Center, Samsung Electronics, Seoul, Rep. of Korea, from 1997 to 2002. He was also with the Communications Lab., Seodu InChip, Seoul, Rep. of Korea, from 2002 to 2006. In 2006, he joined ETRI. His research interests include wireless communications, information theory, and 5G system design.
koyj@etri.re.kr
YoungJo Ko received his BS, MS, and PhD degrees in physics from KAIST, Daejeon, Rep. of Korea, in 1992, 1994, and 1998, respectively. He is currently a director of Wireless Transmission Research Section 1 of the Wireless Transmission Research Department, ETRI. He joined ETRI in 1998 and has been working on mobile communications. His current research interests include LTE evolution and 5G enabling technologies, particularly focusing on wireless transmission and aspects of the physical layer.
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