1
A Multi-hop User Admission Algorithm
for Fixed Relay Stations with Limited Capabilities
in OFDMA Cellular Networks
Jemin Lee† , Hano Wang, Sungmook Lim, Student Members, IEEE,
and Daesik Hong†† , Senior Member, IEEE
E-mail : haessal@yonsei.ac.kr† , daesikh@yonsei.ac.kr††
Abstract—In this paper, a resource management for fixed relay
stations (FRS) with the limited capability is considered in downlink OFDMA multi-hop cellular networks. All of MSs which want
to use a FRS in multi-hop transmission can not be supported when
the capability of the FRS is insufficient. Hence, the multi-hop user
admission (MUA) is required to determine the admitted MSs to
use the FRS because the gain obtained from multi-hop transmission is different to each MS. The problem of MUA is formulated
to maximize the total multi-hop gain which the FRS can achieve
from the admitted MSs, and this problem is proven to be NP-hard.
Hence, two efficient heuristic algorithms for MUA are proposed.
One is the balanced link-MUA (BL-MUA) algorithm which gives
priorities of admission with attaching importance to the load balance between the BS-FRS link and the FRS-MS link. The other is
the focused link-MUA (FL-MUA) algorithm which considers only
the load state of the FRS-MS link in admission. Through the numerical results, it is verified that the FL-MUA algorithm obtains
similar performance to the BL-MUA algorithm with less complexity. In addition, the total number of saved subcarriers in a FRS
increases and more MSs can be supported in a cell with low blocking probability by the proposed algorithms.
I. I NTRODUCTION
Multi-hop cellular networks (MHCN) have been proposed to
enhance throughput and extend coverage [1]. These purposes
can be achieved by deployment of relay stations (RS) in the
conventional single-hop networks. The advantage of MHCN
comes from the reduction in the overall path loss between a base
station (BS) and a mobile station (MS) by a relay station, but the
penalty of transmission with multi-hop is in need for additional
resources (eg. power, bandwidth and etc.) [1]. Hence, according to the MS’s QoS requirements and the channel condition,
some MSs can transmit data with fewer subcarriers compared
to the single-hop transmission [2], and a resource management
algorithms are required for MHCN.
The integrated link scheduling and power control policies are
proposed for throughput maximization [3]. The sub-optimal
subcarrier and power allocation algorithms are proposed for
OFDMA-based multi-hop links [4]. However, those algorithms
do not consider the limitation of the RS’s capability.
The infrastructure cost increases almost linearly with the
equipment capability [5], and it is impossible to change the
capability of the installed equipment flexibly according to the
change of total required capability. Hence, a RS has the limited
and determined capability and the resource managements with
considering the limitation of capability are required.
Fig. 1. The downlink multi-hop cellular architecture with fixed relay stations
Due to the limited capability, some of MSs can not transmit
with multi-hop if all capability of RS are already fully used for
the other MSs. Each MS obtains the different multi-hop gain
which means the saved subcarriers by transmitting in multi-hop
instead of single-hop. For this reason, the limited capability of
RS should be utilized efficiently for the MSs which can maximize the total multi-hop gain in the FRS. Therefore, the multihop user admission (MUA) is required to determine the admitted MSs among all MSs which want to use the RSs.
In this paper, the supportable number of subcarriers is
considered as the limited capability of RS, and the problem of MUA in downlink OFDMA multi-hop cellular networks is formulated. The MUA problem is proven to be the
multi-dimensional knapsack problem kind of NP-hard problem. Hence, two efficient heuristic algorithms for MUA are
proposed. One is the balanced link-MUA algorithm (BL-MUA)
which attaches importance to the load balance between the BSFRS link and the FRS-MS link in multi-hop user admission.
The other is the focused link-MUA algorithm (FL-MUA) only
focused on the load state of the FRS-MS link. The performance
of those algorithms are verified through the numerical results.
II. OFDMA M ULTI - HOP C ELLULAR M ODEL
In this section, the required number of subcarriers for guaranteeing QoS and the limited capability of RS are defined.
A. Cellular Architecture
A downlink OFDMA multi-hop cellular network is considered in this paper. The two-hop relaying system known as the
2
most efficient multi-hop system in the aspect of the system capacity is also adopted [1]. Hence, in this system, it is allowed
to transmit data from a BS to a MS in one of two transmission modes, the single-hop (SH) transmission and the multi-hop
(MH) transmission via a fixed relay station (FRS). An example
of this system’s connectivity is illustrated in Fig. 1.
A number of FRSs are placed on the relay belt. All FRSs are
regenerative relays. In this system, three kinds of links which
are the BS-MS link, the BS-FRS link, and the FRS-MS link are
formed. Based on a FRS, the BS-FRS link and the FRS-MS
link are denoted by the link for receiving data (LRX ) and the
link for transmitting data (LT X ), respectively. The link for the
SH transmission (LS ) denotes the BS-MS link. We assume that
the LRX has a good channel condition as LOS environment and
the LT X and the LS are in NLOS environment. Every link uses
the different frequency band and the frequency band for each
link in the reference cell is reused in the same link of other cell.
In the regenerative relay, the error generated in each hop is
propagated to the next hop. Hence, the sum of the target BER
of each hop in MH transmission should be equal or less than the
2
P
target BER, B in the MH transmission as
B Li ≤ B where
i=1
B Li is the target BER on the link of the ith hop [6].
In addition, the end-to-end data rate from a BS to a MS is
determined by the minimum data rate among the rates in each
hop [7]. Hence, the target data rate of each hop should be equal
or greater than the target data rate, R, as RLi ≥ R where RLi
is the target data rate on the link of the ith hop.
B. Required Number of Subcarriers to Guarantee QoS
For simplification, it is assumed that all of subcarriers in every cell are loaded and the channels are flat fading. Hence,the
ξ/10
channel gain of the link L can be defined as GL = c·d−α
L ·10
where c is constant, dL is the distance between the transmitter
and the receiver on the link L, α is the path loss exponent, and
ξ is a shadowing random variable.
The received signal to interference and noise ratio (SINR) of
the link L can be defined as
GL · PI
ΓL = P
,
(1)
·GIj · PI + η
j6=m
where η is the additive Gaussian noise power. Ij is the link
between a interferer in the jth cell and the target node, and PI
is the transmission power of the transmitter in that link.
In Fig. 1, the kth MS, M Sk , is connected with the mth BS,
i
BSm , and the M Sk uses the ith FRS in the mth cell, RSm
for MH transmission. Hence, in the SH transmission, L is the
BSm -M Sk link, Ij is the BSj -M Sk link and PI = PBS where
PBS is the transmission power of BS. In addition, in the MH
i
i
transmission, L is the BSm -RSm
link, Ij is the BSj -RSm
link
i
and PI = PBS on the first hop. L is the RSm -M Sk link, Ij is
the RSji -M Sk link and PI = PF RS on the second hop where
PF RS is the transmission power of FRS.
With adaptive modulation coding (AMC), the achievable
data rate on the link L is expressed as the function of ΓL and
B L , as follows
µ
¶
−1.5
1
log2 1 +
RL =
· ΓL ,∀L
(2)
Ts
ln(5 · B L )
where Ts is the symbol duration [8]. The number of required
subcarriers of M Sk on the link L to guarantee
§
¨QoS, Ck,L , is
determined by the R and RL as Ck,L = R/RL where dχe is
the least integer equal or lager than χ. Hence, the total numbers
of required subcarriers of M Sk to transmit data with QoS guarantee by the SH transmission and the MH transmission, CkSH
and CkM H , are defined as
CkSH = Ck,LS , CkM H = Ck,LRX + Ck,LT X .
(3)
The number of required subcarriers is changed according to the
used transmission mode, the QoS requirements as well as the
channel condition [2]. For the efficient usage of subcarriers,
it is assumed that the MS do the MH transmission only when
the required subcarriers in the MH transmission are fewer than
those in the SH transmission as CkM H < CkSH . In this case, the
multi-hop gain, Sk , can be defined as the number of saved subcarriers by the MH transmission instead of the SH transmission
as follows
Sk = max{CkSH − CkM H , 0} ∀ k.
(4)
Among all MSs, the MSs which want to transmits in the multihop transmission are denoted by the multi-hop user (MU), and
the other MSs which prefer the SH transmission are denoted by
the single-hop user (SU).
C. Limited Capability of FRS
The number of supportable subcarriers is considered as the
capability of the the FRS. It means that the ith FRS can support
up to Ni,RX subcarriers for receiving on the LRX and Ni,T X
subcarriers for transmitting on the LT X in a time due to the
cost, the limitation of power amplifier and so on. Hence, the
total number of required subcarriers of MUs in each link should
be equal or fewer than the supportable number of subcarriers of
FRS in each link as follows
X
X
Ck,LRX ≤ Ni,RX ,
Ck,LT X ≤ Ni,T X , (5)
k∈MUi
k∈MUi
where MUi is the set of MUs who want to receive data from
the ith FRS. FRSs which have higher capability can generally
support more subcarriers with higher total power.
III. F ORMULATION OF MUA
All FRSs have the limited supportable subcarriers, so a FRS
may not support all of MUs when the required subcarriers of
them are beyond the capability of the FRS. For this reason, the
multi-hop user admission (MUA) is required. The MUs obtain
different multi-hop gains. The problem of MUA is formulated
to determine the admitted MUs to use the FRS among all MUs
with maximizing the total multi-hop gains which can be obtained from the admitted MUs as follows
[MUA] max
F
X
X
xk · Sk
i=1 k∈MUi
s.t
C1,i :
X
xk · Ck,LRX ≤ Ni,RX ,
∀i
xk · Ck,LT X ≤ Ni,T X ,
∀i
k∈MUi
C2,i :
X
k∈MUi
C3 : xk ∈ {0, 1} ,
∀k
3
where F is the total number of FRSs and the xk is the indicator
of admission. If the M Sk is admitted to transmit with multihop using the FRS, xk = 1, otherwise xk = 0 and the M Sk
should transmit in single-hop.
For each FRS, there are two constraints in the [MUA].
Specifically, based on the ith RS, one constraint is C1,i for the
LRX and the other is C2,i for the LT X . The Lagrangian of
[MUA], Lag(u, u0 ), can be defined as
Start
For all k ∈ ΜU i
Caculate Ck , LRX , Ck , LTX and S k
o
Is lRX
> N i , RX
N
o
or lTX
> N i ,TX ?
Y
xk ← 1 ∀k
SU ← { }
F  X
X


Lag(u, u ) =
x k · Sk

BL-MUA
0
i=1
− ui
k∈MUi
− u0i
For all k ∈ MU i ,
k∈MUi
X
X
(xk · Ck,LRX − Ni,RX )
End
Calculate U k in (7) or (8)
(6)


(xk · Ck,LT X − Ni,T X )

k∈MUi
FL-MUA
k ← arg min U k
*
k∈MUi
xk* ← 0
lRX ← lRX − Ck * , L
RX
0
where ui and ui are Lagrangian multipliers. We can rewrite
F
P
0
0
(6) as Lag(u, u0 ) =
Lag(ui , ui ) where Lag(ui , ui ) is the
i=1
formula in the big blanket in (6). Hence, it is shown that the pri0
mal problem can be decomposed into sub-problems Z(ui , ui )
0
0
where Z(ui , ui ) = max Lag(ui , ui ). The parallel MUAs for
each FRS can work independently because the result of one
FRS’s MUA does not affect the other FRSs’ MUAs.
Therefore, the independent MUA for the ith FRS, [MUAi ],
can be formulated as follows.
X
xk · Sk
[MUAi ] max
k∈MUi
s.t C1,i , C2,i , and C3 .
From [MUAi ], it is shown that it has the equivalent form with
the two-dimensional knapsack problem (TDKP) which is a
kind of multi-dimensional knapsack probelm (MDKP) [9]. The
MDKP is a variant of the classical 0-1 knapsack problem (KP)
with more than two knapsack.
IV. P ROPOSED A LGORITHMS FOR MUA
The problem of MUA is the two-dimensional knapsack problem a kind of MDKP. The KP and MDKP are proven to be NPhard, so the optimal solutions of them can not be obtained in a
polynomial time [9]. Hence, in this section, two heuristic algorithms for MUA are proposed.
A. Balanced Link-MUA (BL-MUA) Algorithm
In the MUA, the balance between the used resources on the
LRX and those on the LT X is important. The reason for this
is that no additional MUs can be admitted when at least one of
Ni,RX on the LRX and Ni,T X on the LT X are fully occupied
for other MUs. Hence, the BL-MUA algorithm is proposed
considering both the LRX and the LT X in admission by adopting the primal effective gradient method (PEGM) [10].
The PEGM determines priority of admission using the new
measurement of the aggregate resource. The aggregate resource
is to penalize the MUs which requires many subcarriers in the
lTX ← lTX − Ck* , L
TX
ΜU i ← ΜU i ∪ {k *}
SU ← SU /{k *}
Is lRX > N i , RX
Y
or lTX > N i ,TX ?
N
Fig. 2. Flow chart of the MUA algorithms (BL-MUA algorithm and FL-MUA
algorithm)
more loaded link. The aggregate resource in MUA
.p can be de2
fined as Ak = (Ck,LRX · lRX + Ck,LT X · lT X )
lRX
+ lT2 X
where lRX and lT X are the total numbers of used subcarriers
on the LRX and the LT X by the currently admitted MUs, respectively. The priority function of the BL-MUA algorithm,
UBL,k , is set by the multi-hop gain over the aggregate resources, Sk /Ak , as follows
p
2
Sk lRX
+ lT2 X
UBL,k =
.
(7)
Ck,LRX · lRX + Ck,LT X · lT X
If at least one of Ni,T X and Ni,RX is insufficient, the MU is
rejected to use the FRS in a low-priority order one by one and
the priority function helps to balance the load states between
two links.
B. Focused Link-MUA (FL-MUA) Algorithm
The BL-MUA algorithm attaches importance to the balance
of used resources in the LRX and the LT X . However, when
FRSs are located in LOS environment with BS and the environment of the LT X is NLOS, the number of required subcarriers
to guarantee the same target data rate in the LT X is much more
than that in LRX . This means that no more MUs can be admitted in a FRS generally due to the LT X , not the LRX .
Therefore, the MUA considering both the LRX and the LT X
can be simplified to the MUA which considers the only LT X . In
this case, the problem of the MUA becomes a simple KP, not the
TDKP anymore. Hence, the FL-MUA algorithm is proposed to
be focused on the load state of the only LT X . As the priority
function in the FL-MUA algorithm, the multi-hop gain per the
4
TABLE I
550
System Parameters
Values
System Bandwidth (WBS )
Number of subcarriers (N )
Path loss exponent (LOS/NLOS)
Standard deviation of shadowing(LOS/NLOS)
Transmission Power of BS / FRS
Cell Radius / Radius of the relay belt
Number of cells
Modulation Order
Power control
5M hz
1024
2.35 / 3.76
3.4 dB / 8 dB
43 dBm / 40 dBm
500 m / 250 m
7
BPSK, QAM,
16-,64-,128- QAM
Equal power allocation
QoS Parameters
Values
Target data rate
Target BER
64 kbps, 32 kbps
10−2 , 10−5
Total number of saved subcarriers per FRS
S IMULATION PARAMETERS
w/o MHU
FL-MUA
BL-MUA
500
H-FRS
400
300
L-FRS
200
100
0
5
10
15
20
25
30
35
40
Number of MSs access to a FRS
TABLE II
Fig. 3. The total multi-hop gain obtained from the admitted MUs in a FRS
according to two types of FRSs
D ESCRIPTIONS OF TWO TYPES OF FRS S
Supportable Subcarriers
System Bandwidth
L-FRS
16
WBS /64
H-FRS
64
WBS /16
V. P ERFORMANCE OF THE MUA A LGORITHMS
(9)
In this section, the performances of the BL-MUA algorithm
and the FL-MUA algorithm are evaluated. We assume that the
deployed FRSs have the same capabilities as NR and all capabilities for transmitting and receiving are equal as Ni,RX =
Ni,T X = NR , ∀i. The simulation environments are presented
in Table I. The performances of the MUA algorithms are verified with two types of FRSs as Table II. The L-FRS is the FRS
with the low capability and the H-FRS is that with the high
capability. The performances of the MUA algorithms are compared to the case where MUs are randomly admitted without
the MUA algorithm.
In both MUA algorithms, with the higher priority, the supportable subcarriers of a FRS are used for the MSs which occupy fewer subcarriers with higher multi-hop gain. Hence, the
total multi-hop gain achieved in a FRS and the number of admitted MUs in a FRS can be increased by the proposed algorithms. Those are verified in Fig. 3 and Fig. 4. P
Fig. 3 presents the total multi-hop gain,
xk · Sk ,
o
If lRX
> Ni,RX or lTo X > Ni,T X , then the MUA algorithm
starts.
First of all, the priority values of all MUs are obtained based
on the priority function in (7) or (8). After that, the MU with
the lowest priority is selected and the indicator of admission is
set to zero. The selected MU should do SH transmission, so the
MU is excluded from the MUi and added to the set of SUs,
SU.
If one or both of the Ni,RX and the Ni,T X are still insufficient after one MU exclusion, the MUA process works again.
At this time, the used resources, lRX and lT X , are changed due
to the exclusion of a MU, so the priority function of the BLMUA algorithm should be updated. On the other hand, in the
FL-MUA algorithm, the updating process is not required and
the algorithm just uses the previously determined priorities, so
it is simpler than the BL-MUA algorithm.
The process of the MUA continuously works until both of
Ni,RX and Ni,T X are sufficient for supporting all MUs in
MUi . The performances of the FL-MUA algorithm and the
BL-MUA algorithm are verified at the following section.
achieved by a FRS. The total multi-hop gains of the MUA algorithms are higher than that of the case without MUA for all
types of FRSs. It implies that the MUA algorithms help to admit
MUs which can save more subcarriers by the MH transmission
than the case without MUA algorithm.
The Fig. 4 presents the number of admitted MUs in a FRS
according to two types of FRSs. More MUs can be supported
in a FRS by the MUA algorithms within the limited capability
of FRS compared to the case without MUA algorithm.
From Fig. 3 and Fig. 4, it is also shown that the more significant performance difference between the MUA algorithms and
the case without the MUA algorithm gets as the number of MUs
increases. When the number of MUs is small, the capability of
FRS is generally sufficient for supporting all MUs. Hence, the
MUA is not actually required and the performances of the MUA
algorithms are similar to the case without the MUA algorithms.
However, the MUA becomes meaningful when the FRS can not
support all the MUs due to the insufficient capability.
In addition, the performances of BL-MUA algorithm and FLMUA algorithm are very similar. The reason for this is from the
physical characteristics of the LRX and the LT X . The number
average number of required subcarriers in the LT X is used as
follows
UF L,k = Sk /Ck,LT X .
(8)
When the supportable subcarriers of a FRS are not sufficient,
the MUs are excluded in a low-priority order one by one. The
procedures of the BL-MUA algorithm and the FL-MUA algorithm are discussed in the following subsection.
C. Procedures of MUA Algorithms
The process of the MUA algorithms progresses independently for each FRS, and the overall procedure is shown by the
flow chart in Fig. 2. If MUs which want to use the ith FRS
exist, the total number of required subcarriers in the LRX and
o
the LT X , lRX
and lTo X , can be calculated as
o
lRX
=
X
k∈MUi
Ck,LRX ,
lTo X =
X
Ck,LT X .
k∈MUi
k∈MUi
5
30
w/o MHU
FL-MHU
BL-MHU
0.5
H-FRS
Blocking probability
Total number of admitted MUs
25
20
15
L-FRS
10
5
0
w/o MUA
FL-MUA
BL-MHU
L-FRS
0.4
H-FRS
0.3
0.2
0.1
1
11
21
31
41
51
60
Number of MUs access to a FRS
Fig. 4.
The number of admitted MUs among all MUs access to the FRS
according to two types of FRSs
of required subcarriers in the LT X is much more than that in the
LT X as Ck,LT X À Ck,LRX . In this case, the priority function
of the BL-MUA algorithm in (7) can be approximated to the
priority function of the FL-MUA algorithm in (8) as
p
2
Sk lRX
+ lT2 X
Sk
UBL,k =
≈
= UF L,k .
Ck,LRX · lRX + Ck,LT X · lT X
Ck,LT X
Thus, the similar priority functions are used in both algorithms,
so the performances of them do not have big difference. It implies that the FL-MUA algorithm obtains similar performance
to the BL-MUA algorithm with less complexity.
In Fig. 3 and Fig. 4, the amount of saved subcarriers by the
MH transmission is increased by the MUA algorithms and more
MUs are admitted in a FRS by the MUA algorithms. Hence, in
the aspect of total capacity in a cell, more MSs can be supported
with the limited number of total subcarriers by the MUA algorithms compared to the case without the MUA algorithms. This
can be verified by Fig. 5.
Fig. 5 shows the blocking probability as the number of MSs
per cell is increased when there are six FRSs located symmetrically. The blocking probability is defined as (K − us )/K
where us is the number of supported MSs with 1024 subcarriers
and K is the total number of MSs in a cell. The blocking probabilities of the MUA algorithms are smaller than that of the case
without the MUA algorithm over all range. Specifically, within
0.1 blocking probability, the case without the MUA algorithm
can support at most 135 MSs with L-FRSs and 185 MSs with
H-FRSs. On the other hand, the numbers of supportable MSs
are increased up to 180 MSs with L-FRSs and 223 MSs with
H-FRSs by the MUA algorithms. It implies that 33% and 20%
of the supportable MSs in a cell are increased by the MUA algorithms with L-FRSs and H-FRSs, respectively. Thus, more
MSs can be supported in a cell with low blocking probability
by the MUA algorithms.
VI. C ONCLUSIONS
In this paper, the MUA is considered in downlink OFDMA
multi-hop cellular networks where FRSs with the limited capabilities are deployed. The MUA is required to determine the
admitted MUs to use a FRS in MH transmission with maximizing the total multi-hop gain obtained from the admitted MUs in
a FRS.
0
120
140
160
180
200
220
240
260
280
300
Total number of MSs per cell
Fig. 5. The blocking probabilities according to two types of FRSs
The formulation of the MUA problem is same as the TDKP
kind of NP-hard problem, so the BL-MUA algorithm is proposed to be focused on the load balance between the LRX link
and the LT X and the FL-MUA algorithm is proposed to be only
focused on the load state of the LT X .
Through the numerical results, it is demonstrated that the
multi-hop gain which can be obtained in a FRS and the number of admitted MUs in a FRS are increased by the proposed
algorithms. Hence, more MSs can be supported in a cell with
low blocking probability by the proposed algorithms. In addition, it is verified that the FL-MUA algorithm obtains similar
performance to the BL-MUA algorithm with less complexity.
Hence, the proposed MUA algorithms can be used considering
the acceptable complexity and the required performance in a
system.
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