Evaluation of User-Centric Cell-Free Massive Multiple-Input Multiple-Output Networks Considering Realistic Channels and Frontend Nonlinear Distortion

Abstract

Future 6G networks are expected to utilize Massive Multiple-Input Multiple-Output (M-MIMO) and follow a user-centric cell-free (UCCF) architecture. In a UCCF M-MIMO network, the user can be potentially served by multiple surrounding Radio Units (RUs) and Distributed Units (DUs) controlled and coordinated by a single virtualized Centralized Unit (CU). Moreover, in an M-MIMO network, each transmit frontend is equipped with a Power Amplifier (PA), typically with nonlinear characteristics, that can have a significant impact on the throughput achieved by network users. This work evaluates a UCCF M-MIMO network within an advanced system-level simulator considering multicarrier transmission, using Orthogonal Frequency-Division Multiplexing (OFDM), realistic signal-processing steps, e.g., per resource block scheduling, and a nonlinear radio frontend. Moreover, both idealistic independent and identically distributed (i.i.d.) Rayleigh and 3D ray-tracing-based radio channels are evaluated. The results show that under the realistic radio channel, the novel user-centric network architecture can lead to an almost uniform distribution of user throughput and improve the rate of the users characterized by the worst radio conditions by over 3 times in comparison to a classical, network-centric design. At the same time, the nonlinear characteristics of the PA can cause significant degradation of the UCCF M-MIMO network’s performance when operating close to its saturation power.

1. Introduction

To meet the growing demands of mobile network users, it is not enough to utilize larger bandwidths or densify networks. In addition, advanced transmission techniques that increase spectral efficiency must be used. For currently deployed 5G networks and future 6G networks, such a technique is Massive Multiple-Input-Multiple-Output (M-MIMO) [1], which involves the use of multi-element antenna arrays that allow for the creation of narrow beams of radio signals directed toward individual users. This enables spatial multiplexing of users sharing the same time-frequency resources. Fifth-generation systems employing M-MIMO typically assume that the connection of one user is provided by a single base station (BS), which is referred to as a network-centric architecture. In such an architecture, radio signal coverage is uneven, with users closer to the BS receiving a much stronger signal than those farther away. As a result of this uneven Received Signal Strength (RSS) distribution, there is a significant disparity in throughput between users near the BS and those at the cell edge [2]. Therefore, for 6G systems, a novel, user-centric cell-free architecture combined with M-MIMO (UCCF M-MIMO) is being considered [3]. In a UCCF M-MIMO network, the concept of cells disappears, and following the so-called canonical definition in [4], the user can be served by all surrounding base stations. This effectively places the user in the center of a virtual cell, greatly reducing the throughput disparities among different users. The deployment of UCCF M-MIMO is possible using the open Radio Access Network (RAN) architecture and related 7.2 split [5]. In detail, a UCCF M-MIMO network (or more specifically its part) based on open RAN architecture is constituted by a single virtualized Central Unit (CU), virtualized Distributed Unit (DU), and multiple physical Radio Units (RUs). The virtualized CU–DU coordinates the RUs and is jointly responsible for user scheduling and high physical layer functions, e.g., calculation of precoding weights and modulation and coding scheme (MCS) selection. The physical RUs distributed over the cell area perform low physical layer functions and Radio Frequency (RF) processing of the signal, e.g., modulation, FFT, and application of precoder weights. However, the canonical implementation of UCCF M-MIMO assumes that every user is being served by all RUs. This approach would require enormous computational resources, e.g., to estimate the radio channel coefficients between all RUs and all UEs, compute large matrices of precoding weights, and perform resource scheduling. As in practice, both the virtualized CU–DU and each of the physical RUs have limited computational resources, it is of high importance to ensure reasonable scaling of a UCCF M-MIMO network. Moreover, some RUs that are placed far away from the UE would provide minor performance benefits compared to the required signaling overhead and demand for computational resources. From this perspective, it is of high importance to limit the number of RUs that are serving a single UE to balance performance gains and the growing computational and signaling overhead. In UCCF M-MIMO, this is achieved through the formulation of so-called serving clusters [6]. Serving clusters are dynamically formulated by the centralized CU–DU using various algorithms, e.g., those based on RSS or advanced Machine Learning (ML) solutions, which are aimed at meeting different optimization goals, like load balancing, energy efficiency, or throughput maximization. The architecture of UCCF M-MIMO is summarized in Figure 1.

The user-centric cell-free M-MIMO network is an emerging topic regarding 6G, and numerous works focusing on simulation studies of such systems have already been published. However, most of them, even those coauthored by highly cited experts in the M-MIMO field like [4,7,8,9,10], utilize relatively simple system models. In most cases, these models involve single-carrier, narrowband transmission. In contrast, practical implementations of 5G/6G mobile networks utilize multi-tone modulations, typically Orthogonal Frequency-Division Multiple Access (OFDMA). Moreover, the time-frequency radio resources are often scheduled to users in 5G/6G networks as so-called resource blocks (RBs), which are also typically not considered in recent works. In addition, user throughput in practical 5G/6G communication systems depends on the selected modulation and coding scheme (MCS), not the Shannon rate, as claimed in most recent works, e.g., [11]. Another point is the utilization of simple statistical models of radio channels that neglect the spatial correlations between users, which are crucial for M-MIMO. For example, the independent and identically distributed Rayleigh channel (which, in our work, is shown to be inadequate for simulations of M-MIMO systems), e.g., in [10]. Finally, most current works on both network-centric and UCCF M-MIMO networks neglect the impact of the typically nonlinear Power Amplifier (PA) on users’ throughputs. However, it has been shown that in the worst-case scenario of Line-of-Sight (LoS) communication, the nonlinear distortion is steered toward scheduled users with the same precoding gain as the desired signal [12]. Also, when multiple users are scheduled, spatial intermodulations can occur, further affecting network performance [13]. Only the authors of [14] considered nonlinear distortion in the UCCF M-MIMO network but evaluated it under the Rayleigh channel, which we show is not appropriate for such an analysis. Therefore, there is a need to investigate M-MIMO systems with a user-centric architecture in an environment closely resembling a real network, including the use of OFDMA and a precise radio channel model based on 3D ray tracing. Furthermore, the multi-layer nature of future 6G systems, consisting of various functional blocks responsible for resource allocation, precoding, and the selection of modulation and coding schemes, should be considered. Finally, studies on the UCCF M-MIMO network should take into account the possible nonlinear distortion generated by Power Amplifiers (PAs) installed at M-MIMO RUs.

Compared to previous works, our contribution involves the proposition of an advanced simulation environment of an OFDMA-based UCCF M-MIMO network. This environment utilizes a realistic 3D ray-tracing radio channel model, radio resource allocation performed by a dedicated scheduler entity, throughput calculation based on the MCS, and, most importantly, a realistic model of a Power Amplifier (PA) that relies on the embedded link level to obtain a realistic impact of nonlinear distortion on the user throughput. This paper aims to provide the research community with an advanced system model that can be used to develop and test algorithms within an environment that is far closer to the real world compared to most other proposed system models [4,7,8,9,10]. The solution is described using mathematical formulas and algorithms for easy implementation by other researchers. Moreover, using the proposed advanced computer simulator, we examine the benefits of implementing a UCCF M-MIMO network architecture compared to the traditional network-centric architecture. This comparison is performed under an idealistic independent and identically distributed (i.i.d.) Rayleigh channel model and a realistic one obtained using ray-tracing software. Last but not least, we examine the UCCF M-MIMO network when utilizing nonlinear PAs. The simulation studies show that the results obtained under simplified models, e.g., under a Rayleigh channel or without nonlinear distortion, overestimate the achievable throughput compared to realistic 3D ray-tracing-based simulations. This is consistent with our observations during our previous studies [15], i.e., the antenna selection algorithm optimized under a simplified system model does not perform well under the more realistic one. In the following sections of this work, Section 2 presents the system model. The modeling of nonlinear distortion is described in Section 3. Section 4 provides a detailed description of the proposed simulation environment. The results of computer simulation studies are presented and discussed in Section 5. This paper concludes in Section 6.

2. System Model

In this paper, we consider a downlink in a UCCF M-MIMO network deployed according to the open RAN architecture with a centralized virtual CU–DU managing $N_{\mathrm{RU}}$ RUs. The RU of index l is equipped with an M-MIMO antenna array of $M_l$ elements and has a total maximum radiation power of $P_l$. We assume a full-digital antenna array, i.e., each of the $M_l$ antennas is associated with a dedicated transceiver chain. At the end of the m-th transceiver chain, just before the antenna, there is a PA with a maximum output power (sometimes called saturation power) of $P_{\max ,l}=\frac{P_l}{M_l}$. In the literature, there exists the concept of hybrid beamforming, where a single transceiver chain is connected to several antennas to reduce implementation costs and computational complexity [16]. However, the full digital approach allows us to set precoder weights far more accurately, i.e., individually for each antenna. This enables us to achieve an upper bound of user throughput. While at the current stage of implementation of 5G systems hybrid beamforming is most likely to be practically used, future 6G systems can be expected to utilize more advanced solutions, e.g., due to more optimized hardware design.

The operation point of all PAs can be set to the l-th RU in terms of a so-called Input Back-Off (IBO) ${\gamma }_l$, which is the ratio between the input saturation power of the PA and the average power of the input signal. Lowering the operation point of the PA can avoid signal clipping and reduce the resultant nonlinear distortion, which is discussed in Section 3. In the case of a perfect PA, as considered typically in the literature, it is assumed that the average signal power at the PA output is equal to the saturation power. However, in this case, no nonlinear distortion will be modeled.

The considered UCCF M-MIMO network is OFDMA-based and utilizes bandwidth B allocated at carrier frequency f. The bandwidth is split into $N_{\mathrm{rb}}$ resource blocks (RBs). Each of them exploits 12 OFDM subcarriers in the frequency domain and lasts one time slot of $T_{\mathrm{slot}}$. We assume that within a single RB of index r, the radio channel is flat. Thus, the vector of the complex radio channel coefficients between the i-th single-antenna User Equipment (UE) and the M-MIMO RU l for RB r is given by:

$${\mathbf{h}}_{i,l,r}={\left[\begin{array}{cccc}{h}_{i,l,r,1}& h_{i,l,r,2}& \cdots & h_{i,l,r,M_l}\end{array}\right]}^T.$$

(1)

We assume that each radio channel coefficient already takes into account the antenna gain. The radio channel coefficients are estimated by the RUs and then transferred to the CU–DU for the purpose of centralized formulation of serving clusters, radio resource scheduling, calculation of precoder weights, power allocation, and MCS selection. To reduce the computational complexity of the considered UCCF M-MIMO system, we assume that the calculations of the precoder weights and power allocation are performed independently for each RU, as this allows for avoiding inversions of large matrices while utilizing a Zero-Forcing (ZF) precoder. As we are considering a multicarrier system, we also assume that both the precoder weights and power allocation are calculated independently for each RB r. As a result, RU l transmits the following signal to UE i at RB r if scheduled:

$${\mathbf{X}}_{i,l,r}=\sqrt{\frac{p_{i,l,r}}{12}}{\delta }_{i,r}{\mathbf{D}}_{i,l}\mathbf{A}{\mathbf{w}}_{i,l,r}^T{\xi }_i,$$

(2)

where $p_{i,l,r}$ is the power allocated to UE i by RU l at RB r; ${\mathbf{w}}_{i,l,r}$ is the vertical vector of the precoder weights with a mean power equal to one; ${\delta }_{i,r}$ represents the result of radio resource scheduling (${\delta }_{i,r}=1$ if RB r is allocated to UE i; otherwise, it is equal to zero); ${\mathbf{D}}_{i,l}$ is a matrix that is the result of serving cluster formulation, defined as ${\mathbf{D}}_{i,l}={\mathbf{I}}_{M_l}$ if the i-th UE is being served by the l-th RU and otherwise, ${\mathbf{D}}_{i,l}={\mathbf{0}}_{M_l}$; ${\mathbf{A}}_l$ is a diagonal matrix of size $M_l$, with each element ${\alpha }_{m,l}$ being the nonlinear attenuation of the desired signal for the m-th antenna of RU l (see Section 3); and ${\xi }_i$ is the vector of 12 downlink QAM symbols of UE i, i.e., one symbol per subcarrier. We can treat each element of ${\xi }_i$ as an uncorrelated random variable of zero mean and a variance equal to one. Considering that there are $N_{\mathrm{UE}}$ users in total in the considered UCCF M-MIMO network, the total downlink signal received by UE i at RB r is given by:  

$$\begin{array}{cc}\hfill {\mathbf{y}}_{i,r}=& \sum _{l=1}^{N_{\mathrm{RU}}}\sum _{k=1}^{N_{\mathrm{UE}}}{\mathbf{h}}_{i,l,r}^H·{\mathbf{X}}_{k,l,r}+n_{i,r}+n_{\mathrm{dis},i}\hfill \\ \hfill =& \underset{\mathrm{Desired}\mathrm{Signal}}{\underbrace{\left(\sum _{l=1}^{N_{\mathrm{RU}}}\sqrt{\frac{p_{i,l,r}}{12}}{\delta }_{i,r}{\mathbf{h}}_{i,l,r}^H{\mathbf{D}}_{i,l}{\mathbf{A}}_l{\mathbf{w}}_{i,l,r}^T\right){\xi }_i}}+\hfill \\ \hfill +& \underset{\mathrm{Inter}-\mathrm{user}\mathrm{interference}}{\underbrace{\sum _{\begin{array}{c}k=1\\ k\ne i\end{array}}^{N_{\mathrm{UE}}}\left(\sum _{l=1}^{N_{\mathrm{RU}}}\sqrt{\frac{p_{k,l,r}}{12}}{\delta }_{k,r}{\mathbf{h}}_{i,l,r}^H{\mathbf{D}}_{k,l}{\mathbf{A}}_l{\mathbf{w}}_{k,l,r}^T\right){\xi }_k}}+\underset{\mathrm{Noise}}{\underbrace{n_{i,r}}}+\underset{\mathrm{Distortion}}{\underbrace{n_{\mathrm{dis},i,r}}},\hfill \end{array}$$

(3)

where $n_{i,r}$ denotes the thermal noise, and $n_{\mathrm{dis},i,r}$ denotes the nonlinear distortion term that is the result of RU’s PA characteristics, which is described in Section 3. It can be seen that both the desired signal and inter-user interference terms contain summation over all RUs. In this work, we consider that RUs are perfectly synchronized and connected with a backhaul of negligible latency. This is the best-case scenario in the context of a UCCF M-MIMO network, as it allows for the highest gains in the desired signal. Based on Equation (3), we can formulate the Signal-to-Interference-plus-Noise Ratio (SINR) for UE i at RB r:

$${\mathrm{SINR}}_{i,r}=\frac{{\left|{\sum }_{l=1}^{N_{\mathrm{RU}}}\sqrt{p_{i,l,r}}{\delta }_{i,r}{\mathbf{h}}_{i,l,r}^H{\mathbf{D}}_{i,l}{\mathbf{A}}_l{\mathbf{w}}_{i,l,r}^T\right|}^2}{{\sum }_{\begin{array}{c}k=1\end{array}}^{N_{\mathrm{UE}}}{\left|{\sum }_{l=1}^{N_{\mathrm{RU}}}\sqrt{p_{k,l,r}}{\delta }_{k,r}{\mathbf{h}}_{i,l,r}^H{\mathbf{D}}_{k,l}{\mathbf{A}}_l{\mathbf{w}}_{k,l,r}^T\right|}^2-{\left|{\sum }_{l=1}^{N_{\mathrm{RU}}}\sqrt{p_{i,l,r}}{\delta }_{i,r}{\mathbf{h}}_{i,l,r}^H{\mathbf{D}}_{i,l}{\mathbf{A}}_l{\mathbf{w}}_{i,l,r}^T\right|}^2+{\sigma }_{i,r}^2+{\sigma }_{\mathrm{dis},i,r}^2},$$

(4)

where ${\sigma }_r^2$, and ${\sigma }_{\mathrm{D},i,r}^2$ are the power of the thermal noise and nonlinear distortion per RB, respectively. As the radio channels between the users and precoder weights are known in the CU–DU at the stage of resource scheduling, the SINR can be relatively well approximated. Unfortunately, this is not the case when considering nonlinear distortion. However, the UE is capable of reporting interference levels that can be used to estimate the distortion terms, e.g., interference can be calculated based on Channel Quality Indicator (CQI) reports. Such an estimation is necessary to select the proper MCS by the CU–DU. We assume that a single MCS is allocated for each scheduled user. For this purpose, an effective signal quality metric must be obtained for all RBs allocated to this user, i.e., the so-called effective SINR. It has been shown in the literature that for the considered multicarrier OFDM system that is prone to frequency-selective fading of radio channels, the proper effective SINR metric is Exponential Effective SINR Mapping (EESM) [17]. The EESM for UE i depends on the selected MCS and can be calculated as follows:

$${\mathrm{EESM}}_{i,mcs}=-{\beta }_{mcs}ln\left(\frac{1}{N_{\mathrm{rb}}}\sum _{r\in {\mathcal{R}}_i}exp\left(-\frac{{\mathrm{SINR}}_{i,r}}{{\beta }_{mcs}}\right)\right),$$

(5)

where ${\mathcal{R}}_i$ is a set of indices of the RBs allocated to UE i, and ${\beta }_{mcs}$ serves as an approximate value to adjust for the selected modulation alphabet and coding rate. It will be adjusted by the CU–DU based on the selected MCS (see Section 4.4).

As in practice, both the virtualized CU–DU and each of the physical RUs have limited computational resources, it is of high importance to ensure reasonable scaling of the UCCF M-MIMO network. Following the definition in [3], the UCCF M-MIMO network is scalable when each of the following tasks has finite computational complexity and resource requirements concerning each RU as $N_{\mathrm{UE}}\to \infty$ in the whole network:

• Signal processing for channel estimation.
• Signal processing for data reception and transmission.
• Fronthaul signaling for data and Channel State Information (CSI) sharing.
• Power allocation optimization.

One of the possible solutions to meet scalability tasks 1-3 is to limit the number of users that a single RU can serve. Naturally, the single RU can only serve users that are within range of its reference signals. This limits the number of users for the channel estimation. Moreover, M-MIMO networks usually utilize a limited number of pilot sequences that put a boundary on the channel estimation computational resources, allowing them to meet scalability task 1. In the considered network, the result of serving cluster formulation is not directly related to signal processing for data reception and transmission. It can be that the RU serves many UEs but only a fraction of them currently have radio resources allocated. To set the maximum complexity of data reception and transmission in the considered UCCF M-MIMO network, we assume that there is a maximum number of Multi-User MIMO (MU-MIMO) layers that a single RU can create, i.e., a single RB can be allocated to a maximum of $N_{\mathrm{L}}$ users within a single RU. This allows us to meet the requirements of scalability task 2. With the fixed maximum number of MU-MIMO layers, the size of the precoding matrices will be limited, resulting in finite computational complexity of reception and transmission. As each of the RUs can support only a finite number of pilot sequences for channel estimation and MU-MIMO layers, the fronthaul signaling overhead (task 3) also has finite computational complexity. Finally, the computational complexity of power allocation optimization depends highly on the utilized algorithm. However, one can imagine low-complexity algorithms that can be applied independently for users served by each RU, e.g., an equal-power division that would offer finite computational complexity requirements, meeting scalability task 4.

3. PA Nonlinear Model

Most recent works focusing on M-MIMO networks neglect the impact of hardware impairments, such as the nonlinear characteristics of PAs. However, it has been shown that in the worst-case scenario, the distortion generated by the PAs installed at the M-MIMO’s RU can be steered toward the UE with the same precoding gain as the desired signal. To model this phenomenon in this paper, we consider the so-called Rapp model of the PA [18].

As described in Section 2, every RU is equipped with a fully digital antenna array, meaning that there are $M_l$ transceiver chains and the same number of PAs installed at each RU. While the PA operates on a passband analog signal, our digital signal model creates equivalent distortions. Let us denote the n-th complex sample input to the PA from the m-th transceiver chain at the l-th RU as ${\tilde{x}}_{m,l}\left(n\right)$. This sample has already passed all stages of physical layer processing like precoding, modulation, and IFFT. The output complex sample ${\tilde{y}}_{m,l}\left(n\right)$ of the Rapp-modeled PA is a result of the following nonlinear transformation of the input signal sample ${\tilde{x}}_{m,l}\left(n\right)$ [18]:

$${\tilde{y}}_{m,l}\left(n\right)=\frac{G{\tilde{x}}_{m,l}\left(n\right)}{1+{\left(\frac{{\left|{\tilde{x}}_{m,l}\left(n\right)\right|}^{2p}}{P_{\max ,l}^p}\right)}^{\frac{1}{2p}}},$$

(6)

where G is the amplifier gain (without loss of generality, $G=1$ is assumed from now on); $P_{\max ,l}$ is the saturation power at the output of each PA installed at RU l; and p is the smoothing factor. The higher the p, the closer the PA’s characteristic to the so-called soft limiter. Under the assumption that a complex Gaussian signal is transmitted (valid for OFDM signals [19]), based on the Bussgang theorem, the output sample of PA ${\tilde{y}}_{m,l}\left(n\right)$ can be decomposed into the desired signal sample ${\tilde{x}}_{m,l}\left(n\right)$ scaled by ${\alpha }_{m,l}$ and the nonlinear distortion sample ${\tilde{n}}_{\mathrm{dis},m,l}\left(n\right)$, which is uncorrelated with ${\tilde{x}}_{m,l}\left(n\right)$:

$${\tilde{y}}_{m,l}\left(n\right)={\alpha }_{m,l}{\tilde{x}}_{m,l}\left(n\right)+{\tilde{n}}_{\mathrm{dis},m,l}\left(n\right).$$

(7)

The scaling factor is given by:

$${\alpha }_{m,l}=\frac{\mathbb{E}\left[{\tilde{y}}_{m,l}\left(n\right){\tilde{x}}_{m,l}{\left(n\right)}^{*}\right]}{\mathbb{E}\left[{\tilde{x}}_{m,l}\left(n\right){\tilde{x}}_{m,l}{\left(n\right)}^{*}\right]},$$

(8)

where $\mathbb{E}\left[\right]$ denotes expectation and ${ }^{*}$ is the complex conjugate. For the considered Rapp model of the PA, there is no closed-form expression to calculate ${\alpha }_{m,l}$. However, both the scaling factor ${\alpha }_{m,l}$ and the power of nonlinear distortion can be calculated numerically by simulating the processing of input samples by the Rapp model of the PA. Based on the output nonlinear distortion associated with each RU and taking into account the effect of the radio channel coefficients, one can estimate the power of nonlinear distortion ${\sigma }_{\mathrm{dis},i,r}^2$ for the i-th UE within the band of the r-th RB:

$${\sigma }_{\mathrm{dis},i,r}^2=\mathbb{E}\left[{\left|\sum _{l=1}^{N_{\mathrm{RU}}}\sum _{m=1}^{M_l}{h}_{i,l,r,m}\mathcal{F}{\left\{{\tilde{n}}_{\mathrm{dis},m,l}\left(n\right)\right\}}_r\right|}^2\right],$$

(9)

where $\mathcal{F}{\left\{\right\}}_r$ denotes the Fourier transform at RB r. Similarly, one can estimate the values of ${\alpha }_{m,l}$ that constitute the diagonal matrix ${\mathbf{A}}_l$. Both ${\mathbf{A}}_l$, and ${\sigma }_{\mathrm{dis},i,r}^2$ are necessary for the ${\mathrm{SINR}}_{i,r}$ calculation in Equation (4).

4. Simulation Environment

Unlike the authors of the state-of-the-art works on UCCF M-MIMO networks [7,8,9], we propose an advanced simulation environment to evaluate the network’s behavior. The main part of the simulation environment is the computer simulator, which consists of multiple functional blocks corresponding to the system model described in Section 2. The main loop of the proposed computer simulator for the UCCF M-MIMO network is depicted in Figure 2. Within one iteration of the simulation loop, a period of a single time slot is considered. The loop comprises six steps that are described in the following sections.

4.1. Generation of Radio Channel Coefficients

The simulation loop starts with the generation of the radio channel coefficients. There are two radio channel models implemented within the simulation environment. Both rely on the data from the Wireless InSite 3D ray-tracing software. The ray-tracing software can be controlled by setting different numbers of reflections and diffractions. The first option is to directly obtain the realistic radio channel coefficients from the 3D ray-tracer output. This radio channel model closely reflects the reality of M-MIMO systems because it takes into account the spatial correlations between the radio channels of various users. The second option is to utilize the uncorrelated Rayleigh channel, commonly used in the literature. When this option is used, the radio channel coefficients are generated as uncorrelated complex Gaussian noise with a mean of zero and a variance equal to the average channel gain (including large-scale fading such as path loss) from the 3D ray-tracer output. It should be noted that the Rayleigh channel replaces the small-scale fading from the 3D ray-tracer output. The large-scale fading in both cases is a result of the ray-tracing simulations. This approach enables achieving comparable results between the two considered radio channel models. As such, the computational cost is nearly the same for both radio channels. However, as mentioned above, the channel is precomputed, thereby not increasing the computation time for a single simulator run. Potentially, by replacing the ray-tracing software from the simulation environment with a much simpler empirical large-scale fading model combined with the Rayleigh channel, the simulation time would be reduced at the cost of losing some of the close-to-reality properties of the considered radio environment.

4.2. Formulation of Serving Clusters

The second step of the simulation loop is the formulation of serving clusters. This procedure is run once every $T_{\mathrm{scf}}$ time slots to enable stable radio resource scheduling, which relies on past user bitrates, i.e., the scheduler utilizes information about the past bitrates of users, and frequent reformulation of serving clusters could cause instability in radio resource allocation. We have implemented a state-of-the-art serving cluster formulation algorithm that takes as input the Reference Signal Received Powers (RSRPs) between the i-th UE and all RUs that are within the range of reference signals for this UE. The RSRP between the i-th UE and the l-th RU is denoted as ${\gamma }_{i,l}$ and defined as follows:

$${\gamma }_{i,l}=\frac{P_l}{N_{\mathrm{rb}}}·\frac{{\sum }_{r=1}^{N_{\mathrm{rb}}},{\sum }_{m=1}^{M_l}{\left|h_{i,l,r,m}\right|}^2}{N_{\mathrm{rb}}{M}_l}$$

(10)

where $\frac{P_l}{N_{\mathrm{rb}}}$ is the transmit power per single RB. Based on this input, the serving cluster for the i-th UE is formulated by J RUs characterized by the highest RSRP ${\gamma }_{i,l}$, i.e., for these RUs, ${\mathbf{D}}_{i,l}={\mathbf{I}}_{M_l}$. For the remaining RUs, ${\mathbf{D}}_{i,l}={\mathbf{0}}_{M_l}$. Such an approach is commonly used in related works on UCCF M-MIMO networks, e.g., [20], or with slight modifications introducing an RSRP threshold in [21].

4.3. Scheduling of Radio Resources, Precoding, and Power Allocation

We have implemented a centralized radio resource scheduling algorithm, which is placed within the CU–DU. It is based on the concept of a network-centric approach [22]. However, we have adapted it to the UCCF M-MIMO network architecture. The resulting procedure is presented in Algorithm 1. The scheduling algorithm takes as input the exponential average of UE past rates, inter-cluster interference observed by the UE, radio channel coefficients, and a threshold $\Delta$ in the range $<0;1)$ for the radio channel correlation coefficient, which signifies the minimum requirement for creating a new MU-MIMO layer. The implemented scheduling algorithm independently allocates each RB to users. The allocation is based on the Proportional Fairness (PF) metric, which is defined as the ratio between the maximum expected throughput at a given RB and the user’s past rates. The calculation of the PF metric is performed in steps 2–5 of the scheduling algorithm, resulting in the sequence $\mathcal{K}$ containing the indices of the UEs (denoted as k), which are sorted according to their PF metrics. The user with the highest PF metric (first element of the sequence $\mathcal{K}$) is given the RB. However, due to the utilization of M-MIMO, the same time-frequency resources can be multiplexed in space. Thus, according to the PF metric, the next UEs are allocated, creating a set of $allocatedUEs$ with $N_{\mathrm{L}}$ elements representing spatial layers. This procedure is described in steps 8–25 of the algorithm. Firstly, in step 10 the spatial correlation between all users within the $allocatedUEs$ set is calculated, with the spatial correlation coefficient between the i-th and k-th UE at RB r defined as:

$${\Theta }_{r,i,k}=\left|\frac{{\sum }_{l=1}^{N_{\mathrm{RU}}}{\mathbf{h}}_{i,l,r}{\mathbf{D}}_{i,l}·{\mathbf{D}}_{k,l}{\mathbf{h}}_{k,l,r}^H}{\sqrt{{\sum }_{l=1}^{N_{\mathrm{RU}}}{\parallel {\mathbf{h}}_{i,l,r}\parallel }^2·{\sum }_{l=1}^{N_{\mathrm{RU}}}{\parallel {\mathbf{h}}_{k,l,r}\parallel }^2}}\right|.$$

(11)

Algorithm 1 Radio resource scheduling in a UCCF M-MIMO network

Require: past rate of each UE, inter-cluster interference calculated from the total past interference by each UE, radio channel coefficients, channel correlation threshold $\Delta$ 1: for r in 1 to $N_{\mathrm{rb}}$ do 2:    compute the maximum wanted power for each UE using the Desired Signal term from (3), assuming that a single UE is scheduled, MRT precoder, and $p_{i,l,r}=\frac{P_l}{N_{\mathrm{rb}}}$ 3:    compute the maximum expected UE throughput for RB r using the Shannon formula, with the SINR of each UE being the ratio of its maximum wanted power computed in step 2 and reported inter-cluster interference 4:    compute the PF metric for each UE, being the ratio of its past rate and the current maximum expected throughput for RB r 5:    create a sequence $\mathcal{K}$ containing the indices of UEs, sorted according to their PF metrics in descending order 6:    $sumRate\leftarrow 0$ 7:    $allocatedUEs\leftarrow ⌀$ 8:    for k in $\mathcal{K}$ do 9:         add k to set of $allocatedUEs$ 10:       compute channel correlation coefficients between UEs being within the set of $allocatedUEs$ using (11) 11:       if any correlation coefficient exceeds $\Delta$ then 12:          remove k from set of $allocatedUEs$ 13:       else 14:          set ${\mathbf{D}}_{k,l}={\mathbf{0}}_{M_l}$ for all RUs that reached the maximum number of $N_{\mathrm{L}}$ spatial layers 15:          compute precoding ZF vectors for $allocatedUEs$ 16:          allocate power equally between the $allocatedUEs$ 17:          compute the expected ${\widetilde{\mathrm{SINR}}}_{i,r}$ of $allocatedUEs$ using (4) and reported inter-cluster interference 18:          compute $newSumRate$ of $allocatedUEs$ using the Shannon formula and expected SINR computed in the previous step 19:          if $sumRate>newSumRate$ then 20:             remove k from set of $allocatedUEs$ 21:             break 22:          else 23:             $sumRate\leftarrow newSumRate$ 24:             ${\delta }_{k,r}\leftarrow 1$ 25:          end if 26:       end if 27:  end for 28: end for

If any of the computed channel correlation coefficients exceeds the threshold $\Delta$, the last added user is removed from the set of $allocatedUEs$. This is because the spatial correlation is directly mapped to the interference, e.g., with the Maximum Ratio Transmission (MRT) precoder, the power of the inter-user interference (between the i-th and k-th user) rises proportionally to ${\Theta }_{r,i,k}^2$. The next condition that the k-th user must meet is to increase the $sumRate$ within RB r. This is performed in steps 14-18 of the algorithm. For scalability purposes, each RU has a limit of $N_{\mathrm{L}}$ spatial layers; if this limit is reached, the RU is no longer considered for serving users by setting ${\mathbf{D}}_{i,l}={\mathbf{0}}_{M_l}$ for this RU. Next, the Zero-Forcing (ZF) precoder is calculated for each RU in step 15. Note that the precoding weights are normalized to ensure ${\parallel {\mathbf{w}}_{i,l,r}\parallel }^2=1$. Although the ZF precoder has higher computational complexity than the MRT precoder, it has an important ability to suppress interference between users. This was shown in initial studies to be very beneficial for the considered UCCF M-MIMO network. It should be noted that we assume an architecture where precoding is performed independently for each RU. Moreover, we place a limitation on the number of spatial layers that the scheduler can create. As a result, the radio channel matrix, which is subject to ZF precoding, has a maximum size of $M_l\times N_{\mathrm{L}}$. The maximum number of spatial layers per RU is selected to ensure a reasonable processing time for ZF precoding. In step 16, power is allocated by splitting it equally among all spatial layers, independently within each RU. Power allocation in the UCCF M-MIMO network is a topic of significant importance. While some recent works address this problem, they are not designed for such a complicated system model utilizing an MCS, a scheduler, and a realistic radio channel. Moreover, it remains a challenging issue for the research community [6]. Existing power allocation algorithms are either optimized under a simplified system model, characterized by significant computational complexity, or unscalable. Instead, we utilize baseline power allocation, as presented in [3], which is characterized by low complexity and ensures the scalability of the UCCF M-MIMO network, i.e., equal power allocation among spatial layers within each RU. Having done this, the expected ${\widetilde{SINR}}_{i,r}$ can be computed for each UE that has the r-th RB scheduled using (4). The calculation of the SINR is performed in two places within the simulator: when scheduling users and when calculating the achieved rate. The first application is more challenging as it is based on channel estimates, calculated intra-serving cluster interference, and estimated inter-serving cluster interference. The channel between each UE and its serving RUs is estimated based on the uplink Sounding Reference Signal (SRS), and the knowledge of the utilized precoding can be used to calculate intra-cluster interference. Inter-cluster interference is assumed to be based on a user historical report similar to the Channel Quality Indicator (CQI), Reference Signal Received Quality (RSRQ), or SS-SINR, as outlined in the 5G specifications [23]. Using the expected ${\widetilde{SINR}}_{i,r}$, the $newSumRate$ can be computed based on the Shannon formula. If the $newSumRate$ is higher than the previously computed $sumRate$, the new spatial layer is created and the k-th UE has ${\delta }_{k,r}$ set to 1. Otherwise, it is removed from the $allocatedUEs$, and the loop breaks, as shown in steps 19–25 of the algorithm. After that, the procedure is repeated for the next RB.

4.4. MCS Selection

After the RBs, power, and precoder weights are allocated to the UEs, the proper MCS must be selected. We have implemented an algorithm where a single MCS is selected for all RBs allocated to a particular UE. Each MCS is associated with its spectral efficiency $S{E}_{mcs}$, ${\beta }_{mcs}$, and minimum ${\mathrm{EESM}}_{i,mcs}$, which are necessary to ensure a Block Error Rate (BLER) below 10%. Additionally, two parameters, $c_{mcs}$ and $b_{mcs}$, are required for the BLER calculation. Because parameters suitable for 5G are not easily accessible, we used the values proposed for MCS modeling in LTE. These values are summarized in

Table 1. MCS selection parameters based on [24,25].

MCS	${\mathit{SE}}_{\mathit{mcs}}$ (bit/Hz)	${\mathit{\beta }}_{\mathit{mcs}}$	Required EESM (dB)	${\mathit{b}}_{\mathit{mcs}}$	${\mathit{c}}_{\mathit{mcs}}$
1	0.15	4.73	−6.3	0.19	0.04
2	0.23	2.48	−4.5	0.31	0.05
3	0.38	1.13	−2.8	0.47	0.05
4	0.6	1.52	−0.9	0.74	0.07
5	0.88	1.55	1.1	1.17	0.09
6	1.18	1.58	3.1	1.85	0.14
7	1.48	3.79	5.3	3.06	0.23
8	1.91	4.61	6.9	4.5	0.28
9	2.41	5.92	8.9	7.25	0.46
10	2.73	11.5	10.6	10.8	0.63
11	3.32	16.3	12.5	16.7	0.91
12	3.9	21.6	14.4	25.7	1.36
13	4.52	28.6	16.2	38.3	2.5
14	5.11	31.2	18.1	59.2	3.6
15	5.55	34.5	20.1	95.9	5.4

[24,25]. To select an MCS for a given UE, we compute ${\mathrm{EESM}}_{i,mcs}$ for each value of ${\beta }_{mcs}$ from Table 1 according to (5), using the expected ${\widetilde{SINR}}_{i,r}$ computed during the radio resource scheduling procedure. The selected MCS is the one associated with the highest ${\mathrm{EESM}}_{i,mcs}$ that exceeds the minimum requirement.

4.5. Simulation of Nonlinear Effects at PA

The fifth stage of the main simulation loop is the simulation of the nonlinear effects at the PA. While there exists an analytical framework for nonlinear distortion power calculation [26], it is limited, e.g., it requires the statistical properties of each wireless channel. Instead, link-level simulations are used. This is performed for all RUs and all scheduled UEs in the system. We simulate a batch of random QAM symbols, which are then subjected to precoding using the vectors already computed for all scheduled UEs, RBs, and RUs. These samples are passed through the Rapp model of the PA according to (6). Based on the knowledge of both the input and output samples, one can estimate the power scaling coefficient matrix ${\mathbf{A}}_l$ and the power of nonlinear distortion ${\sigma }_{\mathrm{dis},i,r}$ for each UE i and RB r using (8) and (9).

4.6. Calculation of Real SINR and BLER

During the radio resource scheduling stage (Section 4.3), the expected ${\widetilde{SINR}}_{i,r}$ is used, which is based on the past inter-cluster interference reported by the UEs. However, the interference highly depends on the group of UEs scheduled within a particular time slot. Thus, the reported value usually differs from the real interference observed at a given UE, as well as the nonlinear distortion pattern. Thus, the next step of the main simulation loop is to calculate the real SINR using (4) with full knowledge of the radio channel coefficients, simulated nonlinear distortion, and scaling coefficients. With the calculated real ${\mathrm{SINR}}_{i,r}$ for every UE and RB, along with the ${\beta }_{mcs}$ factor related to the selected MCS, one can calculate the real values of ${\mathrm{EESM}}_{i,mcs}$. During the scheduling phase, it might happen that a particular UE wrongly estimated the inter-cluster interference, e.g., observing much higher real interference. This will influence the achieved rate. The real BLER can be calculated as follows:

$${\mathrm{BLER}}_{i,mcs}=0.5·\mathrm{erfc}\left(\frac{{\mathrm{EESM}}_{i,mcs}-b_{mcs}}{\sqrt{2}{c}_{mcs}}\right),$$

(12)

where $b_{mcs}$ and $c_{mcs}$ are taken from Table 1 based on the MCS selected for the i-th UE.

4.7. Calculation of UE Rate

The final stage of the main simulation loop is the calculation of the user throughput at the considered time slot. This is performed based on $S{E}_{mcs}$, which is associated with the selected MCS, and the calculated ${\mathrm{BLER}}_{i,mcs}$. The throughput of the i-th UE is given by:

$$v_{i,mcs}=\frac{S{E}_{mcs}·12·14·(1-{\mathrm{BLER}}_{i,mcs})}{T_{\mathrm{slot}}}.$$

(13)

The numbers 12 and 14 are related to the fact that, according to the 3GPP specification [27], within a single RB, there are always 12 subcarriers in the frequency domain and 14 OFDM symbols within a single time slot. It should be noted that a UE is not always granted with RBs. Thus, to observe a reliable rate, the throughput should be averaged over multiple time slots.

4.8. Simulation Scenario

To evaluate the considered UCCF M-MIMO network, we utilized an urban scenario developed for the purpose of the METIS project named the Madrid Grid Model, which included both a Line-of-Sight (LoS) park area and narrow street canyons with non-LoS (NLoS) radio conditions [28]. Within this area, we placed six RUs. The RU of index $l=0$ corresponds to a macro-RU installed at a height of 45 m, with a maximal transmit power of $P_0=46$ dBm (128 PAs with $P_{\max ,0}=312.5$ mW) and an antenna array of $M_0=128$ elements (8 rows × 16 columns). The remaining RUs are micro-RUs installed at a height of 6 m, with a maximal transmit power of $P_l=30$ dBm (32 PAs with $P_{\max ,l}=31.25$ mW) and equipped with $M_l=32$ antennas (two panels with 8 rows × 2 columns). The remaining simulation parameters are listed in

Table 2. Simulation parameters.

Parameter	Value
Center frequency f	3.6 GHz
Number of RBs $N_{\mathrm{rb}}$	69
Time slot duration $T_{\mathrm{slot}}$	0.5 ms
Subcarrier spacing	30 kHz
Number of CU–DUs	1 centralized and virtual
Number of RUs $N_{\mathrm{ru}}$	6 (1 macro-RU, 5 micro-RUs)
RU installation height	macro-RU: 45 m; micro-RUs: 6 m
Rapp PA model smoothing factor p	12
Transmit power $P_l$	macro-RU: 46 dBm; micro-RUs: 30 dBm
Number of antennas $M_l$	macro-RU: 128; micro-RUs: 32
Threshold of correlation coefficient $\Delta$	0.7
Maximum number of spatial layers $N_{\mathrm{L}}$	macro-RU: 32; micro-RUs: 8
Wireless InSite configuration	15 reflections, 1 diffraction

.

5. Results

The UCCF M-MIMO network was evaluated using the advanced computer simulator described in Section 4. The simulation studies are divided into three parts: coverage analysis, throughput analysis without nonlinear effects, and throughput analysis considering nonlinear effects.

5.1. Coverage Analysis

The first part of the simulation studies compares the coverage of the state-of-the-art network-centric architecture and that of the novel UCCF M-MIMO architecture. For this purpose, we generated radio channel coefficients for 3542 users uniformly distributed throughout the considered network area, with an inter-user space of 5 m. For each user and a varying number of serving RUs, we computed the Received Signal Strength (RSS) using the term Desired signal from (3), assuming that $p_{i,l,r}=\frac{P_l}{N_{\mathrm{rb}}}$, and the MRT precoder. The results, presented as a map of the RSS averaged over the RBs, for both the network-centric architecture (each user can only be served by one RU providing the highest RSRP calculated using (10)) and the UCCF architecture with six serving RUs, are depicted in Figure 3. The benefits of utilizing the UCCF M-MIMO network architecture are especially visible in the alley on the right, where multiple micro-RUs were deployed. For the UCCF M-MIMO network architecture with six RUs serving the UEs, the radio signal within the alley maintains an average RSS oscillating around −35 dBm. On the other hand, for the network-centric architecture, clear boundaries between cells are visible, with the average RSS dropping below −45 dBm.

To gain better insights into the relationship between the observed RSS and the number of RUs serving a single UE, we examined the ratio between the RSS averaged over the RBs for the UCCF M-MIMO and network-centric architectures under varying numbers of RUs serving a single UE. The Cumulative Distribution Function (CDF) of this ratio is depicted in Figure 4. We can see that the maximal gain related to the utilization of the UCCF M-MIMO network architecture over the network-centric approach is about 11 dB when using six RUs. This observation aligns with the findings from the coverage map. However, it can be seen that while a significant gain in the average RSS ratio can be observed between two and three RUs serving a single UE, for four, five, and six RUs, the gain is marginal. This somehow motivates the idea of forming serving clusters. It is worth mentioning that significant improvements in the average RSS can be observed for about 25% of UEs. This is because in many locations, the RSS from one RU is much higher than from others, e.g., the middle part of the considered area is mostly covered by the macro-RU, and the UEs placed therein benefit marginally from UCCF M-MIMO.

5.2. Throughput Analysis without Nonlinear Effects

After the coverage analysis, we conducted a system-level simulation of the UCCF M-MIMO network without taking into account the nonlinear effects at the PA. For this purpose, we implemented the simulation environment described in Section 4 in MATLAB. We considered 20 users randomly placed in the alley (see Figure 4), where the effects of the selected network architecture were most visible during the coverage analysis. The initial positions of UEs followed a uniform distribution over the alley area. The users moved in random directions at a speed of 1.5 m/s, i.e., the azimuth of each user was uniformly distributed within the range of 0–360 degrees. Individual simulation runs involved continuous service and movement of these 20 users for 500 time slots (250 ms). During each time slot, the main loop depicted in Figure 2 was executed, but the fifth step was omitted. To achieve smooth plots, we conducted 30 independent simulation runs with different random generator seeds. Due to the high computational complexity of radio channel generation in the Wireless InSite 3D ray-tracer software, the realization of users’ movements and the related channel coefficients for all simulation runs were pre-generated. This ensured a fair comparison, i.e., UEs followed the same paths and had identical radio channel coefficients in each simulation run, independent of the number of serving clusters.

5.2.1. Rayleigh Channel

First, we evaluated the UCCF M-MIMO network and compared it against a state-of-the-art network-centric approach under the idealistic i.i.d. Rayleigh channel, which is widely used in the literature, e.g., [4,7]. The resulting CDFs of the average UE rates under the Rayleigh radio channel for both the network-centric approach and the UCCF M-MIMO network architecture, with varying numbers of RUs serving a single UE, are depicted in Figure 5. The CDF for the network-centric architecture exhibits an interesting stair-like shape. The stairs correspond to the maximum user throughput that can be achieved under a given MCS (vertical lines). This is because, under an uncorrelated Rayleigh radio channel, there are no spatial correlations between UEs. More specifically, when a high number of antennas is used, the radio channels between users become orthogonal, and as a result, there is no interference, i.e., the so-called favorable propagation occurs. While the number of UEs is relatively small and each UE can be served by only a single RU, the maximum number of spatial layers is not exceeded. As a result, all UEs experience almost static radio conditions, and in every time slot, the scheduling decision is exactly the same. This is not the case when considering the UCCF approach, where a single UE can create spatial layers within multiple RUs, causing situations where some UEs are not scheduled within a particular time slot (or are granted a limited set of RBs), which affects the decisions of the scheduler in the subsequent time slots. This is why the CDFs for the UCCF M-MIMO network architecture have smooth shapes. However, one can see that only the UCCF architecture with two RUs serving a single UE provides significant gains for users characterized by the worst radio conditions (10th percentile), without deteriorating the median or 90th percentile of the average UE rate distribution. Increasing the number of RUs to three, four, five, and six causes significant degradation. This is the result of equal power allocation, i.e., while there is no interference under an uncorrelated Rayleigh radio channel, the system becomes noise-limited. In such a case, the fact that the transmit power must be distributed among more UEs is not always compensated by the benefits of the joint UCCF network. For example, in the extreme case of six RUs, the median gain in the average RSS from the UCCF network is about 1 dB (see Figure 4), but power is always divided among all spatial layers (in the case of micro-RUs, it is about a 9 dB reduction in the average RSS). Moreover, in some situations, the RU allocates the same power to users who are both close and far away from it. As a result, power allocated to the far UE is “wasted”.

5.2.2. Ray-Tracer Channel

The second step was to repeat the studies within the ray-tracer radio channel, which outputs a channel characterized by spatial correlations causing interference in M-MIMO networks. The resulting CDFs of the average UE rates for the network-centric approach and the UCCF M-MIMO network architecture, with varying numbers of RUs serving a single UE, are depicted in Figure 6. In this case, a significant gain can be observed when adopting the UCCF network architecture. This is because of interference coordination, where a UE served by multiple RUs benefits from ZF precoding suppressing interference between UEs served by the common RU. In the extreme case of six RUs (all RUs serve all UEs), all interference is suppressed by ZF precoding in each RU. However, power allocation can still negatively impact the rates achieved by some UEs, particularly for five and six RUs serving a single UE. On the other hand, the utilization of many RUs causes an effect expected in the literature for UCCF M-MIMO networks: the distribution of average UE rates becomes close to uniform. This means that the Mobile Network Operator (MNO) can guarantee uniform QoS for almost all users. It remains an open question regarding which approach is better from the perspective of the MNO: Is it better to offer network users almost equal throughput at the cost of significant throughput degradation for the best users, or to improve the throughput of median users and those with the worst radio conditions while maintaining the QoS of the best ones? The answer to this question depends on the specific conditions and goals of the MNO. However, the UCCF M-MIMO network can provide flexibility in its implementation through the proper formulation of serving clusters.

5.2.3. Comparison

The results achieved for the Rayleigh and ray-tracer radio channels were compared in terms of the 10th, 50th (median), and 90th percentiles, as shown in Figure 7. The main observation is that the average UE rates achieved under the Rayleigh radio channel are much higher than those achieved under the ray-tracer channel. This is because the Rayleigh channel is not spatially correlated, which plays a crucial role in achieving the full performance of any M-MIMO system. From this perspective, the results obtained for this channel model may be overly optimistic, i.e., the UE rates are overestimated compared to real-world scenarios. However, even after rate normalization, the i.i.d. Rayleigh channel cannot accurately evaluate the relationship between the network-centric and UCCF M-MIMO network architectures. For example, while the highest median rate in the i.i.d. Rayleigh channel is achieved by the network-centric approach or UCCF M-MIMO architecture with two RUs, the ray-tracer-based simulations reveal that it is the best to use the UCCF M-MIMO network architecture with more than three RUs, depending on the MNO’s goal. As a result, accurate radio channel models should be used for the evaluation of any M-MIMO system, especially when demonstrating the opportunities related to the UCCF M-MIMO network. By comparing the plots, it can also be seen that utilization of the UCCF M-MIMO network architecture in the considered network provides greater benefits for the realistic ray-tracer radio channel. This is because it allows for coordinated suppression of interference between RUs (achieved through ZF precoding applied within each RU) and increased array gain through the utilization of M-MIMO transmission from multiple RUs.

5.3. Throughput Analysis Considering Nonlinear Effects

The last studies are related to system-level simulation considering nonlinearities. We followed the same setup and UE distribution used in Section 5.2, i.e., the number of UEs and their spatial distribution. However, here, all the steps of the main simulation loop were executed. We compared the results achieved without nonlinear effects, named Perfect PA, against the system with nonlinear distortion, with the IBO set to 0 dB and 6 dB, respectively. For the Perfect PA scenario, we assumed that the average system transmission power was $P_0=46$ dBm (macro-RU) and $P_l=30$ dBm (micro-RUs, for $l>0$). While this means that the IBO was equal to 0 dB for all RUs, causing severe nonlinear distortion effects, in reality, we omitted these in the Perfect PA scenario. As a result, ${\mathbf{A}}_l={\mathbf{I}}_{M_l}$ for each RU, and no nonlinear distortion appeared, i.e., ${\sigma }_{\mathrm{dis},i,r}^2=0$. We are aware of the fact that in such a case, a comparison between Perfect PA and real frontend cases is unfair, as the Perfect PA case uses higher useful power and is not penalized with nonlinear distortion that would result in higher throughput. However, this allows for a qualitative comparison of both schemes. For comparison under the i.i.d. Rayleigh channel, we selected the network-centric approach and the UCCF approach with two RUs serving a single UE, as it exhibited the highest rate improvements in Figure 7. The results are presented in Figure 8. It can be seen that under a high operation point of the PA (IBO 0 dB), the user throughput significantly degraded compared to the Perfect PA scenario and the results for the case of 6 dB IBO. This is due to the strong nonlinear distortion that was generated when the PA’s operation point was low, i.e., close to 0 dB. On the other hand, lowering the operation point reduced the transmit power, but, as can be seen in this case, it only slightly affected the UE rates. This might be because in most cases, the lower transmit power did not degrade the SINR, resulting in the selection of a lower MCS for a given UE.

The results obtained under the more realistic ray-tracer-based radio channel model are presented in Figure 9. For comparison, we selected the network-centric approach and the UCCF approach with three RUs serving a single UE. This configuration provided high average UE rate gains over the network-centric approach and did not deteriorate the rates achieved by any group of UEs (neither median nor 90th percentile), as visible in Figure 7. The observations are similar to those under the Rayleigh channel. The high operation point of the PA resulted in the generation of significant nonlinear distortion. However, under the realistic ray-tracer radio channel, a small drop in UE rates compared to the perfect PA case can be observed, related to the fact that the transmit power decreased by lowering the operation point of the PA by 6 dB. It might be that while each RU had a lower power to distribute among scheduled UEs, the allocation of a new spatial layer did not meet the condition of sum-rate improvement.

6. Conclusions

In this paper, we evaluated a UCCF M-MIMO network using an advanced computer simulator under both state-of-the-art Rayleigh and realistic 3D ray-tracer-based radio channels, considering nonlinear effects at the PA. The results show that the behavior of the system is different under the idealistic radio channel and the realistic radio channel characterized by the spatial correlations between UEs. Moreover, we demonstrated the impact of the selection of the PA’s operation point on the performance of the UCCF M-MIMO network. The main conclusion is that such a system should be evaluated using advanced computer simulators that consider multiple signal-processing stages and functional blocks within a 5G/6G communication system. Also, to avoid rate overestimation, close-to-real-world radio channels should be used, e.g., those based on 3D ray tracing. The operation point of the PA should be carefully chosen to achieve a balance between the transmit power and nonlinear distortion. Moreover, studies can be extended by evaluating the energy efficiency that depends on PA power consumption as a function of the IBO.