System Level Performance Assessment of Large-Scale Cell-Free Massive MIMO Orientations With Cooperative Beamforming

Received 6 June 2024, accepted 26 June 2024, date of publication 2 July 2024, date of current version 12 July 2024. Digital Object Identifier 10.1109/ACCESS.2024.3422349 System Level Performance Assessment of Large-Scale Cell-Free Massive MIMO Orientations With Cooperative Beamforming PANAGIOTIS K. GKONIS 1, SPYROS LAVDAS2,3, GEORGE VARDOULIAS3, PANAGIOTIS TRAKADAS 4, LAMBROS SARAKIS 1, (Member, IEEE), AND KONSTANTINOS PAPADOPOULOS1 1Department of Digital Industry Technologies, National and Kapodistrian University of Athens, 34400 Dirfies Messapies, Greece 2Department of Computer Science, Neapolis University Pafos, 8042 Paphos, Cyprus 3Department of Information Technology, The American College of Greece, 153 42 Athens, Greece 4Department of Port Management and Shipping, National and Kapodistrian University of Athens, 34400 Dirfies Messapies, Greece Corresponding author: Panagiotis K. Gkonis ([email protected]) This work was supported in part by the project ‘‘Holistic, Omnipresent, Resilient Services for Future 6G Wireless and Computing Ecosystems (HORSE)’’ funded by European Commission, (call for proposal: HORIZON-CL4-2021-DATA-01, funded under: HE | HORIZON-RIA\HORIZON-AG), under Grant 101070177. ABSTRACT The goal of the study presented in this paper is to evaluate the performance of a proposed adaptive beamforming approach in cell-free massive multiple input multiple output (CF-mMIMO) orientations. To this end, mobile stations (MSs) can be served by multiple access points (APs) simultaneously. In the same context, the performance of a dynamic physical resource block (PRB) allocation approach is evaluated as well, where the set of assigned PRBs per active MS is constantly updated according to their signal strength and the amount of interference that cause to the rest of the co-channel MSs. Performance evaluation takes place in a two-tier wireless orientation, employing a system-level simulator designed for parallel Monte Carlo simulations. According to the presented results, a significant gain in energy efficiency (EE) can be achieved for medium data rate services when comparing the cell-free (CF) resource allocation approach to single AP links (non-CF). This is made feasible via cooperative beamforming, where on one hand, the radiation figures of the APs that servea particular MS are jointly updated to ensure quality of service (QoS), and on the other hand, the effects of these updates on the other MSs are evaluated as well. Although EE for high data rate services decreases compared to the non-CF scenario, the proposed dynamic PRB allocation strategy significantly lowers the number of active radiating elements required to meet minimum QoS standards, thereby reducing both hardware and computational demands. INDEX TERMS 5G, cell-free massive MIMO, millimeter-wave transmission, adaptive beamforming. I. INTRODUCTION The full deployment of fifth-generation (5G) networks is expected to support advanced services and applications on a large-scale, such as enhanced mobile broadband (eMBB) [1], ultra reliable low-latency communications (URLLC) [2] as well as massive machine type communications (mMTC) The associate editor coordinating the review of this manuscript and approving it for publication was Tutku Karacolak . [3]. This is made feasible via the coexistence of various novel technologies both in the physical and network layer, such as millimeter wave (mmWave) transmission [4], massive multiple input multiple output (mMIMO) configurations [5] as well as non-orthogonal multiple access (NOMA) [6]. In the case of the mmWave transmission, the corresponding spectrum lies in the 30 GHz to 300 GHz range (with corresponding wavelengths from 10 mm to 1 mm). This spectrum area is of particular interest since it offers an order VOLUME 12, 2024 2024 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/ 92073 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations of magnitude more spectrum than lower bands. In addition, larger bandwidth channels are now possible (i.e., of 2 GHz, 4 GHz, 10 GHz or even 100 GHz). In the case of mMIMO, each antenna array configuration typically consists of hundreds or even thousands of radiating antenna elements. Therefore, there are more degrees of freedom in the design of adaptive beamforming techniques in densely deployed networks. Finally, in NOMA schemes multiple end users can utilize non-orthogonal resources concurrently by achieving a high spectral efficiency while allowing some degree of multiple access interference at the receivers. As the demand for even higher data rates and the support of advanced services and applications is constantly increasing, the discussions on next generation networks are already underway. In this context, sixth-generation (6G) networks are expected to integrate a vast number of heterogeneous technologies and support dynamic network reconfiguration. In 6G communication systems, the use of higher frequency bands (mmWave, THz) and massive antenna arrays will enable high-accuracy and high-resolution sensing, paving the way towards integrated sensing and communication (ISAC) technologies [7],[8],[9]. To this end, the entire network can act as a sensor obtaining various metrics, such as range, velocity, and angle information from the radio signals. Hence, accuracy localization, gesture capturing and activity recognition, passive object detection and tracking, as well as imaging and environment reconstruction can be supported. Indicative use cases include holographic communicationbased services, unmanned mobility, etc. [10],[11]. In this new era of 6G networks, it is expected that the traditional base station (BS) – mobile station (MS) link model will be replaced by a large number of low power access points (APs) over small geographical areas [12] (ultra dense networks - UDNs). In the same context, relay nodes (RNs) that can amplify and retransmit the received signal will also be an indispensable part of 6G networks, especially for cell-edge spatial coverage [13]. The concept of cell-free massive MIMO (CF-mMIMO) orientations has recently emerged as a new approach that can provide on-demand coverage in large geographical areas [14], [15]. In this context, mMIMO configurations are deployed per AP to support a multitude of active MSs via highly directional beams (an MS can be served by multiple APs). CF-mMIMO systems comprise of many distributed, lowcost, and low power access point antennas, connected to a network controller. The complexity and signalling at each AP can be finite even when the number of MSs approaches infinity [16]. This is made feasible via appropriate clustering and power control algorithms that enable scalability. CF-mMIMO configurations are expected to enhance the support of highly demanding mobility patterns, as traffic load can be balanced among the APs and the handover signalling burden can be reduced. Moreover, in realistic wireless orientations signal quality and cell-edge coverage can be improved, due to the multitude of available channels from the various APs. In the same context, appropriate machine learning (ML) approaches can be also applied that can reduce the computational complexity of mMIMO deployments (e.g., optimum beamforming configuration per AP, transmission vector matrix formulation, power allocation, user grouping when mMIMO technology is combined with NOMA) [17],[18]. Despite growing scientific interest in CF-mMIMO systems in recent years, as highlighted by key studies outlined in the next subsection, conducting a comprehensive performance evaluation is crucial to uncover any potential limitations and deployment challenges. Therefore, the goal of this work is to evaluate the performance of CF-mMIMO orientations with respect to conventional centralized mMIMO approaches (non-CF) under the prism of a proposed dynamic physical resource block (PRB) allocation approach and cooperative adaptive beamforming. To this end, various key performance indicators (KPIs) have been considered, such as energy and spectral efficiency (EE, SE), blocking probability (BP), and the number of radiating elements (REs) in the topology. A. INDICATIVE RELATED WORKS Over the last decade, various research activities have focused on the performance evaluation of CF-mMIMO orientations. In [19], the main challenges, solutions, and opportunities for user-centric CF-mMIMO networks are presented. The work in [20] considers practical measurements of CF-mMIMO systems. In this context, three different co-located and widely distributed radio unit (RU) configurations have been analyzed in terms of time-variant delay-spread, Doppler spread, path-loss, and the correlation of the local scattering function over space. Results indicate that various performance metrics can be improved, such as signal-to-interference-plus-noise ratio (SINR). Moreover, as the authors point out, CF systems are less susceptible to channel aging than distributed or conventional mMIMO systems. The work in [21] deals with more flexible architectures that are based on wireless fronthaul operating at a higher band compared to the access links. Results indicate that these architectures can achieve comparable data rates to those obtained with optical fiberbased fronthaul. Hence, installation complexity and related costs can be reduced. In [22], the performance of CF-mMIMO systems is examined in an industrial indoor scenario to assist inspection robots. To this end, AP selection, power control and scalability issues are examined. In [23], the authors investigate isolated and cumulative failures on the hardware of CFmMIMO networks, concluding that system performance degradation can be significantly increased as the MS density increases. Therefore, appropriate protection schemes are required that can mitigate failure effects. In [24], the performance of asynchronous CF-mMIMO systems with rate-splitting has been evaluated. In this context, closed-form expressions have been derived in the presence of channel estimation errors. Results indicate that asynchronous reception can have a severe impact on the pilot orthogonality 92074 VOLUME 12, 2024 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations and coherent data transmission. Hence, suitable precoding schemes have been designed to maximize the SE. In [25], a new CF architecture is proposed for virtualized cloud radio access network (V-CRANs). In this context, end to end power consumption is minimized, by optimally selecting APs and distributed units (DUs) per active MS. In [26], the resource allocation for a CF-mMIMO enabled URLLC downlink system is studied, and closed-form solutions are derived for the lower bound data rate based on imperfect channel state information (CSI). The derived non-convex problem is transformed to a discrete set of subproblems, that are iteratively solved via a proposed low complexity approach. In [27], the concept of hybrid beamforming (HBF) is considered, where fewer radio frequency (RF) chains are employed compared to the number of active antenna elements in the topology. Hence, signalling burden and computational complexity of mMIMO configurations can be reduced. To achieve that, the subset of antennas that are associated with a specific RF chain can adjust their phases in an analogue mode. Thus, when considering multiple APs equipped with HBF, for each possible MS, a set of candidate RF chains that have the highest received signal power is defined, without considering the specific APs these RF chains are associated with. According to the presented results, the proposed approach can significantly improve SE and reduce the complexity of centralized beamforming. In [28], data-assisted channel estimation has been considered. In this context, the analytical achievable uplink SE for minimum mean-squared error (MMSE) combining has been derived. In [29], a multi-CPU CF-mMIMO orientation is considered, where the effect of quantization noise caused by capacity-limited backhaul links is investigated. Also, a new MMSE beamformer and clustering methods have been developed, where the joint resource optimization problem is solved. In [30] the authors have derived closed-form expressions for the lower-bound achievable rate and SE under maximum ratio combining (MRC) and imperfect CSI, considering a CF-mMIMO internet of things (IoT) network. Moreover, a low-complexity power control approach is presented, based on local CSI. As the authors point out, the addition of more transmit antennas can enhance the achievable rate but may degrade the achievable SE due to the increased pilot overhead. In [31], a two-layer large scale fading precoding method is proposed in a downlink CF-mMIMO system. In this context, in the first layer the distributed APs are responsible for designing distributed precoding and power control coefficients for the MSs. In the second layer, the CPUs perform zero forcing processing to mitigate the interference caused by pilot contamination. Finally, the work in [32] considers hardware impairments in an uplink CF-mMIMO system. In this context, closed-form expressions of SE have been derived, which prove that the effect of hardware impairments can be mitigated in the case of MSs with multiple antennas. B. CONTRIBUTIONS In all the aforementioned studies, either limited network topologies have been considered (i.e. single-cell scenarios) or a limited number of active MSs. In this work, a two-tier topology (19 active cells) is taken into consideration, with three APs per cell. An MS can be served either by one AP that is selected according to total losses minimization (centralized provision of service, non-CF) or in a CF mode. In the same context, a dynamic PRB allocation scheme is also considered, that is based on a continuous resource reconfiguration according to channel conditions and overall interference. Therefore, the main contributions of our work can be summarized as follows: •Performance evaluation of CF-mMIMO orientations takes place in large-scale wireless environments. For this purpose, a system level simulator has been developed that can execute independent Monte Carlo (MC) simulations in parallel. In this context, various system orientations are generated (each one corresponding to a different MS distribution and channel generation of the corresponding PRBs) where dynamic PRB assignment and power allocation procedures take place. At each MC snapshot various KPIs are extracted, such as EE, SE, BP and number of REs. •A PRB allocation approach is presented and evaluated, that can further improve performance metrics. This approach is based on a dynamic update of the allocated PRBs, according to channel conditions and interference levels. As it will also be explained in Section IV, PRB assignment is based on the SINR per MS and PRB as well as on the amount of interference that this MS causes to the rest of co-channel MSs. •Transmission in mmWave frequency band has been also considered (i.e., 28 GHz), incorporating recent 3GPP channel modelling guidelines [33]. To the best of the authors’ knowledge, this is the first scientific attempt where realistic radiation patterns are used for the performance evaluation of CF-mMIMO orientations. The rest of this paper is organized as follows: In Section II, the 5G mmWave multicellular mMIMO orientation is presented (channel modelling and transceiver procedures), while in Section III the antenna design aspects per AP are highlighted. In Section IV, the proposed resource allocation and adaptive beamforming approaches are analyzed, for both considered orientations (centralized provision of service as well as CF transmission mode). Results are presented in Section V, where the previously mentioned KPIs have been considered. Finally, concluding remarks and proposals for future work are provided in Section VI. The following notation is used in the paper. An italic variable aor Adenotes a scalar, whereas boldface lowercase and uppercase variables aand Adenote vectors and matrices, respectively (the (i,j) element of Ais denoted as A(i,j)). Moreover, ||a||Fstands for the Frobenius norm of vector a. A calligraphic variable Adenotes a set of |A|elements (A VOLUME 12, 2024 92075 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations TABLE 1. List of acronyms. is the complementary set), while AHdenotes the conjugate transpose of matrix A. II. 5G MILLIMETER WAVE MASSIVE MIMO ORIENTATION We consider the downlink of a 5G mMIMO multicellular orientation with BBSs, as shown in Fig. 1. To this end, there are three APs per BS that can provide sufficient signal coverage. The total available bandwidth is denoted as Wand is divided to a discrete number of PRBs [34]. MSs enter the network sequentially following a predefined spatial distribution. In CF-mMIMO mode, PRBs may be allocated from adjacent APs as well. Throughout the rest of this paper, the term adjacent APs will indicate the set of APs that belong to geographically adjacent BSs (i.e., first tier BSs with respect to the specific AP) and their radiation patterns might have an impact on co-channel interference (CCI). It should be emphasized at this point that since two operational modes have been considered (non-CF and CF), the BS concept with three APs in its area of service is adopted for the non-CF case. Each MS that enters the network is assumed to request a specific type of service that is translated to an equivalent number of assigned PRBs, as it will be later described in Section IV. In each AP there are 441 REs, that are deployed in an orthogonal configuration (21 arrays per dimension) able to formulate a multitude of radiation diagrams that can be steered across the AP’s serving area, as it will be described in in the following section. In the non-CF mMIMO operational mode, blocking occurs if there are no available PRBs in the serving BS of the candidate MS. On the contrary, in the CFmMIMO case, this happens either if there are no available PRBs in the adjacent APs, or their potential allocation would result in excessive downlink transmission power. In the following two subsections, channel modelling issues along with transceiver procedures are described. In particular, in Subsection A the main 3GPP guidelines for mmWave transmission are summarized, while in Subsection B signal transmission and reception over all APs are highlighted. A. CHANNEL MODELLING Considering a non-line of sight (NLOS) environment, the channel impulse response for an arbitrary pair of 92076 VOLUME 12, 2024 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations FIGURE 1. Deployed mMIMO multicellular orientation. transmitting-receiving antennas (denoted as qand u, respectively, 1≤q≤Nt, 1≤u≤Nr) is given by [33]: HNLOS u,q(τ, t)= 2 X n=1 3 X i=1X m∈Ri HNLOS u,q,n,m(t)δt−τn,i + N X n=3 HNLOS u,q,n(t)δ(t−τn)(1) where τn,i,τnrepresent the delay of the ith subcluster of the nth cluster and the delay of the nth cluster, respectively, and δ stands for the Kronecker delta. It is important to note that for the first two dominant clusters three additional sub-clusters are defined. The subpaths per sub-cluster are stored in the set Ri. Moreover, HNLOS u,q,n,mand HNLOS u,q,nare given by: HNLOS u,q,n,m=rPn MFT rx,n,m2n,mFtx,n,me j2π(ˆrT rx,n,m·drx,u) λo ×e j2π(ˆrT tx,n,m·dtx,q) λo(2) HNLOS u,q,n= M X m=1 HNLOS u,q,n,m(3) where: Frx,n,m=Frx,u,θ θn,m,ZOA, φn,m,AOA Frx,u,φ θn,m,ZOA, φn,m,AOA(4) Ftx,n,m=Ftx,q,θ θn,m,ZOD, φn,m,AOD Ftx,q,φ θn,m,ZOD, φn,m,AOD(5) 2n,m=  exp j8θθ n,mqκ−1 n,mexp j8θφ n,m qκ−1 n,mexp j8φθ n,mexp j8φφ n,m (6) In the above set of equations, θn,m,ZoD and θn,m,ZoA represent the angles of departure (AoD) and arrival (AoA), respectively, in the vertical plane for the mth subpath (1 ≤ m≤M) of the nth cluster (1 ≤n≤N). The corresponding parameters for the horizontal plane are φn,m,AoD and φn,m,AoA, respectively. Moreover, Pnis the power of the nth cluster, the set n8θθ n,m, 8θφ n,m, 8φθ n,m, 8φφ n,mocorresponds to initial phases uniformly distributed in (-π, π) while κn,mparameter is the generated cross polarization power ratio (XPR) for each ray mof cluster n. In addition, ˆrrx,n,mis the spherical unit vector with azimuth arrival angle φn,m,AOA and elevation arrival angle θn,m,ZOA, while ˆrtx,n,mis the spherical unit vector with azimuth departure angle φn,m,AOD and elevation departure angle θn,m,ZOD. Moreover, Ftx /Frx represent the field pattern of transmitting/receiving antenna element q/u, respectively, drx,uis the location vector of receive antenna element uand dtx,qis the location vector of transmit antenna element q. Finally, λois the carrier wavelength. Note that in cases of LOS environments 2n,mis a diagonal matrix with elements +1 and −1 appearing on the diagonal. B. TRANSCEIVER PROCEDURES The Nt×1 transmitted signal in the CF-mMIMO orientation can be expressed as: xk(t)=X s∈Uk √pk,T(k,s),stk,T(k,s),sXk,sej2πfst,0<t<Ts (7) where the set Ukindicates the assigned PRBs to the kth MS (1 ≤k≤K). Moreover, T(k,s) is the corresponding entry of 2D matrix Tthat indicates the serving AP of the kth MS with respect to the sth PRB, pk,T(k,s),sis the corresponding downlink transmission power and tk,T(k,s),sis the Nt×1 transmission weight vector. It should be emphasized at this point that diversity combining transmission mode is assumed. Moreover, Xk,sis the transmission symbol over the sth PRB selected from a predefined signal constellation (i.e., QPSK, 16QAM, 64QAM), fsis the frequency of the sth PRB and Tsis the symbol duration. In reception mode, the corresponding Nr×1 signal after matched filtering over the sth PRB can be expressed as: Yk,s=rpk,T(k,s),s TLk,T(k′,s)rk,T(k,s),sHk,T(k,s),stk,T(k,s),sXk,s + K X k′=k,s∈Uk′rpk′,T(k′,s),s TLk,T(k′,s)rk,T(k,s),sHk,T(k′,s),s ×tk′,T(k′,s),sXk′,s+rk,T(k,s),snk,s(8) The first term is the desired MS signal, while the second/third term denote CCI and noise, respectively. In the same context, Hk,T(k,s),sis the Nr×Ntchannel matrix of the kth MS with respect to the sth PRB and rk,T(k,s),sis the 1×NrMRC multiplying vector. Finally, TLk,T(k,s)represents the total losses (including shadowing and attenuation due to radiation patterns). The SINR per MS and PRB in CF allocation (CFA) mode averaged over a frame duration can be expressed as (assuming that E(Xk,sXk′,s)=δk,k′, where E(x) is the mean value of x): (9), as shown at the bottom of the next page, where Iois the thermal noise level. VOLUME 12, 2024 92077 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations FIGURE 2. Two square subarray beamforming configurations: 3 ×3 (left) and 11 ×11 (right) with corresponding azimuth radiation patterns for 0◦, 30◦, and -30◦spatial coverage (red outlines indicate positive gain in the left panel, doubling the values in gain in the right panel). From (9), it follows that the ratio of the desired signal power of a particular MS to the total amount of interference that causes to the of rest co-channel MSs (also referred as jamming) can be expressed as: (10), shown at the bottom of the next page. Assuming that each MS requests RkMbps from the serving APs, then SE and EE can be defined as follows: SE = K P k=1 Rk W(11) EE = K P k=1 Rk K P k=1P s∈Uk pk,T(k,s),s (12) III. ANTENNA DESIGN The current work employs a cost-effective antenna array configuration to minimize hardware complexity. Specifically, the suggested mmWave antenna setup features a 21×21 array of rounded crossed bowtie REs, as illustrated in Fig. 2. To achieve a unidirectional radiation pattern with minimal energy wastage through the back lobe, two ground planes are positioned beneath each RE at distances of λo/4 and λo/2, respectively, with reference to each rounded bowtie antenna [35]. Notably, the crossed rounded bowtie antennas, serving as exciters of the reflector, are rotated at ±45◦ to enhance the formulation of an adaptive dual-polarized radiation pattern which is crucial for cellular network communications [36]. In particular, the former rotation of the exciters, coming with a phase difference of 90◦, facilitates the creation of circular polarization, achieving high XPR values more than 20 dB for the desired spatial coverage. This occurs because right-hand circular polarization (RHCP), which is the current main polarization, and left-hand circular polarization (LHCP) are naturally well-isolated. High XPR values, in concert with circular polarization, reduce not only the sensitivity to the orientation of the receiving antenna—which is beneficial in mobile communications where antenna orientations can significantly vary—but interference levels as well, and at the same time improve signal integrity. To this end, such an antenna scheme leads to improved overall system performance. It is essential to mention at this point that the detailed electromagnetic characteristics of this array configuration are thoroughly covered in our recent publications [37],[38] (radiation diagrams and technical details about the REs have been included as well). The analysis employs the method of moments (MoM) [39] in a 3D computational model [40], accounting for the deleterious effects of mutual coupling among REs. The adoption of different phases for each RE, coupled with activating either the entire array or a subarray, facilitates the deployment of efficient beamforming techniques. This enhances the manipulation of the radiation pattern, allowing changes in both desired directions (azimuth or elevation level) and gain [39]. Fig. 2illustrates an example of the applied beamforming configurations, demonstrating 2 out of 51 different possible configurations, including square and rectangular arrays [38]. SINRk,s= pk,T(k,s),s TLk,T(k,s),rk,sHk,T(k,s),stk,T(k,s),s 2 P k′=k,s∈Uk′ pk′,T(k′,s),s TLk,T(k′,s)rk,sHk,T(k′,s),stk′,T(k′,s),s 2+rH k,T(k,s),srk,T(k,s),sIo (9) 92078 VOLUME 12, 2024 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations The choice of the right array configuration takes into consideration three key parameters: the number of activated REs, the desired quality of service (QoS), and the required spatial coverage. In this context, six representative scenarios showcasing the mutual dependence of these parameters are presented in Fig. 2. In particular, the left panel demonstrates three different radiation patterns in azimuth where all of them are derived from the same 3 ×3 square subarray. As it has already been mentioned, the appropriate applied phase difference among the REs leads to an efficient beamforming configuration, namely achieving a spatial coverage between +30◦and −30◦. In the same context, the right panel of Fig. 2 illustrates the same spatial coverage by employing a larger square subarray of 11 ×11 REs. However, the developed radiation patterns are not only significantly more directional but also offer greater spatial gain. As a result, this setup is ideally suited for cellular network applications that require high service standards. Therefore, by adapting to various QoS levels, the algorithm can effectively choose the optimal subarray configuration in terms of power consumption, gain efficiency, and spatial coverage. Specifically, the underlying principle of the employed algorithm for activating the appropriate radiating subarray is to effectively provide the required services while minimizing energy consumption. By dynamically adjusting the active subarrays based on real-time demand, the algorithm ensures optimal performance and energy efficiency, thereby enhancing the overall performance of the communication channel. It’s important to highlight that changes in the configuration can be made using affordable pin diodes to activate the necessary REs. Additionally, integrating ML techniques could further enhance these configurations [38]. IV. COOPERATIVE ADAPTIVE BEAMFORMING IN CELL-FREE MASSIVE MIMO ORIENTATIONS A. ALGORITHM DESCRIPTION The proposed resource allocation approach in CF-mMIMO orientations is described in Algorithm 1. At the first step, all active BSs are initialized with the same number of PRBs (i.e., the set Sbindicates the available PRBs in the bth BS, 1 ≤ b≤B). In the same context, the REs per AP are initialized as well (i.e., the set T Eb,lindicates the transmitting elements in the lth AP of the bth BS, 1 ≤l≤3, while all potential beamforming configurations are stored in the set BCb,l). There are two possible modes during PRB allocation: In the first case, which will be denoted as BS allocation (BSA), PRB assignment is based on the active PRBs of the specific BS. In the second case, denoted as CFA allocation (CFA), all APs of the adjacent BSs participate in PRB allocation. In the same context, a dynamic PRB allocation approach is also examined, that is based on PRB switching according to channel conditions and overall interference levels. In this approach, for every new MS that tries to access the network, all PRBs of adjacent APs are considered as available, even the occupied ones. The adjacent APs with respect to the bth BS are stored in the set Jb. If channel gain (stored in matrix CG) is maximized for a particular PRB that has already been assigned to another MS, then PRB switching might take place: In this case, it is examined if in the new state, where the potential new MS is allocated with the PRB that maximizes its channel gain and the other MS is allocated with the next available PRB, the product of SINR and SJR is maximized. In all cases, the indexes of the sorted channel gains are stored in the set Uk, which indicates the allocated PRBs to the kth MS, as previously mentioned. As described in Algorithm 1, the kth MS tries to enter the network in the serving area of the bth BS requesting Rk Mbps with a specific modulation order (MOk) per PRB. This request is translated into an equivalent number of PRBs with the help of function define_PRBs. In step 4, control flag cf indicates either the BSA (cf=0) or the CFA mode (cf=1). In both cases, the Pequivalent channel gains are sorted, and the results are stored in the set Uk(or Uk,opt ). In Step 6, considering the dynamic PRB allocation approach (df=1), if the selected PRB is already assigned to another MS (i.e., the k´th MS), then a temporal allocation is performed according to which this PRB is assigned to the new potential MS and the k´th MS is assigned with the next available PRB. In this new state, if the product of the updated SINR and SJR values for both MSs is increased compared to the previous state, then PRB allocation as previously described takes place. Otherwise, the new potential MS is assigned with another PRB that has already been calculated in Step 4. In both cases, beamforming and power assignment calculations take place (i.e., x(λm(A)) is the eigenvector corresponding to the maximum eigenvalue of matrix A). In the same context, it is essential to examine if power outage in at least one of the active MSs takes place. In this case, additional beamforming configurations are examined (i.e., the set MSbdenotes the active MSs in the bth BS). To this end, the term P s∈Uk′ pk′,s≤pmindicates total downlink transmission power from the k′th MS, which is upper limited by pm. SJRk,s= tH k,T(k,s),sHH k,T(k,s),sHk,T(k,s),stH k,T(k,s),s tH k,T(k,s),s P k′=k,s∈Uk′ HH k′,T(k,s),sHk′,T(k,s),sTLk,T(k,s) TLk′,T(k,s)+IoTLk,T(k,s)!tk,T(k,s),s (10) VOLUME 12, 2024 92079 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations Algorithm 1 The Proposed Cooperative Adaptive Beamforming and Resource Allocation Approach in Cell-Free Massive MIMO Orientations 1: Sb←{1:NPRB},initialize T Eb,l,1≤l≤3 2: k←k+1. The kth MS enters the network in the bth BS requesting RkMbps with a specific modulation order (MOk) per PRB 3: P←define_PRBs(Rk,MOk) 4: if(cf=0) (BSA mode) CGSb←  HH k,Sb   2 F/TLk,Sb,∼,Uk←sort(CGSb,P) else (CFA mode) CGSJb←  HH k,SJb   2 F/TLk,SJb ∼,Uk←sort(CGSJb,P) end if 5: if (df=1) (the proposed dynamic PRB approach) CGSJb∪SJb←    HH k,SJb∪SJb    2 F /TLk,SJb∪SJb ∼,Uk,opt ←sort(CGSJb∪SJb ,P) end if 6: for s∈Uk(or sopt ∈Uk,opt , if df=1) if sopt /∈Sb(which means that df=1 and the selected PRB is occupied by the k′th MS) s1←sopt ,s2←Uk′(P+1),s3←s,s4←sopt if SINRk,s1·SJRk,s1·SINRk′,s2·SJRk′,s2> SINRk,s3·SJRk,s3·SINRk′,s4·SJRk′,s4 Uk←Uk∪sopt ,Uk′←Uk′−sopt end if end if tk,T(k,s),s←xλmHH k,T(k,s),sHk,T(k,s),s,pk,T(k,s),s←SNRth·Io·TLk,T(k,s) ∥Hk,T(k,s),stk,T(k,s),s∥2 F update pk′,T(k′,s),s,1≤k′≤K,s∈Uk′or sopt ∈Uk′,opt end for 7: if P s∈Uk′ pk′,T(k′,s),s≤pm, 1≤k′≤Kthen rf ←0 else for every b∈Jb while {BCb,l>0and (rf >0) T Eb,l←argmin Q′∈BCb,lQ′,BCb,l←BCb,l−T Eb,l update Hk′,T(k′,s),s,tk′,T(k,s),s,pk′,T(k′,s),sfor every k′∈MSb,s∈Uk′ if P s∈Uk′ pk′,T(k′,s),s≥pmfor an arbitrary k′∈MSb, then rf ←1, restore Hk′,T(k′,s),s,tk′,T(k′,s),s,pk′,T(k′,s),sand BCb,l end if end while end for end if 8: ifrf=0, then Sb←Sb−Uk,MSb←MSb∪k Set Pt,b←P k′∈MSb,s∈Uk′ pk′,T(k′,s),s(1≤b≤B) if Pt,b>Pmor |Sb|<P(cf=0) or SJb<P(cf=1) then MC simulation terminates else go to Step 2 end if end if It should be emphasized at this point that a joint beamforming approach among the active APs is considered. In this case, for each MS in CFA mode, all beamforming configurations of the APs that contribute to PRB allocation are jointly updated, along with the corresponding APs. MS rejection will take place only in the case where there is not any available configuration to serve all active MSs. In the opposite case, all related sets are updated (Step 8) and reject flag (rf) is set to zero. FIGURE 3. Two propagation scenarios in terms of QoS regarding heavy activity of online streaming and light activity of texting, left and right panel, respectively. The corresponding similar radiation patterns of both scenarios are illustrated on the upper left and right part of each panel. MC simulation comes to an end either if power outage occurs in an AP, or if there are no available PRBs for a new potential MS to arrive. In the BSA allocation mode, as previously mentioned, this happens if there are no available PRBs in the bth BS. In the CFA mode, PRB availability considers the adjacent APs of the candidate MS. B. BEAMFORMING PROCEDURES In this subsection, the proposed beamforming approach will be further explained with the help of Fig. 3. It should be emphasized at this point that the REs per mMIMO configuration gradually increase starting from the activation of the central element (i.e., 1 ×1 configuration) until the desired QoS is met for all active MSs of the considered AP. To this end, and with respect to Fig. 3, two traffic scenarios have been considered: In the first scenario, MSs are assumed to heavily engage in online streaming activities, which are characterized as bandwidth and energy-hungry applications. To meet this demand, a subarray consisting of 21×3 elements is activated, offering a high gain of 22.8dBi as shown in Fig. 3, ensuring seamless transmission and reception of highbandwidth content. In contrast, in the second scenario where MSs engage in less bandwidth-intensive texting activities, the requirement for high-quality service is remarkably reduced. Here, a smaller subarray configuration of 3×3 elements will suffice, featuring a lower gain of 14.6dBi, as shown in Fig. 3. Note that both of the former scenarios require identical spatial coverage as MSs are distributed in the same way. Consequently, both antenna configurations form similar radiation patterns, as shown in Fig.3. The need for similarity in radiation patterns, as previously highlighted, constitutes one of the most critical parameters of the current work. Specifically, while the radiation patterns exhibit similarity in terms of directivity, there is a significant difference in terms of gain. This is clearly illustrated 92080 VOLUME 12, 2024 P. K. Gkonis et al.: System Level Performance Assessment of Large-Scale CF-mMIMO Orientations FIGURE 4. Antenna array geometry with potential activated configurations highlighted in the right panel using corresponding colors. The right panel columns describe the number of activated REs per row and per column, the gain of each array configuration, the total number of REs, and the maximum/minimum azimuth beamwidth of each configuration. in Fig. 4, which presents various indicative antenna configurations along with their maximum and minimum obtained azimuth beamwidth and corresponding gain (dBi). Notably, the activation of a single RE can form a beamwidth of 106◦ with a gain of 7.5 dBi. In contrast, the activation of a 21 × 2 subarray achieves a comparable beamwidth of 86◦but with a substantially higher gain of 21 dBi. Although similar spatial coverage can be achieved with these two different antenna array configurations, the required services will ultimately dictate the most appropriate array scheme. This adaptive deployment of antenna array underscores the system’s ability to tailor resource allocation not only to the specific MS demands but also to the distinct MS locations, thereby optimizing energy efficiency. C. PRACTICAL CONSIDERATIONS AND COMPLEXITY CALCULATIONS In Fig. 5, typical radiation patterns are depicted in the first tier BSs of the central BS (labelled as 1), as in this case CCI is maximized. The red outlines in each pattern indicate the pointing direction of the specific beam. Considering an arbitrary AP in the first BS (i.e., the one corresponding to the pointing direction of the vertical arrow), then the set of adjacent APs takes into consideration only the APs of the neighboring BSs whose radiation patterns might have an impact on CCI (with respect to Fig. 5, these include nine APs that belong to BSs labelled as 2,3,4,5,6 and 7). Therefore, all SINR and SJR calculations consider only a very small subset of the entire APs, that further reduces the computational complexity of the presented calculations. In realistic CF-mMIMO deployments, if the aforementioned BSs are connected to the same CPU, then latency is minimized for the MSs in the area of the first BS, since all KPI-related calculations (i.e., channel measurements, SINR and SJR, transmit vector matrices, etc.) are executed locally. However, even in the case where adjacent APs belong to different CPUs, virtual clusters can be formulated. For example, with respect to Fig. 1, the virtual cluster for the specific AP of the first BS includes nine adjacent APs, as previously menFIGURE 5. Radiation patterns in the considered topology (first tier worst case scenario). FIGURE 6. Multicellular orientation with non-uniform traffic. tioned. The related parameters for each cluster can be locally stored in the corresponding CPUs (i.e., all CPUs that are associated with one or more BSs of the specific cluster) and be updated according to the coherence time of the channel. Furthermore, by employing cooperative adaptive beamforming, as previously mentioned, that takes into account all APs serving a specific MS and considering the interference (jamming) to other co-channel MSs, the impact of pilot contamination can be minimized. This is also depicted in Fig. 5, since as it becomes apparent there are signals from adjacent APs (i.e., the one from the fifth BS) that are received from the backlobe of the radiation pattern under consideration. As a final remark on this issue, it should be noted that the generated beams in Fig. 5cover a wide angular space per AP, to depict a worst-case scenario in terms of interference. The effects of cooperative beamforming in the topology are more significant when highly directive beams are generated, since in this case the APs per virtual cluster can be minimized VOLUME 12, 2024 92081