![](https://csdnimg.cn/release/download_crawler_static/16056078/bg3.jpg)
ZHU et al.: WPT IN MASSIVE MIMO-AIDED HetNets WITH USER ASSOCIATION 4183
TABLE I
N
OTATION
and uses the harvested energy for WIT in the uplink. Let
T be the duration of a communication block. The first and
second sub-blocks of duration τ T and
(
1 − τ
)
T are allocated
to the downlink WPT and uplink WIT, respectively, where
τ
(
0 ≤ τ ≤ 1
)
is the time allocation factor. We assume that
the first tier represents the class of macrocell BSs (MBSs),
each of which is equipped with a large antenna array [32].
The locations of the MBSs are modelled using a homogeneous
Poisson point process (HPPP)
M
with density λ
M
[33]. The
locations of the small-cell (such as micro/picocell, femtocell,
etc.) BSs (SBSs) in the i-th tier (i = 2,...,K ) are modelled
by an independent HPPP
i
with density λ
i
. It is assumed
that the density of users is much greater than that of BSs so
that there always will be one active mobile user at each time
slot in every small cell and hence multiple active mobile users
in every macrocell.
2
In the macrocell, S single-antenna users
communicate with an N-antenna MBS (assuming N S ≥ 1)
in the uplink over the same time slot and frequency band.
3
In the small cell, only one single-antenna user is allowed
to communicate with a single-antenna SBS at a time slot.
We assume that perfect channel state information (CSI) is
known at the BS,
4
and the effect of pilot contamination on
channel estimation is omitted. As mentioned in [7] and [35],
pilot contamination is a relatively secondary factor for all but
colossal numbers of antennas, and various methods to mitigate
pilot contamination via low-intensity base station coordination
have already been proposed in the literature such as [35].
In addition, universal frequency reuse is employed such that all
of the tiers share the same bandwidth and all the channels are
assumed to undergo independent identically distributed (i.i.d.)
quasi-static Rayleigh block fading.
2
In reality, there may be more than one active users in a small cell and this
can be dealt with using multiple access techniques.
3
We note that in [14], the probability mass function of the number of users
served by a generic BS was derived by approximating the area of a Voronoi
cell via a gamma-distributed random variable. However, the result in [14]
cannot be applied in this paper, since the Euclidean plane is not divided into
Voronoi cells based on the considered user association methods. We highlight
that it is an important work to study the case of the dynamic S following a
certain distribution in less-dense scenarios.
4
In the practical TDD massive MIMO systems, the downlink CSI can be
obtained through channel reciprocity based on uplink training.
A. User Association
We introduce two user association algorithms: (1) a user is
associated with the BS based on the maximum DRSP at the
user, which results in the largest average received power; and
(2) a user is associated with the BS based on the maximum
URSP at the BS, which will minimize the power loss of user’s
signal during the propagation.
5
Considering the effect of massive MIMO, the average
received power at a user that is connected with the -th MBS
( ∈
M
) can be expressed as
P
r,
= G
D
a
P
M
S
L
X
,M
, (1)
where G
D
a
denotes the power gain obtained by the user
associated with the MBS, P
M
is the MBS’s transmit power,
L
X
,M
= β
X
,M
−α
M
is the path loss function, β is
the frequency dependent constant value,
X
,M
denotes the
distance, and α
M
is the path loss exponent. In the small cell,
the average received power at a user that is connected with
the j-th SBS ( j ∈
i
)inthei-th tier is expressed as
P
r,i
= P
i
L
X
j,i
, (2)
where P
i
denotes the SBS’s transmit power in the i-th tier and
as above L
X
j,i
= β
X
j,i
−α
i
is the path loss function
with distance
X
j,i
and path loss exponent α
i
.
For DRSP-based user association, the aim is to maximize
the average received power. Thus, the serving BS for a typical
user is selected according to the following criterion:
BS : arg max
k∈
{
M,2,...,K
}
P
∗
r,k
, (3)
where
P
∗
r,M
= max
∈
M
P
r,
, and P
∗
r,i
= max
j∈
i
P
r,i
. (4)
By contrast, for URSP-based user association, the objective
is to minimize the uplink path loss, and as such, the serving
BS for a typical user is selected by
BS : arg max
k∈
{
M,2,...,K
}
L
∗
(
|
X
k
|
)
, (5)
where
L
∗
(
|
X
M
|
)
= G
U
a
max
∈
M
L
X
,M
, (6)
L
∗
(
|
X
i
|
)
= max
j∈
i
L(
X
j,i
). (7)
Here, G
U
a
is the power gain of the serving MBS and L
∗
(
|
X
M
|
)
can be viewed as compensated path loss due to the power gain.
B. Downlink WPT Model
For wireless energy harvesting, the RF signals are inter-
preted as energy. Therefore, in the massive MIMO macrocell,
we adopt the simplest linear MRT beamforming
6
to direct the
5
Although user association for the downlink and uplink can be decoupled
to maximize both the DRSP and URSP, the main drawback for the decoupled
access is that channel reciprocity in massive MIMO systems will be lost [36].
6
Since there is no interference concern in the downlink power trans-
fer, other beamforming methods involving interference mitigation such as
zero-forcing (ZF) will reduce power gain and increase the power consumption
of the MBS.