Robust Beamforming for Multiuser MISO
Interference Channel with Energy Harvesting
Constraint
Zhengyu Zhu
‡
, Yuanyuan Zhang
‡
, Zhongyong Wang
‡
, Yanbin Zhang
‡
, Xiangchuan Gao
‡
, Zheng Chu
†
‡
School of Information and Engineering, Zhengzhou University, Zheng Zhou, China
†
School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, U.K.
Email: zhuzhengyu6@gmail.com, iezywang@zzu.edu.cn, iexcgao@zzu.edu.cn, z.chu@newcastle.ac.uk
Abstract—In this paper, we study the robust transmit beam-
forming and receive power splitting design for simultaneous
wireless information and power transfer in multiuser multiple-
input single-output interference channel with imperfect channel-
state information at the transmitter. We consider two types of
receivers, namely Type I and Type II receivers according to
the ability of eliminating the interference from received signals.
Following the worst-case model, we minimize the average total
transmit power subject to a set of energy harvesting constraint
and SINR constraint for Type I receiver or SNR constraint for
Type II receiver, respectively. Based on the Lagrangian multiplier
method, we propose a lower and upper bounds algorithm that is
able to achieve a global optimum for Type I receiver. For Type II
receiver, we transform this problem into a relaxed semidefinite
programming problem, which can be solved efficiently. It is shown
from simulation results that our proposed method outperform the
non-robust scheme.
Index Terms—Simultaneous wireless information and power
transfer (SWIPT), MISO-IFC, robust beamforming, power split-
ting, energy harvesting (EH)
I. INTRODUCTION
Simultaneous wireless information and power transfer
(SWIPT) is a promising method to deal with the energy scarci-
ty problem in energy constrained wireless networks [1]-[14].
The idea of the SWIPT for a single-input-single-output system
was firstly studied in [1]. Motivated by this idea, SWIPT
was later expanded to multiple-input-multiple-output (MIMO)
and multiple-input-single-output (MISO) broadcast systems in
[3]-[7]. However, receiver should not simultaneously decode
information and harvest energy from the same receive signal.
Under such constraint, a practical co-located receiver design
was proposed as the power splitting (PS) receiver in [2]. To
allow SWIPT at the PS receiver side, the transmit power
minimization problem for MISO broadcast channel (BC) and
interference channel (IFC) with SWIPT scheme was first
considered in [3] and [4], respectively. A MISO-IFC SWIPT
system with multiple power splitting-based receivers was also
considered in [5].
In addition, these literatures only considered the perfect
channel-state information at the transmitter (CSIT), which
cannot meet the practical implementation in general. Ro-
bust transmit beamforming design problems for the SWIPT
have been investigated in some scenarios [6]-[8]. For secure
communication in multiuser MISO systems with SWIPT, [7]
proposed an efficient semidefinite programming (SDP) to ob-
tain the global optimal beamforming. [8] studied multicasting
MISO SWIPT system with both perfect and imperfect CSIT
cases. However, its algorithm only is available for the SNR
constraint for each user.
In contrast to the assumption of perfect CSIT for MISO-BC
[3] and MISO-IFC [4], we consider the worst-case optimiza-
tion with spherical uncertainty by jointly optimal design of
transmit beamforming at each transmitter and receive power
splitting factors at each receiver, our objectives are to mini-
mize the total transmit power under individual EH constraint
and SINR constraint at two types of receivers, respectively.
For Type I receiver, the optimization problem under SINR
constraint and EH constraint is non-convex. To solve this
problem, we reformulate the initial design problem and convert
the channel uncertainty to the uncertainty in its covariance
matrix. We propose a efficient approach by choosing exact
lower and upper bounds on the numerator and denominator
terms of SINR. The final problem become convex and can
be efficiently solved by the existing interior point method
[10]. For Type II receiver, the original problem has infinite
nonconvex constraints due to the channel uncertainties. Ap-
plying certain transformation techniques, this problem convert
into an easier one with finite constraints, but still non-convex.
By using the SDR technique, we can obtain a relaxed SDP
problem which can be solved efficiently. Simulation results
are presented to assess the performance advantages of the
proposed robust design schemes.
Notations: A
H
, ∥A∥, tr(A) and rank(A) denote the conju-
gate transpose, Frobenius norm, trace and rank of the matrix A,
respectively. vec(A) denotes to stack the columns of a matrix
A into a single vector a. ∥a∥ denotes the Euclidean norm of
a. A circularly symmetric complex Gaussian (CSCG) random
vector a with mean
¯
a and covariance matrix Σ is denoted
as x ∼ CN(
¯
a, Σ). ∇
a
f(·) stands for the differentiation of a
function f with respect to a. E{·} describes the mathematical
expectation.
II. SYSTEM MODEL
As shown in Fig. 1, we consider K-user MISO-IFC with
SWIPT scheme. Different from the conventional IFC, each
receiver can simultaneously decode information and harvest