MSEQoS约束下的多用户MIMOSWIPT收发器和功率分配联合优化资源-CSDN文库

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本文研究的是在平均平方误差（MSE）服务质量（QoS）约束下，针对下行链路多用户多输入多输出（MU-MIMO）同时无线信息和功率传输（SWIPT）系统的收发器设计和功率分配（PS）的联合优化问题。作者通过联合优化基站（BS）的发射器和功率分配因子以及移动站（MSs）上的信息解码（ID）接收器，目的是在满足预先设定的MSE QoS约束和给定的能量采集（EH）约束的情况下最小化发射功率。提出的优化问题是一个非凸优化问题，无法直接解决。为了解决这个问题，提出了一种迭代优化框架，包括发射器和PS因子的联合优化子问题（JTxPS）以及接收端最小均方误差（MMSE）最小化子问题。通过迭代求解这两个子问题，可以解决原始的优化问题。对所提出的JTDPS和JTxPS问题的可行性的充分必要条件进行了分析。理论分析表明，JTxPS子问题也是非凸的，可以通过凸半定规划（SDP）来解决。考虑到基于SDP方案的高计算复杂性，还提出了一种基于传统MMSE收发器设计的低复杂度次优方案。通过模拟结果验证了理论分析，并且结果表明所提出的方案的有效性。通过这段文字，我们可以梳理出以下知识点： 1. 多用户多输入多输出（MU-MIMO）技术：一种通信技术，利用多个天线同时传输多个数据流，以提高频谱效率和数据吞吐量。 2. 同时无线信息和功率传输（SWIPT）：这是一种新兴的通信技术，旨在通过无线信号同时传输信息和能量，从而解决移动设备的充电问题。 3. 平均平方误差（MSE）：一种衡量信号质量的指标，用于评估信号在经过传输或处理过程中的失真程度。 4. 服务质量（QoS）：在通信网络中，QoS定义了传输数据流所需满足的服务水平标准，包括延迟、带宽、丢包率等参数。 5. 能量采集（EH）：指无线设备从接收到的无线信号中提取能量，用于自身供电的技术。 6. 发射器和功率分配（PS）优化：在无线通信系统中，发射器的优化和功率分配方案对于提升系统性能至关重要，包括调整功率水平和分配策略以降低能耗、提高传输效率。 7. 非凸优化问题：在数学优化中，非凸优化问题是目标函数或约束条件中存在多个局部极小值的优化问题，这使得找到全局最优解变得复杂。 8. 迭代优化框架：一种通过迭代求解多个子问题，逐步逼近整体优化问题最优解的方法。 9. 最小均方误差（MMSE）：一种统计算法，用来估计一个随机变量，使得估计值与真实值之间的均方误差最小化。 10. 半定规划（SDP）：一种凸优化问题，广泛应用于控制理论、信号处理和通信等领域，它是关于半定矩阵变量的线性目标函数的最大化或最小化问题。 11. 低复杂度次优方案：在解决复杂问题时，由于某些算法可能计算成本过高，寻找计算复杂度较低的算法是一种实用的方法，虽不一定是最佳解，但在实际应用中更为可行。 12. 理论分析与模拟验证：在提出新的算法或系统设计后，通常需要通过理论分析和计算机模拟来验证其有效性和可行性。这些知识点详细阐述了本论文的研究背景、目标、方法和结果，提供了对多用户MIMO SWIPT系统中的收发器设计和功率分配联合优化问题的深入理解。

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Joint Transceiver and Power Splitting Optimization

for Multiuser MIMO SWIPT under

MSE QoS Constraints

Haixia Zhang, Senior Member, IEEE, Anming Dong, Member, IEEE, Shi Jin, Member, IEEE, and

Dongfeng Yuan Senior Member, IEEE

Abstract—This paper studies the joint transceiver design and

power splitting (JTDPS) for a downlink multiuser multiple-input

multiple-output (MU-MIMO) simultaneous wireless information

and power transfer (SWIPT) system. Aiming to minimize the

transmit power by jointly optimizing the transmitter at a base

station (BS), the power splitting (PS) factors and information

decoding (ID) receivers at mobile stations (MSs) subject to

both the predeﬁned mean-square error (MSE) and the given

energy harvesting (EH) constraints. The formulated problem is

a nonconvex JTDPS optimization problem, which can not be

solved directly. To solve it, an iterative optimization framework

composed of joint transmitter and PS factor optimization (JTxP-

S) subproblem and a receiver side minimum mean-square error

(MMSE) minimization subproblem is proposed. By iteratively

solve the two subproblems, the original optimization problem is

solved. The sufﬁcient and necessary conditions for the feasibility

of the formulated JTDPS and the JTxPS problems are analyzed.

Theoretical analysis show that the JTxPS subproblem is also

nonconvex and can be solved by using convex semideﬁnite pro-

gramming (SDP). Considering the high computational complexity

of the SDP based scheme, a low-complexity suboptimal scheme

based on traditional MMSE transceiver design is also proposed.

Simulation results are done to validate the theoretical analysis,

and results show the effectiveness of the proposed schemes.

Index Terms—Energy harvesting; mean-squared error (MSE);

multi-input multi-output (MIMO); quality of service (QoS);

semideﬁnite programming (SDP); semideﬁnite relaxation (SDR);

simultaneous wireless information and power transfer (SWIPT);

transceiver design.

I. INTRODUCTION

Eliminating the power line connecting mobile devices to

the grid for recharging is an envisaged future communication

scenario [2]–[6]. Simultaneous wireless information and power

transfer (SWIPT) has been regarded as a promising solution

to realize this envision. It has also been expected to bring

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

This work was partly presented at the IEEE International Conference on

Communications (ICC) 2016 [1].

The work was supported in part by the International S&T Cooperation

Program of China under Grant 2014DFA11640; by the National Natural

Science Foundation of China under Grant 61622111, Grant 61671278 and

Grant 61371109.

H. Zhang and D. Yuan are with the Shandong Provincial Key Laboratory of

Wireless Communication Technologies, Shandong University, Jinan 250100,

China. (e-mail: haixia.zhang@sdu.edu.cn; dfyuan@sdu.edu.cn)

A. Dong is with the School of Information, Qilu University of Technology,

Jinan 250353, China. (e-mail: donganming@gmail.com)

S. Jin is with the National Communications Research Laboratory, Southeast

University, Nanjing 210096, China. (e-mail: jinshi@seu.edu.cn)

fundamental changes and new challenges in the design of

future wireless communication networks [7]–[9]. Since the

work in [10] and [11], which characterized the fundamental

limits on rate and energy of point-to-point SWIPT systems

from the perspective of information theory, there has been

a great interest in constructing practical SWIPT transmission

schemes and protocols [12]–[16]. Power splitting (PS) is one

of the methods that achieve SWIPT by dividing the received

signal at the receive antennas into two parts for information

retrieval and energy storage, respectively and simultaneously.

In such architecture, it is proﬁtable to achieve SWIPT by

jointly optimizing the transceivers for information decoding

(ID) and PS factors for energy harvesting (EH). Moreover,

because of its ability in providing spatial multiplexing and

diversity [16], [17], multiple antenna system has the potential

to improve the performance of SWIPT transmission. Con-

sequently, transceiver design and power splitting for multi-

input multiple-output (MIMO) SWIPT systems has received

considerable attentions recently.

The prior work on transceiver design and PS for a variety

of multiple-input multiple-output (MIMO) scenarios can be

found in literature [16]–[26]. The concept of PS was ﬁrst

proposed for a point-to-point MIMO system in [16]. Joint

transmit beamforming and PS optimization was investigated to

minimize the transmit power under signal-to-interference-and-

noise ratio (SINR) and EH quality of service (QoS) constraints

for multiuser multiple-input single-output (MISO) systems in

[17]. A semideﬁnite programming (SDP) relaxation technique

was developed to obtain the globally optimal solution, but

with high computational complexity. [18] further proposed a

second order cone programming (SOCP) relaxation solution,

which can decrease the computational complexity signiﬁcantly

compared with the SDP scheme. Recently, robust counterparts

of this problem have been investigated in [19] and [20] to

combat channel imperfection. Related work has also been

extended to interference channel (IC) networks. [21] jointly

optimized the beamforming and power allocation scheme to

minimize the transmit power for a PS-based MISO interference

channel under the SINR and EH QoS constrains. Both SDP

and SOCP based solutions were derived. [22], [23] and [24]

investigated more general MIMO IC networks by employ-

ing interference alignment. For multicell multiuser downlink

SWIPT systems, [25] studied the joint transceivers and PS

design to optimize the energy efﬁciency. In [26], an energy

harvesting system with PS-based relay station was considered.

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

is an N ×N identity matrix. A

, A

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

and k·k

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

antennas. It is assumed that user k is served with N

data

streams, and the total number of data streams in the system

is d =

k=1

≤ M. Suppose that s

∈ C

×1

is the

data vector to be transmitted to user k, ∀k, the data vector

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