WU et al.: QOE AND ENERGY AWARE RESOURCE ALLOCATION IN SMALL CELL NETWORKS WITH POWER SELECTION 7463
II. SYSTEM MODEL AND PROBLEM FORMULATION
A. System Model
Let us consider a dense SCN, where L SBSs are indepen-
dently deployed in random locations. There are N SUs in the
SCN. We assume that small cells transmit on orthogonal chan-
nels with macrocells, thus the cross-tier interference is avoided
in this network. There are M dedicated channels for small cells
to transmit. For presentation, denote the SU set as N , i.e.,
N = {1, 2,...,N}, the SBS set as L, i.e., L = {1, 2,...,L},
and the dedicated channel set as M, M = {1, 2,...,M}. Each
SBS can operate at a power level selected from the power set P
in all channels,
1
i.e., P = {0,p
1
,p
2
,...,p
K
}, where p
k
<p
k
for k<k
.
It is assumed that the coverage ranges of all SBSs are vary-
ing with their transmission power levels. Concretely, the trans-
mission range D
l,k
tx
of each SBS l at power level p
k
is de-
fined as the range within which the received signal power
from SBS l is higher than some threshold RSS
tx
. Formally,
let rss(l, k, d) denote the received signal power at distance d
from SBS l sending beacons at power level p
k
, then the trans-
mission range D
l,k
tx
= max{d : rss(l, k, d) ≥ RSS
tx
}. It is clear
that D
l,k
tx
<D
l,k
tx
for k<k
.
It is assumed that these N SUs can be covered by these
L SBSs, i.e., max
n,l
{d
nl
}≤D
l,K
tx
, where d
nl
is the distance
between SU n and SBS l. When the transmission power level of
SBS l is determined, the transmission range of each SBS l can
be expressed as D
l
tx
for simplicity.
Due to the spatial distribution and low transmission power
of SBSs, each SBS can only directly affect the transmission of
neighboring SUs. Similarly, the interference range D
l,k
int
of each
SBS l at power level p
k
is defined as the range within which
an SU associated with another SBS will receive an interference
power from SBS l that is higher than threshold RSS
int
(RSS
int
≥
RSS
tx
), i.e., D
l,k
int
= max{d : rss(l, k, d) ≥ RSS
int
}. It is clear
that D
l,k
int
<D
l,k
int
for k<k
.
Thus, when a given SBS transmits signal to a selected associ-
ated SU, such a transmission link would only cause significant
effect to the rest associated SUs of the given SBS and a few SUs
associated with other neighboring SBSs.
An interference graph can characterize the potential inter-
ference relationship among SUs. The interference graph is dif-
ferent from the traditional interference graph of SBSs: When
SU i associates with one of its available SBS l who trans-
mits at power level k and another SU j transmits in the same
channel with SU i, if the distance between SBS l and SU
j is smaller than D
l
int
, then SU i would interfere SU j, and
vice versa.
A summary of key notations is presented in Table I.
1
The coverage ranges of SBSs are determined by the selected power levels
without considering the effect of channel carrier frequencies. In the following,
we assume that the coverage ranges of an SBS in all channels are identical for
convenience, i.e., there is only one coverage range for an SBS at one time. The
power allocated in the dedicated channels can also be different. Then, the action
space will be much larger.
TABLE I
S
UMMARY OF KEY NOTATIONS
Notation Physical Interpretation
N ,N SU set, number of S Us
L,L SBS set, number of SBSs
M,M Dedicated channel set, number of channels
P,K Power level set, number of nonzero power level
p
k
,p
l
The power of level k, the power of SBS l
D
l
tx
(D
l,k
tx
) Transmission range of SBS l (at power level p
k
)
rss(l, k, d) Received signal power at distance d
from SBS l at power level p
k
d
nl
Distance between SU n and SBS l
˜
N
l
,
˜
N
l,k
Available severed SU set of SBS l
at current power level/at power level p
k
˜
L
n
Available candidate SBS set of SU n
at current power level
D
l
int
(D
l,k
int
) Interference range of SBS l (at power level p
k
)
N
cov
, N
uncov
Covered SU set, uncovered SU set
SU
l
Selected SU set of SBS l
su
li
The ith SU of SBS l’s selected SU set
C
l
Allocated channel set to SU set SU
l
C
li
Allocated channel set for su
li
C
l
All channels used by SBS l
A,A
l
Action profile of all SBSs, action of SBS l
γ
m
l,n
Received SINR of SU n from SBS l in channel m
h
m
l,n
Channel gain from SBS l to SU n in channel m
σ
m
n
Noise power at SU n in channel m
δ
m
l,n
Intercell interference indicator function
r
m
l,n
Data rate attained by SU n from SBS l in channel m
m
n,su
lh
Intracell interference indicator function
R
su
li
,R
n
Achieved aggregate throughput of SU su
li
and SU n
s
n
,F
n
() QoE of SU n, satisfaction function of SU n
κ Operational cost for each SBS
˜κ
n
Split part of the operational cost to SU n
ν (p
l
) The energy cost transmitting with power level
p
l
in one channel
π Penalty for a unserved SU
U, u
n
Global utility, utility of SU n
A1,A2 Action profile of subproblem i (G1) and ii (G2)
L
dec
Decision maker SBS set
L
fol
Follower SBS set
L
fol,l
Follower set of SBS l
ˆ
N
dec,l
Possible affected SUs of decision maker l
ˆ
N
fol,l
Possible affected SUs of follower l
sbs
n
SBS allocated to SU n by decision maker
ˇ
N
dec,l
Unaffected SU set of decision maker l
B. Problem Formulation
First, each SBS l chooses a power level p
l
from the power
set P for transmitting. When power levels of all SBSs are
determined, all SUs can be divided into two SU sets, the
covered set N
cov
= {n : d
nl
≤ D
l
tx
, ∃l ∈L} and the uncov-
ered set N
uncov
= {n : d
nl
>D
l
tx
∀l ∈L}, N
cov
∪N
uncov
= N .
The available severed SUs of SBS l can be denoted as
˜
N
l
= {n : d
nl
≤ D
l
tx
,n∈N}. Each covered SU n can only
be associated with an SBS from the candidate SBS set
˜
L
n
=
{l : d
nl
≤ D
l
tx
,l ∈L}. Then, SBS l selects a set of available
served SUs SU
l
= {su
l1
,su
l2
,...,su
ln
l
} from
˜
N
l
in a coop-
erative manner with its neighboring SBSs, SU
l
⊂
˜
N
l
. Particu-
larly, there have N
cov
= SU
1
∪ SU
2
∪···∪SU
l
and SU
l
∩ SU
l
= ∅, ∀l = l
. Finally, each SBS l allocates channels to all its
served SUs. The allocated channel set can be denoted as
C
l
= {C
l1
,C
l2
,...,C
ln
l
}, where C
li
is the allocated channel set
for SU su
li
(C
li
⊂M, |C
li
|≥1). Then, the all channels used