Downlink and Uplink Decoupling in Heterogeneous Networks for 5G and Beyond 3
ε = 1, the pathloss is completely compensated by the power
control and if ε = 0, no channel compensation is applied and
all users transmit with the same power. The symbol X
v
is the
distance between a user and its associated vBS. The vector
h
v
∈ C
L
v
×1
is the Rayleigh fading channel between vBS and
a user associated to it. s
v
is the normalized transmitted signal
of the user. The first term represents the received signal while
the second and third terms are the intra-cell interference and
inter-cell interference, respectively. Φ
0
v
and Φ
0
w
represent the
point processes formed by the thinned PPP of the scheduled
users of the vBSs and the wBSs tier, respectively, n ∈ C
L
v
×1
is a vector of the complex additive white Gaussian noise at the
tagged BS.
Nonetheless, the inter-cell interference could also be ig-
nored reasonably for the sake of convenient analysis
[17,18]
in
UL. Since the MBS tier and the SBS tier operate on differ-
ent frequency bands, inter-tier interference can be eliminated.
Besides, adjacent small cells are assumed to use different op-
erating frequencies, which leads to the fact that no inter-cell
interference exists at SBSs. Moreover, inter-cell interference
at MBSs can be neglected due to the large coverage area of
MBSs and the low transmit power level of users. Therefore,
by neglecting the inter-cell interference in Eq. (2), a simplified
signal model for MISO is given by
y
v
=
q
QX
−α
v
h
v
s
v
+ n, (3)
where the first term
p
QX
−α
v
h
v
s
v
represents the received sig-
nal of the vBS from the user associated to it. Then, the re-
ceived signals will go through the detectors such as maximal
ratio combining (MRC) and zero-forcing (ZF), which is dif-
ferent from that in SISO
[11,19]
.
C. MIMO
In two-tier multiuser MIMO HetNets, vBSs deploy L
v
an-
tennas, which is the same as the assumption in MISO HetNets
(see Fig. 2). Nevertheless, instead of serving single user in one
resource block (i.e., MISO), BSs are assumed to serve mul-
tiple users simultaneously in each resource block in MIMO
scenario. Note that each user still associates with one BS in
UL/DL.
Let s
v
∈ C
K
(·)
v
×1
be the normalized transmit signal across
the K
(·)
v
users, where K
(·)
v
(K
(·)
v
6 L
v
) is the number of users
associated with vBSs in UL with (·) = (DA) for DA scenario
and (·) = (CA) for CA scenario. Besides, the set of K
(·)
v
users
is denoted by ϕ
(·)
v
. Fast fading is considered here while the
shadowing is neglected for simplicity. Then, the received sig-
nal at vBS, i.e., y
v
∈ C
L
v
×1
, is given as
y
v
= H
v
Q
1/2
v
s
v
+
∑
j∈Φ
u
\ϕ
(·)
v
q
QX
−α
v, j
h
v, j
s
j
+ n. (4)
The term H
v
Q
1/2
v
s
v
represents the received signal of vBS
from users associated to it where H
v
∈ C
L
v
×K
(·)
v
is the channel
matrix with each component obeying the Rayleigh distribu-
tion. Moreover, the diagonal matrix Q
v
with [Q
v
]
kk
= QX
−α
v,k
is the received signal power of vBS from users associated to
it. The second term on the right hand side is the interference
from all the users associated to other BSs, where X
v, j
is the
distance from vBS to the jth user which is not associated to it.
Besides, the channel vector h
v, j
is an i.i.d. complex Gaussian
distributed vector, representing the channel between vBS and
the jth user. Furthermore, the transmit signal of the jth user
is denoted as s
j
.
Since most of the works in DL and UL decoupling in Het-
Nets are based on the system models described above, two
most important UL user association policies for DA will be
introduced.
III. PATHLOSS-BASED
ASSOCIATION POLICIES
In UL, users are associated to the BS which achieves the
highest UL average power. Due to the fact that the fading-
induced variations can lead to ping-pong effects in the asso-
ciation process, the average power is obtained by averaging
over the received signals in Eq. (1) with respect to the fading,
which is given as
E
h
[s
v,U
] = QX
−α
v
. (5)
Then, a user associates with the BS that offers the highest av-
erage power, i.e., the user is associated to MBS in UL if
QX
−α
M
> QX
−α
S
. (6)
Otherwise, the user is associated to SBS. The association rule
described in Eq. (6) is called minimum pathloss association
policy.
According to the PDF of X
v
[20]
and the minimum pathloss
association policy described in Eq. (6), the association proba-
bility of associating to vBS under the minimum pathloss pol-
icy, represented by A
PL
v
, can be calculated as
A
PL
v
=
λ
v
λ
v
+ λ
w
. (7)
It can be seen that the association probability A
PL
v
under the
minimum pathloss policy is only related to the densities of
vBSs and wBSs.
Next, with the biased factor considered in the association
policy, i.e., the user is associated to MBS in UL if
Qη
M
X
−α
M
> Qη
S
X
−α
S
, (8)