2
Aiming at exploiting the benefit of multiple-antenna relay, the
outage probability and ergodic capacity over different linear
receiving schemes were investigated therein. Besides the PS-
based schemes, transceiver designs for system with separated
ID and EH receivers can be found in [27]–[31]. All the
aforementioned work has been done to optimize either the
information rate or the output SINR.
As one of the main quantitative performance metrics in
the field of wireless communications, the mean-square er-
ror (MSE) has been a standard criterion for the assessment
of signal quality and fidelity [32], and it has been widely
adopted in traditional transceiver designs [33]–[35]. Since it
offers good compromise between the performance and the
implementation complexity, MSE based transceiver design for
SWIPT systems has also been widely investigated recently
[36]–[38]. [36] studied the MSE-based transceiver design
for a downlink multiuser MIMO (MU-MIMO) system with
separated EH and ID receivers. In [36], two schemes were
studied, one was to minimize the worst MSE among all ID
receivers subject to the given EH constraints, and the other was
to maximize the energy harvested subject to the given MSE
QoS constraints. The weighted minimum MSE (MMSE) based
MIMO SWIPT transceiver designs were investigated in [37],
which also studied the separated ID and EH receivers case. A
sum MSE minimization problem was investigated in [38] for
two-user MIMO IC networks. All these work has been done
without considering the PS factors, and unfortunately cannot
be extended to PS-related systems directly. Therefore, to
develop joint transceiver design and power splitting (JTDPS)
schemes based on MSE criterion is of both practical and
theoretical significance.
In this work, we study the joint transceiver and PS design for
the downlink of MU-MIMO SWIPT systems, where each MS
has individual QoS constraints on both the harvested energy
and MSE of the received information. This work aims at
jointly optimizing the transmitter at the BS, the PS factors and
ID receivers at MSs, such that the consumed transmit power is
minimized and the MSE and energy harvesting constraints of
each MS are satisfied. Analysis reveals that the formulated
JTDPS problem is nonconvex on the transceivers and PS
factors and difficult to solve. To overcome this, an iterative
framework is established by iteratively optimizing two sub-
problems, i.e., a joint transmitter and PS factors optimization
(JTxPS) problem and a minimum MSE receiver optimization
problem. The feasibility of both the JTDPS problem and the
JTxPS subproblem is studied, and the sufficient and necessary
conditions to guarantee the feasibility of these problems are
derived. To solve the nonconvex JTxPS sub-problem, SDR
technique is adopted to reformulate it to a convex SDP
problem, which can be solved effectively. Considering the
high computational complexity of the SDP based scheme, a
low-complexity suboptimal scheme based on the traditional
MMSE transceiver design is proposed. The performance of
the proposed schemes is validated and compared through
simulations.
The main contributions of this work are listed as follows:
1) The research on MSE-based transceiver design for
SWIPT is extended from point-to-point MIMO to MU-
MIMO scenarios.
2) A novel JTDPS problem is formulated by minimizing
the transmit power subject to both the MSE and EH
constraints. The formulated problem is jointly non-
convex on the precoder, receivers and PS ratios. Besides,
the products of these variables poses huge challenges on
not only analyzing but also solving the problem.
3) Analysis reveals that the feasibility of the formulated
JTDPS problem is independent of the EH and PS con-
straints. This makes it possible to check the feasibility
of the formulated problem.
4) An alternative optimization framework to solve the for-
mulated nonconvex problem by iteratively optimizing
the receivers and the transmit precoder together with
PS factors. To make the framework practical, the sub-
problem of precoder and PS factors design is casted as
a convex SDP, and thus the solutions for the original
problem can be obtained efficiently.
5) A low-complexity optimization scheme is proposed for
large systems by first designing the transceivers which
can satisfy the MSE constraints and then calculating the
transmit power and PS factors in closed-form. Compared
with the SDP-based scheme, the proposed scheme is of
quite low computational complexity for large number of
antennas and users.
The remainder of this paper is organized as follows.
Section II presents the MU-MIMO SWIPT system model.
Section III formulates the JTDPS problem and analyzes the
feasibility of formulated problem. In Section IV, an iterative
optimization framework is established to solve the JTDPS
problem and the feasibility of the JTxPS subproblem is
analyzed. An SDP-based solution is proposed to solve the
JTxPS subproblem in Section V. Section VI presents the low-
complexity design scheme. Simulations results are presented in
Section VII for performance evaluation. Finally, Section VIII
concludes the whole paper.
Notations: C represents the complex field. Bold uppercase
and lowercase letters represent matrix and column vectors,
respectively. Non-bold italic letters represent scalar values. I
N
is an N ×N identity matrix. A
H
, A
T
and A
−1
represent the
Hermitian transpose, transpose and inverse of A, respectively.
The Kronecker product is ⊗. vec(A) is a vector formed by
stacking the columns of A. Tr(A) and rank(A) is the trace
and rand of matrix A, respectively. E[·] denotes the statistical
expectation. k·k
2
and k·k
F
denote the 2- and Frobenius-norm,
respectively. card(G) denotes the cardinality of set G.
II. SYSTEM MODEL
The downlink of a multiuser MIMO system with K users
as shown in Fig. 1 is considered. It is assumed that the base
station (BS) serves K mobile stations (MSs) through spatial
multiplexing in the considered system. The BS is equipped
with M antennas and user k, k = 1, . . . , K is equipped with
L
k
antennas. It is assumed that user k is served with N
k
data
streams, and the total number of data streams in the system
is d =
P
K
k=1
N
k
≤ M. Suppose that s
k
∈ C
N
k
×1
is the
data vector to be transmitted to user k, ∀k, the data vector