Application of cell-free massive MIMO in 5G and beyond 5G wireless networks: a survey

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 high-capacity demands and broad network coverage is quite challenging due to inter-cell interference and significant rate variations. Cell-free massive MIMO (CF-mMIMO), a key enabler for 5G and 6G wireless networks, has been identified as an innovative technology to address this problem. In CF-mMIMO, 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 CF-mMIMO in the ubiquitous 5G, and the envisioned 6G wireless networks. First, a foundational background on massive MIMO solutions-cellular massive MIMO, network MIMO, and CF-mMIMO is presented, focusing on the application areas and associated challenges. Additionally, CF-mMIMO architectures, design considerations, and system modeling are discussed extensively. Furthermore, the key areas of application of CF-mMIMO such as simultaneous wireless information and power transfer (SWIPT), channel hardening, hardware efficiency, power control, non-orthogonal multiple access (NOMA), spectral efficiency (SE), and EE are discussed exhaustively. Finally, the research directions, open issues, and lessons learned to stimulate cutting-edge 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 data-hungry applications [1]. In recent times, the emergence of the Internet of Things (IoT) has ushered in new-age internet-enabled smartphones and machine-to-machine 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

Related work
Cell-free 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 in-depth 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 long-term 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 CF-mMIMO 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 CF-mMIMO 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 CF-mMIMO 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 CF-mMIMO 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 cell-edge effects are studied [70]. References [11,71] have reported novel scalable and distributed algorithms used for initial access and cooperation cluster formation in CF-mMIMO. The authors also proposed scalable signal-to-leakage-and-noise ratio precoding to address the scalability issues in CF-mMIMO. 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 CF-mMIMO 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 CF-mMIMO 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 CF-mMIMO, there is no detailed study on CF-mMIMO systems that captures entirely cellular massive MIMO, network MIMO, and CF-mMIMO 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 CF-mMIMO is vitally important. Therefore, the current paper presents an extensive survey on CF-mMIMO 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 phase-coherent transmitting/receiving antennas, thus suppressing inter-cell and intra-cell 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 near-optimal linear processing [96]. Motivated by the benefits mentioned above, various massive MIMO-based solutions significantly gained traction in academia and industry [97]. A brief discussion on cellular mMIMO, network MIMO, and CF-mMIMO focusing on their architectures, strengths, and applications are presented in the following subsections.

Cellular massive MIMO
Massive MIMO time-division duplex (mMIMO-TDD) systems have been reported to boost the throughput of wireless networks [83,86]. Since the multiple antennas used in mMIMO-TDD are much smarter, it presents a practical means to outperform partial multiuser MIMO (MU-MIMO) systems. BS antennas could be substantially larger than Table 1 Limitations of some related works

Ref. Focus and coverage
Limitations Contributions [78] The work quantifies the improvement of CF-mMIMO over cellular massive MIMO in EE using max-min power control and CB.
▪ Optimization techniques not presented. ▪ Channel estimation not clearly outlined.
▪ This paper outlines useful techniques to improve the overall EE of CF-mMIMO. ▪ This paper examines the most recent research trends and future directions on EE in CF-mMIMO. [79] The authors examine the performance of CF-mMIMO systems with limited fronthaul capacity.
▪ A perfect hardware transceiver that is not satisfied in practice is considered.
▪ An extensive analysis of transceiver HI, most recent research trends on the performance of CF-mMIMO systems with limited fronthaul capacity are presented. [80] This paper analyzes the UL SE of CF massive MIMO with multiple antennas at the APs and users, zero-forcing (ZF) combining, and data power controls.
▪ ▪ Challenges with the use of multi-antenna are not clearly outlined. ▪ Security and privacy issues of multi-antenna users are not discussed elaborately.
▪ Presents a detailed outline of the application of CF-mMIMO in improving the SE. ▪ Security and privacy issues of wireless networks are clearly outlined. Also, UL SE of CF-mMIMO with multiple antennas at the APs and users are broached.
[81] The authors propose an ANNbased UL power control technique to assess power allocation in a CF-mMIMO network to maximize the sum rate or the min rate.
▪ Applications of power control in CF-mMIMO not clearly outlined.
▪ Power optimization techniques are limited to just a deep learning approach.
▪ Presents a robust discussion on the application of power control in CF-mMIMO. ▪ Power optimization techniques such as alternative optimization, second-order cone program (SOCP), and machine learning (ML)-based approaches are discussed [82].
[83] The work considers maximizing the total EE of CF massive MIMO using a well-established DL power consumption model. Additionally, AP selection schemes are covered to minimize the power consumption caused by the backhaul links.
▪ Channel estimation not clearly outlined. ▪ Open research issues and future research directions are not discussed elaborately.
▪ This paper examines the most recent research trends and future directions in CF-mMIMO. ▪ A robust discussion on AP selection schemes aimed at minimizing power consumption is presented.
[84] The authors examine a generalized UL CF-mMIMO in the presence of radio frequency (RF) impairments and ADC imperfections. Also, the study provides novel insights on implementing low-quality transceiver RF chains and low-resolution ADCs.
▪ Technical propositions to minimize hardware costs in practical systems are limited. ▪ Signal detection is not clearly outlined.
▪ Instructive insights to optimize the system's performance in practical scenarios are clearly discussed. ▪ Sophisticated signal detection techniques such as ML, deep learning-based techniques, and sphere decoder are highlighted.
[69] The work characterizes the coexistence and underlying issues of SWIPT and CF massive MIMO.
▪ Open research issues and future research directions in CF-mMIMO are not discussed clearly.
▪ Research activities capturing the most recent research trends and lessons learned related to SWIPT in CF massive MIMO are outlined.
[85] The work presents the UL performance of CF-mMIMO systems with multiple antennas and least-square (LS) estimators considering the effects of spatially correlated fading channels.
▪ The security and privacy threats to multi-antenna users are not considered. ▪ Pilot contamination effects were not discussed.
▪Security and privacy issues of wireless networks are captured. Future research directions and lessons learned are outlined. ▪ This paper also provides a holistic review of pilot contamination and the UL performance of CF massive MIMO systems.
[86] The paper considers using an NCB scheme in CFm-MIMO subject to short-term average power constraints. The work also considers the effects of channel estimation errors and pilot contamination. 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 interference-limited performance of cellular networks. Specifically, by jointly designing the DL beams to multiplex multiple users spatially, intra-cluster 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 cell-edge 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.

Cell-free 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 inter-cell interference, high QoS variations, and hand-offs [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 cell-free 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 next-generation 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 domain-centric NOMA integrated with CF-mMIMO emerged as a viable solution to address the conflicting demands on high SE, EE, high reliability with user-fairness, increased connectivity, and reduced latency in 5G wireless networks [105][106][107]. In CF-mMIMO, the number of simultaneously served users can be increased by supporting the users to utilize the same time-frequency resource effectively and invoking superposition-coded transmission and successive interference cancelation (SIC) decoding [108][109][110].
Cell-free 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, CF-mMIMO 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 signal-to-noise 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 CF-mMIMO network, and Table 2 presents a performance comparison among cellular massive MIMO, network MIMO, and CF-mMIMO. 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 CF-mMIMO is shown in Fig. 5. For the cellular condition, hundreds and even thousands of BS antennas are

System model of cell-free massive MIMO
The CF-mMIMO network arbitrarily distributed over a wide coverage area operating on a one-time 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 edge-cloud processors, called the CPU. Data-decoding 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 Interference management 30% 50% 70% [2,46] EE 70% 30% 85% [78,103] Hardware efficiency 30% 50% 70% [48,112] Channel hardening 85% 30% 50% [62,103] Uniform coverage 30% 50% 70% [103] Macro-diversity 30% 50% 70% [103,113] Number of antennas 85% 70% 85% [103,114] Favorable propagation 85% 30% 50% [103,115] SE 70% 50% 85% [116,117] where g k~C N(0, 1) denotes the transmit data symbol for UE k, and z k $ CN ð0; σ 2 k I N Þ 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 signal-to-interference-plus-noise 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 pilot-aided channel state information (CSI) acquired at the BSs, and the UEs are considered.

Uplink pilot-aided 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 UL−1 b is given by (4) and (5) where Z UL 1 b ∈ℂ MÂρ denotes the AWGN at BS b having elements distributed as (0; σ 2 b Þ. Likewise, the LS estimate of d b, k is given by (6) and (7) Downlink pilot-aided channel estimation Let the effective DL channel vector between all the BSs and UE k be denoted by h k ≜ P b∈ß H H b;k y b;k ∈ℂ NÂ1 . 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 DL k is given by (9) where Z DL k ∈ℂ NÂρ denotes the AWGN at UE k with elements distributed as (0; σ 2 k Þ. Likewise, the LS estimate of h k is given by (10) and (11) There exist several pilot-based channel estimators, namely LS estimator, minimum mean-squared error (MMSE), element-wise minimum mean-squared error (EW-MMSE), phase-aware minimum mean-squared error (PA-MMSE), and linear MMSE. Table 4 presents a summary of pilot training-based 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 user-centric (UC) massive MIMO architecture. Let τ c represent the length of the channel coherence time in discrete-time samples and τ s represent the length of the UL training phase, also in  discrete-time 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 ∅ k ∈C sÂτ s . While the rows of ∅ k are assumed to be orthogonal, i.e., ∅ k ∅ D k ¼ 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 In this case, the gradient of the MSE concerning the complex matrix Q Ã k;m 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 fĥmk Ë C g , and beamforming it to all users, the mth AP precodes the pilot sequences φ k Ë C ∈ℂ τ v;l Â1 ; k Ë C ¼ 1; …; 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. φ D k φ k Ë C ¼ 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 η l;k ≜ D k y vl;k $ CNð0; 1Þ. Given xˇv l;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.
Areas of application of cell-free 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 CF-MIMO are detailed in the following subsections.

SWIPT in cell-free massive MIMO
The ultra-high transmission rate of wireless networks has been identified as a significant challenge that decreases the lifetime of battery-powered devices. SWIPT is considered an innovative candidate for the energy-limited 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 thejth user which depicts a typical energy user, the ambient harvested energy Ej 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 Rj can be expressed as (28) where γj denotes the SNR of thej-th user and is expressed as (29) γ~j ¼ Now, Rj can be modeled as (30) where Ej is given by (27). Thus, Rj is obtained as (31) after some modifications.
Further, the distribution of Ej is approximated with the Gamma distribution employing moment matching. The scale parameters which define the Gamma distributions are which can be simplified numerically.

Channel hardening and favorable propagation in cell-free 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 flat-fading 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 inter-user and intra-cell 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 small-scale 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 CF-mMIMO 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) )→1 as the number of antennas N ap →∞ ð33Þ As a result, the impact of the small-scale fading variations on the communication performance is minimized while the challenge of large-scale fading remains. The degree of channel hardening in CF-mMIMO 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 cell-free 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 energy-hungry it becomes. This bottleneck, a trade-off between the quality of hardware components and cost, is usually considered a breakthrough. Nonetheless, this technique inevitably introduces hardware and channel impairments, including amplifier non-linearities, 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 non-ideal 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 Efjw Ç jg ¼ Efjw i Ç jg indicates the equivalence of the variance of both the input and output signals for the non-ideal 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 τ-length orthogonal pilots represented as ψ k ∈ ℂ τ × 1 are assigned to UEs, where τ = K ≤ T, and ψ D k ψ k Ë C ¼ δðk−k Ë C Þ for k, k´∈ {1, 2, …, K}. As a result, the pilot signal ffiffiffiffiffiffiffi ffi τP p p ψ 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 non-ideal 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 cell-free 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 CF-mMIMO systems. Furthermore, Table 10 shows a more concise account of power control/algorithms (alternative optimization, successive convex approximation (SCA), GP, bisection, SOCP, fractional, and ML-based 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 (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) ▪ The pilot contamination effect is generally reduced. ▪ Notably, the 95% likely throughput in both UL and DL transmission is considerably improved. ▪ The case without pilot power control is sub-optimal at all times compared to the case with pilot power control.
▪ Pilot power control is a multiobjective optimization problem and providing an optimal solution that simultaneously optimizes each objective is quite challenging.
2018 [81] The authors present power allocation techniques in the UL of a CF-mMIMO network. The work aims at maximizing the sum rate and the minimum rate of CF massive MIMO systems using the ANN-based power control method.
▪ The effect of pilot contamination on the learning capabilities of deep neural networks (DNN) is highly minimal, as near-optimal performance is obtained.
▪ The shadowing effect degrades the performance of the suggested ANN-based power control considerably.
2019 [125] The DL performance of a partially distributed CF massive MIMO network under the assumption of different power control policies is investigated. These policies are extended to cover the case when the power control is coordinated only within subsets of APs and not across the subsets.
▪ The SCA policy is shown to outperform other power control policies in terms of the SE gains. ▪ Moreover, the gain in SE for SCA is higher for CB precoding compared to ZF precoding.
▪ Computational complexity and loss in sum SE are major bottlenecks to the optimal performance of the SCA policy.
2019 [138] In this correspondence, a DNNbased power allocation for CF massive MIMO is proposed. Particularly, DNNs are trained to perform both centralized and distributed power allocation with reduced computational complexity.
▪ A properly trained framework is shown to improve power allocation significantly.
▪ The gap between the distributed and centralized methods is substantial and requires further improvement.
2019 [129] The UL data transmission of a NOMA-aided CF-mMIMO is investigated. An optimal backhaul combining scheme to enhance the worst SINR among users in the network is proposed. The work is further analyzed using a max-min QoS power control problem which is iteratively solved by a successive inner approximation technique.
▪ A significant performance improvement is obtained with the proposed OBC compared to equal-gain combining and ZF combining.
▪ The SINR degrades dramatically as the number of antennas on each BS grows large.

2020
[139] A novel unsupervised learningbased to address the max-min rate problem in CF massive MIMO is proposed. A DNN is adopted and trained in an unsupervised manner to learn user power allocations. An online learning stage is further introduced to maximize the minimum user rate.
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 onD 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 P K k¼1;k≠i G ki . Solving for p i yields (45)

NOMA-aided cell-free 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 non-orthogonal resources to users to manage interference. Considering the enormous benefits of CF-mMIMO 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 NOMA-aided 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 large-scale 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 cell-free massive MIMO The need to improve the SE by network service providers owing to an ever-increasing 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 closed-form 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)   [55] The work presents the effect of multi-antenna users on CF massive MIMO networks. The work aims at optimizing the multiplexing gain, as well as improving the SE. In order to achieve this, a simple CB scheme is considered. By using the max-min data power control and mutually orthogonal pilot sequence, the effect of the proposed model is analyzed.
▪ In terms of per-user net throughput, the multiple antennas at both APs and users outperform a single antenna. ▪ Also, the array gain is improved while the inter-user interference is minimized.
▪ A decrease in the per-user net throughput value is imminent due to an increase in antennas per user.
2018 [104] A comprehensive survey of CF massive MIMO under different cooperation levels is presented. Specifically, four different levels of implementation, from fully centralized to fully distributed with arbitrary linear processing and spatially correlated fading, are examined. In addition, the achievable SE expression for the different CF implementations is presented.
▪ The proposed scheme significantly outperforms cellular massive MIMO and SC systems, however, with MMSE processing.
▪ For centralized implementation with MMSE, the SE is generally minimized in the regime of fewer APs equipped with multiple antennas. ▪ Notably, the distributed implementation is marginalized and requires further improvement.
2019 [80] This survey characterized the UL performance of CF massive MIMO with multi-antennas at both APs and users. Motivated by the gaps in CF systems with multi-antenna users, the work aims at maximizing the UL SE using ZF combining at the APs and data power control at users.
▪ The UL SE of CF systems with ZF combining is substantially improved. ▪ Integration of CF systems with maximum-ratio (MR) combining is sub-optimal compared to its ZF combining counterpart. ▪ Notably, additional antennas at users provide significant performance gain is minimal active users in the system.
▪ The results indicate that the interference increases when the number of active users grows large, and the SINR of each antenna generally decreases, which is undesirable in practice.
2019 [85] This work considers the impact of spatially correlated fading channels on the UL performance of CF architecture. The LS estimator is used, and a rigorous closed-form expression is designed to analyze the effects of the system's parameters-number of users. The number of APs and the fronthaul on the SE and EE is developed, considering the spatial correlation matrices and the number of APs antennas.
▪ The low-complexity LS estimator optimizes the SE and EE significantly as opposed to collocated massive MIMO. ▪ A compromise between the number of APs and the number of users is essential to maximize the performance of SE and EE. ▪ In addition, the performance of SE and EE in correlated Rayleigh fading channels is sub-optimal compared to the uncorrelated Rayleigh fading channel.
▪ The system is significantly impacted by spatial correlation.
2019 [131] The authors considered limited-fronthaul CF massive MIMO system in the presence of quantization errors, imperfect channel acquisition, and pilot contamination. By exploiting the max algorithm and Bussgang decomposition, an optimal uniform quantization model is presented under the assumption of estimate and quantize, quantize and estimate, and decentralized scheme. Moreover, analytical Thus, the SE is obtained as (55) Energy efficiency of cell-free massive MIMO While state-of-the-art technologies are consistently developed to address data, QoS, and capacity demands, issues related to environmental concerns and high-power 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 CF-mMIMO has been characterized by is enough to achieve optimal performance.
[163] The work considers improving the spectral/energy efficiency of wireless communication systems using intelligent multiobjective optimization techniques. Multi-objective genetic algorithm, multi-objective particle swarm optimization, and multi-objective differential evolution algorithms are proposed and applied at different circuit power levels.
▪ The SE-EE trade-off is generally maximized with the proposed intelligent optimization scheme compared to some other schemes investigated. 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 CF-mMIMO. 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 ultra-reliability 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 CF-mMIMO.

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 large-scale antenna arrays may not be sufficient to satisfy the demands for increased throughput, ubiquitous QoS, and ubiquitous connectivity. The so-called 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 ultra-dense wireless network, CF-mMIMO, and the less-congested terahertz

Hardware impairments
Most literature on CF-mMIMO has centered on perfect hardware components, which are unrealistic in practice due to high financial cost, bulkiness, and energy-hungry devices [171]. Achieving ideal hardware in both transceiver and receiver under practical implementation remains a general challenge. In order to alleviate this detrimental imperfection, an insight into the impact of RF impairments and ADCs imperfections on CF massive MIMO systems is presented in [84]. Results obtained show that the hardware expenses can be minimized by limiting the quality of transceiver RF chains and the quantization bits of lowresolution ADCs, however, at the cost of significant performance degradation. The effect of HI on the performance of CF-mMIMO has been considered extensively [134,135]. The adverse impact of HI at UE is not well accounted for, though the SE is shown to be significantly boosted as the hardware qualities increases. Further research s required to investigate the detrimental influence of HI.

Channel estimation
Acquiring CSI is an important part of any telecommunication system for resource allocation and detecting user signals. Unfortunately, the complex architecture of the transceiver and the plethora of distributed antennas in CF massive MIMO has made channel estimation quite challenging [172]. DL, ML, and compressed sensing have recently been proposed to predict statistical channel characteristics during channel estimation [173][174][175][176]. Thus, obtaining an efficient estimation method is one of the crucial areas requiring further investigation.

Security and privacy
The security and privacy of user data are essential in deploying 5G and B5G wireless networks due to the need to support billions of connected devices and deliver reliable Gigabit connection speeds [177]. As a result, investigations toward finding new approaches to improve trust and security of future wireless networks are exciting for research. More precisely, combining quantum communication (frequencies higher than 300 GHz) with CF massive MIMO is an excellent area worthy of further investigation.

Signal detection
In massive MIMO systems, signal detection requires sophisticated processing due to the massive number of antennas, thus incurring a high computational complexity. High-quality research aimed at obtaining an optimal trade-off between computational complexity and its performance has been proposed [178]. To further downplay this challenge, ML, deep learning-based techniques, sphere decoder, and SIC techniques have been explored for signal detection [9,179,180]. The design of cutting-edge signal detection algorithms is an exciting area calling for further research.

Pilot contamination
Here, non-orthogonal pilot sequences need to be employed by the users due to the limited length of the coherence interval in the UL training phase. This, in turn, causes a so-called severe effect identified as pilot contamination which presents a significant bottleneck to the performance of CF massive MIMO [85,101,181,182]. Specifically, the channel hardening effect is primarily affected by pilot contamination, particularly for a small coverage area [64]. The authors in [128] demonstrated that pilot contamination severely impacts the performance of CF-mMIMO-NOMA considerably. A new insightful pilot assignment scheme utilizing graph coloring is investigated in [183]. Indeed, the throughput is improved dramatically with the proposed graph coloring-based pilot assignment scheme. At the same time, a modest throughput complexity trade-off is obtained. To further optimize the performance of CF massive MIMO, developing optimal models that reduce the effect of pilot contamination is an interesting area worthy of further investigation.
Energy efficiency EE has become a major concern for network operators owing to increased power consumption, carbon emissions, and global warming related to wireless communication technologies. Although CF massive MIMO is a natively greener technology than its cellular counterpart, power consumption in 5G networks is relatively higher than 4G networks [78,184]. In order to address the crucial demanding green specifications, simplified deployment, and efficient energy-saving in next-generation wireless systems; there is a need for more advanced, low complexity, and low-cost optimization models and algorithms for greener CF massive MIMO systems. band is a crucial enabler to much larger bandwidths and a basic pillar to sustain the SE and EE. Terahertz-enabled CF-mMIMO will be a key enabler for next-generation wireless communication systems.

Lesson three
Compared to earlier generations of wireless communication networks, the total power consumption of 5G and beyond-5G 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 next-generation wireless standards is NOMA. The power domain-based 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 trade-off between complexity and performance (sum rate), high-quality 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 low-cost components, the hardware imperfections increase, which is detrimental to the overall system's performance. These imperfections consisting of phase noise, I/Q imbalance, amplifier non-linearities, and more are referred to as HIs. There is a need for an optimal trade-off 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 5G-aided SWIPT networks presents an entirely new challenge. Therefore, there is a need to find proper allocation schemes to optimize the rate-energy trade-off between information retention and energy allocation.

Conclusions
Cell-free massive MIMO has been proposed as a novel architecture to address the ever-increasing 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, CF-mMIMO enables the deployment of dense APs over a wide network area to communicate with several UEs cooperatively. Motivated by the distinctive benefits of CF-mMIMO, 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 CF-mMIMO, covering the UL/DL pilot-aided channel estimation, UL/DL training, and channel hardening, is discussed elaborately. Additionally, the performance characteristics of CF-mMIMO using key design metrics like EE, channel hardening, SE, and more, are discussed extensively. Furthermore, the viable application areas of CF-mMIMO are outlined, and an up-todate review of key findings and current research trends in CF-mMIMO is presented. Finally, open research issues and key take-away lessons are drawn from the survey to explore this exciting area of wireless communications systems deeply.