YIN et al.: INTERFERENCE COORDINATION FOR D2D COMMUNICATIONS IN CELLULAR NETWORKS 1521
signal-to-interference-plus-noise ratio (SINR) at the receiver
(denoted as D2DR
k
) can be expressed as
SINR
k,n
=
p
k,n
H
k,n
I
(ia)
k,n
+ I
(ir)
k,n
+ N
k,n
, (1)
where p
k,n
and H
k,n
are the transmit power and the channel
gain of D2D
k
on subchannel n, respectively, N
k,n
is the noise
power, I
(ia)
k,n
and I
(ir)
k,n
stand for intra-layer interference and inter-
layer interference experienced by D2D pair k, respectively.
Then, accordingly, I
(ia)
k,n
≥ 0 and I
(ir)
k,n
=0 in the overlaying
mode, I
(ia)
k,n
≥ 0 and I
(ir)
k,n
≥ 0 in the underlaying mode. Ob-
viously, interference coordination for the underlaying mode
is much more complicated than that in the overlaying mode
since both intra-layer and inter-layer interference need to be
addressed to guarantee the QoS of both CUs and D2D pairs.
Therefore, we will focus on the distributed interference coordi-
nation scheme for the underlaying mode. The other scenarios
should be easy to deal with once the underlaying mode is
resolved.
In this paper, we assume only uplink channels are shared with
D2D pairs. For uplink channel reusing, the victim of inter-layer
interference at the cellular side is the BS, which is typically
capable of dealing with co-channel interference, for example,
using smart antenna techniques [19]. Thus, reusing uplink
channel in D2D layer can bring more performance gain with
less challenge than reusing the downlink resources according
to [20], [21].
If the subchannel n allocated to CU m is reused by the kth
D2D pair, then intra-layer and inter-layer interference experi-
enced on subchannel n of D2D pair k can be written as
I
(ia)
k,n
=
K
j=1
j=k
p
j,n
˜
H
j,k,n
, and I
(ir)
k,n
=ˆp
m,n
ˆ
H
m,k,n
, (2)
respectively, where
˜
H
j,k,n
is the interference channel gain from
D2DT
j
to D2DR
k
on subchannel n, ˆp
m,n
is the transmission
power of CU
m
on subchannel n, and
ˆ
H
m,k,n
denotes the inter-
ference channel gain from CU m to D2D pair k on subchannel
n. Since we focus on spectrum allocation and power control
in D2D layer, inter-layer interference, I
(ir)
k,n
, will be treated as
noise.
Then, with (1) and (2), the achievable data rate on D2D link
k can be expressed as
R
k,n
(p
k,n
)=log
2
1+
SINR
k,n
Γ
k
=log
2
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
1+
p
k,n
Γ
k
⎛
⎝
K
j=1
j=k
p
j,n
α
j,k,n
+σ
k,n
⎞
⎠
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
, ∀k ∈K,
(3)
where α
j,k,n
Δ
=
˜
H
j,k,n
H
k,n
is the normalized intra-layer interference
channel gain from D2DT
j
to D2DR
k
, σ
k,n
Δ
=
ˆp
m,n
ˆ
H
m,k,n
+N
k,n
H
k,n
is the normalized noise power, Γ
k
is a constant SINR gap,
which is based on the bit-error-rate (BER) requirement in
practical systems and can be expressed as [22]
Γ
k
= −
ln(5BER
k
)
1.5
, (4)
where BER
k
is the desired BER for D2D link k.
In the cellular layer, two cases will be studied. In the first
case, we assume that the transmission power of CUs on each of
its occupied subchannels is fixed while the second case is that
they can be adapted according to inter-layer interference. Since
only the uplink channels are allowed to be reused in the D2D
layer and there is no intra-layer interference, the achievable
SINR at the BS from CU m on subchannel n in the uplink
will be
SINR
B
m,n
=
ˆp
m,n
h
m,n
K
k=1
p
k,n
˜
h
k,n
+
˜
N
m,n
, (5)
where h
m,n
is the channel gain between CU m and the BS on
subchannel n,
˜
h
k,n
is the interference channel gain between
D2D pair k and the BS,
˜
N
m,n
is the received noise power at
the BS on subchannel n. Then, similar to (3), the data rate of
CU m on subchannel n can be expressed as
R
B
m,n
(ˆp
m,n
)=log
2
⎛
⎜
⎜
⎜
⎝
1+
ˆp
m,n
ˆ
Γ
m
K
k=1
p
k,n
˜α
k,n
+˜σ
m,n
⎞
⎟
⎟
⎟
⎠
, (6)
where ˜α
k,n
Δ
=
˜
h
k,n
h
m,n
, ˜σ
m,n
Δ
=
˜
N
m,n
h
m,n
, and
ˆ
Γ
m
is also derived
according to (4).
III. P
RICING BASED DECENTRALIZED
INTERFERENCE COORDINATION
In this section, we will apply a pricing based game-
theoretical model to develop a decentralized joint power and
subchannel allocation framework for D2D pairs. Inter-layer
and intra-layer interference in D2D communications has to be
mitigated. Therefore, the BS, treated as a supervisor, maintains
a “price” vector θ =(θ
n
)
N
n=1
, where θ
n
represents the price
charged for inter-layer interference brought by D2D transmis-
sion on subchannel n. D2D pairs are treated as subordinates.
With the price vector, θ, the competition for the reuse of uplink
spectra among D2D pairs is modeled as a non-cooperative
game. When the NE is reached, the data rate requirements of
D2D pairs are satisfied. Therefore, in order to guarantee the
QoS of both CUs and D2D pairs, the pricing strategy at BS in
the cellular layer should be carefully designed and the sufficient
conditions for the existence and uniqueness of the NE in the
game of the D2D layer should be investigated. In the following,
the non-cooperative game among D2D pairs and the pricing
strategy at the BS will be studied, respectively.
A. Non-Cooperative Game Among D2D Pairs
With the price vector, θ, the non-cooperative game for the
D2D layer is defined as
G =
K, (p
k
)
k∈K
, (U
k
(θ, P))
k∈K
, (7)