Simulation and Analysis of Mobile Access (SAMA): Cellular Radio Access Network Simulator and Performance Evaluator Applied to 5G

Abstract

ABSTRACT

The different use‐case scenarios for mobile networks make radio access network (RAN) assessment using only coverage (radio link) prediction inadequate since channel capacity and latency play vital roles in some scenarios. To correctly evaluate the RAN performance, the flexible assignment of the spatial (beamforming) and time‐frequency resources of the physical layer frame must be accounted for. This paper presents a RAN simulator for 5G mobile networks that can evaluate different performance indicators of the base stations (BS) arrangement supporting a user equipment (UE) distribution in the region where the mobile network operates. The BS may have multiple sectors and antenna arrays for beamforming in the simulator. The simulator supports both uplink and downlink. Each simulation round considers a physical layer frame when the UEs' positions are assumed static for the assignment between BS beams and UEs. The tool also encompasses some standard schedulers for the radio resources. Besides the UEs–BSs assignment and scheduling, which depend on the BS arrangement and the distribution of UEs and the scheduler, the simulator returns performance indicators as the capacity, throughput, and latency for each UE. The performance accounts for the interference in the radio environment. Consequently, the presented simulation tool helps with system design and evaluation. The many resources encompassed in the simulator can be configured for many different scenarios. We exemplify the simulator usage by comparing the RAN's performance for different network usages under various network configurations and resource schedulers.

Introduction

The different use-case scenarios and verticals for 5G networks impose different service requirements [1, 2]. The complexity of the radio access network (RAN) design increases due to the large coverage area, the many pieces of equipment that may be employed, and virtualization techniques [3]. To design a RAN guaranteeing the desired quality of service (QoS), a very detailed characterization of the links from base stations (BS) to UEs (and vice-versa) is necessary, for example, to assess the resulting channel capacity, throughput, and general network latency [4, 5].

To support the design and evolution of the RAN, emulating diverse scenarios and assessing the requirements of the different use cases is essential. For example, the enhanced mobile broadband (eMBB) [6] has been proposed for real-time video and gaming requiring reasonable data rates for downlink and uplink, the ultra reliable low latency communications (URLLC) [6] considers autonomous-vehicle applications and the massive machine type communications (mMTC) [6] aims at IoT and smart cities use-cases where a multitude of devices must be connected. Each scenario presents different requirements to the mobile network and thus to its RAN. Consequently, simulation tools must encompass multiple performance indicators to evaluate the network under diverse situations.

In the literature, one finds system-level and link-level simulators for the RAN. Link-level simulators evaluate link-related indices like the bit error rate; meanwhile, system-level simulators provide performance indices for the RAN and maybe for individual users. Among the simulators encountered in the literature, perhaps the most well-known physical-layer simulator is the Vienna simulator [7, 8]. It is a successor to the Vienna LTE-A SL simulator [9] and is implemented using Matlab and may be used for link-level and system-level analyses; it is modular and can be used and adapted for many use cases. It provides 2D and 3D stochastic-channel models, schedulers as the best channel quality index (BCQI) and round-Robin, beamforming, single-input-single-output, multiple-input-multiple-output, and non-orthogonal-multiple-access features. Nevertheless, it does not provide any automation for the UE and BS placement and requires the user to configure it in detail. Despite being developed for academic usage, the MATLAB requirement may hinder its use. Other simulators derive from it, as, for example, [10]. Another physical-layer simulator is the Simu5G [11], a successor of SimuLTE [12]. Unlike the Vienna simulator, it focuses on the so-called end-to-end paradigm with IP protocol and the network's core entities. It is developed using C++ (on the framework OMNeT++ [13]). Nevertheless, the entailed complexity limits the scale of the simulations, and it is restricted to constrained scenarios with few BSs. Other simulators of similar scope but still more limited usages are 5G-LENA [14] and 5G-air-simulator [15].

Nonetheless, to evaluate the mobile network service, a tool capable of simulating the multiple access of UEs to the physical layer frame resources, considering the spatial arrangement of the RAN elements and their equipment characteristics, is necessary. Such a tool could allow evolution from legacy infrastructure sites (cabinets and poles) to support a new RAN deployment. Besides, the tool must also consider the channel's variability between BSs and UEs. It is only possible to evaluate the different quality requirements in the service area by considering those aspects. Consequently, we develop a system-level simulator based on the channel state information (CSI, or, equivalently, the channel quality indicator, CQI) between UEs and BSs [16]; it is named SAMA1. SAMA simulates the allocation of resources in a RAN composed of multiple BSs with beamforming capability. The radio-link CSI from a BS to a UE is the proxy for the link's (channel) capacity. SAMA analyzes the performance of a complete RAN with multiple BSs and UEs, accounting for the interference between them; therefore, it is a system-level simulator. SAMA does not evaluate indices like the bit error rate in the link as expected for link-level simulators, but instead uses the CSI of each link as a proxy for its capacity. SAMA computes key performance indices for individual UEs to evaluate the quality of service (QoS). This makes it possible to define levels for the QoS, and the simulated network to schedule resources for the UEs depending on the satisfaction of the QoS. Thus, the RAN performance for different services like eMBB, URLLC, and mMTc can be evaluated using SAMA.

The associations between UEs and the BS's beams are obtained from the CSI, spatially portraying the RAN's radio links among UEs and BSs. Subsequently, the RAN performance is evaluated as the scheduling of the time-frequency resources of a physical layer frame among the UEs takes place, since, for a given association between BSs and UEs, the performance will most commonly depend on the scheduling employed [17]. The simulator returns UEs–BSs-beams associations and the resulting links' path losses and data rates, which are independent of the scheduler, besides the channels' capacities, UE throughput, and latency, which are scheduler dependent. The result is a snapshot of the RAN during a physical layer frame. The RAN's performance can be accessed using the Monte Carlo approach, considering many physical layer frames. SAMA provides a 5G RAN open simulation tool considering spatially distributed UEs, arbitrary BS arrangements, and the intrinsic variability of the wireless channel between UEs and BSs. SAMA is developed in Python and can run different simulation scenarios since it encompasses the necessary minutiae to conduct simulations under different systemic configurations and equipment characteristics with little user input [18].

Following, Section 2 describes the models for the RAN equipment. Section 3 describes using the RAN resources to serve the users connected to it. Section 4 presents the indicators used to evaluate the RAN performance considering different use-case scenarios. Section 5 describes how the entities, models, and algorithms are implemented in the simulator using an object-oriented approach. Its use is demonstrated in Section 6 under diverse simulation scenarios. Section 7 concludes the paper.

Equipment and Physical Models

To simulate the radio links, one must correctly represent the main elements of the RAN—the BSs and UEs and their arrangements. The RAN connects $$U$$ UEs inside a region of interest (ROI) to the mobile network through the BS beams. There are $$N$$ BSs that may present sectors with beamforming capacity. In principle, as represented in Figure 1, SAMA receives the ROI, the distribution of UEs, the UE's characteristics, the BS's arrangement or criteria for finding it, the BS's characteristics, and a path-loss model. SAMA outputs UEs–BSs-beams assignments and path-losses/CSI, which are independent of the scheduler.

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SAMA users can define the fraction of active UEs. This allows the simulation to be adjusted to diverse scenarios. Once the UE is active, it shares the resources with the other active UEs. SAMA framework assumes that there is always data available for transmission for an active UE (i.e., it considers a full buffer model). The user of SAMA defines the target data rate (throughput) for the UEs during 1 s, and SAMA verifies whether the target has been achieved individually. Different schedulers were implemented, varying how the resources are shared, and the transmission times are also traced so that peak rates, latency, and the eventual overflow of the buffer could be signaled.

SAMA can run one or iterate across multiple runs. The UE positions are drawn randomly (defining a probability density, i.e., we adopt a stochastic model) so that the metrics resulting from multiple runs present statistical confidence—SAMA can evaluate that through a hypothesis test. Meanwhile, the BSs' arrangement can be obtained from the UEs' positions or direct input. In this section, we discuss the system entities, their interactions, the assumptions employed in SAMA, and some of its ongoing and future enhancements.

Region of Interest

The region of interest (ROI) delimits the geographical region the RAN should cover. It can be a free-form clip of a geographic region, a municipality, a state, or else. A consistent model for the UE distribution in the ROI is of utmost importance for judiciously evaluating the RAN performance. A possible approach is to derive the distribution for the UEs sampling relevant socio-economic and other population-related data as a proxy for the user distribution [19] and demands. Below, Section 2.2 describes the procedure.

User Equipment

One expects the useful information to consume most network resources instead of encapsulation and protocol data. Consequently, applying an effective and flexible representation of the UE distribution and radio characteristics is essential for reliable data rate estimates. The RAN is intended to serve $$U$$ UEs in the ROI. Usually, these UEs have different power profiles, device characteristics, and priorities. For example, while the UEs belonging to eMBB subscribers may employ more powerful transceivers, the opposite may be observed for the ones used by mMTC UEs. For URLLC, the latency of the RAN is of great importance, while for eMBB, it is not an issue.

SAMA considers that $$U$$ active UEs demand the RAN in each simulation run. Nevertheless, it allows modelling the active UE distribution over the ROI differently. It can be modelled by drawing the UE positions from a uniform probability density function (PDF) in the ROI or using a PDF composed of a sum of parametrized 2D Gaussian or Gamma PDFs. In addition, SAMA can receive an arbitrary density for the UEs in the ROI. SAMA reads a file with the relative chances of the ROI's pixels containing active UEs. Let $$\text{pr}(x,y)$$ be the relative chance for the existence of an active UE at the pixel $$(x,y)$$; let $$x^{\prime }$$ and $$y^{\prime }$$ be auxiliary variables, then the cumulative distribution function (CDF) of UEs being placed in the ROI pixel having coordinates $$(x,y)$$ is 1 $$$\begin{equation} \text{F}(x, y) = \sum _{x^{\prime }\le x}\sum _{y^{\prime } \le y} \text{pr}(x^{\prime },y^{\prime }). \end{equation}$$$One draws a random variable (RV) drawn from a uniform distribution over [0,1), computes its CDF, and places the UE at the $$(x,y)$$ leading to $$\text{Pr}(x,y)$$ closest to the CDF of the drawn value. Repeating this procedure $$U$$ times, one obtains the positions for the $$U$$ UEs. Notice that this formulation can be applied to a ROI of arbitrary shape by sorting its pixels using a predefined order.

BS Model

The BSs provide the radio links from the UEs to the network. It is usual for mobile-network BSs to present multi-sector coverage capacity. Mobile network standards and, consequently, the BSs have been evolving to use the resources better and, in consequence, improve the quality of service (QoS) for the different use-case scenarios and applications. The 5G BS can employ spatial multiple-access through beams to direct the transmission power and improve the link quality for the UEs. Contemporary networks employ an active antenna system (AAS), a highly dense antenna array with radio integration for improved spectrum usage by employing beamforming and MIMO techniques [20]. Attempting to reproduce a convincing representation of an actual mobile network, we consider BS divided into sectors employing beamforming antennas.

Sectorial Antennas

We use the recommendation ITU-R F.1336-5 [21] to obtain standard radiation patterns for the antenna sectors. Let ($$\theta,\phi$$) denote the elevation and azimuth angles tandem; the radiation pattern is given by 2 $$$\begin{align} G(\phi,\theta) = G_0 + G_{\text{h}}(\chi _h) + R \cdot G_{\text{v}}(\chi _v), \end{align}$$$where $$G_0$$ is the maximum gain, $$G_{\text{h}}(\chi _h)$$ is the reference-antenna gain (in dB) in the azimuth plane in the normal direction to $$(x_h,0)$$, $$R$$ is the horizontal gain compression ratio, and $$G_{\text{v}}(\chi _v)$$ is the reference-antenna gain (in dB) in the elevation plane (perpendicular to $$(0,x_v)$$). The complete calculations are in ITU-R F.1336-5 [21].

Beamforming

Beamforming employs an array of antenna elements to produce directional irradiation patterns. The pattern is determined by the physical arrangement of the antenna elements and the array coefficients [22, 23]. We simulate beamforming antennas using the 3GPP TR 37.840 [23], where the complete specification can be found, to model an array composed of $$H \times V$$ (horizontal $$\times$$ vertical) antenna elements lying along the z-axis [22]. The antenna array pattern/gain $$G_{b}(\theta,\phi)$$ in the $$b$$-th beam results from the contribution of the $$H\times V$$ elements in the array [22, 23] and the beam gain is given by 3 $$$\begin{equation} G_b(\theta,\phi) = G_{\text{Max}} - \min {{\left\lbrace -|A_{H}(\phi) + A_{V}(\theta)|,\nobreakspace A_m \right\rbrace} }, \end{equation}$$$where $$A_{H}(\phi)$$ and $$ A_{V}(\theta)$$ are the horizontal and vertical attenuation, respectively, $$G_{\text{Max}}$$ is the maximum directional gain of the single irradiating element, and $$A_m$$ is its front-to-back ratio. The attenuations $$A_{H}(\phi)$$ and $$ A_{V}(\theta)$$ depend on the horizontal and vertical 3 dB beamwidths, $$\phi _{3dB}$$ and $$\theta _{3dB}$$, and are given by 4 $$$\begin{align} A_{H}(\phi) &= -\min {\left\lbrace 12 {\left(\frac{\phi }{\phi _{3dB}}\right)}^2,\nobreakspace A_m \right\rbrace}, \end{align}$$$5 $$$\begin{align} A_{V}(\theta) &= -\min {\left\lbrace 12 {\left(\frac{\theta -90}{\theta _{3dB}} \right)}^2,\nobreakspace \text{SLA}_V \right\rbrace}, \end{align}$$$where $$\text{SLA}_V$$ is the side-lobe suppression limit [22, 23]. The beam gains are used to construct the grid of beams (GoB).

Grid of Beams (GoB)

The GoB gives a low-complexity beam-based simulation strategy to link the UE to the sectors' beams that may serve it [24]. It lists the azimuth and elevation bearings of the centers of the coverage areas of the beams [24] w.r.t the corresponding antenna sector. The beams present different irradiation patterns, and superposition occurs when creating the GoB [25]. In SAMA, the beams are arranged to form complementary regions that segment the sector azimuth range using the beams' half-gain beamwidth—a customized beam configuration is also possible. We can obtain the beam serving a UE by evaluating the received power and the CSI.

Channel State Information

The models for the equipment previously discussed can be used to estimate the CSI and evaluate many of the RAN aspects. SAMA considers that the BS transmits a downlink pilot, a reference signal [17], and that the UE measures it to obtain the CSI. The higher the CSI value, the better the channel condition. The CSI at the $$u$$-th UE from the $$b$$-th beam of the $$n$$-th sector (although a BS is composed of several sectors, it is easier to include the BS index in the sector and ignore the BS number) is (in dB) 6 $$$\begin{equation} \text{CSI}(u,n,b) = P_{\text{Tx}}(n) + G(u,n,b) + \text{PL}(n,u), \end{equation}$$$where $$P_{\text{Tx}}(n)$$ is the transmission power at the $$n$$-th sector, $$G(u,n,b)$$ is the gain from the $$b$$-th beam of the $$n$$-th sector toward the $$u$$-th UE (calculated using Equations 2 or 3, for $$\theta$$ and $$\phi$$ between the UE and the BS), and $$\text{PL}(n,u)$$ is the correspondent path loss (PL). Note that this CSI definition may refer to a collection of different channel indicators reported by the UE in the 5G technology as the CQI, PMI (precoding matrix indicator), CRI (CSI-RS resource indicator), SSBRI (SS/PBCH resource block indicator), LI (layer indicator), RI (rank indicator) and/or L1-RSRP [26]. They are currently not addressed by SAMA, simplifying the model without impacting the channel attenuation modelling by Equation (6). Besides, this also does not affect the assessment of the RAN performance and resulting comparative analyses.

Path-Loss Model

SAMA encompasses the alpha-beta-gamma (ABG) model [27] for path loss (PL). It is a simple empirical method for large-scale PL by means of [27] 7 $$$\begin{align} \text{PL}(f,d) = 10\alpha \log _{10}(d) + \beta + 10 \gamma \log _{10}(f) + \mathcal {X}_{\sigma }\nobreakspace \text{[dB]} \end{align}$$$where $$\alpha$$ and $$\gamma$$ express the angular dependence of the PL on the distance ($$d$$) between the transmitter (BS) and the receiver (UE) and the frequency ($$f$$), respectively; meanwhile, $$\beta$$ is a linear coefficient used to improve the model's agreement to empirical data, and $$\mathcal {X}_{\sigma }$$ represents the large-scale signal fluctuations caused by shadowing and modeled using a log-normal distribution. We do not specifically account for uncertainty in the UE measurements. However, employing different random shadowing $$\mathcal {X}_{\sigma }$$ values in the PL model may account for this [28].

UE Sensitivity

The UE sensitivity threshold follows the 3GPP's recommendation ETSI TS 138 101-1 [29]. If $$\text{CSI}(u,n,b)$$ is smaller than the threshold, then the $$u$$-th UE cannot connect to the beam $$b$$ of the BS $$n$$.

UE–Beam Association

The $$u$$-th UE is associated with the beam $$b_u$$ in the sector $$n_u$$ when 8 $$$\begin{equation} (n_u,b_u) = \arg \max _{(n,b) \in \lbrace 1\dots N \rbrace \times \lbrace 1,\mathcal {B}_n\rbrace }{\text{CSI}(u,n,b)}. \end{equation}$$$The $$u$$-th UE is associated with the RAN's beam offering the best CSI. At the moment, SAMA assumes that the UEs remain fixed during a time frame and the association among UEs and serving beams, BS, and CSI do not change over the time frame interval.

BS Arrangement

The arrangement of the BSs (and their sectors) on the ROI impacts the network performance since the beam associated with a given UE (and vice versa) will depend on the radio path between the UE and the different transceivers of the RAN infrastructure. In each simulation run, SAMA considers that the RAN is composed of $$N$$ BSs (and, consequently, it is composed of $$N\times S/BS$$ sectors—$$S/BS$$ is the number of sectors per BS). They can be arranged using different approaches.

Arbitrary BSs Arrangement

To evaluate the RAN using the existing or legacy network sites, SAMA can read the BS positions from a file.

Random BSs Arrangement

Another option is to place the BSs randomly over the ROI using a uniform distribution to draw the BSs' coordinates.

UEs-Dependent BSs Arrangement

To assess the best possible RAN performance, the influence of the arrangement of BSs shall be mitigated; thus, we reduce the average distance between the UEs and the closest BS to each UE. For this purpose, SAMA positions the BS by clustering the UEs using the Euclidean distance [30] into $$N$$ sets and using the centroids of the clusters for the BSs' positions. Since, in general, a UE is expected to connect to the network using the closest BS, this approach reduces the expected radio link path loss. Figure 2 presents a sample of 800 UEs drawn from a UE-density map (constructed using the density of residences presenting wireless broadband connection [31, 32]) and the resulting arrangement of four BSs using the clustering of UEs.

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Duplexing Schemes

Duplexing refers to the strategy of providing two-directional links. Frequency-division duplexing (FDD) and time-division duplexing (TDD) are the cases supported by wireless mobile networks [33]. FDD employs different frequency bands for the downlink and the uplink. Therefore, there is no control parameter for the FDD besides the bandwidths in each direction that are parameterized in the configuration file.

Meanwhile, TDD shares the same bandwidth for both. Depending on the case, one can be more advantageous than the other [34]. To allow more flexibility, irrespective of the duplexing scheme, SAMA assumes independent scheduling (Section 3.3) in the downlink and uplink in every BS. SAMA uses TDD with the duplexing ratio 9 $$$\begin{equation} r_{\text{duplex}}=t_{\text{up}}/(t_{\text{up}} + t_{\text{down}}). \end{equation}$$$to assign the air interface resources for uplink or downlink.

5G RAN Resources

Resource Blocks

In this section, considering a 5G air interface, we present how SAMA obtains the UEs-beams-BSs associations and allocates the resources for a given RAN.

The air interface provides resource blocks (RBs). An RB encompasses the smallest resource that can be given to a UE. Figure 3 shows a typical representation of the time-frequency resources in an RB. In the long term evolution (LTE) specification, the resource block is composed of twelve neighbouring subcarriers of seven subsequent orthogonal frequency division multiplex (OFDM) symbols, resulting in 84 resource elements (RE)—the tiniest fraction of an RB.

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Each BS beam can use the same resources to serve the UEs connecting with it. The activation table $$\zeta (t,f,u,n,b)$$ indicates if the beam $$b$$ in the sector $$n$$ during the timeslot $$t$$ is using the $$f$$-th carrier to serve the UE $$u$$. Note that if the whole OFDM symbol is being employed, then $$\zeta (t,f,u,n,b) =1\nobreakspace \forall f=1\dots F$$, and if the beam is active during the whole time frame, then $$\zeta (t,f,u,n,b) =1\nobreakspace \forall t=1\dots T$$.

The role of the scheduling algorithm is to obtain the activation table guaranteeing that 10 $$$\begin{align} \text{{$\zeta (t,f,u_i,n,b) \ne \zeta (t,f,u_j,n,b) \nobreakspace \forall \nobreakspace t,f,n,b, \nobreakspace \text{with}\nobreakspace {i \ne j}$}} \end{align}$$$that is, two UEs $$i$$ and $$j$$ served by the same BS beam $$(n,b)$$ cannot use the same RE $$(t.f)$$. Note that the association among BS, beams, and UEs imposes similar restrictions, while $$\zeta (t,f,u,n,b)$$ is used for the uplink and downlink when in TDD mode.

Activation Table Model

Some aspects are simplified to reduce the computational demands. In this regard, SAMA employs two simplifications regarding power allocation and beam activation. Although SAMA is intended to develop and evolve them, they allow us to evaluate the RAN performance under different configurations and schedulers fairly, not impacting the analyses of the performances of the possibly different RAN configurations and schedulers.

Beam Activation

We assume that in every timeslot, only one beam is active per sector. Using different subcarriers, the active beam may simultaneously serve several UEs in its reach during the timeslot.

Power Control

We assume that all sectors operate at the maximum output power $$P_{\text{max}}$$ and distribute the power equally over the whole bandwidth. Therefore, 11 $$$\begin{align} P_{\text{Tx}}(t,f,u,n,b) = \frac{P_{\text{max}}}{\text{{BW}}} \end{align}$$$where BW is the system bandwidth.

Let $$\mathcal {B}_n$$ list the beams in the sector $$n$$ that are associated with active UEs, and $$\mathcal {U}_{n,b}$$ list the UEs served by the beam $$b$$ in sector $$n$$. If $$\zeta ^\prime (t,n,b) = \max _{f,u}\zeta (t,f,u,n,b)$$, (i.e., it is equal to 1 (one) if the $$b$$-th beam at the $$n$$-th sector is active in the timeslot $$t$$, and, equal to 0 (zero), otherwise) the above assumptions lead to the scheduling conditions 12 $$$\begin{align} {\begin{cases} C_1\text{:} & \displaystyle \sum _{b \in \mathcal {B}_n}{\zeta ^\prime (t,n,b)} \le 1,\nobreakspace \forall \nobreakspace t,\nobreakspace n \\[12pt] C_2\text{:} & \displaystyle \sum _{u\in \mathcal {U}_{b,n}} {\sum _f P_{\text{Tx}}(t,f,u,n,b)}\le P_{\text{max}} \nobreakspace \forall \nobreakspace t,\nobreakspace b,\nobreakspace n \end{cases}} \end{align}$$$The first condition ($$C_1$$) restricts the number of active beams to one in every sector during the timeslot $$t$$. Meanwhile, $$C_2$$ restricts the power to be smaller than the maximum output power in every beam time slot.

Resource Allocation

The scheduling algorithm allocates the shared resources among the UEs. It determines which UE accesses an RB (the smallest resource that can be assigned) at every transmission time interval (TTI). Three of the most common scheduling algorithms are round-robin (RR), best channel quality indicator (BCQI), and proportional fair (PF) [17, 35–37]. In SAMA, the RB is configurable and can be adjusted to arbitrary time slot values and bandwidth.

Round-Robin (RR)

The RR scheduler assigns resource blocks randomly and recursively to the UEs. Therefore, it is highly fair from the UEs' viewpoint since scheduling does not depend on the UEs; consequently, it is widely used in many deployments due to its additional simplicity [38]. Nevertheless, the uniformed (it ignores CSI or CQI) management of the resources may degrade the overall performance. We consider a beam-oriented RR, prioritizing the beams with the longest UE queues, as in [39].

Best Channel Quality Indication (BCQI)

In mobile networks, the BS periodically receives CQI from the UEs. The BCQI scheduler allocates RBs to the UE that presents the best CQI at every TTI. Thus, it can achieve the most significant cell throughput. Nevertheless, it lacks fairness [38] since the UEs with the worst CSI may never receive an RB [17].

Proportional Fair (PF) Like

The PF scheduler is the most used scheduling algorithm for network equipment. It optimizes the logarithmic utility function of the throughput/data rate among users, assigning resources to the user leading to the largest utility [35]. As a result, in each slot, resources are allocated to the UE with the highest ratio between instantaneous achievable rate (capacity) and throughput before the current slot [40]. Note that in the first slot, all data rates are zero, and PF mimics the BCQI scheduler. Therefore, to achieve a good trade-off between user throughput and fairness, we employ an algorithm that assigns resources to the UE with the best CQI in the first slot and, subsequently, uses RR to allocate RBs to the UEs in the remaining slots [41]. We refer to it as PF-like due to the reasonable trade-off fairness among users it provides [41].

Evaluation of the RAN Performance

Different mobile services impose different requirements. For example, when the RAN attends subscribers of the eMBB service, it is necessary to account for the throughput of the UEs to accurately asses and evaluate the RAN performance. Meanwhile, in the URLLC scenario, the delay between the data transfer start and the instruction for the transfer, the so-called latency, is a critical network performance indicator. We define these indicators below.

Indicators of UE Performance

Capacity

The Shannon law provides the channel capacity [bits/s] for each UE during the timeslot $$t$$ [42] 13 $$$\begin{equation} C_{\text{timeslot}}(t,u) = \text{BW}(t,u) \log _2{(1+ \text{SNIR}(t,u))}. \end{equation}$$$The throughput (the total of bits transmitted) for the $$u$$-th UE up to the $$t$$-th timeslot is given by the summation of the timeslot capacities—Equation (13)—multiplied by the timeslot duration over the timeslots in which the UE is active up to $$t$$ (inclusive). The expression depends on the Signal to Noise plus Interference Ratio (SNIR), the ratio between the received power and the sum of the contributions (interference) of any other active transmitter plus noise. The SNIR is defined below in Section 4.1.4. We point out that although SAMA does not apply a specific modulation scheme, it provides a comprehensive and reasonable evaluation of the available channel capacity since it uses Shannon's formula as ceiling.

If $$\Delta _T$$ is the slot duration and $$\mathcal {T}(t,u)$$ lists the timeslots when a beam serves $$u$$, the troughput [bits] of $$u$$ during the time frame up to the timeslot $$t$$ is 14 $$$\begin{equation} \text{{$R$}}(t,u) = \sum _{\tau \in \mathcal {T}_u}C_{\text{timeslot}}(\text{{$\tau $}},u)\times \Delta _T. \end{equation}$$$We use $$R(u)$$ for $$R(T,u)$$, that is, for the user throughput in the whole time frame.

Throughput Deficit

If the RAN must be designed to provide a minimum target throughput $$\text{{$R$}}_{\text{{target}}}$$ [in bits] for one or multiple UEs, the throughput deficit [in bits] for the $$u$$-th UE up to the timeslot $$t$$ is 15 $$$\begin{align} \text{{$RD$}}(t,u) = \text{{$R$}}_{\text{{target}}} - \text{{$R$}}(t,u) \end{align}$$$We use $$\text{{$RD$}}(u)$$ for $$\text{{$RD$}}(T,u)$$, that is, for the user throughput deficit [in bits] in the time frame after the last timeslot. When $$\text{{$RD$}}(u)$$ is positive, the throughput provided to the $$u$$th UE is still smaller than $$\text{{$R$}}_{\text{{target}}}$$; it becomes negative when the provided throughput surpasses the target.

Latency

Latency can be defined as the time between successive accesses to the channel. Thus, in the uplink, the latency for the $$u$$-th UE in $$t$$ is defined as 16 $$$\begin{align} \text{{$L(t,u) = \min _\tau {((\zeta (t, f, n, b, u) =1) \nobreakspace \wedge \nobreakspace (\zeta (t-\tau, f, n, b, u) =1)}$}}, \end{align}$$$in words, it is the distance between two consecutive active instants for the UE. We can obtain the minimum, average, and maximum latency from the formulation for individual UEs and among all UEs.

Signal to Noise Plus Interference Ratio

For the UE $$u$$, placed at $$p_{\text{u}} = (x_{\text{u}},y_{\text{u}})$$, associated with the BS $$n_u$$ and the beam $$b_u$$, during the timeslot $$t$$, at the carrier $$f$$, the downlink SNIR is given by 17 $$$\begin{align} & \text{SNIR}_{\text{DL}}(t,f,u) = \\ & \nobreakspace \nobreakspace \nobreakspace \frac{\text{P}_{\text{Rx}}^{\text{DL}}{(u,n_u,b_u)}}{\sum _{(n,b) \ne (n_u,b_u)}{\zeta (t,f,u,n,b)\text{P}_{\text{Rx}}^{\text{DL}}{(u,n,b)}}+P_{\text{N}}\text{BW}(t,f,u)}. \nonumber\end{align}$$$Note that the expression considers the received power $$\text{P}_{\text{Rx}}^{\text{DL}}{(u,n_u,b_u)}$$ at the $$u$$-th UE from the $$b$$-th beam of the $$n$$-th sector, $$P_{\text{N}}$$ is the power density of the noise and $$\text{BW}(t,f,u)$$ the bandwidth allocated for the user $$u$$ during $$t$$. Note that $$\zeta (t,f,u,n,b)$$ and $$\text{BW}(t,f,u)$$ depend on the resource allocation. The interference at the receiving UE originates from other beams in the same sector and other sectors, and, in principle, the sectors are not coordinated in time.

Similarly, at the uplink, the SNIR at the beam $$b_u$$ of the sector $$n_u$$ through which the $$u$$-th UE sends data is 18 $$$\begin{align} & \text{SNIR}_{\text{UL}}(t,f,n_u,b_u) \nonumber\\ & \quad = \frac{\text{P}_{\text{Rx}}^{\text{UL}}(u,n_u,b_u)}{\sum _{u^{\prime } \ne u}{\zeta (t,f,u^{\prime },n,b) \text{P}_{\text{Rx}}^{\text{UL}}{(u^{\prime },n_u,b_u)}} + P_{\text{N}}\text{BW}(t,f,u)}. \end{align}$$$This expression considers the received power $$\text{P}_{\text{Rx}}^{\text{UL}}(u,n,b)$$ at the beam $$b$$ of the sector $$n$$ from the UE $$u$$. The interference at the receiving beam originates from other UEs served by the RAN.

RAN (Aggregate) Indicators of Performance

Appropriate indicators for network performance are essential. Beforehand, UE's SNIR, capacity, and latency were mentioned. These indicators address the performance of an individual UE. From them, we define aggregate indicators for the performance of the RAN.

RAN Throughput

RAN throughput is the bit total the whole RAN provides (all BSs, sectors, and beams), considering all user equipment. It is the summation of the throughput for all the UEs (during one time frame) 19 $$$\begin{align} \text{{$R$}}_{\text{RAN}}= \sum ^{U}_{u=1}{\text{{$R$}}(u)} \qquad \text{[bits]} \end{align}$$$In SAMA, the throughput can be assessed for smaller elements, such as the sector, focusing on different RAN components.

Average Throughput Deficit

The average throughput deficit [in bits] for all the UEs is 20 $$$\begin{align} \overline{\text{{$RD$}}} = \sum ^U_{u=1}{\text{{$RD$}}(u)} = U \text{{$R$}}_{\text{{target}}} - \sum ^U_{u=1}{\text{{$R$}}(u)} = U \text{{$R$}}_{\text{{target}}} - \text{{$R$}}_{\text{RAN}} \end{align}$$$

Spectral Efficiency

Spectral efficiency [in bits/s/Hz] evaluates the usage of the bandwidth. For a UE, it is the UE throughput divided by the bandwidth employed, leading to $$ S_u = \sum ^{T}_{t=1} \frac{ R_{\text{timeslot}}(t,u)}{\text{BW}(t,u)}$$. For the whole RAN, the spectral efficiency averages the spectral efficiency of the UEs 21 $$$\begin{align} \text{{$S = \sum\limits ^U_{u=1}{\sum\limits ^{T}_{t=1} \frac{ R_{\text{timeslot}}(t,u)}{\text{BW}(t,u)}}$}} \end{align}$$$

Fairness Index

It assesses the equity of the network: a proxy for the ratio of UEs that are satisfied ($$F$$) or starving UEs ($$1-F$$). We use Jain's fairness index [43] to evaluate it. For the user throughput, the fairness index is 22 $$$\begin{align} F_{\text{{$R$}}} = \frac{{\left(\sum _{u=1}^{U}{\text{{$R$}}(u)} \right)}^2}{U\sum _{u=1}^{U}{\text{{$R$}}(u)^2}} . \end{align}$$$

The Simulator

SAMA simulator is coded in Python in a modular fashion, and its configuration is done by editing a .yml (yaml) file [44]. The entities described in Section 2 are mocked as classes. The associations between classes mimic the responsibilities of the RAN components, as depicted in Figure 4. The network object is responsible for instancing the BSs and UEs, calling the interference calculations, and computing and storing the performance indicators, among other functionalities. The UE disposition object represents a collection of UEs (which can have different characteristics). Its primary function is to verify if the CSI is within the sensitivity threshold and then to inform the UEs' statuses (channel matrix and demands as the throughput target). The simplicity of a UE (as compared to the BS), together with the possibility of processing them jointly in a batch, is the main reason for using the object for the set of UEs instead of individual UEs, saving memory and execution time while not impacting the assessment of the RAN performance. These design decisions make SAMA easy to scale for more extensive networks, with more UEs and BSs, without significantly impacting memory and computing requirements (as we show later, in Section 6.6, SAMA complexity increases linearly with the number of UEs and BSs). To better illustrate the link budget simulations, we refer to the flowchart in Figure 5. Simulation execution goes through three stages: network definition, interference simulation, and indicators storage. Algorithm 1 describes the processing sequence in the first two stages at a high level of abstraction. Following, we delve into some details of the process.

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Network Definition

The network creation stage consists of instantiating the network entities using the configurations from the parameters file. The configuration parameters affect the algorithm execution, BS and UE types, and their numbers and disposition. Subsequently, the UE object is instantiated, and the positions for the UEs are obtained according to the selected method. The BS positions are then defined to instantiate the BS objects. Other auxiliary components exist, but they are omitted to keep this description short. For more details, please refer to the code [18].

Once all the entities are instantiated, the simulator creates a matrix of CSI estimates for all UEs within the HPBW (half power beamwidth) for every beam using Equation (6). Note that if the RAN is appropriate (in the sense of the combined coverage for the BSs), then every UE in the ROI should lie inside the HPBW with at least one beam in the GOB. Since GOB may present superposed beams (Section 2.3.3), the UE is assigned to a beam using Equation (8), and the association is stored for use in the scheduling phase. If TDD is used, the duplex controller builds uplink and downlink activation tables (as described in 2.7) before the simulator advances to the interference calculation.

Interference Calculation

We evaluate the RAN's performance using a time frame containing $$T$$ timeslots. To assess the RAN's performance, the simulator addresses the interference in the timeslots used to assign RBs. Therefore, interference calculation must be aware of the scheduling of the RAN resource, that is, the UE-beam activation table over time and frequency.

The computation of the SNIR must account for the relevant specificities. When in downlink timings, the interference came from other BS antennas. In contrast, the calculated interference in the uplink came from other active UEs transmitting during the same timeslot. Besides, in principle, the carriers employed for the UE to transmit (BS to receive) differ from the ones the BS uses to transmit (UE to receive). Consequently, in the timeslot $$t$$, SNIR is estimated using equations (17) and (18). In both cases, the simulator considers inter-sector (from the same and different BSs) interference. The process is iterated for all timeslots within the time frame. In the case of TDD, the uplink and downlink timings are assumed to be controlled and synchronized among all BSs in the ROI. Note that process 4 in Figure 5 informs changes in UEs–beams relationship (active UEs during $$t$$, active beams, UE that demand alterations, which can be used to model the effects of UE mobility) for updating the schedulers, depending on the algorithm. During this set, many indicators (Section 4) over the time index $$t$$ are stored in memory with the format $$ \text{indicator}\times UE_{\text{ index}} \times t (\text{timeslot index})$$ (process 8 in Figure 5). When $$t$$ reaches the time frame duration $$T$$, the simulator saves the indicators obtained to a file.

Indicators Storing

In process 9 in Figure 5, SAMA builds matrices containing indicators with the format $$ \text{indicator} \times UE \text{ index}$$. Since saving all the raw data demands a large storage capacity, the raw data is organized and summarized by groups of active UEs, BSs, and beams, depending on the user's needs. An association table in the format $$UE \times Sector \times beam \times CSI$$ can also be stored.

Stop Criteria

SAMA can be configured to stop after a pre-defined number of time frames. Nevertheless, this does not guarantee trustworthy performance indicators. Consequently, SAMA can be set up to apply the Mann-Whitney U-test [45, 46] using a configurable batch size. The Mann-Whitney U-Test is a non-parametric statistical test of the null hypothesis that two random variables have the same distribution [46]. We use the Mann-Whitney U-Test to verify if the distribution of the selected performance index is not varying, that is, if the distribution of the performance index has stabilized. The simulation halts when the U-test accepts the null hypothesis after some rounds. For example, one compares the samples of the user throughput indicator every 20 rounds using the U-test; by default, SAMA employs the $$p$$-value equal to 0.05 to apply for the indicator configured to be tested.

1

ALGORITHM

Simple (one time-frame) interference, capacity computation, and UE-dependent indicators simulation algorithm.

Require: parameter file
1:	$$[ p_{\text{UEs}}, p_{\text{BS}}, p_{\text{RAN}}]$$ $$\leftarrow$$ Read(parameter)
2:	$$\lbrace \text{UE}\rbrace$$ $$\leftarrow$$ Create UE($$p_{\text{UEs}}$$)
3:	$$\lbrace (\text{BS}, \lbrace \text{Sectors} \rbrace) \rbrace$$ $$\leftarrow$$ Create BS($$p_{\text{BS}}$$)
4:	$$\lbrace \text{Beams}\rbrace$$ $$\leftarrow$$ $$G_b(\theta, \phi)$$ using (3)
5:	Network $$\leftarrow$$ Create Network($$\lbrace \text{UE}\rbrace$$, $$\lbrace (\text{BS}, \lbrace \text{Sectors} \rbrace)\rbrace$$, $$\lbrace \text{Beams}\rbrace$$, $$p_{\text{RAN}}$$) ▹ UEs' positions are in $$\lbrace (x_u,y_u)\rbrace$$ and BSs' positions are in $$\lbrace (x_n,y_n)\rbrace$$
6:	for (BS, UE) $$\in$$ RAN do
7:	Compute $$PL ({\rm BS}$$, UE) using (7)
8:	for $$beam \in \lbrace \text{Beams}\rbrace$$ do
9:	Compute CSI(BS, beam, UE) using Equation (6)
10:	end for
11:	end for
12:	Associate UE–(BS, beam) using Equation (8)
13:	while $$1 \le t \le T$$ do
14:	for Sector $$\in$$ RAN do
15:	Apply scheduler within the sector
16:	end for
17:	for UE scheduled during timeslot $$t$$ do
18:	Compute $$\text{SNIR}_{\text{DL}}$$ with (17)
19:	Compute $$\text{SNIR}_{\text{UL}}$$ with (18)
20:	Compute individual UE indicators (Section 4.1)
21:	end for
22:	Compute aggregate indicators (Section 4.2)
23:	$$t++$$
24:	end while
25:	Compute latency with (16)

Application Example

To illustrate the usage of SAMA, we employ different analyses. First, we employ SAMA to simulate a completely synthetic RAN operating in a rectangular ROI. This scenario is employed to assess and compare the performance of the scheduling algorithms in the downlink when the number of BSs varies. Then, we evaluate how the TDD ratio affects the compromise between the uplink and the downlink throughputs. Then, we simulate the RAN service in the $${\rm S}\tilde{a}{\rm o}$$ José de Ubá municipality. Following, we evaluate the RAN's latency (necessary for URLLC use cases resulting from different schedulers) in a synthetic RAN using different numbers of BSs. At last, we consider the mMTC scenario and evaluate the network performance when the number of UEs vastly increases but under low UEs' data-rate demand. In all simulations, besides the URLLC, we use the air interface configuration and equipment models defined in Table 1.

TABLE 1 Configuration parameters.

RAN's parameters
Central frequency	3.5 GHz
Bandwidth	100 MHz (reused in every sector)
Number of BS in the RAN	Varies
RAN's service target
$$\text{{$R$}}_{\text{{target}}}$$ (Mbps)	$$[30, 10]$$ [downlink, uplink]
BS's parameters
BS height	30 m
Number of sectors per BS	3
BS sectors bearings ($$\phi$$, $$\theta$$)	$$\phi$$=$$(60^{\text{o}}, 180^{\text{o}}, 300^{\text{o}})$$, $$\theta$$=$$(0^{\text{o}}, 0^{\text{o}}, 0^{\text{o}})$$
Sector's parameters and model
Transmission power per sector	100 W
Sector antenna array	8 x 8 (0,5$$\lambda$$ spacing)
Sector antenna array gain	As in Section 2.3.2
Array element gain	5 dBi
Number of beams	20 per antenna
UEs's parameters and model
UE height	1.5 m
UE transmission power	400 mW
UE antenna diagram	omnidirectional
UE antenna gain	0 dBi
Simulation parameters
Path-Loss model variance	6 dB
Timeslot duration	1 ms
Round duration $$T$$	1000 timeslots
Stop criterion
Mann-Whitney U-test on	$$C_{\text{u}}$$
Batch size	20 rounds
$$p$$-value	0.05

Comparison of Scheduling Algorithms

To assess the performance of the scheduling algorithms, 1000 UEs are randomly distributed, assuming a uniform 2D distribution, over a square ROI of $$30\times 30$$ $${\rm km}^2$$ (the ROI is divided into 1000$$\times$$1000 pixels of 30$$\times$$30 $${\rm m}^2$$ each). We configure SAMA to cluster UE's positions to place the BSs as described in Section 2.2. This is applied for $$N=[1, 2, 3, 4, \ldots, 18, 19, 20]$$ BSs having three sectors and beamforming capacity. Figure 6 shows the distribution of the CSI for a few values of $$N$$; one sees that the average CSI increases with $$N$$. The channel capacity is expected to follow this channel improvement, although interference and schedule may impact the UE capacity in the timeslot and consequently the attained throughput. Thus, we evaluate the RAN performance under the scheduling algorithms in Section 3.3.

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We evaluate the downlink throughput in an eMBB scenario. The RAN must provide the target throughput for all the UEs it serves, and it is considered that the throughput $$\text{$R$}_{\text{target}}$$ = 30 Mbits during 1 s, that is, a target rate $$R_{\text{target}}$$ = 30 Mpbs. The top graph in Figure 7 shows the percentage of UEs reaching $$\text{{$R$}}_{\text{{target}}}$$. A pattern is shown in Figure 7. The RR scheduler may be worse in serving the UEs when there is a low density of BSs, but, at the same time, it is fairer (more significant fairness index); BCQI is the least fair; meanwhile, PF-like presents a middle term between the previous two. The ratio of UEs that reach the target throughput is smaller for RR, but it improves over the BCQI and PF-like for many BSs. The reduction in the SNIR, as depicted in the middle graph in Figure 7, may explain that. The BCQI strategy allocates most (if not all) channel resources for the UE having the best channel condition. It reflects on the interference since beams pointing toward UEs near the BSs are most likely being used, providing a larger SNIR when the number of BSs is not too large. However, the BCQI criterion is inherently less fair to this, as seen in the bottom graph in Figure 7. For low to medium density of BSs, the PF-like scheduler presents a good compromise between the fraction of UEs that achieve the target throughput and fairness. Although the average SNIR under the PF-like scheduler is the worst, the PF-like indicators expectantly lie between the RR and BCQI indicators since it simply applies a combination of RR and BCQI. Meanwhile, the overall throughput does not change much across the different schedulers; see the bottom graph in Figure 7.

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In Figure 8, we evaluate the SNIR and the percentage of UEs reaching the target throughput when the BSs' transmission power changes. One sees that higher power levels can slightly increase the SNIR, independently of the scheduler. Nevertheless, this difference in SNIR does not strongly affect the fraction of UEs reaching the $$\text{{$R$}}_{\text{{target}}}$$. When the number of BSs increases, the difference in the SNIR between different power levels reduces for all three schedulers. Probably, this derives from the fact that increasing the number of BSs decreases the average distance between a UE and the assigned BS, increasing the relevance of the antenna gain compared to the path loss for defining the BS-UE association and interference calculation.

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In the following experiments, we employ the PF-like scheduler since it is well suited for most use cases [41] and, as we saw, it presents good $${\rm indicators}\times{\rm fairness}$$ compromise.

Time Division Duplexing Effect

Considering the same RAN and ROI, we evaluate the performance under TDD. We consider TDD ratios of $$r_{\text{duplex}} = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]$$ (e.g., if $$r_{\text{duplex}}=0.3$$, the channel is employed for downlink during 70% of the total time and uplink in the remaining 30%). The results in Figure 9 show that as this time-sharing factor reduces, fewer UEs achieve the $$\text{{$R$}}_{\text{{target}}}$$ in the uplink. When $$r_{\text{duplex}}=0.5$$, a similar percentage of UEs attain the $$\text{{$R$}}_{\text{{target}}}$$ in the downlink and the uplink.

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The bottom graph in Figure 10 shows that $$r_{\text{duplex}}$$ effectively accommodates different throughputs in the RAN's uplink and downlink. One notes that for the successive 10% increase in $$r_{\text{duplex}}$$, the resulting increases in the throughput are greater in the DL than in the UL. The differences come from the SNIR levels. The top graph in Figure 10 shows that the uplink presents an SNIR around 40 dB smaller than the downlink, translating into less capacity and, consequently, in a smaller throughput. The difference in SNIR levels results from the non-directional radiation pattern (causing more interference) and smaller transmission power (smaller signal intensity) of the transmissions irradiated by the UE. One also sees that the downlink's SNIR achieves a limit after a sufficient number of BSs is employed—this does not occur in the uplink. As expected, one also observes that the SNIR does not greatly vary when $$r_{\text{duplex}}$$ varies, although it depends on the number of BSs composing the RAN.

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RAN Design for a Municipality

To test the simulator for a more realistic scenario, we chose the region of $${\rm S}\tilde{a}{\rm o}$$ José de Ubá, a mostly rural municipality in Rio de Janeiro State, Brazil. The UE density data is extracted from [31, 32] with a map resolution of approximately 30$$\times$$30 $${\rm m}^2$$. We draw 750 UEs (approximately one-tenth of the population) for the eMBB scenario. We evaluate the RAN performance for $$[1, 2, 3, 4, \ldots, 23, 24, 25]$$ BSs, the PF-like scheduler, $$r_{\text{duplex}}=0.4$$, and the equipment configuration in Table 1. We set the hypothetical goal of 70% of the UEs being correctly satisfied, that is, achieving $$\text{{$R$}}_{\text{{target}}}=[30,10]$$ ([DL, UL]). Figure 11 shows that this goal is achieved with 23 BSs. Figure 12 illustrates the resulting association between UEs and BSs, following the formulation in Section 2.5. One notes that a UE is not always associated with the nearest BS. This results from the log-normal shadowing that introduces randomness in the path loss, the arrangement of the sectors, and the beams' bearings that are not perfectly complementary or pointing to the area below the BS's tower. They produce irregular cell contours and superimposed GOBs.

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URLLC Scenario

We also evaluate SAMA's ability to assess the performance of the RAN in the URLLC scenario. In this case, we evaluate the latency indicator using the different schedulers. Figure 13 presents an aggregate view of the results. The results indicate a large difference between the BCQI and the other schedulers. Since the BCQI only serves the UEs with the best channel conditions, it leaves the rest unattended, resulting in superposed minimum, maximum, and average latency. The RR and PF-like present lower latency values. Figure 14 shows the latency distributions for the RR and the PF-like (BCQI is excluded since, as seen before, it is much worse than the two with respect to this performance indicator). The latency distribution is more concentrated at lower latency values for the RR, following the graphs in Figure 13. Besides, one notes that the latency variability reduces as the number of BSs increases. Although a reliable evaluation of the URLLC service should consider moving UEs at different speeds, as discussed in Section 6.7, this can be included in SAMA by classifying UEs into grades of movement speed and adjusting the propagation models accordingly.

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mMTC Scenario

An mMTC network must serve many UEs with low data rates and activity. In this case, connectivity is the most critical performance indicator, even under reasonable latency and low throughput. Although connectivity can be ensured if large latency is possible; however, if the machines have storage limitations, then a minimum throughput needs to be provided for the machines' memories not to overflow. Therefore, we assess the percentage of machines achieving a minimum throughput as an indicator to evaluate the mMTC scenario.

Consequently, we use SAMA to evaluate the RAN when the number of UEs increases ($$U = [500, 1000, 1500, \ldots, 9500, 10000]$$) for a fixed number of BSs ($$N=10$$). We set $$\text{{$R$}}_{\text{{target}}}$$ = 10 kbps, low BS transmission power (10 W), and the UE transmission power is also reduced to 200 mW. Figure 15 compares the RAN's ability to provide the UEs with the minimum throughput. When the BCQI, PF-like, and RR are employed to schedule the RAN resources, the three attain the target throughput for nearly 100% of the UEs in the downlink. Nevertheless, in the uplink, the lower transmission power and the higher interference affect the achieved capacity and thus the throughput—a similar behaviour was reported in Figure 8. Figure 15 shows that the RR scheduler provides the minimum throughput for more users, but when the number of UEs is too large, it also fails.

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Figure 16 shows the total RAN throughput in this mMTC scenario. All curves present the same behaviour. Despite the number of UEs achieving $$\text{{$R$}}_{\text{{target}}}$$ reduces, the RAN throughput is higher the more UEs $$U$$ exist—since the number of UEs near the BSs resulting in better channel conditions increases, augmenting the total throughput.

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Simulation Time

Figure 17 presents the mean (in stronger color) and the dispersion (the graphs were obtained using 20 executions with 200 rounds each) of the simulation time—the expected runtime for one physical time frame in SAMA is the corresponding average in the graph divided by 200. The simulations are executed on a Core i7 12700F CPU with 64 gigabytes of RAM running Ubuntu 24. Although the dispersion of the simulation time increases as the numbers of BSs and USs increase, one notices an almost linear behaviour for the simulation time w.r.t the numbers of BSs and UEs considered; the linear coefficients of the first-order fittings for the different mean-time curves in Figure 17 lie within  .28 and  .34.

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As previously stated in the Introduction, the Vienna 5G system level simulator provides tools similar to SAMA. However, their underlying software architectures and parallelization strategies differ significantly. While Vienna 5G SL is based on Matlab and SAMA is coded in Python, their performance discrepancy is primarily rooted in their design philosophy. SAMA is architected to execute multiple, independent simulation runs in parallel–an approach that maximizes throughput for large-scale statistical assessments and is advantageous for capturing the stochastic nature of the RAN. In contrast, the Vienna 5G simulator employs parallelization to accelerate the computational tasks within a single, complex simulation, a design aimed at reducing the latency of a single run. The current version of SAMA includes essential features to provide valuable results on RAN performance in urban scenarios, employing the Mann-Whitney U-test to provide reliable and meaningful performance indices. A comparison between the execution times for the two simulators, presented in Table 2 [8], confirms this trade-off: while the execution times are comparable under high-load, single-threaded conditions, SAMA is significantly faster in the parallel case, whereas Vienna 5G performs better in the smaller-scale, single-thread scenario. On the other hand, SAMA is currently absent from multiple input multiple output (MIMO) channel models and non-orthogonal multiple access (NOMA) resources allocation and evaluation; the support for these techniques is under development, as well as more channel and user mobility models.

TABLE 2 Comparison between SAMA and Vienna 5G SL (lite) for single-thread and parallel simulations in SISO scenario.

1000 UEs and 100 BSs
	SAMA	Vienna 5G
Parallel (5 threads)	403 s	583 s
Single	2018 s	1895 s
100 UEs and 10 BSs
	SAMA	Vienna 5G
Single	35 s	19 s

On the Model Limitations and Evolution (Future Developments) of SAMA

SAMA has the advantage of presenting a highly automated approach to creating the simulation scenarios, requiring little input from the user. The application examples show a fraction of the analyses obtained using SAMA. Others can be made by altering the parameter files provided with the code; new models and features to complement SAMA are currently under development.

We note that the performance results may not perfectly match actual data. However, SAMA provides valuable insights by modelling key system behaviours under controlled assumptions, offering a solid foundation for further validation in real-world scenarios. SAMA provides a benchmark that can be used as a starting point for 5G RAN design, for example, when using the locations of existing RAN equipment for future 5G deployments. Also, it can be used to assess if a given distribution of base stations in a given ROI is adequate for offering the services of a specific vertical or if an expansion of the number of base stations is necessary.

Antenna Model

The (more straightforward) particular case of an antenna sector that does not support beamforming corresponds to the single-beam case.

Multiple Breams

The presented formulation can accommodate multiple active beams simultaneously by dividing the total transmit power by the number of active beams per sector. In the future, we intend SAMA to consider more than one beam active per sector.

Activation Table Model

The fixed-transmission-power and the one-active-beam-per-time-slot conditions do not compromise the evaluation of the RAN adequacy since they lead to using most of the resources during every active beam. One notices that the model in Equation (12) leads to the maximum channel capacity (the resource block is used at the maximum power density) for the active UE.

Transmission Power Allocation

Alternatively, an arbitrary power during a fixed bandwidth quantum could be employed. Meanwhile, the fixed-transmission-power assumption employed does not impose a tight limitation. The model can be iterated while reducing the transmission power if spare bandwidth is available in the sector serving the UE. This process can also start using a small transmission power and increase it until the activation table is satisfactory. Nonetheless, in any case, the power allocation process should be considered together with the performance, which depends on the resource allocation/scheduling algorithm employed.

UE Mobility

SAMA can classify UEs into grades (static, slow-moving, and fast-moving). This makes the UEs to move more or less rapidly from one time frame to another. However, the UEs' coordinates do not change, that is, UEs do not move during a time frame. Future developments are planned to include channel models for fast-fading and the Doppler frequency shift, allowing for a more accurate evaluation of scenarios with high-speed users. If the UEs move across timeslots, in addition to fading and Doppler effects, UE-beam association may have to be revisited in every time slot.

UE QoS Requirements

Another improvement refers to a more complex model of the UE's QoS requirements, besides a target throughput $$\text{{$R$}}_{\text{{target}}}$$. Service models to be considered in this case can be seen in [1, 2].

Microcell Network

Currently, SAMA does not support microcells and picocells operating at higher frequencies and using ultra-dense arrays [47]. Specific propagation models must be employed. The goal is to provide a tool for Hetnet (Heterogeneous networks) simulation using a mix of different BS types [48].

Propagation Model

More complex propagation models considering uncertainty in predicting the path-loss [49] are being developed with the appropriate models for different frequency ranges. Besides, MIMO channel support is being included in SAMA.

BS Arrangement

SAMA can be modified to include location-allocation strategies [19, 50] to optimize the BS arrangement depending on the UEs' distribution in the ROI and the use case scenario.

Conclusion

For the design and implementation of cellular networks, it is important to have a simulation tool with reliable models for the physical layer, which may evolve to include technological advances and provide reliable models for the equipment. SAMA is intended to fit into this concept. It is a free and open-source Python-based simulator. The code for SAMA is available for download [18]. SAMA is set up using a text file (and simple initial configuration examples for different scenarios are provided) to simulate a RAN's physical layer and evaluate its performance using diverse indicators such as the SNIR, channel capacity, throughput, latency, fairness, etc. Being an open-source project with a modular and object-oriented approach, SAMA can incorporate other channels, performance indicators, schedulers, and equipment models. It can also expand to include tailored functionality and models.

To outline SAMA's functionality, we presented different simulation scenarios for the RAN. Initially, the downlink performance of round Robin, best channel quality indicator, and performance fairness index schedulers is assessed using a synthetic RAN model. SAMA was also used to evaluate the RAN performance under different TDD ratios and BS transmission power. We also assessed (using SAMA) the number of BSs necessary to serve the users under the eMBB service requirement in an actual county. Another simulation considered using SAMA to evaluate a RAN for the URLLC service through the latency. Lastly, SAMA was employed to evaluate the RAN performance for the mMTC scenario, with many UEs being served. These examples show SAMA's versatility in assessing the performance of a 5G RAN under different systemic parameters and equipment models.

Author Contributions

Christian Fragoas F. Rodrigues: conceptualization, methodology, software, validation, data curation, visualization, writing – original draft, writing – review & editing. Lisandro Lovisolo: conceptualization, data curation, writing – original draft, writing – review and editing. Luiz Alencar Reis da Silva Mello: conceptualization, writing – review & editing.

Conflicts of Interest

The authors declare no potential conflicts of interest.

Data Availability Statement

All data is available upon request.

References

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