In this paper, we investigate the performance of Signal to Leakage and Noise Radio (SLNR) based user scheduling in uplink of multicell with largescale antenna system. Large antenna array is desired to improve the performance in future system by providing better beamforming capability. However, some studies have found that the signal channel is ‘hardened’ (becomes invariant) when the antenna number goes extremely large, which implies that the signal channel aware user scheduling may have no gain at all. With the mathematic tool of order statistics, we analyzed the signal and interference terms of SLNR in a homogeneous multicell network. The derived distribution function of signal and interference shows that the leakage channel’s variance is much more influential than the signal channel’s variance in largescale antenna regime. So even though the signal channel is hardened, the SLNRbased scheduling can achieve remarkable multiuser diversity (MUD) gain due to the fluctuation of the uplink leakage channel. By providing the final SINR distribution, we verify that the SLNRbased scheduling can leverage MUD in a better way than the signal channel based scheduling. The Monte Carlo simulations show that the throughput gain of SLNRbased scheduling over signal channel based scheduling is significant.
1. Introduction
U
ser scheduling has been widely adopted in the uplink of MIMO multicell networks to improve system throughput. It can get significant multiuser diversity gain if the varying in channel is large and the channel state is known by scheduler. The latest engineering advances allow the multiple antennas to be extended to extremely large antenna array in a practical and affordable way
[1]
. This technology is named largescale antenna system (a.k.a. massive MIMO). The large number of antennas is desired to improve the performance in future system by providing better signal capture capability. However, some studies have found that the signal channel is ‘hardened’ (becomes invariant)
[2]
when the antenna number goes extremely large. Moreover, the acquisition of channel state information (CSI) which is the prerequisite of scheduling becomes challenging since the channel size is large while the resources for channel training is limited. Thus, whether to schedule users or not in massive MIMO is a subject of particular interest. In this work, we investigate the performance of Signal to Leakage and Noise Ratio (SLNR)based scheduling which is aware of the channel condition in both signal and leakage channels in largescale antenna system.
Recent works show that accurate CSI is available in massive MIMO system, so the scheduling performance in high CSI accuracy regime is of particular intrerest. The pilot contamination was considered as a serious problem for massive MIMO
[3]
. The inaccurate CSI causes the hardening in both signal and interference channel so that the user scheduling gain vanishes. Recently, planty of researches show that accurate is acquirable for massive MIMO
[4]
[5]
[6]
. Thus, channel aware user scheduling is viable for massive MIMO system.
Moreover, we notice that, when the scheduled user in other cell is different from the user causes the pilot contamination, the precoding will be also uncorrelated with the interfering channel. It also implies that the interference channel will not be hardened like the signal channel.
Motivated by knowing that the interference power flactuates significantly, we consider deploying user scheduling to reduce the interference in multicell massive MIMO systems. The user scheduling schemes in
[7]
[8]
exploit the users’ channel diversity on largescale to implement cooperative downlink massiveMIMO transmission. Thus, the interference can be turned into signal. However, the exchanging of CSIs among cells faces numbers of challenges, e.g. delay, backhaul overhead (especially for very large antenna system). Thus, we are interested at the scheme which doesn’t need coordination among cells.
The SLNRbased scheduling can aware of the interference produced by localcell user without assitance from other cells. It can suppresse intercell interference opportunistically while boost signal
[9]
. The performance of SLNRbased scheduling has been studied in traditional multiantenna system. In traditional multiantenna system, the signal channel fluactuates much more signicantly than intereference channel. Our early study shows it can provide significant throughput gain
[10]
. However, in massive MIMO system, the channel hardening effect causes signal channel fluactuate less significantly. Whether the SLNRbased scheduling could still provide performance gain has not yet known.
In this work, we study the performance of user scheduling in high CSI accuracy regime. When the impact of interference on pilot is suppressed, the data receiving will be less affected by the mislead channel estimation. However, the interference on data becomes a nonnegligible factor. Unlike the signal channel based scheduling scheme whose gain vanishes in masssive MIMO, we find that the SLNRbased scheduling can still provide profound performance gain even when the signal channel is hardened. The major contributions of this paper are as follows:

1) By the mathematic tool ofOrder Statistics, we analyzed the signal and interference terms in SLNR of a homogeneous multicell network. The way that signal is enhanced and interference is suppressed is illustrated.

2) We find that, for largescale antenna system, the leakage channel’s variance is much more influential than the signal channel’s variance in largescale antenna regime based on the derived distribution function of signal and interference. So, even though the signal channel is hardened, the SLNRbased scheduling can achieve remarkable multiuser diversity (MUD) gain due to the fluctuation of the leakage channel.

3) By providing the eventual SINR distribution, we verify that the SLNRbased scheduling can leverage MUD in a better way than the signal channel based scheduling. The Monte Carlo simulations show that the throughput gain of SLNRbased scheduling over signal channel based scheduling is significant.
This paper is organized as follows. Section 2 introduces the system model, describes MRC detector and uplink. Section 3 discusses the relationship between CSI accuracy and the fluctuation characteristics in effective signal and interference channels. After discovering the fluctuation in massive MIMO interference channel of multicell uplink, we provide a simple review of SLNRbased user scheduling, which can effective exploiting the channel fluctuation opportunistically, in Section 4. In Section 5, the distribution of scheduled user’s SINR is derived. And the effect of multiuser diversity in interpreted. The Monte Carlo simulation results are presented in Section 6. And Section 7 concludes the paper. .
We use following notations in the paper.
ƒ_{X}
(•) and
F_{X}
(•) is the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of a Random Variable (RV), correspondingly.
2. System Model
We consider the uplink of a multicell system with
M
BSs. Denote the BS in cell
m
as B
_{m}
. BS is equipped with
N_{r}
antennas. Each BS serves
K
singleantenna users. The users are identified by their index in cell and cell index jointly, e.g. the
k
th user in cell
m
is denoted by U
_{m,k}
. The BS with multiple antennas can support more than one uplink data streams simultaneously. Due to the large antenna size, the interuser interference is considered as being trivial for massive MIMO. Since we are particularly interested at intercell interference, we assume a BS serves one user on each uplink resource block for the sake of simplicity and tractability.
We consider the propagation channel with largescale path loss and smallscale channel fading. Assume OFDM is deployed so that each subcarrier can be considered as flat fading. The largescale pathloss power gain of the channel between BS B
_{m}
and the user U
_{n,k}
is
τ_{m,n,k}
, 1 ≤
m,n
≤
M
and 1 ≤
k
≤
K
. For the signal channel between BS B
_{m}
and its user U
_{m,k}
, the small scale fading coefficient vector can be denoted by
h
_{m,k}
∈ C
^{Nr × 1}
. For the interfering channel between BS B
_{m}
and any user from other cell, U
_{n,k}
,
m
≠
n
, the small scale fading coefficient vector can be denoted by
g
_{m,n,k}
∈ C
^{Nr × 1}
. We assume independent Rayleigh fading for all channels, then the elements in
h
_{m,k}
and
g
_{m,n,k(n)}
follow i.i.d. complex Gaussian distribution
CN
(0,1).
We assume that all BSs and users are perfectly synchronized and operate in Time Division Duplexing (TDD) mode with universal frequency reuse. So, the channel has downlinkuplink reciprocity after TxRx hardwares are calibrated.
Denote the scheduled user of BS B
_{m}
ak
k
(
m
). The signal transmitted by the scheduled user of BS B
_{m}
is
x_{m,k(m)}
. All user send signal with uniform transmit power
P^{UL}
, so
The received signal at BS B
_{m}
is the superposition of the signal from the scheduled users in all cells,
where, the last term is the white Gaussian Noise at BS
m
,
We assume a simple singleuser detector with linear filtering. All interference is treated as noise. Both the Maximal Ratio Combining (MRC) and the MMSE detector are commonly used in conventional MIMO systems. However, due to extremely large
N_{r}
, the matrix inversion operation in MMSE has high computational complexity. MRC receiver is considered here. For the signal of BS B
_{m}
’s scheduled user, the output of MRC receiver is
where,
is the normalized MRC receiving weight vector.
is the estimated channel vector.
Then, the uplink SINR of BS B
_{m}
can be represented by
where,
σ
is the normalized noise power,
Since both the signal and interference have been processed by vector
v
_{m,k(m)}
, we are interested at the effective channel that the signal and interference propagate through.
is effective channel for signal while
is the effective channel for interference. They jointly determines the achievable rate of this transmission, log
_{2}
(1+
p_{m}
). The system performance can be evaluated by the average throughput per cell,
Here, we assume the duration of the channel measurement, feedback and the scheduled transmission is much less than the coherent time of the varying channel. So, the channel measurement/feedback overhead can be omitted. The channel can be seen as constant within a scheduling period.
3. Relation between CSI Accuracy and Signal/Interference Channel Characteristics
The CSI accuracy, and the coupling between user scheduling and pilot allocation, jointly determines the characteristics of effective signal and interference channel. In this section, we show that in different level of CSI accuracy, the effective signal and interference channel will present different level of fluctuation. Further, we find the oppurtunistic user scheduling can help decorrelating the precoding with interference channels, so that the interference channel has fluctuation independent of
N_{r}
.
To depict the CSI accuracy in multicell MIMO system with pilot contamination, we begin with examination of the fundemantal channel estimation process. We assume MBS acquires channel state via uplink training according to the channel reciprocity in TDD mode.
J
orthogonal pilot sequences are reused among users. Denote the set of users using
j
th pilot sequence in cell
m
is Ω
_{j,m}
. Assume each set has equal number of users,
For the case that the number of users in cell is larger than the number of pilot sequences (
K
>
J
), pilot sequences will be reused within a cell, Ω
_{j,m}
>1.
Due to the pilot reuse in interference channel, the estimated signal channel is contaminated by the interfering channels which use the same pilot sequences. In the most serious case, the estimated signal channel is the superposition of local signal channel and interference channel
[5]
. And in other cases, the pilot contamination is alleviated
[4]
[6]
. The signal and interference channel can be seems as orthognal to each other as
N_{r}
goes extremely large (from Lemma 1 in
[5]
),
Thus, generally, the estimated signal channel of user U
_{m,k(m)}
can be expressed as
where,
α_{m,k(m)}
,
φ_{(m,k(m)), (m,u)}
and
φ_{(m,k(m)), (n,l)}
are the scalar projection of
on
h
_{m,k(m)}
,
h
_{m,u}
and
g
_{m,n,l}
, respectively. Since the vector
h
_{m,k(m)}
,
h
_{m,u}
and
g
_{m,n,l}
are not normalized, the above scalar projection of
a
on
b
shall be calculated by
a
^{H}
b
/
b

^{2}
. The coefficients
α_{m,k(m)}
,
φ_{(m,k(m)), (m,u)}
and
φ_{(m,k(m)), (n,l)}
are determined by the performance of deployed pilot transmission design and channel estimation schemes jointly.
υ
_{m,k(m)}
is the residual part which can be calculated by
Note that when
N_{r}
is small,
h
_{m,k(m)}
,
h
_{m,u}
and
g
_{m,n,l}
are not strictly orthogonal with each other, and that (4) is not a strict orthogonal decomposition of vector
is weakly correlated with
h
_{m,k(m)}
,
h
_{m,u}
and
g
_{m,n,l}
.
Then, we consider the data receving with the estimated CSI. Combining (1) and (2), we can rewriten the received signal in form of
First, we consider the signal term of above equation. From (4), we can know the component
in the signal term has
h
_{m,k(m)}
is uncorrelated with
h
_{m,u}
and
g
_{m,n.l}
. And residual term
υ
_{m,k(m)}
is neglectable. The pilot contamination’s impact on the signal term can be evaluated by
is much larger than 
α_{m,k(m)}

^{2}
, which means the pilot contamination is severe, the precoding vector
can’t match the signal channel
h
_{m,k(m)}
. In this case (CSI Accuracy level I in
Table 1
), the gain of effective signal channel will fluctuate. Despite fluctuation exists in level I, this is case is not desirable at all due to the loss of multiantenna beamforming gain. So, this case will be avoided in practical system. When the factor 
α_{m,k(m)}

^{2}
is significant,
is dominant in (6). So the signal channel becomes hardened when
N_{r}
goes larger (CSI Accuracy level II and III in
Table 1
).
Relation between CSI Accuracy and Signal/Interference Channel Characteristics in massive MIMO System
Relation between CSI Accuracy and Signal/Interference Channel Characteristics in massive MIMO System
Then, we consider the interference term in (5). The component
in interference term has
Obviously,
is uncorrelated with
g
_{m,n,k(n)}
. So, the impact of intracell pilot contamination can be neglected.
When the characteristics which exist in realistic propogation channels are not exploited at all, the signal channel and interference channel are indistinguishable
[5]
. In such case, 
α_{m,k(m)}

^{2}
and
σ
^{2}
_{m,k(m)}
are comparable and the pilot contamination is serious. The work in
[5]
assumes all users reusing the same pilot sequence are scheduled simultaneously. The term
causes the hardening in interference channel (CSI accuracy level II in
Table 1
). Obviously, there is also hardening in interference channel for the CSI accuracy level I.
Recent works show that, by exploiting the channel statistical feature in realistic environment, the sophisticated pilot sequence assignment
[4]
and pilot stage allocation scheme
[5]
can estimate the signal channel quite accurately. The simulation in shows that the mean square error of the estimation,
can be extremely small and the estimation result even approaches the interferencefree case. We denote it as the accuracy level III in
Table 1
. A pilot sequence allocation scheme has been proposed in
[4]
which shows that the contamination factor is small and
α
approaches 1 (
σ
^{2}
_{m,k(m)}
→ 0, correspondingly). In this CSI accuracy level, the correlation between
and
g
_{m,n,k(n)}
is small and the interference channel become fluctuating.
Moreover, we find that the interference channels are no longer hardened when multiuser scheduling is deployed. Assuming the scheduled user in cell
m
using the
j
th pilot sequence,
k
(
m
) ∈ Ω
_{j,m}
and all user has equal scheduling oppurtunities. The pilot contamination is most damaging when
k
(
n
) ∈ Ω
_{j,n}
as in
[5]
. The receiving vector will partial match the direction where the interference comes from. In fact, the probability of this event is small,
P
{
k
(
n
)∈Ω
_{j,n}
}=Ω
_{j,n}
/
K
=
J
^{1}
. The case that the user using other pilot seqeunce in cell
n
is more probable,
P
{
k
(
n
)∈Ω
_{j,n}
}=(
K
Ω
_{j,n}
)/
K
=1
J
^{1}
. The interfering channel
g
_{m,n,l}
from cell
n
is uncorrelated with the channel which causes the pilot contamination
g
_{m,n,k(n)}
. So the interference channels are no longer hardened when
N_{r}
goes larger.
The scheduling performance in CSI accuracy level III has not yet been studied by any existing papers. In later of this work, we consider the CSI accuracy level III and exploit the channel characteristics to achieve throughput gain.
4. Exploiting Channel Fluctuation in MIMO Multicell System
In this section, we study how SLNRbased scheduling helps boosting the SINR in multicell system. Since the SLNRbased user scheduling in uplink affects the SINR distribution in indirect way, to obtain of distribution of the resulting SINR, we shall first know the distributions of scheduled user’s signal and interference which are associated with the maximal SLNR. And these distributions rely on the distribution of maximal SLNR which is affected by the number of candidate users. So we derive the distribution of the scheduled user’s SLNR, signal, interference and SINR, one by one.
The SLNRbased scheduler has the benefit of exploiting the fluctuation in both signal and interference channels
[10]
. The SLNR of user U
_{m,k}
is
The SLNR aware scheduler can pick the user with highest SLNR,
The SLNRbased scheduling gain relies on the small scale channel fluctuation in (7). To simplify the notation and ease the analysis, we define the smallscale power gain of effective channel for both signal and interference channel. The smallscale power gain of effective signal channel of user U
_{m,k}
is
stands for the chisquared distribution with 2
N_{r}
degrees of freedom. The smallscale power gain of the effective leakage channel between user U
_{m,k}
and a BS interfered by it, B
_{n}
,
n
≠
m
, is
For the sake of tractability, we assume a homogeneous largescale channel model in all cells. We consider the same pathloss for all users’ signal channels,
τ_{m,m,k}
=
g_{s}
, 1 ≤
m
≤
M
, 1 ≤
k
≤
K
. Similarly, the pathloss gains in all interfering channels are also the same,
In uplink, the aggregated leakage produced by user U
_{m,k}
to all BSs interfered by it is
So, the SINR in (7) can be rewriten as
 4.1 The Impact of Scheduling on SLNR
First, we consider the distribution of RVs before scheduling, which is call prescheduling distribution. The signal and pollution’s channel distributions,
ƒ_{Sn,m}
(
s
) and
ƒ_{Pn,m}
(
p
), jointly determine the distribution of prescheduling SLNR. For any user U
_{m,k}
, it has prescheduling SLNR
λ_{m,k}
which has PDF of
By taking
and the assumed PDF of
s_{n,m}
and
p_{n,m}
into (10), we can get
Further, by expending the term (
σ
+g
_{p}P
)
^{Nr}
, we can get
The Eq. (12) can be rewritten as
Finally, by applying
to (13), we can get the exact form of
λ_{m,k}
’s PDF
Thus, the CDF of
λ_{m,k}
can be derived as
where,
For the special case that
N_{r}
=1, it has simple closed form
Based on the distribution of prescheduling RVs and the behavior of scheduling, the distribution of the postscheduling RVs can be obtained. We consider the impact of user scheduling. The event that the maximal SLNR in cell
m
has value of
λ
is equivalent to the event that any other users in cell have SLNRs smaller than
λ
,
Besides, this user
k
(
m
) can be any one of
K
users. So, by order statistics
[11]
, the PDF of the scheduled user’s SLNR can be derived as
And the CDF of
λ
_{m,k(m)}
is
The CDFs of scheduled users’ SLNR, calculated by (16) for the cases of
M
= 4,
K
= 10 and
N_{r}
= 1,16,256 is shown in
Fig. 1
. The variance of SLNR becomes smaller with the increase of BS’s antenna number. It can be interpreted by the hardening of signal channel at large
N_{r}
. Considering the performance of median user, the postscheduling SLNR has 2.9dB gain over the prescheduling SLNR.
The CDF of pre and postscheduling SLNRs with various antenna configurations for g_{S} / g_{P} = 3dB and g_{P} / σ = 5dB. The theoretical results are shown by solid lines, while the Monte Carlo results of PreScheduling and PostScheduling are presented by the markers □ and +, respectively. The markers are all coincident with their corresponding lines.
 4.2 Analysis of Scheduling’s Effect on Signal Enhancement and Interference Suppression
Since the
λ_{m,k(m)}
is the largest among all
K
users’ SLNRs, the signal term in it,
s_{m,k(m)}
, tends to be large while the pollution term,
q_{n,m,k}
, tends to be small.
First, we consider the distribution of signal term,
s_{m,k(m)}
. The signal channel power gain of the selected user
s_{m,k(m)}
is associated with the SLNR
λ_{m,k(m)}
greater than the other
K
 1 users. So the
s_{m,k(m)}
’s PDF is
In (17), the multiplier
K
comes from
which means that any user could be the one with highest SLNR. When
p_{m,k}
traverses over the range (0, + ∞) the value of
λ_{m,k(m)}
is adjusted to
accordingly.
F_{λm ,k}
^{K1}
(
λ
) is the probability that all users other than
k
(
m
) in cell
m
have SLNR smaller than
λ
.
The CDF of effective signal power gain in smallscale channel fading. The theoretical results are shown by solid lines, while the Monte Carlo results of PreScheduling and PostScheduling are presented by the markers □ and +, respectively.
Unfortunately, there’s no closed form expression for the integral result in (17). By taking (14) and (15) into (17),
s_{m,k(m)}
’s PDF can be calculated by numerical method. The CDFs of scheduled users’ signal channel power gain
s_{m,k(m)}
and all users’ signal channel power gain
s_{m,k}
(1 ≤
k
≤
K
) are presented in
Fig. 2
. When
N_{r}
is small,
s_{m,k}
has significant fluctuation. The scheduler can easily exploit the channel diversity to enhance the signal channel power gain of scheduled users. However, when
N_{r}
goes large, the hardening effect of massive MIMO’s signal channel emerges. For
N_{r}
=256, the varying of
s_{m,k}
is so small that SLNRbased scheduler could hardly pick any user with higher
s_{m,k}
.
While the higher SLNR tends to be associated with a higher signal channel gain
s_{m,k}
, it also pursues a lower leakage channel gain
q_{n,m,k}
. However, the situation for
q_{n,m,k(m)}
is more complicate than for
s_{m,k(m)}
, since in
λ_{m,k(m)}
the channel power gains of leakage to several BSs are summed,
First, we consider the aggregated pollution by the user
k
in cell
m
to all interfered BSs except a interfered BS
i
≠
m
, which is denoted as
The PDF of
is
Obviously, from the definition in (9), we can know
By (18) and (19), we can get
There is no closed form expression for the scheduled pollution channel power gain’s expression either. We calculate (20) by numerical integration. The CDF of individual interference channel’s smallscale gain at BS is shown in
Fig. 3
. The distribution of prescheduling interference channel gain
q_{n,m,k}
is independent of
N_{r}
. After scheduling, the interference channel gain is suppressed effectively. And the suppression is more significant when
N_{r}
is large. It is because that when signal channel is hardened at large antenna number regime, the fluctuation in SLNR is dominated by the varying in pollution channel.
Distribution of individual interference channel’s small scale gain q_{n,m,k}, under various antenna configurations. The theoretical results are shown by solid lines, while the Monte Carlo results of PreScheduling and PostScheduling are presented by the markers □ and +, respectively.
Denote the aggregate interference in uplink data SINR (3) as
We can get its CDF based on (20),
Aggregate interfering channels’ smallscale gain under various antenna configurations (N_{r}=1,16,256). The theoretical results are shown by solid lines, while the Monte Carlo results of PreScheduling, MinLeakage Scheduling and MaxSLNR Scheduling are presented by the markers □, ○ and +, respectively.
The consequent aggregate interference channel gain’s distributions are shown in
Fig. 4
. The most left CDF curve (green) is from
minleakage scheduling
scheme,
We compare the result of maxSLNR scheduling with it. At
N_{r}
=256, the
ω_{m,k(m)}
’s CDF curve under maxSLNR scheduling is almost aligned with the curve under minleakage scheduling. It is because that the signal channel becomes hardened as shown in
Fig. 2
. The fluctuation in
λ_{m,k}
is primarily contributed by the variance of
q_{n,m,k}
. So, in large antenna regime, maxSLNR scheduler behaves similar to minLeakage scheduler.
Note that we consider the interference is much more significant than noise. Although in energy effient (“green”) regime, the BS’s transmit power for masive MIMO may be low enough that the intercell interference is drown in thermal noise, the achievable rate for each spatial stream is also low. To achieve extreme high data rate and satisfy user’s applicatin demand, the perstream rate must be high since the supportable spatail stream number at each user is limited. Thus, highorder modulations are used. The interference will be significantly above the noise level.
We can conclude that

1) The SLNRbased scheduling exploits the fluctuations in signal and interference channel.

2) It always tends to find a user with larger signal channel power gain and smaller leakage channel power gain among all users in a BS. And the preference is adapted to the variances in signal and leakage channels.
 4.3 The impact of Scheduling on SINR
The SINR’s PDF can be derived in similar way of obtaining
ƒ
_{λm,k}
(
λ
),
The average percell capacity in system is
The final SINRs’ CDF under various scheme and different antenna configurations is shown in
Fig. 5
. By opportunistically selecting the user with high SPR, the spectrum efficiency of all users is increased, especially in high spectrum efficiency region. The SLNR based scheduling’s SINR is always beyond the SINR under maxSignal scheme and minLeakage scheme.
SINR distribution under various antenna configurations. The theoretical results are shown by solid lines, while Monte Carlo results of Random Scheduling, MaxSignal Scheduling, MinLeakage Scheduling and MaxSLNR Scheduling are presented by the markers ×, □, ○ and +, respectively.
From the analysis above, we conclude the main differences between the SLNRbased scheduling in traditional MIMO and Massive MIMO in
Table 2
.
Comparison of SLNR based scheduling in massive MIMO and traditional MIMO
Comparison of SLNR based scheduling in massive MIMO and traditional MIMO
5. Simulation Results
We compare the performance of various schemes by Monte Carlo simulations. Unless specified otherwise, we assume the percell user number is
K
= 10. And the major interfered BS number
M
 1 is 3. The total BS number is
M
= 4. The large scale signal to interference power ratio is
g_{S}
/(
M
1)
g_{P}
=3
dB
. The large scale interference to noise ratio is (
M
1)
g_{P}
/
σ
=5
dB
.
The average percell throughputs with increasing BS antenna number is show in
Fig. 6
. It shows that the maxSLNR scheduling scheme has the highest throughput for all BS antenna configurations. We provide
Fig. 6
(b) to give a detailed view of the throughputs in low antenna number cases. Initially, when BS antenna number is small, the maxSLNR scheduling scheme achieves 1.87 times throughput of the random scheduling scheme. And the gain of maxsignal scheduling over random user selection is also significant. By recalling the result from Section 4.2, we can find that the variance in signal channel is much larger than the variance in interference (leakage) channel, so the maxsignal can achieve almost the same performance as maxSLNR scheme.
The throughputs in various schemes with increasing antenna number
When BS antenna number becomes extremely large (
N_{r}
=128), the gain of maxsignal scheduling over random user selection vanishes. It can be interpreted as that users’ signal channels are hardened with increasing antenna number.
Comparing to the performance gap between maxsignal scheduling and random scheduling at
N_{r}
=128, the performance gain of maxSLNR scheduling over maxsignal scheduling is preeminent. It is because that the fluctuation in leakage channel does not vanish with the increasing of BS antenna number. The varying in leakage channel becomes dominant when the signal channel power gain is almost fixed.
It is worth noting that the MUD gain from signal channel is so limited while the cost of acquiring signal channel state increases linearly with
N_{r}
[12]
. This cost may outweigh the MUD gain benefit within it when
N_{r}
→ ∞. However, the cost of acquiring effective leakage channel does not increase with
N_{r}
. The throughput of minLeakage scheduling is very approaching the throughput of maxSLNR scheduling. It suggests that the gain of MUD in leakage channel is dominant in largescale antenna regime.
We evaluate the throughput achieved by various scheduling schemes with increasing percell user number
K
. To show how throughput is improved with
K
, we use the dual capacity of uplink MAC channels, the sum rate of the downlink broadcast channel, as the baseline. It is well known that, the percell sumrate of the
maxSINR scheduling
in downlink demonstrates the growth rate of log log
K
, asymptotically with increasing number of users percell
K
[13]
. From
Fig. 7
we can see that the log log
K
like MUD gain is also achieveable in multicell uplink. The achievable rate of log log
K
like has been found in early work
[14]
. It adopts a leakagethreshold based prequalifying stage to preclude the user who may cause strong leakage to be the candidate. Then, the user with best signal channel is scheduled. However, it is hard to be applied to the multicell uplink with largescale antenna because of the signal channel hardening. In contrast with it, SLNR based scheme can adapt to the varying of fluctuation characteristics in channels smoothly.
Percell Throughput vs. User Number
Percell Throughput vs. BS Number M
Fig. 8
shows the impact of BS number’s impact on throughputs. We can see that all scheduling schemes’ percell throughputs decrease with the increasing of
M
. It is because that the aggregated leakage tends to be less fluctuating when
M
is large, as we can see from (9). Its impact on leakageaware schemes including our SLNRbased scheduling is significant when
M
= 10 . However, in practical networks, the number of BSs that cause strong interference to local cell is small. For all cases of
M
= 2, 3 and 4, the performance gains of SLNRbased scheduling compared with MaxSignal scheduling are over 10%.
6. Conclusion
In this work, we investigate the performance of the SLNRbased user scheduling in uplink of multicell with largescale antenna system. We find that in high CSI accuracy regime, with awareness of not only signal power but also the leakage power, the SLNRbased scheduling can try best efforts to suppress users’ interference power leakage to other cells’ BS when the signal channel is hardened in massive MIMO regime. So, generally, the SLNRbase scheduling can provide excellent performance in all antenna number configurations. With the mathematic tool of Order Statistics, we analyzed the signal and interference terms in SLNR of a homogeneous multicell network. The derived distribution function of signal and interference shows that the leakage channel’s variance is much more influential than the signal channel’s variance in largescale antenna regime. So, the SLNRbased scheduling can leverage MUD in a better way than the scheduling schemes which only focus on signal channels. The Monte Carlo simulations show that the throughput gain of SLNRbased scheduler over signal channel based one is significant.
BIO
Yanchun Li received the B.Sc. degrees in Electronics and Information Engineering from Huazhong University of Science and Technology (HUST), China, in 2006. He was graduate intern in the Communication Technology Laboratory of Intel Crop., where he participate research on WiMAX 2, from 2007 to 2008. He was research assitant in Computer Science and Engineering department at Hong Kong University of Science and Technology, where he participate the research on Green Network, from 2010 to 2011. He is currently pursuing his PhD at the Electronics and Information Engineering Department at HUST. His research interests are in the areas of Communication Theory, Information Theory and Signal Processing.
Guangxi Zhu received his B.S. in radio engineering from Huazhong Institute of Technology, China, in 1969. He is the expert of assessment group in Academic Degrees Committee of China State Council for Information and Communication Engineering, cosponsor and director of Future Mobile Communication FuTURE Project Forum, a Committee for National Technical Standardization. He is a professor and chairman of the academic board of the Department of Electronics and Information Engineering, HUST. His research interests include wireless communication and media signal processing. He has published over 300 papers.
Chen Hua is a associate professor in Wuhan Textile University. Her main research field is Network Communications, include optimization theory and technology, etc. From 2005 to now, her presided more than 3 Hubei natural science fund projects and more than 2 Hubei youth fund projects, published more than 15 papers in the field of network communications.
Minho Jo received his Ph.D. in Dept. of Industrial and Systems Engineering, Lehigh Univ., USA in 1994. He received his BA in Industrial Engineering, Chosun University, S. Korea. He is now Professor of Department of Computer and Information Science at Korea University, Sejong. He is one of founding members of the LCD Division, Samsung Electronics in 1994. He is the Founder and Editor inChief of KSII Transactions on Internet and Information Systems. He is an Editor of IEEE Network and an Editor of IEEE Wireless Communications, respectively. He is an Associate Editor of Wiley’s Security and Communication Networks and an Associate Editor of Wiley’s Wireless Communications and Mobile Computing, respectively. He has published many refereed academic publications in very high quality journals and magazines. He is now the Vice President of the Institute of Electronics and Information Engineers. Areas of his current interest include cognitive radio, network algorithms, optimization and probability in networks, network security, wireless communications and mobile computing in 5G and 6G, wireless body area network (WBAN), and wireless organ network (WON).
Yingzhuang Liu is a professor of Huazhong University of Science and Technology (HUST). His main research field is broadband wireless communication, including LTE and IMT Advanced system, etc., especially its Radio Resource Management. From 2000 to 2001, he was a postdoctoral researcher in Paris University XI. From 2003 up to now, he has presided over 10 national key projects, published more than 80 papers and held more than 30 patents in the field of broadband wireless communication. He is now the group leader of broadband wireless research of HUST, which has more than 10 young teachers and more than 20 PhD students.
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