1 Energy-Efﬁcient Cell-Free Network Assisted by Hybrid RISs

2025-04-27 0 0 2.43MB 6 页 10玖币

侵权投诉

Energy-Efﬁcient Cell-Free Network

Assisted by Hybrid RISs

Wanting Lyu, Yue Xiu, Songjie Yang, Chau Yuen, Fellow, IEEE, and Zhongpei Zhang, Member, IEEE

Abstract—In this letter, we investigate a cell-free network

aided by hybrid reconﬁgurable intelligent surfaces (RISs), which

consists of a mixture of passive and active elements that are

capable of amplifying and reﬂecting the incident signal. To

maximize the energy efﬁciency (EE) of the system, we formulate

a joint transmit beamforming and RIS coefﬁcients optimization

problem. To deal with the fractional objective function, Dinkel-

bach transform, Lagrangian dual reformulation, and quadratic

transform are utilized, with a block coordinate descent (BCD)

based algorithm proposed to decouple the variables. In addition,

successive convex approximation (SCA) method is applied to

iteratively to tackle the non-convexity of the sub-problems.

Simulation results illustrate the effectiveness and convergence

of the proposed algorithm through analyzing the EE and sum

rate performance with varying parameter settings. The proposed

hybrid RISs schemes can achieve 92% of the sum rate but 188%

of EE of active RISs schemes. As compared with passive RISs,

11% gain in sum rate can be achieved with comparable EE.

Index Terms—Beamforming, cell-free, convex optimization,

energy efﬁciency, reconﬁgurable intelligent surfaces.

I. INTRODUCTION

CELL-FREE network has gained great attractiveness in

beyond ﬁfth-generation mobile communications (B5G)

without cell boundaries [5]. It has great potential in next

generation indoor and hot-spot environment, such as shopping

malls, train stations, hospitals and subways. In addition, cell-

free network is particularly effective in high-mobility scenarios

like vehicular networks without handover cost [7]. Despite

the above advantages, conventional cell-free network requires

massive access points (APs), resulting in high power consump-

tion both for AP transmit power and hardware power [8].

Recently, reconﬁgurable intelligent surface (RIS), as a

promising technology to overcome obstacles, enhance channel

capacity and improve energy efﬁciency [33] in various scenar-

ios [26], [27], [29]–[32], [34], has been integrated into cell-free

networks to replace some of the APs [8] [18] [2]. However,

the ideal capacity gains provided by RIS is difﬁcult to achieve

practically owing to the ”multiplicative fading” effect caused

by RIS, causing extremely large path loss in the cascaded

channels. Considering this, a new structure of RIS, namely

active RIS has been proposed by authors of [11] [12], where

active reﬂecting elements are conﬁgured with radio frequency

Wanting Lyu, Yue Xiu, Songjie Yang and Zhongpei Zhang are with

National Key Laboratory of Science and Technology on Communications,

University of Electronic Science and Technology of China, Chengdu61173,

China (E-mail: lyuwanting@yeah.net; xiuyue12345678@163.com; yang-

songjie@std.uestc.edu.cn; zhangzp@uestc.edu.cn).

C. Yuen is with the Engineering Product Development (EPD) Pillar,

Singapore University of Technology and Design, Singapore 487372 (e-mail:

yuenchau@sutd.edu.sg).

Fig. 1. System model of the hybrid RIS-aided cell-free network.

(RF) chains and power ampliﬁers to alleviate the severe

fading effect. The active RIS, however, requires higher power

consumption, and introduce non-negligible self-interference

and thermal noise. Considering the trade-off between the

signal amplifying effect and power consumption, a hybrid RIS

architecture has been proposed [14]. In this architecture, only a

few reﬂecting elements are activated, introducing a lower level

of transmit power and effective noise than active RIS, while

signiﬁcantly enhancing the signal strength compared with full

RIS. Hybrid RIS provides a reliable, sustainable solution to

the wireless network design with an acceptable level of cost

and power consumption.

To the best of our knowledge, conventional passive RISs

have been used in cell-free networks to reduce the power

consumption, but the data rate is limited by the severe

double-fading effect. To improve the energy efﬁciency (EE)

of cell-free networks while alleviating the fading effect, we

consider hybrid RISs with a few active elements capable

of amplifying the incident signal to replace a part of APs.

Thus, we consider a downlink cell-free network assisted by

hybrid RISs to achieve a trade-off between EE and sum rate

performance. A highly coupled non-convex EE maximization

problem constraint on the minimum rate requirement is for-

mulated by optimizing the digital beamforming and hybrid

RIS coefﬁcients design. Then, we propose a block coordinate

descent (BCD) based algorithm to decouple the variables. To

deal with the fractional objective function, Dinkelbach method,

Lagrangian dual reformulation, and quadratic transform are

applied. Particularly, successive convex approximation (SCA)

method is used to tackle the non-convexity of the subproblems.

Simulation results show the effectiveness of the proposed

algorithm in terms of improving energy efﬁciency.

arXiv:2210.01440v1 [eess.SP] 4 Oct 2022

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. Transmission Model

Consider a downlink cell-free network with LAPs each

conﬁgured with Ntantennas serving Ksingle-antenna users

as shown in Fig. 1. To enhance the communication quality and

improve the energy efﬁciency, Rhybrid RISs are deployed in

the network, each with Nsreﬂecting elements. For each RIS,

NaNsactive reﬂecting elements are predetermined in the

set Ar, where |Ar|=Na. The RIS coefﬁcient matrix of RIS

ris deﬁned as Θr=diag{ar,1, . . . , ar,Ns}, where ar,ns=

|ar,ns|ejθr,nsdenotes the coefﬁcient of the nth

selement, with

the amplitude |ar,ns| ≤ amax if the element (r, ns)is in the

set Ar, and |ar,ns| ≤ 1otherwise. To combine the elements

in all RRISs together and for ease of exposition, deﬁne n=

Ns(r−1) + ns,1≤n≤N, where N=RNs. The elements

in set A=∪

rArare the active reﬂecting elements in all R

RISs. Then, the overall RIS matrix can be written as Θ=

blockdiag{Θ1,...,ΘR}. To distinguish the active and passive

elements, rewrite Θas Θ=Ψ+Υ, where Ψ=AΘ and

Υ= (IN−A)Θdenote the coefﬁcient matrices of active and

passive elements, respectively, where the selection matrix A

is an N×Ndiagonal matrix with the elements corresponding

to set Ato be 1, and others to be 0.

Assume that all APs and all RISs serve all users over

the same time-frequency resource, such that data symbol

s∈CK×1satisfying E{ssH}=IKis transmitted from

the APs simultaneously. A central processing unit (CPU)

connected to all APs generates the digital beamformers based

on perfectly known channel state information (CSI) of all

the links. The transmitted signal at the AP lcan then be

expressed as xl=Wls, where Wl∈CNt×Kdenotes the

transmit beamforming matrix at AP l. The links from AP l

to user k, from AP lto RIS r, and from RIS rto user kare

denoted as dH

l,k ∈C1×Nt,Gl,r ∈CNs×Ntand fH

r,k ∈C1×Ns,

respectively. Thus, the received signal of user kcan be

expressed as

yk=

l=1

(dH

l,k +

r=1

r,kΘrGl,r )Wls+

r=1

r,kΨzr+nk,(1)

where nk∼ CN(0, σ2

0)is the additional white Gaussion noise

(AWGN) at user k, and zr∼ CN(0, σ2

rArINs)is the effective

noise caused by the active elements of RIS r, including the

AWGN and self-interference due to the full-duplex mode. Or

we can write (1) in a more compact form as

yk= (dH

k+fH

kΘG)Ws +fH

kΨz +nk,

=˜

kWs +fH

kΨz +nk,(2)

where dH

k= (dH

1,k,...,dH

L,k)∈C1×LNt,fH

(fH

1,k,...,fH

R,k)∈C1×RNs,W= (WT

1,...,WT

L)T∈

CLNt×K,z= (z1,...,zR)∈CRNs×1, and

G=





G1,1··· GL,1

.....

G1,R ··· GL,R





∈CRNs×LNt.(3)

Hence, the received signal-to-interference-plus-noise

(SINR) at user kcan be expressed as

γk=|˜

kwk|2

Pj6=k|˜

kwj|2+PR

r=1 ˜σ2

r+σ2

,(4)

where wkis kth column of the digital beamforming matrix

W, and ˜σ2

r=σ2

r||fH

r,kΨr||2is the effective RIS noise power.

B. Energy Efﬁciency

The total power consumption includes transmit power at

APs, transmit power at active elements of RISs and hardware

circuit power. Therefore, the total power consumption of the

cell-free system can be expressed as

Ptot(W,Ψ) =

l=1

l,tx(Wl)

| {z }

transmit power of APs

r=1

r,a(Ψr,W)

| {z }

transmit power of active RIS elements

l=1

l,c +

r=1

r,c +

k=1

| {z }

circuit power of APs, RISs and UEs

.(5)

Speciﬁcally, transmit power of AP lis PA

l,tx(Wl) =

Tr(WH

lWl)

µA, and transmit power of the active elements of

RIS ris PR

r,a(ΨrW) = 1

µRE{||Ψr(GrWs +zr)||2}=

µRTr(WHGH

rΨH

rΨrGrW) + Pns∈Ar|ar,ns|2σ2

r,

where µA, µR∈(0,1] denote the ampliﬁer efﬁciency factors

of AP and RIS, respectively.

Thus, the energy efﬁciency of this system can be written as

η=PK

k=1 Rk

Ptot

,(6)

where Rk= log2(1 + γk)is the data rate of user k.

C. Problem Formulation

To maximize the system energy efﬁciency, the optimization

problem can be formulated as

(P1) max

W,Θη(7a)

s.t. PA

l,tx(Wl)≤PA

max,∀l∈ {1, . . . , L},(7b)

0≤θn≤2π, ∀n, (7c)

|an| ≤ amax, n ∈ A (7d)

|an| ≤ 1, n /∈ A (7e)

Rk≥Rth,∀k, (7f)

r,a(Ψr,W)≤PR

max,∀r, (7g)

where (7b), (7g) are the transmit power constraints for AP

land RIS r. (7c), (7d) and (7e) are the phase shift and

amplitude constraints for all RIS elements, respectively. (7f)

is to guarantee the data rate of user k.

However, problem (P1) is difﬁcult to solve due to the

strongly coupled variables, non-convex fractional objective

function (7a), and non-convex constraints (7f). To solve this

problem, we proposed an iterative BCD algorithm in section

III.

III. JOINT OPTIMIZATION ALGORITHM

In this section, we ﬁrst transform the complex fractional

objective function into equivalent concave form, and propose a

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1Energy-EfcientCell-FreeNetworkAssistedbyHybridRISsWantingLyu,YueXiu,SongjieYang,ChauYuen,Fellow,IEEE,andZhongpeiZhang,Member,IEEEAbstractInthisletter,weinvestigateacell-freenetworkaidedbyhybridrecongurableintelligentsurfaces(RISs),whichconsistsofamixtureofpassiveandactiveelementsthatarecapableof...

展开>> 收起<<

1 Energy-Efﬁcient Cell-Free Network Assisted by Hybrid RISs.pdf

共6页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

1 Energy-Efﬁcient Cell-Free Network Assisted by Hybrid RISs

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: