1 Integrated Access and Backhaul in Cell-free Massive MIMO Systems

2025-04-30 0 0 477.03KB 14 页 10玖币

Integrated Access and Backhaul in Cell-free

Massive MIMO Systems

Ali Hosseinalipour Jazi, S. Mohammad Razavizadeh, and Tommy Svensson

Abstract

One of the major challenges with cell-free (CF) massive multiple-input multiple-output (MIMO) networks is providing backhaul

links for a large number of distributed access points (APs). In general, providing ﬁber optics backhaul for these APs is not cost-

effective and also reduces network scalability. Wireless backhauling can be a promising solution that can be integrated with wireless

access links to increase spectrum efﬁciency. In this paper, the application of integrated access and backhaul (IAB) technique in

millimeter-wave (mmWave) CF massive MIMO systems is investigated. The access and backhaul links share a frequency spectrum

in the mmWave bands, and in both, hybrid beamforming techniques are adopted for signal transmission. The bandwidth allocation

(division) parameter between the two link types as well as the beamforming matrices are optimized to maximize the end-to-end

data-rate. This leads to a non-convex optimization problem for which an efﬁcient solution method is proposed. The simulation

results show the effectiveness of the IAB technique and our proposed scheme in CF massive MIMO systems. These simulations

also compare the proposed hybrid beamforming method with a fully digital solution in terms of the number of radio frequency

(RF) chains and the volume of backhaul trafﬁc. Finally, the effect of increasing the number of APs on the users’ data rates in

terms of wireless access and backhaul links constraints is also examined.

Index Terms

Integrated Access and Backhaul (IAB), massive MIMO, millimeter-wave (mmWave), cell-free (CF), hybrid beamforming.

I. INTRODUCTION

During past years, there have been increasing demands for new wireless services like enhanced mobile broadband (eMBB) and

ultra-reliable and low latency communication (URLLC) that motivate researchers to develop new technologies for efﬁcient and

reliable transmission of more data in minimal time and frequency resources. Massive multiple-input multiple-output (MIMO) is

one of the promising techniques for accommodating these demands [1]. However, implementation of a large number of antennas

of massive MIMO on a limited space base station (BS) is not easy in practice and leads to a degradation in the expected

performance. In addition, in the centralized implementation scenarios of the massive MIMO arrays, there is a signiﬁcant

difference in the signal powers of cell-edge and cell-center users. This motivates distributed or cell-free (CF) massive MIMO

systems in which the antennas of the massive MIMO are distributed among a number of access points (APs) in a wide area [2].

CF massive MIMO systems can provide uniform quality of service (QoS) over a cell region and reduce multi-user interference

[3]. It is also a good choice for implementing new services like massive machine type communication (mMTC) and internet

of things (IoT), in which devices are distributed in a wide service area [4].

In spite of these advantages, CF networks face many challenges, including synchronization among the APs, user association,

and backhaul link provisioning for the APs [5]. In general, existing cable and optical ﬁber-based backhaul links are less

suitable for future cellular networks due to implementation costs and low ﬂexibility. Hence, the wireless backhaul has attained

much attention due to its lower implementation complexity and higher ﬂexibility [6]. Microwave backhaul links that operate

in line-of-sight (LOS) conditions have been used for a long time, utilizing dedicated international telecommunications union

(ITU) frequency bands [7]. However, in 5G, millimeter-wave (mmWave) frequency bands are a potential candidate to meet

the growing bandwidth demand in the future wireless backhaul link. In addition, due to the wide bandwidth in the mmWave

access spectrum, there is a new interest to share radio resources between the wireless backhaul and access links, leading to

the concept of integrated access and backhaul (IAB) [8].

There are many papers that study wireless backhauling and IAB techniques in wireless cellular networks. For example, in

[9], the authors consider a cellular heterogeneous network (HetNet) with wireless backhaul links and design the beamforming

matrices for this network. The authors in [10] maximize the wireless backhaul link rate in the mmWave bands and then use

this rate as a constraint in maximizing the rate of users in the access link that operate in the sub-6 GHz frequency band.

The design of IAB networks by multiplexing the access and backhaul links in time domain is studied in [11]. The authors in

[12] maximize end-to-end sum rate of users (i.e., from the central processing unit (CPU) in the network core to the users) in

a mm-wave cellular network by optimizing the dedicated bandwidth for the access and backhaul links and power allocation

coefﬁcients in the macro-cell BS (MBS). In addition, the authors in [7] and [13] evaluate the coverage probability of a

cellular network equipped with IAB by considering different backhaul scenarios (ﬁber, wireless/ﬁber, and IAB). In the case

Ali Hosseinalipour ans S. Mohammad Razavizadeh are with the School of Electrical Engineering, Iran University of Science and Technology (IUST),

Tehran 16846-13114, Iran (e-mail: {alihosseinalipour, smrazavi}@iust.ac.ir)

Tommy Svensson is with the Electrical Engineering Department, Chalmers University of Technology, 412 96 Gothenburg, Sweden, (e-mail:

tommy.svensson@chalmers.se)

arXiv:2210.12633v1 [cs.IT] 23 Oct 2022

of wireless backhauling, the small-cell BSs (SBSs) in the backhaul link and users in the access link are served by different

carrier frequencies. In most of the references, the authors do not optimize the bandwidth allocation coefﬁcient between the

access and backhaul connections and use a frequency division multiplexing in the access and backhaul links.

There are also a few papers that assume wireless backhauling in the CF networks. For example, in [14] and [15], the wireless

backhaul links parameters are considered as the constraints for the access link optimization in the CF networks. In [16] the

authors optimize end-to-end rate in a user-centric CF massive MIMO network by jointly optimizing the beamforming matrix

in the backhaul link and the power allocation coefﬁcients in the access link. This paper considers different frequency bands

(mm-wave band and sub-6 GHz) for the access and backhaul links. However, to the best of our knowledge, the IAB technique

and specially frequency multiplexing between backhaul and access links in the CF networks has not been studied before in

the literature.

In this paper, we study the use of IAB in the downlink of a CF massive MIMO network in which the wireless backhaul and

access links are multiplexed in the frequency domain. In the considered network, there is one CPU (IAB-donor) and multiple

APs (IAB-nodes) that serve a large number of users at the same time and frequency resource. In this paper, we use the terms

CPU/APs and IAB-donor/IAB-nodes interchangeably. Both wireless access and backhaul links operate at the same mm-wave

frequency band, and hybrid beamforming techniques are used for signal transmission at both of them. For optimal design

of the IAB scheme, the bandwidth allocation coefﬁcient between the access and backhaul links is optimized to maximize

the minimum end-to-end rate over them. At the same time, the hybrid beamforming matrices at the CPU and APs are also

optimized, which ﬁnally leads to a non-convex optimization problem that cannot be solved efﬁciently. Hence, we propose a

solution method that optimizes the above variables for access and backhaul links alternatively. We also derive a closed-form

expression for dividing the mm-wave frequency band between the access and backhaul links. We verify the performance of the

proposed scheme through computer simulations. The results show the effectiveness of using IAB in the CF massive MIMO

systems. We also evaluate the performance of the proposed hybrid beamforming optimization scheme by comparing it with

fully digital beamforming and centralized beamforming at the CPU, which illustrates the effectiveness of using this technique

in conjunction with IAB. Then, we investigate the impact of the number of APs on coverage enhancement of the CF network

in the access link and also on the rate of the backhaul link. Finally, by considering the effects of both the access and backhaul

rates on the end-to-end rate of the networks, we show that in the CF massive MIMO systems with wireless backhaul, there is

an optimal number of APs achieving the best performance.

The rest of this paper is organized as follows. The system model is described in Section II. Following the deﬁnition of the

main problem in Section III, the parameters of the backhaul and access links are optimized in Sections IV and V, respectively.

Section VI speciﬁes a closed-form equation for the bandwidth allocation coefﬁcient. Section VII presents the numerical results

of the proposed algorithms. In Section VIII, the paper is summarized.

Throughout this paper, the following notations are used: a,a, and Astand for a scalar, a column vector, and a matrix,

respectively; [A]i,j denotes the (i;j)-th element of matrix Aand the i-th element of vector ais denoted by [a]i;rank(A)is

the rank of A;(A)∗,(A)T, and (A)H, denote conjugate, transpose, and Hermitian transpose of A, respectively. The Euclidean

and Frobenius norms of Aare denoted by k.kand k.kF, respectively. Furthermore, we use T r {},<{}, and E{} to respectively

represent the trace, real part taking, and expectation operators. diag {a}forms a diagonal matrix of the vector a, and INdenotes

the N×Nidentity matrix. z∼CN(0, σ2)denotes a circularly symmetric complex Gaussian random variable zwith zero

mean and variance σ2. Further, Cand Cm×ndescribe a complex value and a complex matrix of dimension m×n, respectively.

The amplitude and phase of a complex value zare denoted by |.|and ∠, respectively.

II. SYSTEM MODEL

As depicted in Fig. 1, we consider a CF massive MIMO system consisting of M NA-antenna APs (i.e., IAB-nodes) that

serve Ksingle-antenna users. All the IAB-nodes are connected to an NC-antenna CPU (i.e., IAB-donor). Both the access

and backhaul links operate at the same frequency band in the mmWave frequencies. Assuming that Band η∈(0,1] indicate

the total available bandwidth in the network and the bandwidth allocation coefﬁcient between access and backhaul links,

respectively, dedicated bandwidth to the access and backhaul links will be ηB and (1 −η)B, respectively. In the following,

we discuss signal transmission and reception in the access and backhaul links.

A. Access link

Let xk∈Cdenotes the k-th user’s signal in the access link, which is transmitted from all the APs and E{|xk|2}= 1. The

received signals at the k-th user is

Fig. 1: System Model.

yk=

m=1

j=1

hk,mWRF

mwBB

j,mxj+nk

m=1

hk,mWRF

mwBB

k,mxk

|{z }

Desired signal

m=1

j=1

j6=k

hk,mWRF

mwBB

j,mxj

| {z }

Interference

+nk,

(1)

where Wm=WRF

mWBB

m∈CNA×Kdenotes the hybrid beamforming matrix of the m-th AP which is product of an analog

beamforming matrix WRF

m∈CNA×NA

RF and a baseband digital beamforming matrix WBB

m∈CNA

RF ×K(where wBB

k,m is the

k-th column of WBB

m). NA

RF is the number of RF chains at each AP. The analog beamforming matrix has a unit-module

constraint (i.e., WRF

mi,j =1

√NA) and the digital beamforming matrix must satisfy AP power constraint 

WBB

m

2

F≤PA

where PAis the total AP’s power constraint for the access link. In addition, nk∼CN(0, σ2

k)is the additive white Gaussian

noise at the k-th user.

The channel gain of the m-th AP to the k-th user is denoted by hk,m ∈C1×NAthat has Saleh-Valenzuela (SV) channel

model [17] and is deﬁned as

hk,m =pNAϑL

k,m aL(ϕAoD

k,m )

Lk,m

l=1 sNA

Lk,m

ϑN

l,k,m aL(ϕAoD

l,k,m).(2)

In this equation, Lk,m,ϕAoD

k,m (ϕAoD

l,k,m), and aL(.)represent the number of non-line-of-sight (NLOS) paths, the angle of departure,

and the normalized array response vector, respectively. Without loss of generality, we consider a uniform linear array (ULA)

at each AP and CPU. For an N-element ULA, the array response can be expressed as

aL(ϕ)∆

√Nh1, ej2π

λdAsin(ϕ), ..., ej2π

λdA(N−1) sin(ϕ)i

∈C1×N,

(3)

where λis the wavelength, and dAindicates inter-element spacing. Also, ϑL

k,m ∈CN 0, I(d) 10−0.1κindicates path loss of

the channel between the m-th AP and the k-th user in the LOS link in which I(d)is a parameter that shows the existence of

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1IntegratedAccessandBackhaulinCell-freeMassiveMIMOSystemsAliHosseinalipourJazi,S.MohammadRazavizadeh,andTommySvenssonAbstractOneofthemajorchallengeswithcell-free(CF)massivemultiple-inputmultiple-output(MIMO)networksisprovidingbackhaullinksforalargenumberofdistributedaccesspoints(APs).Ingeneral,provi...

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