A Review on Cell-Free Massive MIMO Systems

Abstract

Cell-free massive multiple-input multiple-output (CF mMIMO) can be considered as a potential physical layer technology for future wireless networks since it can benefit from all the advantages of distributed antenna systems (DASs) and network MIMOs, such as macro-diversity gain, high channel capacity, and link reliability. CF mMIMO systems offer remarkable spatial degrees of freedom and array gains to mitigate the inherent inter-cell interference (ICI) of cellular networks. In such networks, several distributed access points (APs) together with precoding/detection processing can serve many users while sharing the same time-frequency resources. Each AP can be equipped with single or multiple antennas, and hence, can provide a consistently adequate service to all users regardless of their locations in the network. This paper presents a detailed overview of the current state-of-the-art on CF systems. First, it performs a literature review of the conventional CF and scalable user-centric (UC) CF mMIMO systems in terms of the limited capacity of the fronthaul links and the connection between APs and user equipments (UEs). As beyond networks will rely on higher frequency bands, it is of paramount importance to discuss the impact of beamforming techniques that are being investigated. Finally, some of the CF promising enabling technologies are presented to emphasize the main applications in these networks.

1. Introduction

The vision of a networked society with unlimited access to information and data sharing at any time and anywhere, for everyone and everything, necessitated a re-evaluation of current cellular-based deployments to accomplish this vision [1]. In the past, bandwidth expansion (sub-6 GHz and millimeter Wave (mmWave) frequencies) and network densification (ultra-dense networks (UDNs)) were the primary means to provide more sophisticated broadband services and improve network scalability, spectral efficiency (SE) and energy efficiency (EE) [2].

1.1. Bandwidth Expansion

Nowadays, the demand for mobile data traffic is increasing rapidly each year due to the extensive use of smartphones and other wireless devices, and thus, sub-6 GHz bands are extremely crowded. Therefore, using a higher frequency spectrum, such as mmWave was one of the key physical layer solutions for 5G and beyond systems [3]. With sub-6 GHz, the systems generally implement a full-digital baseband beamforming, i.e., each antenna element is connected to one dedicated radio frequency (RF) chain [4]. However, the high cost and energy consumption of the large number of RF chains force mmWave systems to rely on hybrid analog–digital beamforming, where the number of RF chains is much less than the number of antennas. In such hybrid architectures, some signal processing is carried out at the digital domain and some left to the analog one [5]. Indeed, different hybrid beamforming schemes have been presented in the literature for narrowband [6,7] and wideband [8,9,10] mmWave-based systems.

1.2. Network Densification

Network densification (by deploying a large number of small cells (SCs)) allows for each user to be tracked by a base station (BS). However, the number of BSs must increase exponentially, leading to a significant increase in the investment required, and thus requires advancements in hardware miniaturization and cost reduction [11]. On the other side, both inter-cell interference (ICI) and poor signal quality at cell-edges have caused notable performance degradation problems [12]. Therefore, the improved interference mitigation techniques, such as distributed antenna systems (DASs) [13], network multiple-input multiple-output (MIMO) [14], coordinated beamforming [15], and coordinated multi-point (CoMP) [16] have been proposed to deal with the users near the cell borders (cell-edge users) by adding cooperation between the closely located access points (APs), and hence mitigating ICI. Although these techniques may boost system performance as well as provide micro- and macro-diversity gain, the distributed APs into cooperative clusters led to cluster interference [16,17]. In addition, despite the high peak data rates available to each user in the cell centers, the significant variations within each cell render quality of service (QoS) are unreliable [18]. For that reason, the primary goal for future mobile networks (B5G/6G) is to guarantee rates to the vast majority of locations within the geographical coverage region rather than increase the peak rates [19]. Therefore, it is crucial to start research on beyond 5G/6G wireless systems and design a non-cellular-based network architecture with intelligent cooperation and coordination capabilities to meet future performance requirements.

1.3. Cell-Free Massive MIMO Systems

By integrating the benefits of both DAS and MIMO technologies, a new disruptive network architecture, based on cell-less deployment, called cell-free massive MIMO (CF mMIMO) has been designed to fulfill the desired goals of consistently high data rates everywhere and uniform QoS, ultra-high reliability, and the avoidance of cells interference since the concept of cell boundaries does not exist [20,21]. As shown in Figure 1, in CF mMIMO, a very large number of distributed APs connected to the central processing unit (CPU) via fronthaul connections serve, simultaneously and jointly, all user equipments (UEs)) that share the same resources [22]. However, the conventional CF mMIMO system is not scalable and has some issues with fronthaul signaling, high computational complexity, and makes large-scale networks unfeasible [23]. Therefore, the user-centric (UC) approach has been proposed to deal with the scalability problem and build a realistic deployment, where each UE is only served by a small number of cooperative APs, leading to a minimization in the amount of information sent to the CPU [23,24]. UC CF mMIMO topologies may serve as the basis for B5G networks since they achieve EE and robust connectivity to guarantee that all UEs enjoy consistent coverage and performance through the network area [24].

1.4. Paper Organization

The remainder of this paper is organized as follows: Section 2 presents the scalable CF mMIMO systems in terms of the limited fronthaul capacity constraints and the AP–UE association methods. Then, Section 3 defines the full-digital and hybrid analog–digital beamforming techniques for both conventional and UC CF mMIMO systems. In Section 4, different promising technologies for CF networks are discussed. Finally, the main conclusions are drawn in Section 5.

2. Scalable Cell-Free mMIMO Systems

The assumption of CF mMIMO, in which each UE can be served by all APs, resulted in massive fronthaul signaling, high computational complexity, and power consumption. For that reason, many studies have evaluated their systems under limited fronthaul capacity constraints [25,26,27,28,29,30,31,32,33,34,35], while others adopted different AP–UE selection techniques [36,37,38,39,40,41,42,43,44,45,46,47]. Based on that, the following subsections present in detail different solutions to build scalable systems with less fronthaul requirements, as shown in Figure 2, where each user can be served by a group of APs for more practical implementation.

2.1. Limited Fronthaul Capacity

In the following, research on CF mMIMO systems with limited fronthaul capacity links that connect the APs to the CPU are described.

Table 1. A literature comparison for CF mMIMO systems with limited fronthaul capacity.

Ref.	Year	Transmission	Channel Model	Coordinated Beamforming	Performance
[25]	2018	Downlink	Block fading channel	Centralized	Improve power weight allocation
[26]	2019	Uplink	Block fading channel	Distributed	Improve SE and EE
[27]	2019	Uplink / Downlink	mmWave	Semi-centralized	Improve average max–min user rate
[28]	2020	Uplink / Downlink	Block fading channel	Distributed	Improve average max–min user rate
[29]	2021	Uplink	Rayleigh fading channel	Distributed	Improve BER
[30]	2021	Uplink	Flat fading channel	Distributed	Improve overall system SINR
[31]	2021	Uplink	Rician fading channel	Distributed	Improve average max–min user rate
[32]	2022	Downlink	Rayleigh fading channel	Distributed	Improve average max–min user rate
[33]	2022	Uplink	mmWave	Centralized	Improve SE and EE
[34]	2022	Uplink	mmWave	Distributed	Improve average max–min user rate
[35]	2022	Downlink	Block fading channel	Distributed	Improve coverage user rate and EE

compares the research [25,26,27,28,29,30,31,32,33,34,35], in terms of the data transmission, the channel model, the coordinated beamforming schemes, and finally the performance of the proposed systems. More precisely, the authors of [25] solved the joint problem of power weight allocation and quantization distortion under the capacity fronthaul links constraint by considering three different joint optimization problems with the zero-forcing (ZF) beamforming scheme. In [26], the closed-form achievable rates for three different transmission techniques at the APs were evaluated. Then, they proposed an efficient low-complexity fronthaul-rate-allocation algorithm in order to share the capacity of fronthaul connections for transmitting channel state information (CSI) and data signals from the APs to the CPU. Finally, data transmission power control was addressed using two optimization strategies to control the signal to interference and noise ratio (SINR). The same authors of [27,28] computed the closed-form max–min power allocation and fronthaul quantization problems, where in [27], the optimization problems were solved by integrating block coordinate descent (BCD) techniques with sequential linear optimization algorithms, resulting in a uniformly high QoS over the whole network coverage region, while in [28], the solution of the optimization expressions of both the achievable user rates and the fronthaul bandwidth consumption was found using low-resolution analog-to-digital converters (ADCs) with various AP–CPU functional splits to quantize the signals/samples shared among the APs and CPU during the transmission phase. The work of [29] designed two robust receivers to mitigate the impacts of limited capacity fronthaul by exploiting the knowledge of the heteroscedastic covariance of the associated effective noise. The high-complexity first receiver was built using an expectation propagation algorithm, which led to the best performance results, while the low-complexity second receiver used the effective noise heteroscedastic covariance in a generalized least squares variation of the maximum likelihood detection problem. Ref. [30] looked at another approach that considers point-to-multipoint fronthaul architecture, where the research is concentrated on developing a new optimization problem for joint power control and AP scheduling, aiming to achieve maximum power to each user and to a limited amount of shared fronthaul bandwidth. The authors of [31] addressed the achievable rate of a limited fronthaul system with a mean square error (MSE) receiver under the assumption of uncorrelated quantization distortion on two different scenarios, the exact uplink per-user rate and the uplink per-user rate, without taking into account the correlation between the inputs of the quantizers. In [32], the authors proposed an orthogonal frequency division multiplexing (OFDM)-based system that takes into consideration the transmitting power and fronthaul capacity constraints of each AP. Two quadratic transform optimization techniques are proposed to optimize the minimum rate of each user and the sum rate performance. In [33], the authors addressed the channel estimation error and the precoding processing, considering the low-ADC/digital-to-analog converter (DAC) resolution and low-capacity fronthaul connections. First, they reduced the channel estimation error by optimizing the minimum MSE-achieving codebook associated with the fronthaul compression. Then, they proposed an alternative optimization approach to alternate between two sub-problems, the power allocation and codebook design problems, in order to deal with the max–min fairness problem for the maximum ratio (MR) and ZF precoding schemes. Another approach was considered in [34], where the proposed architecture has a number of CPUs and APs, where the APs are connected to each CPU according to their respective distance. Based on this assumption, two expressions were derived, the density of the activated APs as a function of the blockage and CPU densities, and the achievable fronthaul capacity distribution, assuming an equal AP fronthaul bandwidth. Finally, Ref. [35] employed conjugate beamforming and stochastic geometry methods to analyze the proposed networks under a finite fronthaul capacity constraint. For conventional CF mMIMO architecture, they computed the coverage user rate using independent binomial point processes, while in the UC case, they determined the load for a subset of APs that serve a given user using independent homogeneous poisson point processes to model the locations of the APs and users in the network.

2.2. AP–UE Association Techniques

This subsection presents different AP–UE selection methods [36,37,38,39,40,41,42,43,44,45,46,47], considering UC approach that allows each user to be served by a subset of APs. Specifically, the authors of [36,39,40,42,47] adopted a simple AP–UE association method based on the largest large scale fading (LSF) coefficients or maximum channel gain. Besides the LSF-based approach, the authors of [36] proposed another method that is based on the received power from each AP to a particular UE. In [37] the authors proposed two different allocation algorithms, the effective channel gain from all UEs to all APs and the channel quality of each UE. Herein, each user is connected to the most appropriate AP in the geographical coverage area. The AP–UE connections in [38] are based on several switch-on/switch-off techniques to dynamically activate/deactivate some of the APs in the network. Namely, the pure random switching method, three selection algorithms that aimed to maintain consistent locations of the group of active APs, another strategy that used the availability of time-dynamic information in short-term traffic variations, and finally a greedy optimal EE selection strategy. In [41,43,44,45], the AP–UE connections are determined by considering the channels with the largest Frobenius norm, i.e., the users are connected to its nearest AP. Finally, in [46], each user is assigned to a limited number of APs based on a threshold received signal-to-noise ratio (SNR) method. First, the received SNR between each AP–UE pair is computed and then it is compared with a given threshold in order to limit the fronthaul load.

3. Beamforming for Cell-Free mMIMO Systems

Coordinated beamforming is an efficient method to improve mobile communication system performance by regulating ICI, particularly in the cell-edge area. In coordinated beamforming, in order to control the induced ICI, each data stream is transmitted from a single BS (or AP), and hence, the transmissions are effectively coordinated between multiple BSs/APs. Coordinated beamforming can be either centralized or decentralized (also called distributed) [48,49]. In the centralized approach, the coordination is carried out by the CPU that requires access to the global CSI, i.e., the information between all BSs/APs and all users, while in the decentralized (distributed) approach, part of the coordination process is performed at the BSs/APs and part at the CPU based on local CSI, i.e., the knowledge of the channels between a BS/AP and all users. Therefore, recent studies have focused on evaluating the performance of beamforming algorithms, namely, those designed for conventional CF and UC-CF mMIMO systems either with sub-6 GHz frequencies or mmWave communications channels. The following subsections present a detailed literature review of CF mMIMO systems with beamforming techniques for both Sub-6 GHz and mmWave bands.

3.1. Sub-6 GHz

This subsection presents a literature review about conventional CF systems [50,51,52,53,54,55] and UC CF mMIMO [36,37,38,39,40,41,42] under sub-6GHz frequencies.

Table 2. A literature comparison for CF mMIMO systems under sub-6 GHz frequency bands.

Literature Review		Conventional CF mMIMO						User-Centric CF mMIMO						Both
		[50] 2017	[51] 2019	[52] 2019	[53] 2022	[54] 2021	[55] 2022	[36] 2018	[37] 2020	[38] 2020	[39] 2022	[40] 2022	[41] 2022	[42] 2021
Data Transmission	Uplink		✓	✓	✓					✓	✓	✓
	Downlink	✓				✓	✓	✓	✓	✓	✓		✓	✓
Channel Model	Rayleigh fading			✓	✓	✓	✓	✓		✓	✓		✓	✓
	Flat fading	✓	✓						✓			✓
Digital Beamforming	at UEs				✓						✓
	at APs/CPU	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
Coordinated Beamforming	Distributed	✓		✓	✓		✓	✓	✓	✓	✓	✓	✓	✓
	Semi-centralized			✓	✓
	Centralized		✓	✓	✓	✓					✓			✓

summarizes the main similarities and differences among the cited studies [36,37,38,39,40,41,42,50,51,52,53,54,55], in terms of the data transmission, the fading channel model, the use of digital beamforming, and finally the coordinated beamforming implementation.

3.1.1. Conventional Cell-Free

The work of both [50,51] considered the conjugate beamforming and ZF schemes to evaluate the proposed systems. In [50], the authors designed low-complexity optimal and sub-optimal power optimization algorithms using max–min criteria with those simple linear precoders, while in [51], a tight approximation rate expression was computed to evaluate the effects of the multiple antenna AP, channel estimation error, pilot contamination, and power control. Herein, two power control algorithms were proposed. The first method focused on optimizing the total rate while taking the QoS and each user’s power constraints into consideration. The second attempted to maximize the one user’s rate, making sure that the other users could meet their QoS requirements. The work of [52,53] analyzed the SE of four different coordinated beamforming implementations, where in [52], the authors considered global and local minimum MSE. Meanwhile, in [53], they used minimum MSE successive interference cancellation detectors and an arbitrary combining technique. They also computed closed-form SE expressions for two-layer decoding processing with a maximum-ratio combining scheme. In [54], the exact closed-form expression for the achievable SE of a dubbed, enhanced, normalized conjugate beamforming system was derived. Besides, they developed an optimal max–min fairness power control algorithm that is only dependent on LSF quantities. Different iterative matrix inversion algorithms were designed in [55], aiming to avoid the direct matrix inversion for the linear ZF precoder scheme in order to obtain a near-optimal performance with less computational complexity.

3.1.2. User-Centric Cell-Free

Indeed, a lot of research work evaluated the digital beamforming schemes with UC CF mMIMO systems to achieve more practical deployments. In [36], data transmission from the APs to the users was performed using a simple conjugate beamforming technique, where the authors developed a closed-form SE expression, considering the impacts of channel estimation errors, power control, non-orthogonality of pilot sequences, and backhaul power consumption. The optimal power control algorithm sought to maximize the overall EE, under the constraints of a per-user SE and a per-AP power constraint. In [37,38], the emphasis was on the AP selection problem, where data transmission was carried out using the maximum ratio and ZF precoding schemes, respectively. More precisely, the authors of [37] considered the effective channel gain and the channel quality of each UE. In [38], they developed different techniques to switch some of the APs on/off based on the traffic load in the network. The authors of [39] also derived the closed-form SE, as in [36], but for a full-duplex system with an MR beamforming scheme and optimal uniform quantization. Then, they optimized the weighted sum EE power control by using a two-layered iterative algorithm that integrated the successive convex approximation and the alternating direction method of multipliers. The work in [40] proposed a power allocation algorithm for data transmission with conjugate beamforming under both proper and improper Gaussian signaling. Herein, the power allocation method aimed to increase the geometric mean of user rates. Then, they developed a novel method to evaluate the network EE with the users’ rates balanced by exploiting the relationship between the user rates’ geometric mean and the total transmit power. The work of [41] considered the MR technique and introduced novel EE maximization problems for both coherent and non-coherent transmissions schemes, subject to the fronthaul capacity and power consumption constraints. For that, they used a single framework that combined successive convex approximation with the Dinkelbach algorithm to derive closed-form expressions in order to obtain sub-optimal solutions for both strategies. Finally, the research of [42] focused on evaluating both the conventional CF and UC CF mMIMO systems, where the authors considered indoor industrial scenarios to investigate the power control algorithms along with several beamformers (MR, ZF, and partial ZF), aiming to maximize the minimum SINR among users.

3.2. Millimeter Wave

Together with CF mMIMO, mmWave communications have the potential to achieve multi-Gbps data rates, due to its frequency being several times higher than current systems. The propagation of mmWave communications is characterized by high free-space path-loss (PL), which requires the consideration of spatial selectivity or scattering in channel modeling. To accurately model these systems, the Saleh–Valenzuela model [56] has been extended and forms the foundation of mmWave mMIMO channel models. This section provides a brief overview of the clustered wideband [57] and narrowband [6] channel models.

3.2.1. Wideband Channel Model

The frequency domain clustered-wideband channel matrix of the uth UE and mth AP at the subcarrier k can be expressed as

$${\mathbf{H}}_{m,u,k}=\sum _{d=0}^{D-1}{\mathbf{H}}_{m,u,d}{e}^{-j\frac{2\pi k}{N_c}d},$$

(1)

where ${\mathbf{H}}_{m,u,d}\in {\mathbb{C}}^{N_r\times N_t}$ is the channel in time domain, such that the average received power $\mathbb{E}\left[{∥{\mathbf{H}}_{m,u,d}∥}_F^2\right]=N_r{N}_t$, and can be given by

$$\begin{array}{c}{\mathbf{H}}_{m,u,d}=\sqrt{{\rho }_{\mathrm{PL},m,u}\gamma }{\displaystyle \sum _{q=1}^{N_{cl}}}{\displaystyle \sum _{r=1}^{N_{ray}}}{\alpha }_{q,r}^{m,u}{p}_{rc}\left(d{T}_s-{\tau }_q^{m,u}-{\tau }_{q,r}^{m,u}\right)\hfill \\ {\mathbf{a}}_{rx,m,u}^{}\left({\varphi }_q^{m,u}-{\phi }_{q,r}^{m,u}\right){\mathbf{a}}_{tx,m,u}^H\left({\theta }_q^{m,u}-{\vartheta }_{q,r}^{m,u}\right),\hfill \end{array}$$

(2)

with $N_{cl}$ as the scattering clusters, $N_{ray}$ as the propagation paths per cluster, and with $N_t$ and $N_r$ representing the transmitting and receiving antennas, respectively.

The PL constant ${\rho }_{\mathrm{PL},m,u}$ between the transmitter and the receiver can be represented as ${\rho }_{\mathrm{PL},m,u}=G_a/{\beta }_{mu}$, where $G_a$ is the antenna gain, and ${\beta }_{mu}$ is the PL between the uth UE and mth AP, which is given in dB as

$${\beta }_{mu}\left[\mathrm{dB}\right]={\beta }_0+10\epsilon \mathrm{lo}{\mathrm{g}}_{10}\left(\frac{d_{mu}}{d_0}\right)+A_{\xi },$$

(3)

where ${\beta }_0=10\mathrm{lo}{\mathrm{g}}_{10}{\left({\lambda }^{-1}4\pi d_0\right)}^2$, $d_{mu}$ is the distance between the users and the APs, $\lambda$ is the wavelength, $d_0=1\mathrm{m}$, $\epsilon$ is the average PL exponent, and $A_{\xi }$ is a zero mean Gaussian random variable with a standard deviation $\xi$ in dB, representing the shadow fading effect.

The remaining variables are $\gamma =N_r{N}_t/N_{cl}{N}_{ray}$, which is the normalization factor; ${\alpha }_{q,r}^{m,u}$ is the complex path gain at the rth ray of the qth cluster; $p_{rc}\left(.\right)$ denotes the pulse-shaping filter function; $T_S$ corresponds to the sampling interval; ${\tau }_q^{m,u}$ is the time delay of the qth scattering cluster; and ${\tau }_{q,r}^{m,u}$ denotes the relative time delay. Then, ${\mathbf{a}}_{rx,m,u}^{}\left({\varphi }_q^{m,u}-{\phi }_{q,r}^{m,u}\right)$ and ${\mathbf{a}}_{tx,m,u}\left({\theta }_q^{m,u}-{\vartheta }_{q,r}^{m,u}\right)$ denote the normalized receiving and transmitting array response vectors, respectively, with an angle of arrival (AoA) ${\varphi }_q^{m,u}$, a relative AoA ${\phi }_{q,r}^{m,u}$, an angle of departure (AoD) ${\theta }_q^{m,u}$ and a relative AoD ${\vartheta }_{q,r}^{m,u}$ at the rth ray of the qth scattering cluster.

3.2.2. Narrowband Channel Model

The clustered narrowband-based channel model between the UEs and APs has the same underlying principles as the wideband model, and can be represented as

$$\begin{array}{c}{\mathbf{H}}_{m,u}=\sqrt{{\rho }_{PL,m,u}\gamma }{\displaystyle \sum _{q=1}^{N_{cl}}}{\displaystyle \sum _{r=1}^{N_{ray}}}{\alpha }_{q,r}^{m,u}{\Lambda }_{rx,m,u}\left({\varphi }_q^{m,u}-{\phi }_{q,r}^{m,u}\right){\Lambda }_{tx,m,u}\left({\theta }_q^{m,u}-{\vartheta }_{q,r}^{m,u}\right)\times \hfill \\ {\mathbf{a}}_{rx,m,u}\left({\varphi }_q^{m,u}-{\phi }_{q,r}^{m,u}\right){\mathbf{a}}_{tx,m,u}^H\left({\theta }_q^{m,u}-{\vartheta }_{q,r}^{m,u}\right),\hfill \end{array}$$

(4)

where the main difference between the wideband and narrowband is that the latter has the functions ${\Lambda }_{rx,m,u}\left(.\right)$ and ${\Lambda }_{tx,m,u}\left(.\right)$ which correspond to the receiving and transmitting antenna element gain at the corresponding AoA and AoD.

Therefore, the recent research trends made an effort to evaluate the performance of hybrid analog–digital beamforming, which was particularly designed for conventional CF mMIMO systems [27,58,59,60,61,62,63] and UC CF mMIMO [43,44,45,46,47] with mmWave communication channels. Figure 3 shows the architecture of multi-user hybrid analog–digital beamforming, and

Table 3. A literature comparison for CF mMIMO systems under the mmWave frequency band.

Literature Review		Conventional CF mMIMO							Both Conv. & UC CF mMIMO
		[27] 2019	[58] 2020	[59] 2021	[60] 2022	[61] 2022	[62] 2022	[63] 2022	[43] 2017	[44] 2018	[45] 2019	[46] 2021	[47] 2022
Data Transmission	Uplink	✓	✓			✓	✓	✓	✓		✓
	Downlink	✓	✓	✓	✓		✓		✓	✓	✓	✓	✓
Channel Model	Narrow-band	✓	✓	✓	✓	✓			✓	✓	✓	✓	✓
	Wide-band						✓	✓
Hybrid Beamforming	at UEs	✓	✓				✓	✓
	at APs/CPU	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
Coordinated Beamforming	Distributed		✓	✓	✓	✓		✓	✓	✓	✓
	Semi-centralized	✓				✓						✓
	Centralized						✓						✓

summarizes the main similarities and differences among the aforementioned studies [27,43,44,45,46,47,58,59,60,61,62,63], in terms of data transmission, the mmWave channel model, the use of hybrid beamforming, and finally the coordinated beamforming implementation.

• Conventional Cell-Free

In [27], low-complexity multi-user hybrid beamforming algorithms were designed with respect to various constraints, including imperfect CSI estimation, limited capacity of fronthaul links, max–min power allocation, and the non-orthogonality of pilot sequences. Herein, the analog part of the precoder/decoder relies on large-scale second-order CSI, while the ZF scheme is used to implement the digital part based on small-scale instantaneous CSI. The same switch on/off APs concept, used in [38], is considered in [58] but under mmWave frequencies, where the authors evaluated the EE and SE of different AP sleep-mode strategies with the non-uniform spatial distribution of users using hybrid ZF precoding/combing techniques. The work of [59] proposed three different analog precoding schemes combined with ZF digital precoding. Then, they investigated how the correlated shadowing and pilot assignment techniques may affect the average SE performance of the proposed precoding algorithms under both indoor and outdoor scenarios, while [60] concentrated on maximizing the weighted sum rate of a near-optimal hybrid precoding system, under two constraints: the transmit power for each AP and the constant modulus for the analog precoder phase shifters. The optimization problem of the hybrid precoding was solved iteratively using a low-complexity BCD algorithm. The authors of [61] investigated two hybrid beamforming architectures and proposed low-complexity algorithms to dynamically activate and deactivate the RF chains, the associated analog to digital converters, and phase shifters at the APs to minimize power consumption and maintain the total achievable rate while increasing the system EE. In [62], the authors designed hybrid beamforming architecture based on a beam squint-aware channel covariance for OFDM systems. They proposed high-dimensional single- and double-phase shifter-based analog precoder/combiner techniques, considering different beam squint awareness assumptions. Finally, [63] designed a low-complexity AoD-based analog precoder, while the AP hybrid equalizer and CU combiner were jointly designed by minimizing the average MSE between the transmitted and CPU estimated signals. A cyclic minimization algorithm was used to iterate between the AP hybrid equalizer and CPU combiner, where the information is exchanged between them based on a set of error variances to enhance detection performance.

• User-Centric Cell-Free

The work on such hybrid systems with UC CF mMIMO under mmWave frequencies is scarce but ongoing. In particular, the authors of [43] proposed a multi-user channel estimation scheme that takes into account channel correlation for the nearby users along with a low-complexity hybrid analog–digital partial ZF beamforming at the APs, while a very simple channel-independent 0-1 beamforming process was used at the UEs. The same system model and assumptions from [43] are considered in [44,45], which proposed an optimal power control algorithm to maximize global EE. The main difference here is that [44] only addressed the downlink power control, while [45] additionally considered the uplink power control. The authors of [46] proposed hybrid precoding schemes based on a simplified sum MSE objective function, where two heuristic algorithms were developed to design the analog part of the hybrid precoder, considering different knowledge of statistical CSI to fulfill the rate requirements of each UE. Another aspect is considered in [47] to deal with the infrastructure cost and installation complexity of such CF mMIMO systems, where the authors proposed two dual-band architectures, i.e., mmWave wireless fronthaul channels between CPU and APs, and sub-6 GHz wireless access channels between APs and UEs. Efficient low-complexity analog-hybrid beamforming and resource allocation algorithms were proposed, considering the UC–AP-grouping approach to serve each user. Then, they evaluated the proposed architecture with mixed wireless and wired mmWave fronthaul links, in which only the leaders of the wired clusters were chosen as the nearest APs to the CPU with wireless fronthaul links.

As an example, Figure 4 compares the bit error rate (BER) performance of both centralized and distributed coordinated beamforming, where C-SC, C-CF, and D-CF refer to the centralized SCs, centralized CF, and distributed CF, respectively. In both figures, the main simulation parameters can be seen in [64,65], where the CF system considers 4 APs, 2 UEs, and 2 receiving RF chains, with the same number of antennas—16 antennas in the transmitter and 16 in the receiver. In the case of SCs, we considered 2 SCs—each one has an AP that can serve a UE. The left-hand side figure (Figure 4a) evaluated the hybrid analog–digital receiver under a narrow-band channel [64], while the right-hand side figure (Figure 4b) adopted the wide-band channel [65]. In Figure 4a, the performance of the CF hybrid system is quite close to that of the full-digital one, meaning CF systems where channels are sparse hybrid architectures are more energy-efficient than full-digital counterparts achieving similar performance. Regarding the performance of the distributed CF system (Figure 4b), the D-Cf and C-CF full-digital performances are very close to each other. These results demonstrate the effectiveness of the distributed processing techniques for CF systems, thus reducing the fronthaul requirement.

4. Cell-Free Promising Technologies

This section presents some of the research trends that investigate the combination of CF mMIMO with promising enabling technologies for 6G networks. As depicted in Figure 5, these include reconfigurable intelligent surface (RIS), radio stripe (RS), large intelligent surface (LIS), unmanned aerial vehicle (UAV), and artificial intelligence (AI) techniques. Indeed, integrating CF mMIMO systems with these technologies has the potential to provide a wide-range of new possibilities for upcoming wireless networks services and applications.

4.1. Reconfigurable Intelligent Surface (RIS)

RIS, also known as intelligent reflecting surface (IRS), is a potential cost- and energy-efficient technology to deal with the high costs of hardware and power sources of CF systems [66]. It might enhance the CF network performance and EE by re-configuring the wireless propagation environment between the transmitter and receiver through highly software-controlled signal reflections [67]. RIS is a flat surface with a large number of low-cost passive reflecting components. These components can independently adjust amplitude and/or the phase of the incident signals and reflect them in a controllable way [68]. The intelligent transmission method of RIS is based on the principle of wavefront control, which involves using mathematical algorithms to optimize the configuration of the components on the RIS in real-time, according to the desired transmission requirements and environmental conditions. These algorithms are commonly based on optimization techniques, such as gradient-based optimization or reinforcement learning [69,70], which are used to find the optimum possible component configuration that may be employed to achieve the intended transmission goals. The wavefront control algorithms must consider various factors, including the frequency and bandwidth of the signals, the channel characteristics, the available power resources, and the computational and time constraints. Unlike conventional CF systems, RIS-aided CF does not need any additional hardware implementation, like complicated digital phase shift circuits, which significantly reduces energy consumption and signal processing complexity. Hence, compared to conventional CF systems, with RIS, less power is needed to achieve the same level of QoS [67]. In addition, RIS-aided wireless systems have some benefits and challenges [66,71], such as:

• Since RIS acts as antenna arrays, it can boost network capacity and data rates in inexpensive and energy-efficient way due to the tuning of various passive reflecting elements.
• As RIS is passive, it is not possible to use the traditional channel estimation techniques to estimate the reflected channels of RIS-aided wireless communication systems.

4.2. Radio Stripe (RS)

RSs are one of the promising technologies for CF networks to cope with the high costs/complexity deployment, as well as the limited capacity of both the fronthaul and backhaul links. Unlike RIS, RSs have active antenna elements. They employ a sequential topology, which is considered to be a quite interesting technique for deploying the CF mMIMO network in congested areas and indoor locations such as stadiums, train stations, factories, and shopping centers with multiple APs and UEs in such areas [68]. It should be noted that the conventional CF mMIMO network requires a star topology, i.e., separate fronthaul cables are needed to connect the APs and the CPU [72]. This results in high implementation costs and an unscalable system performance, while in CF systems with RSs, many APs are integrated into a single cable to more efficiently perform the synchronization, data transmission, and power supply operations than in a conventional CF system configuration [68]. Then, each radio stripe is connected to a single or multiple CPUs. Such CF networks with RSs have some advantages/disadvantages [72,73], including:

• Flexible deployment and cable routing in real-world applications to achieve more practical and scalable systems.
• The network can be fault-tolerant by using routing mechanisms that might reduce the impact of node failures.
• RSs improve robustness and resilience, and thus decrease maintenance expenses.
• Low heat dissipation simplifies and reduces the cost of cooling systems.
• The crucial requirement of CF network with RSs is the specific and accurate synchronization and coordination between antennas and antenna processing units.

4.3. Large Intelligent Surfaces (LIS)

LIS is a new concept in wireless communication. Similar to RSs, it assumes active elements, where it is used as a large active antenna array, and can be considered as an extension of mMIMO technology [74]. LIS consists of a continuous radiating surface that can send and receive information to and from the nearby users. It performs as a radio access point, and facilitates direct user communication. LIS serves as an adjustable reflector between the BS/AP and the users, where it occupies a part of the channel [71]. With LIS, there is a reduction in route loss, but a high antenna gain, since the user and the LIS are close to each other. Therefore, it is expected that the transmit power would be low in both sides of the communication. This enables such an active component to be widely used due to its low-cost and high EE [71]. Therefore, it is quite interesting to integrate CF systems with LIS technology, since the resource allocation in CF systems (also in LIS) can lead to multi-objective optimization problems, including the min and sum rate per user, as well as the transmit power [75].

The main challenge in LIS technology is the high level of implementation and computational complexity [71]. However, it has been suggested that adopting a panel-based LIS configuration (each panel has fewer antenna elements) instead of using a single LIS is a practical alternative solution to provide effective communication with much implementation flexibility at an affordable rate of computational complexity [76,77]. Therefore, the work of [77] addressed two different approaches for deploying panel-based LISs. One approach is to install several panels, and only activate a subset of them. Another option is to consider sparse deployment, i.e., deploy fewer panels but with full activation. Therefore, LIS-aided wireless communication systems have some benefits [74], such as:

• LIS provides maximum data rates with a traditional large antenna array for a certain surface area.
• LIS has high performance when the number of terminals increases and can mitigate interference. Therefore, it is a promising candidate for data transmission in wireless networks that go beyond mMIMO technology.

4.4. Unmanned Aerial Vehicle (UAV)

UAVs, commonly known as drones, have recently attracted a lot of interest due to their ability to provide high mobility, flexibility, adaptive altitude, and cost-effective wireless access in areas with no wireless coverage [78,79]. UAV functions as a flying BS/AP that has the ability to dynamically update its location in order to fill the coverage gaps in the network and increase capacity [68]. Among the diverse applications enabled by UAVs, the use of UAVs for high-speed wireless communications is likely to play a significant role in beyond systems. The UAVs can be employed as an effective temporary alternative in circumstances of overcrowding events, weather monitoring, forest fire detection, traffic control, military services, and in disaster-hit areas where part of the existing infrastructure is destroyed, and there is a need to provide emergency services [78,79].

In fact, the adoption of CF architectures for supporting wireless communications with UAVs, instead of conventional cellular mMIMO systems, has attracted a substantial data rate performance to support the communication links for UAVs in the presence of terrestrial users [80]. The fact that the user will benefit from the employment of UAVs in the network more than from the deployment of more ground APs is one of the key advantages of doing so. This results in avoiding the obstacles and enhancing the probability of achieving line-of-sight communication links with the served users in the network [68]. Not only that, UAV-aided CF topologies do not suffer from the cell-edge issue that exists in conventional mMIMO deployments [80]. However, there are some critical requirements that UAVs must meet to transfer data between APs and users [78], such as:

• Having solid connections between APs and UAVs, to ensure particular QoS criteria in terms of data rates, latency, and reliability, can be considered a prerequisite to fulfill the anticipated benefits of UAVs.
• It is necessary to build new communication protocols, taking into consideration the risk of sparse and intermittent network connectivity.
• The issues resulted from the high signal processing complexity and the high costs associated with power consumption make it highly expensive to use multiple antennas in UAVs due to the size, weight, and power constraints.

4.5. Artificial Intelligence (AI)

AI is one of the promising technologies to improve the performance of 5G and beyond networks since it enables connections for millions of internet-connected mobile devices [81,82]. The main goal of AI is to make it possible for machines and systems to operate with intelligence levels that are equivalent to those of humans. Despite all intensive research into AI learning techniques, it still experiences improvements and challenges, especially in recent years due to the significant progress in modern computing and data storage technologies [81]. Nowadays, research merging AI with 5G and beyond networks has piqued a lot of interest from both sides, academia and industry [82]. Therefore, many novel studies on AI-based communication technologies have combined recently, promising higher data rates, enhanced QoS, and low implementation costs [82]. In fact, applying machine/deep learning techniques to CF wireless communication systems has attracted many advantages, such as recognizing unknown patterns, minimizing complexity, achieving better reliability and sustainability, as well as producing performance results that are equivalent to/better than traditional approaches [83,84,85].

5. Conclusions

Recently, more innovative technologies are required to pave the way for a cell-less disruptive network infrastructure due to the increasing demands for high system throughput, ultra-reliability, and near-instant connections. For that reason, the so-called CF networks have been lately proposed to overcome the problem of user performance and user location in the conventional cellular networks. This paper addressed some of the foreseen key enabling techniques for the evolution of mobile networks towards B5G/6G, such as UDNs, mMIMO, and mmwave communication bands. This review paper started by describing the main reason behind CF and its scalable UC systems. Then, three main sections followed: The first described the state-of-the-art of scalable systems under fronthaul capacity links between AP and UE constraints, as well as the AP-user association methods. The second part concentrated on addressing the full-digital and hybrid beamforming architectures at sub-6 GHz and mmWave frequencies. Finally, some of the prospective CF technologies were discussed, such as RIS, RS, LIS, UAV, and AI. Consequently, CF mMIMO can be considered as a promising enabling technology for 6G wireless communication networks since it may demonstrate impressive performances and can provide uniform connectivity to all users within the coverage area.