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Application of cellfree massive MIMO in 5G and beyond 5G wireless networks: a survey
Journal of Engineering and Applied Science volume 68, Article number: 13 (2021)
Abstract
In recent times, the rapid growth in mobile subscriptions and the associated demand for high data rates fuels the need for a robust wireless network design to meet the required capacity and coverage. Deploying massive numbers of cellular base stations (BSs) over a geographic area to fulfill highcapacity demands and broad network coverage is quite challenging due to intercell interference and significant rate variations. Cellfree massive MIMO (CFmMIMO), a key enabler for 5G and 6G wireless networks, has been identified as an innovative technology to address this problem. In CFmMIMO, many irregularly scattered single access points (APs) are linked to a central processing unit (CPU) via a backhaul network that coherently serves a limited number of mobile stations (MSs) to achieve high energy efficiency (EE) and spectral gains. This paper presents key areas of applications of CFmMIMO in the ubiquitous 5G, and the envisioned 6G wireless networks. First, a foundational background on massive MIMO solutionscellular massive MIMO, network MIMO, and CFmMIMO is presented, focusing on the application areas and associated challenges. Additionally, CFmMIMO architectures, design considerations, and system modeling are discussed extensively. Furthermore, the key areas of application of CFmMIMO such as simultaneous wireless information and power transfer (SWIPT), channel hardening, hardware efficiency, power control, nonorthogonal multiple access (NOMA), spectral efficiency (SE), and EE are discussed exhaustively. Finally, the research directions, open issues, and lessons learned to stimulate cuttingedge research in this emerging domain of wireless communications are highlighted.
Introduction
The exponential growth of wireless network service users worldwide orchestrates the need to deploy novel enabling technologies to satisfy billions of datahungry applications [1]. In recent times, the emergence of the Internet of Things (IoT) has ushered in newage internetenabled smartphones and machinetomachine communications (M2M) for the growing mobile users [2]. However, the current network infrastructure is already overstretched, and there is a need for novel technologies to improve the existing wireless network architecture [3]. From managing security and privacy challenges, network spectrum issues, traffic spikes, complex network configuration, prohibitive operating costs, network failure, to hardware compatibility issues and more, the ubiquitous fifthgeneration (5G) wireless network architecture needs to be enhanced to accommodate these growing concerns optimally [4, 5]. Recently, key enabling technologies for the envisioned beyond 5G and 6G wireless systems have been proposed [6,7,8,9]. Interestingly, these enablers include cellfree massive MIMO (CFmMIMO) technology [10,11,12], mmWave communication [13,14,15], terahertz communication [16,17,18], quantum communication [19, 20], directional beamforming [21], reconfigurable intelligent surfaces (RIS) [22,23,24], and more.
The concept of CFmMIMO introduced in [25] presents a promising alternative to guarantee high quality of service (QoS) to all UEs. CFmMIMO leverages the idea of smallcells (SC), massive MIMO, and userbased joint transmission coordinated multipoint (JTCoMP) [26] to deal with intercell interference [27]. Additionally, CFmMIMO provides massive macrodiversity to mitigate path loss [28] via minimizing the adverse effects of spatially correlated fading and shadowing [29]. In this case, several ubiquitous access points (APs) with single or multiple antennas jointly serve a smaller number of distributed UEs over the coverage area in timedivision duplex (TDD) mode [30]. CFmMIMO has been described as an embodiment of network MIMO and is regarded as an alternative network MIMO [31]. Compared to the fully distributed SC system and massive cellular MIMO, CFmMIMO has improved performance under several practical conditions, including but not limited to favorable propagation and channel hardening with spatially wellseparated UEs and APs. This results in increased macrodiversity gain from the low distance between UEs and APs [3, 32, 33].
Currently, there is a growing interest in the implementation of sustainable and greener CFmMIMO systems [34] to boost the energy efficiency (EE) [35, 36] of wireless systems, offset the power consumption cost [37], and minimize the environmental impacts of wireless systems [38]. Several optimization techniques, EEsaving algorithms, and robust power control models [39, 40], such as energy cooperation [41], reconfigurable intelligent surface (RIS) [23, 42, 43], and more, have been explored. Combining CFmMIMO and simultaneous wireless information and power transfer (SWIPT) technique is considered to drive energylimited user devices and improve the EE of nextgeneration wireless networks [44,45,46]. Given that several APs and several users are involved in a CF system [47], the deployment cost and energy consumption may rise, and more energy resources [48, 49] would be required. In order to realize CFmMIMO in practice, carrier frequency and sampling rate offsets, Inphase/quadraturephase (I/Q) imbalance, phase noise, and analogtodigital converter distortions need to be examined [50, 51]. Toward this end, this paper provides an extensive survey on the areas of application of CFmMIMO in nextgeneration wireless communication systems. A comprehensive layout of the paper is presented in Fig. 1. Furthermore, different massive MIMObased solutions, massive cellular MIMO, and network MIMO are examined critically. The design and system configurations, system modeling, application scenarios, potentials, and associated challenges of CFmMIMO are discussed extensively. Additionally, open research issues, lessons learned, and future research directions are outlined.
This survey is focused on applying CFmMIMO in 5G and beyond 5G (B5G) wireless networks. The key highlights of the survey are outlined as follows.

1.
We present a background on the evolution of CFmMIMO in emerging wireless communication systems.

2.
We present an overview of cellular massive MIMO, network massive MIMO, and CF massive MIMO, highlighting their areas of application, strengths, limitations, and performance comparison of these architectures with reference to key design metrics, interference management, channel hardening, and SE, among others.

3.
We examine the configuration details and system modeling of CFmMIMO, emphasizing the uplink/downlink (UL/DL) pilotaided channel estimation, UL/DL training, channel hardening, and outage probability.

4.
We highlight key areas of application of CFmMIMO such as in SWIPT, power control, NOMA, SE, and EE.

5.
We present key research findings and current trends in CFmMIMO, highlighting their focus, coverage, prospects, and limitations.

6.
We highlight open research issues, future research directions, and key takeaway lessons on CFmMIMO deployment in 5G and B5G wireless networks.
The rest of this paper is organized as follows. The literature review is presented in the “Related work” section. A comprehensive description of the traditional MIMO architecture, massive cellular MIMO, network MIMO, and CFmMIMO is presented in the “Overview of massive MIMO systems” section. The “System model of cellfree massive MIMO” section offers a detailed account of the CFmMIMO system modeling and configuration. The application of CF massive MIMO in channel hardening, NOMA, EE, and more are discussed in the “Areas of application of cellfree massive MIMO” section. Open research issues and lessons learned are highlighted in “Open research issues and lessons learned” section. Finally, the “Conclusions” section gives a concise conclusion to the paper.
Related work
Cellfree massive MIMO has attracted considerable research interest in the past decade, and it is currently regarded as a key 5G and beyond 5G physical layer technology [52,53,54,55]. The authors in [56] provide an indepth exposition into simulation platforms and insightful schemes for emerging 5G interfaces. An extensive overview of several solutions for 5G infrastructures including, but not limited to massive MIMO, millimeterwave (mmWave), NOMA, and also the latest achievements on simulator capabilities, are clearly outlined. Also, artificial intelligence (AI)based discontinuous reception (DRX) technique for greening 5G enabled devices have been proposed in [57]. The proposed mechanism significantly outperforms the conventional longterm evolution (LTE)DRX technique in efficient energy savings. In recent times, the use of deep learning techniques to perform power control in wireless communication networks has been studied in [58,59,60]. Reference [61] advocate using deep neural networks to perform joint beamforming and interference coordination at mmWave.
Additionally, the authors in [62] consider incorporating channel hardening in CFmMIMO using stochastic geometry and evaluated the potential constraints to its practical implementation. It suffices that the channel hardening effect is more noticeable in massive cellular MIMO than in CFmMIMO and depends mainly on the number of antennas per AP and the pathloss exponent of the propagation environment [63]. Fortunately, the authors [64] have shown that significant improvement in channel hardening is achievable with the normalized conjugate beamforming (NCB) precoder compared to the conjugate beamforming (CB) scheme. The works [65,66,67] characterized the coexistence of CFmMIMO and SWIPT utilizing the Poisson point process (PPP) model.
Furthermore, an insight into the achievable harvested energy, channel variations due to fading and path loss, and UL/DL rates in closed form are considered [68, 69]. The detrimental effects of pilot contamination on the performance of CFmMIMO are highlighted in [70, [1]. The authors in [53] proposed allocating pilot power for each user in the network to palliate this defect. Interestingly, interference management and joint user association aimed at minimizing celledge effects are studied [70]. References [11, 71] have reported novel scalable and distributed algorithms used for initial access and cooperation cluster formation in CFmMIMO. The authors also proposed scalable signaltoleakageandnoise ratio precoding to address the scalability issues in CFmMIMO. Currently, federated learning (FL) frameworks are introduced in [72, 73], and FL optimization techniques have been presented in [74,75,76]. A detailed account recapitulating the impact of hardware impairments (HI) on the performance of CFmMIMO is characterized [48]. By employing a hardware scaling law, the impact of HI on APs is shown to vanish asymptotically. The authors in [77] analyzed the UL and DL CFmMIMO performance under the classical HI model to gain further insights.
Most of the literature provides valuable information on massive MIMO deployment in 5G wireless networks. Though some of these papers present several aspects of CFmMIMO, there is no detailed study on CFmMIMO systems that captures entirely cellular massive MIMO, network MIMO, and CFmMIMO system modeling, architecture, strengths and limitation, and applications in terms of SWIPT, channel hardening, hardware efficiency, power control, NOMA, SE, and EE. To this end, the need for a comprehensive paper covering the aspects mentioned above of CFmMIMO is vitally important. Therefore, the current paper presents an extensive survey on CFmMIMO as a candidate enabler for 5G and B5G wireless networks. Specifically, the limitations of some selected literature are outlined, and the contributions of the current paper are highlighted, as presented in Table 1.
Overview of massive MIMO systems
The concept of massive MIMO has received considerable attention due to its deployment to meet the demands of wireless capacity and higher data rates [89]. Massive MIMO offers improved spectral and energy efficiency and adopts optimal signal processing schemes [90]. Moreover, massive MIMO can spatially multiplex many user equipment (UE) by using many phasecoherent transmitting/receiving antennas, thus suppressing intercell and intracell interference [91, 92]. These unique features have revitalized studies leading to the discoveries of several massive MIMO solutions [93]. Massive MIMO technology, empowered with several antennas at each cell site, offers tremendous improvements in the radiated EE, power efficiency, and SE compared to the traditional MIMO systems [94, 95]. Moreover, by operating in either a centralized or distributed fashion, favorable propagation facilitates the realization of nearoptimal linear processing [96]. Motivated by the benefits mentioned above, various massive MIMObased solutions significantly gained traction in academia and industry [97]. A brief discussion on cellular mMIMO, network MIMO, and CFmMIMO focusing on their architectures, strengths, and applications are presented in the following subsections.
Cellular massive MIMO
Massive MIMO timedivision duplex (mMIMOTDD) systems have been reported to boost the throughput of wireless networks [83, 86]. Since the multiple antennas used in mMIMOTDD are much smarter, it presents a practical means to outperform partial multiuser MIMO (MUMIMO) systems. BS antennas could be substantially larger than the number of transmitter terminals. Recently, the attractive features of cellular networks, including exploiting channel reciprocity, especially as more antennas do not necessarily lead to a corresponding increase in the feedback overhead, have been investigated. The traditional cellsize shrinking technique is eliminated via the installation of extra antennas to existing cell sites. Furthermore, UL and DL transmit powers are considerably reduced due to increased antenna aperture and coherent combining. Nonetheless, cellular networks face significant challenges, including estimating the criticality of coherent channels, bandwidth, and interference limitations. Additionally, the substantial cost associated with a large number of transmitting/receive chains and power amplifiers is a major setback. An illustrative description of a typical cellular massive MIMO system is given in Fig. 2. The mobile station (MS) is connected to a central base station (BS) in each cell.
Network MIMO
Network MIMO system, which allows for coordination of a set of APs that jointly serve all users in the network, has often been hailed as an exciting alternative to achieving the capacity limit of cellular networks [98, 99]. Network MIMO or multicell MIMO signaling is considered a potential physical layer technique for 5G wireless networks. A plethora of interfering transmitters share user messages in a network MIMO system and enable joint precoding to be performed. Additionally, network MIMO could be referred to as cooperative communications used to improve the interferencelimited performance of cellular networks. Specifically, by jointly designing the DL beams to multiplex multiple users spatially, intracluster interference can be eliminated. This concept has recently been introduced under a new network structure named CF massive MIMO [3]. It is considered a key enabling technology for 5G and beyond 5G wireless systems. Besides, the celledge problem inherent in cellular massive MIMO is eliminated, and all antennas jointly serve all users (UEs). Figure 3 presents the architecture of a typical network MIMO system.
Cellfree massive MIMO
The cellular topology has been the traditional way of covering the subscribers in a given geographical area with wireless network service for many decades. Each BS serves a given set of UEs using highly directional beamforming techniques [94]. This network topology has shown desirable performance gains, spectral efficiency, and energy efficiency [100,101,102]. However, the technology inevitably limits further performance improvements due to intercell interference, high QoS variations, and handoffs [78, 103]. In order to address this problem, a viable option is to eliminate the inherent cell characteristics and take a considerable number of distributed APs densely deployed over a given coverage area to serve a smaller number of UEs optimally [53]. This novel communication architecture is described as cellfree massive MIMO, and it has been identified as a candidate enabling technology for future wireless communication systems [83, 104].
Currently, key disruptive technologies have been deployed to cater to throughput, coverage, EE, and ubiquity requirements of nextgeneration wireless networks. In particular, having multiple antennas at the APs for several users has been observed as a promising technique to boost the multiplexing gain and enhance the SE in CF massive MIMO [55, 80]. Recently, power domaincentric NOMA integrated with CFmMIMO emerged as a viable solution to address the conflicting demands on high SE, EE, high reliability with userfairness, increased connectivity, and reduced latency in 5G wireless networks [105,106,107]. In CFmMIMO, the number of simultaneously served users can be increased by supporting the users to utilize the same timefrequency resource effectively and invoking superpositioncoded transmission and successive interference cancelation (SIC) decoding [108,109,110].
Cellfree massive MIMO leverages a distributed antenna system’s unique features, coordinates beamforming, joint transmission, and scheduling to provide multiuser interference suppression and achieve stronger diversity gains. Moreover, due to the welldesigned network topology, CFmMIMO allows for favorable propagation and high quality of service throughout the coverage area [25, 52, 103, 111]. Compared to conventional cellular networks, some of the fascinating features of CF networks include uniform signaltonoise ratio (SNR) with smaller variations, improved interference management, increased SNR due to coherent transmission [12], high EE, high SE, low latency, low complex linear processing, minimal power consumption, flexible and costefficient deployment, and high reliability, among others [9, 103]. Figure 4 presents a pictorial representation of a CFmMIMO network, and Table 2 presents a performance comparison among cellular massive MIMO, network MIMO, and CFmMIMO. According to its performance level, several critical performance metrics are selected, and each metric has been weighted (in percentage), as discussed in Section 5 of the current paper. Last, a pictorial comparison of cellular mMIMO and CFmMIMO is shown in Fig. 5. For the cellular condition, hundreds and even thousands of BS antennas are selected to serve UEs within disjoint cells, thus achieving considerable throughput and coverage improvement. However, for the CF scenario, a plethora of geographically distributed single APs are chosen to serve a smaller number of UEs. The coverage area is not divided into disjoint cells leading to a CF network where signals from surrounding APs only influence each UE. The distributed AP antennas are connected via a fronthaul network to one or multiple central processing units (CPUs), facilitating effective coordination.
System model of cellfree massive MIMO
The CFmMIMO network arbitrarily distributed over a wide coverage area operating on a onetime frequency resource is discussed in this framework. Let there be K UEs and M randomly located APs, each equipped with N_{ap} antennas, where N_{ap}≥1. It is often assumed that M ≫ K. Besides, all APs are connected through an unlimited backhaul network to edgecloud processors, called the CPU. Datadecoding is performed, ensuring that the UEs’ coherent joint transmission and reception in the coverable area are enabled. Remarkably, the pathloss between a user and any AP antenna is unique. The pathloss matrix possesses distinct diagonal elements, and as a result, performance analysis is generally challenging and considerably different from related prior works. TDD protocol with channel reciprocity and a single data stream transmitted per UE is assumed. The communication protocol is usually divided into several phases. These include UL training, UL payload data transmission, DL training, and DL payload data transmission. For the overview of the system model of CFmMIMO networks captured in this survey, a concise list of relevant mathematical notations used and their meanings are presented in Table 3.
First, by taking into consideration a DL CF massive MIMO system, let a set of BSs ß ≜ {1, …, B}, each equipped with M antennas serves a set of UEs К ≜ {1, …, K},each loaded with N antennas. Moreover, let H_{b, k} ∈ ℂ^{M × N}denote the UL channel matrix between BS b ∈ ß and UE k ∈ К, while \( {H}_k\triangleq {\left[{H}_{1,k}^T,\dots, {H}_{B,k}^T\right]}^T\in {\mathbb{C}}^{BM\times N} \) represents the global UL channel matrix seen by UE k. More so, let Y_{b, k} ∈ ℂ^{M × 1}denote the BSSpecific precoding vector utilized by BS b for UE k, while \( {Y}_k\triangleq {\left[{Y}_{1,k}^T,\dots, {Y}_{B,k}^T\right]}^T\in {\mathbb{C}}^{BM\times 1} \) represents the global precoding vector utilized UE k.
Thus, the received signal at UE k reads as (1)
where g_{k}~CN(0, 1) denotes the transmit data symbol for UE k, and \( {z}_k\sim CN\ \left(0,{\sigma}_k^2{I}_N\right) \) represents the average AWGN at UE k. When p_{k}is collected, UE k employs the combining vector q_{k} ∈ ℂ^{N × 1}. The resulting signaltointerferenceplusnoise ratio (SINR) [118] is given by (2)
In addition, the sum rate is expressed as R ≜ ∑_{k ∈ K}log_{2}(1 + SINR_{k}). Next, the realistic pilotaided channel state information (CSI) acquired at the BSs, and the UEs are considered.
Uplink pilotaided channel estimation
Let the effective UL channel vector between UE k and BS b be denoted by d_{b, k} ≜ H_{b, k}q_{k} ∈ ℂ^{M × 1}. Likewise, let the pilot assigned to UE k be denoted by l_{k} ∈ ℂ^{ρ × 1}, where  l_{k}² = ρ. In this phase, each UE k jointly transmits its pilot precoded with its combining vector and is expressed as (3)
Thus, for each BS b, \( {X}_b^{UL1} \)is given by (4) and (5)
where \( {Z}_b^{UL_{\bar{\mkern6mu}}1}\in {\mathbb{C}}^{M\times \uprho} \) denotes the AWGN at BS b having elements distributed as Ϲ (\( 0,{\sigma}_b^2\Big) \). Likewise, the LS estimate of d_{b, k} is given by (6) and (7)
Downlink pilotaided channel estimation
Let the effective DL channel vector between all the BSs and UE k be denoted by \( {h}_k\triangleq {\sum}_{b\in \mathrm{\ss}}{H}_{b,k}^H{y}_{b,k}\in {\mathbb{C}}^{N\times 1} \). In this phase, each BS jointly transmits a superposition of pilots after they have been precoded with the corresponding precoding vector and is expressed as (8)
Thus, for each UE k, \( {X}_k^{DL} \) is given by (9)
where
\( {Z}_k^{DL}\in {\mathbb{C}}^{N\times \uprho} \)denotes the AWGN at UE k with elements distributed as Ϲ (\( 0,{\sigma}_k^2\Big) \). Likewise, the LS estimate of h_{k}is given by (10) and (11)
There exist several pilotbased channel estimators, namely LS estimator, minimum meansquared error (MMSE), elementwise minimum meansquared error (EWMMSE), phaseaware minimum meansquared error (PAMMSE), and linear MMSE. Table 4 presents a summary of pilot trainingbased channel estimators [119]. Next, the UL training phase, DL training phase, and outage probability of the communication protocol are considered.
Uplink training
In the uplink training phase, the UEs send UL training pilot sequences to allow channel estimation at the APs. The uplink training phase also applies to the usercentric (UC) massive MIMO architecture. Let τ_{c} represent the length of the channel coherence time in discretetime samples and τ_{s} represent the length of the UL training phase, also in discretetime samples. At all times, τ_{s} < τ_{c}. The matrix has on its rows the pilot sequences transmitted by the kth UE is denoted by \( {\varnothing}_k\in {C}^{s\times {\tau}_s} \). While the rows of ∅_{k} are assumed to be orthogonal, i.e., \( {\varnothing}_k{\varnothing}_k^D={I}_S \), assuming there is no orthogonality for the pilot sequences directed to other UEs. Of course, by employing orthogonal pilot tout court, a robust system to the effects of pilot contamination is achievable. However, the peak value of the product KS that can be taken in the channel coherence time would be primarily limited. Thus, we define the N_{AP} × τ_{s} dimensional matrix X_{m} by (12)
where F_{k, m} = D_{k, m}L_{k}, Y_{m} denotes the matrix of thermal noise samples. Next, we explore the structure of the LMMSE channel estimator briefly. Defining parameters, x_{m} = vec(X_{m}), y_{m} = vec(Y_{m}), f_{k, m} = vec(F_{k, m}), the vectorized model is given as (13)
where \( {R}_k={\varnothing}_k^T\otimes I. \)We process x_{m} by a matrix \( {Q}_{k,m}^D \), i.e., \( {\hat{f}}_{k,m}={Q}_{k,m}^D{x}_m \). Thus, the MSE is obtained as (14)
In this case, the gradient of the MSE concerning the complex matrix \( {Q}_{k,m}^{\ast } \) is assumed to be equal to zero. Solving for Q_{k, m},the LMMSE estimator is given by (15)
Downlink training
In this section, the scalable beamforming training scheme is adopted. Let τ_{v, l} denote the length of the DL training duration per coherence interval; it suffices that τ_{v, l} < τ − τ_{u, l}. By exploiting the channel estimates \( \left\{\hat{h}m{k}^{\acute{\mkern6mu}}\right\} \), and beamforming it to all users, the mth AP precodes the pilot sequences \( {\varphi}_{k^{\acute{\mkern6mu}}}\in {\mathbb{C}}^{\tau_{v,l}\times 1},{k}^{\acute{\mkern6mu}}=1,\dots, K. \) Thus, the τ_{v, l} × 1 pilot vector w_{m, l} sent from the mth AP is obtained as (16)
where σ_{v, l} is the normalized transmit SNR per DL pilot symbol and {φ_{k}} assume mutual orthonormality i.e. \( {\varphi}_k^D{\varphi}_{k^{\acute{\mkern6mu}}}=0, \)for k^{´} ≠ k, and ‖φ_{k}‖^{2} = 1. This requires that τ_{v, l} ≥ K. The kth user receives correspondingly, τ_{v, l} × 1 pilot vector which is given by (17)
where y_{vl, k} denotes a vector additive noise at the kth user. The effective channel gain r_{kk}, k = 1, …, K is estimated via the processing of the received pilot first by the kth user as (18)
where \( {\eta}_{l,k}\triangleq {\mathit{\mathsf{\varphi}}}_{\mathit{\mathsf{k}}}^{\mathit{\mathsf{D}}}{\boldsymbol{\mathsf{y}}}_{\mathit{\mathsf{vl}},\mathit{\mathsf{k}}}\sim CN\left(0,1\right) \). Given \( {\overset{\check{} }{x}}_{vl,k}, \) linear MMSE estimation of r_{kk}is performed, which is obtained as (19)
Outage probability
Obtaining the exact expression for outage probability is quite challenging due to the computational complexity in determining the cumulative distribution function (CDF) of the SINR at the APs [120]. The only exception for massive MIMO systems applies to perfect CSI and identically distributed channels unsatisfied in practice [121, 122]. Therefore, an alternate approach, approximate outage probability, is selected to provide the outage probability of massive MIMO networks where all the APs are collocated. Hence, β_{mk} = β_{k}, γ_{mk} = γ_{k}, ∀_{m, k}. The outage probability approximation of the kth user is obtained as (20) and (21)
for \( T\le \frac{\rho_u\left(M1\right){\gamma}_K}{\left(1+{\rho}_u\left({\beta}_K{\gamma}_K\right)\right)} \) and
for \( T>\frac{\rho_u\left(M1\right){\gamma}_K}{\left(1+{\rho}_u\left({\beta}_K{\gamma}_K\right)\right)}, \)
where \( {c}_1^i,{c}_2^i,{c}_3,{c}_4 \) and c_{5} are given by (22), (23), (24), (25), and (26).
Areas of application of cellfree massive MIMO
The wireless research community has explored the outstanding features of the mutually beneficial combination between CF structure and massive MIMO technology to enable seamless transfer from theory to practical implementation. Of course, significant progress in signal processing, communication, and optimization algorithms developed has further deepened the range of applications of this technology. Table 5 presents a summary of CF massive MIMO application areas alongside their strengths and limitations. A concise account of the past findings and current research trends based on SWIPT, channel hardening, hardware efficiency, power control, NOMA, SE, and EE for the CFMIMO are detailed in the following subsections.
SWIPT in cellfree massive MIMO
The ultrahigh transmission rate of wireless networks has been identified as a significant challenge that decreases the lifetime of batterypowered devices. SWIPT is considered an innovative candidate for the energylimited environment through energy reclamation. It offers an effective solution to enable a guaranteed energy level and minimize backhaul resources and energy consumption. Compared to traditional massive MIMO, CF massive MIMO presents a new paradigm to boost the performance of SWIPT. A summary of recent advances on SWIPT technology in CF massive MIMO is presented in Table 6.
Additionally, the energy harvest and DL achievable rate for an energy user under a linear scheme are presented. First, for the harvested energy, it is assumed that the harvesting circuitry operates with an efficiency represented as η. With reference to the \( \overset{\sim }{j} \)th user which depicts a typical energy user, the ambient harvested energy \( {E}_{\overset{\sim }{j}} \) during a time slot is obtained as (27)
In this case, the noise factor is neglected to owe to its low comparative strength instead of other terms. As a step further, the DL achievable rate for a typical energy user is derived. The average achievable rate \( {R}_{\overset{\sim }{j}} \) can be expressed as (28)
where \( {\gamma}_{\overset{\sim }{j}} \) denotes the SNR of the \( \overset{\sim }{j} \)th user and is expressed as (29)
Now, \( {R}_{\overset{\sim }{j}} \) can be modeled as (30)
where \( {E}_{\overset{\sim }{j}} \) is given by (27). Thus, \( {R}_{\overset{\sim }{j}} \) is obtained as (31) after some modifications.
Further, the distribution of \( {E}_{\overset{\sim }{j}} \) is approximated with the Gamma distribution employing moment matching. The scale parameters which define the Gamma distributions are obtained as \( {k}_h={\left(\mathbbm{E}\left[{E}_{\overset{\sim }{j}}\right]\right)}^2/\mathbbm{VAR}\left[{E}_{\overset{\sim }{j}}\right] \) and \( {\theta}_h=\mathbbm{VAR}\left[{E}_{\overset{\sim }{j}}\right]/\mathbbm{E}\left[{E}_{\overset{\sim }{j}}\right] \). Consequently, (31) can be remodeled as (32)
which can be simplified numerically.
Channel hardening and favorable propagation in cellfree massive MIMO
Two essential virtues that appear in the regime of hundreds or even thousands of antennas: channel hardening and favorable propagation, are defined and analyzed. By increasing BS antennas, the propagation is assumed to happen through a quasideterministic flatfading equivalent channel. In light of the above, the fading channel behaves as though it was not a fading channel (almost deterministically) [50]. This phenomenon is referred to as channel hardening. Also, when the channel directions of two UEs become spatially orthogonal, the interuser and intracell interference vanishes automatically using a relatively simple signal processing technique called maximumratio processing (MRP). This desirable property is termed favorable propagation. The channel hardening effect has been exploited by massive MIMO to decrease the problem of smallscale fading in wireless communication systems to guarantee desirable reliability and low latency. However, channel hardening conditions have also been observed and remain valid for CF massive MIMO systems, with reduced pathloss exponent and increased antenna density. Table 7 presents a summary of recent trends and advances on channel hardening in CFmMIMO systems.
The mathematical representation of channel hardening and favorable propagation in CF massive MIMO is presented. Let d_{jk} reflects the propagation channel response between the UE k and AP m. The channel hardening effect is defined as (33)
As a result, the impact of the smallscale fading variations on the communication performance is minimized while the challenge of largescale fading remains. The degree of channel hardening in CFmMIMO is dependent mainly on the number of antennas per AP and the geographical AP distribution [12]. The favorable propagation is expressed as (34)
Hardware impairments and pilot transmission in cellfree massive MIMO systems
Using practical systems with perfect hardware components during production could result in enormous energy consumption and prohibitive hardware costs, which are not satisfied in practice. In short, the closer to ideal a hardware transceiver is, the more costly, bulkier, and energyhungry it becomes. This bottleneck, a tradeoff between the quality of hardware components and cost, is usually considered a breakthrough. Nonetheless, this technique inevitably introduces hardware and channel impairments, including amplifier nonlinearities, phase noise, I/Q imbalance, and ADC distortions into the system. Analyzing CF massive MIMO under the effects of HI has gained significant research interest. Table 8 presents a summary of progress made in this regard. Additionally, mathematical models of the hardware impairment and pilot transmission are presented.
Hardware impairment model
In order to model the combined effect of hardware distortions, the transmitted/received signal is assumed to be distorted by an additive Gaussian noise [92]. The distorted signal is expressed as (35)
where w refers to the input signal to the nonideal hardware. Moreover, ξ_{i} ∈ [0, 1], i = {t, r} reflects the hardware quality coefficient. The distortion noise is obtained as (36) and is independent of the input signal w.
The term \( \mathbbm{E}\left\{\leftw\right{}^2\right\}=\mathbbm{E}\left\{\left{w}_i\right{}^2\right\} \) indicates the equivalence of the variance of both the input and output signals for the nonideal hardware device. Besides, the hardware quality is obtained through ξ_{i} ∈ [0, 1], where ξ_{i} = 1 and ξ_{i} = 0 denotes perfect and useless hardware, respectively.
Pilot transmission
In this context, it is assumed that τlength orthogonal pilots represented as ψ_{k} ∈ ℂ^{τ × 1} are assigned to UEs, where τ = K ≤ T, and \( {\psi}_k^D{\psi}_{k^{\acute{\mkern6mu}}}=\delta \left(k{k}^{\acute{\mkern6mu}}\right) \)for k, k^{´} ∈ {1, 2, …, K}. As a result, the pilot signal \( \sqrt{\tau {P}_p}{\psi}_k \) is transmitted by UE_{k,} and the signal modeled as (37) is received by the mth AP
where P_{p} refers to the pilot power, z_{t, k} expressed as (38) accounts for the distortion caused by a nonideal hardware device, z_{r, m} expressed as (39) denotes the distortion caused by hardware impairment at the mth AP and n_{m} represented as (40) indicates the additive noise [92, 137]
Power control in cellfree massive MIMO
Power control has appeared as a key feature and one of the most impacting algorithms in mobile networks. It entails an intelligent selection of transmitter power output to improve the overall performance of wireless systems. The power control techniques find handy applications in CF massive MIMO to limit the generated interference, minimize pilot contamination, maximize the power of the desired received signal, and provide a more uniform QoS to the UEs. Table 9 presents a survey of various areas of application of power control in CFmMIMO systems. Furthermore, Table 10 shows a more concise account of power control/algorithms (alternative optimization, successive convex approximation (SCA), GP, bisection, SOCP, fractional, and MLbased techniques) used in solving specific utility optimization problems [119].
Additionally, an insight into different power control policies is highlighted. In particular, the equal transmits power policy, equal receive power policy, and inverse leakage policy are considered. In all policies, it is assumed that \( {G}_{ik}={f}_k^D{V}_i{f}_k \).

(1)
Equal Transmit Power Policy: In this policy, the same power is transmitted to each UE i, taking into consideration the power constraints and can be expressed as (41)
where C denotes a constant chosen to satisfy the power constraints. The maximum value of C is obtained as (42)
Thus, the total power p_{i} transmitted to any UE i, for i = 1, …, K, can be written as (43)

(2)
Equal Receive Power Policy: This policy ensures that the average received signal power that is conditioned on \( \hat{D} \) remains the same for all UE by selecting power scaling factors. Therefore, p_{i}G_{kk} = C,for i = 1, …, K. The constant C is also selected to satisfy the power constraints. After some mathematical analysis, p_{i} can be obtained as (44)

(3)
Inverse Leakage Policy: This policy allocates lower powers to UEs to minimize the interference in the system, resulting in higher leakage to other UEs. In this policy, it is assumed that p_{i} is inversely proportional to \( \sum \limits_{k=1,k\ne i}^K{G}_{ki} \). Solving for p_{i} yields (45)
NOMAaided cellfree massive MIMO
Currently, there is a growing interest in implementing NOMA in 5G and beyond 5G systems due to its attractive SE gains and potential to support low latency massive connectivity. NOMA technique, a paradigm shift from the OMA scheme, primarily seeks to allocate nonorthogonal resources to users to manage interference. Considering the enormous benefits of CFmMIMO and NOMA, integrating these two techniques is envisioned to reap further gains. Recent research efforts on this hybrid combination are summarized in Table 11.
The channel model of a NOMAaided CF massive MIMO system is presented. The DL channel between the kth user and the mth AP in the nth cluster, where k ∈ {1, …, K}, m ∈ {1, …, M} and n ∈ {1, …, N} can be expressed as (46)
where ζ_{mnk} accounts for the largescale fading, which changes at a prolonged rate [162]. Besides, the circularly symmetric Gaussian assigned with zero mean unit variance can be written as (47)
Spectral efficiency of cellfree massive MIMO
The need to improve the SE by network service providers owing to an everincreasing number of users and high rate expectations in B5G wireless networks cannot be overemphasized. Interestingly, massive and dense antennae deployment has been at the forefront, and thanks to its ability to upgrade the BS hardware rather than the deployment of new BS sites. Compared to conventional massive MIMO systems, CF has a great potential of substantially improving the SE by employing additional antennas at users, power allocation, and the receiver filter coefficient design. Table 12 presents certain areas of application of CF massive MIMO in improving the SE.
Additionally, a closedform expression for the UL SE of CF massive MIMO with the LS estimator is presented. In this context, spatially correlated Rayleigh fading channels are taken into consideration. The received signal r_{u, k} at the CPU is expressed as (48)
where v_{k} depicts the desired signal detected by r_{u, k}. The received signal in (48) can be further expressed as (49)
where the desired signal (DS) is given by (50), the beamforming uncertainty gain (BU) is given by (51), the multiuser interference (UI) is given by (52), and the noise interference (NI) is given by (53).
The UL SINR of the kth user is given by (54)
Thus, the SE is obtained as (55)
Energy efficiency of cellfree massive MIMO
While stateoftheart technologies are consistently developed to address data, QoS, and capacity demands, issues related to environmental concerns and highpower consumption are escalating rapidly. EE has become an essential criterion in designing future wireless networks, and its importance has been realized even more. The cellular configuration can deliver higher EE, and it is widely recognized as naturally energyefficient. As a step further, the EE of CFmMIMO has been characterized by researchers worldwide, and several sophisticated optimization techniques and comprehensive power models have been developed accordingly. Table 13 presents a summary of research efforts and future research directions on the EE of CFmMIMO.
Furthermore, the total EE model of a CF massive MIMO network is presented. From correspondence [168], the total power consumption can be written as (56)
where P_{A} represents the power amplifier’s power consumption and P_{C} represents the circuit power consumption. The power consumption P_{A} and P_{C} is obtained as (57) and (58), respectively
where ζ reflects the power amplifiers efficiency at each user, P_{f} denotes the fixed power consumption at each AP, P_{U} accounts for the power required to run circuit components at each user, and P_{b, m} denotes the backhaul power consumption from the mth AP to the CPU and is expressed in the following [169, 170]
where P_{BT} accounts for the total power to operate the backhaul traffic at full capacity, R_{b} refers to the backhaul rate between the mth AP and the CPU, and C_{b} reflects the capacity of the backhaul link between the mth AP and the CPU. More precisely, the backhaul rate R_{b} can be expressed as (60)
where σ_{m} represents the quantization bits of the mth AP. Thus, the total EE is obtained as (61)
Open research issues and lessons learned
The concept of CF massive MIMO has received considerable research efforts to understand its essential features and immense benefits. While significant progress has been made, many open questions, unresolved practical, and various deployment challenges persist, requiring substantial research efforts before realizing its promised gains. Table 14 presents an outline of some research directions in HI, signal detection, EE, channel estimation, pilot contamination, and security and privacy issues. As a step further, we highlight vital lessons learned for future research exploration in the area of CF massive MIMO.
Lessons learned
In this section, a comprehensive summary of lessons learned from this survey is presented. The summary covers CF massive MIMO, mmWave, Terahertz, EE, NOMA, security and privacy, HI, and SWIPT, as outlined briefly.
Lesson one
The current wireless network infrastructure is faced with unprecedented demand for ultrareliability and higher data rates. CF massive MIMO, where many APs are densely deployed across the entire coverage area linked to a CPU, has been proposed to address this problem. However, there are still issues to contend with in network management, hardware design, and practical implementation of CFmMIMO.
Lesson two
By a careful analysis of the current 5G wireless systems, employing the highly congested microwave frequency band spanning from about 300 MHz to 6 GHz alongside the use of largescale antenna arrays may not be sufficient to satisfy the demands for increased throughput, ubiquitous QoS, and ubiquitous connectivity. The socalled mmWave frequency band, though a promising physical layer solution to the envisioned beyond 5G wireless communication network, is susceptible to high molecular absorption. This lends the terahertz band a natural candidate for 6G wireless networks. However, distance is a major problem in terahertz communication. However, the combined use of an ultradense wireless network, CFmMIMO, and the lesscongested terahertz band is a crucial enabler to much larger bandwidths and a basic pillar to sustain the SE and EE. Terahertzenabled CFmMIMO will be a key enabler for nextgeneration wireless communication systems.
Lesson three
Compared to earlier generations of wireless communication networks, the total power consumption of 5G and beyond5G systems have increased greatly. This is primarily due to the higher density of APs, larger bandwidths, and larger antenna numbers, resulting in increased environmental and economic concerns. Thus, EE has become a critical requirement in the design of emerging wireless networks. In order to address this issue, highly comprehensive power models, efficient energy management strategies, and more sophisticated optimization techniques are required. Specifically, these systems may be enabled with energy harvesting and energy exchange capabilities. The grid source will be incorporated to compensate for the random and intermittent nature of the harvested energy owing to uncontrollable environmental conditions. Also, the possibility of turning off inactive APs is another useful technique to improve the overall EE of CF massive MIMO systems.
Lesson four
An indispensable candidate technique for nextgeneration wireless standards is NOMA. The power domainbased concept represents a paradigm shift from OMA, which is fast approaching its fundamental SE limit. An interplay of the distinctive benefits of NOMA and CF massive MIMO is expected to substantially boost the system’s performance with respect to bandwidth efficiency, spectral and energy efficiency, massive connectivity with low latency, and concurrent transmission from multiple users. Nonetheless, the additional hardware complexity due to error propagation and SIC processing is undesirable in practice. In order to tackle the tradeoff between complexity and performance (sum rate), highquality optimization techniques are required.
Lesson five
From the inception of wireless communication networks, security and privacy threats have been a real concern for network operators. With the deployment of 5G and the emerging beyond 5G systems to support billions of connected devices and drive high user mobility, threats to availability and integrity of networks, besides the growing concerns for user privacy, will become more visible. The security threat is envisaged to be greater than ever. There is a need for advanced cryptographic schemes to provide a robust security architecture in wireless networks to protect user privacy. More needs to be done in blockchain technology and quantum communication to tackle the confidentiality and privacy threats posed to future wireless networks.
Lesson six
Deployment of CF massive MIMO depends on multiple antenna elements, which increase the system complexity, energy consumption, and hardware design cost. By using lowcost components, the hardware imperfections increase, which is detrimental to the overall system’s performance. These imperfections consisting of phase noise, I/Q imbalance, amplifier nonlinearities, and more are referred to as HIs. There is a need for an optimal tradeoff between the quality of the transceiver hardware design and cost. Additionally, there is a need for suitable compensation algorithms to minimize the effects of HI.
Lesson seven
Compared to traditional energy storage methods, SWIPT is considered a potential solution to ease the transmission rate and minimize the energy consumed by batterypowered devices. However, the exponential growth in the number of connected devices coupled with the issues posed by mmWave communication in 5Gaided SWIPT networks presents an entirely new challenge. Therefore, there is a need to find proper allocation schemes to optimize the rateenergy tradeoff between information retention and energy allocation.
Conclusions
Cellfree massive MIMO has been proposed as a novel architecture to address the everincreasing demands for high SE, coverage probability, green output, and uniformly distributed throughput for all network users. In the ubiquitous 5G and the envisioned beyond 5G wireless communication systems, CFmMIMO enables the deployment of dense APs over a wide network area to communicate with several UEs cooperatively. Motivated by the distinctive benefits of CFmMIMO, this paper attempted to give a concise survey of the design, application scenarios, potentials, and deployment challenges of this disruptive technology. The system model of CFmMIMO, covering the UL/DL pilotaided channel estimation, UL/DL training, and channel hardening, is discussed elaborately. Additionally, the performance characteristics of CFmMIMO using key design metrics like EE, channel hardening, SE, and more, are discussed extensively. Furthermore, the viable application areas of CFmMIMO are outlined, and an uptodate review of key findings and current research trends in CFmMIMO is presented. Finally, open research issues and key takeaway lessons are drawn from the survey to explore this exciting area of wireless communications systems deeply.
Availability of data and materials
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Abbreviations
 5G:

Fifth generation
 6G:

Sixth generation
 ADC:

Analogtodigital converter
 ADMM:

Alternating direction method of multipliers
 AI:

Artificial intelligence
 ANN:

Artificial neural networks
 AP:

Access point
 B5G:

Beyond 5G
 BE:

Bandwidth efficiency
 BS:

Base station
 BU:

Beamforming uncertainty gain
 CB:

Conjugate beamforming
 CDF:

Cumulative distribution function
 CF:

Cellfree
 CS:

Central station
 CPU:

Central processing unit
 CSI:

Channel state information
 DCC:

Dynamic cooperation cluster
 DE:

Deterministic equivalent
 DL:

Downlink
 DNN:

Deep neural network
 DRX:

Discontinuous reception
 DS:

Desired signal
 ECB:

Enhanced bormalized conjugate beamforming
 EE:

Energy efficiency
 EMCF:

Estimatemultiplycompressforward
 EPC:

Equal power control
 EWMMSE:

Elementwise minimum meansquared error
 FD:

Fullduplex
 FL:

Federated learning
 fpZF:

Fullpilot zeroforcing
 GP:

Geometric programming
 HD:

Halfduplex
 HI:

Hardware impairment
 IA:

Inner approximation
 IoT:

Internet of Things
 I/Q:

Inphase/quadrature
 JTCoMP:

Joint transmission coordinated multipoint
 LMMSE:

Linear minimum meansquared error
 LOS:

Lineofsight
 LS:

Leastsquare
 LTE:

Longterm evolution
 MF:

Matched filtering
 MIMO:

Multiple input multiple output
 ML:

Machine learning
 mMIMO:

Massive MIMO
 MMSE:

Minimum meansquared error
 MR:

Maximum ratio
 MRC:

Maximum ratio combining
 MRT:

Maximum ratio transmission
 MS:

Mobile station
 M2M:

Machinetomachine
 NCB:

Normalized conjugate beamforming
 NI:

Noise interference
 NOMA:

Nonorthogonal multipleaccess
 OBC:

Optimal backhaul combining
 OMA:

Orthogonal multipleaccess
 PAMMSE:

Phaseaware minimum meansquared error
 PN:

Phase noise
 PPP:

Poisson point process
 QoS:

Quality of service
 RIS:

Reconfigurable intelligent surface
 RSI:

Residual selfinterference
 RF:

Radio frequency
 RMMSE:

Robust minimum meansquared error
 RZF:

Regularized zeroforcing
 SC:

Smallcell
 SCA:

Successive convex approximation
 SE:

Spectral efficiency
 SIC:

Successive interference cancelation
 SINR:

Signaltointerferenceplusnoise ratio
 SLNR:

Signaltoleakageandnoise ratio
 SOCP:

Secondorder cone program
 SNR:

Signaltonoise ratio
 SWIPT:

Simultaneous wireless information and power transfer
 TDD:

Timedivision duplex
 TRLSFD:

Timereversal largescale fading decoding
 TRMRC:

Timereversal maximumratio combining
 TS:

Tabu search
 UE:

User equipment
 UI:

Multiuser interference
 UL:

Uplink
 WPT:

Wireless power transfer
 ZF:

Zeroforcing
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Agbotiname Lucky Imoize is supported by the Nigerian Petroleum Technology Development Fund (PTDF) and the German Academic Exchange Service (DAAD) through the NigerianGerman Postgraduate Program under grant 57473408.
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The manuscript was written through the contributions of all authors. Conceptualization, A.I.; methodology, H.O., A.I., and F.A.; writing—original draft preparation, H.O. and A.I.; writing—review and editing, H.O., A.I., F.A., and K.K.; supervision, A.I.; project administration, A.I., F.A., and K.K.; funding acquisition, A.I. The authors have read and approved the final manuscript.
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Obakhena, H.I., Imoize, A.L., Anyasi, F.I. et al. Application of cellfree massive MIMO in 5G and beyond 5G wireless networks: a survey. J. Eng. Appl. Sci. 68, 13 (2021). https://doi.org/10.1186/s4414702100014y
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DOI: https://doi.org/10.1186/s4414702100014y