1 Introduction

A significant increase in the number of mobile users, various mobile apps, interconnected devices, and related services is driving the growth of mobile data traffic [1]. In recent years, there has been massive growth in the global mobile user base and data volume. It was predicted that by 2023, there could be tens of billions of mobile devices worldwide. By the end of 2023, global mobile data traffic, not including fixed wireless network traffic, was estimated to reach 130 Exabytes (EBs) per month and could reach 403 EBs per month by 2029. When fixed wireless networks are included, total mobile network traffic expected to reach approximately 160 EB per month by the end of 2023, with a climb to 563 EB per month by 2029. On the other hand, it was predicted that the proportion of mobile data traffic linked to 5G would increase from \(15\%\) in late 2022 to \(25\%\) by the end of 2023, and is forecasted to reach \(76\%\) by 2029 [2].

The increasing need for wireless mobile data service has made it clear that traditional wireless mobile network setups will not be sufficient. The optimal solution to address the growing demand is the implementation of an Ultra-Dense Small Cell (UDSC) Heterogeneous Network (HetNet). This involves the deployment of several low-power small Base Stations (BSs) with smaller coverage areas [3]. In HetNets, Small Cells (SCs) can encompass various types, such as microcells, picocells, femtocells, and relay nodes, and they can vary in size from ten meters to hundreds of meters [4]. These SCs can be deployed in diverse locations such as shopping malls, parking lots, airports, sports stadiums, homes, and offices. By adopting this approach, the link quality between the User Equipment (UE) and the serving BSs will be significantly enhanced, and the capacity of the network will be increased [5]. However, this solution will also pose various sincere challenges like spectrum allocation, interference, security and privacy concerns, power consumption, cost, and Handover (HO) management [6, 7].

HO is the main advantage of the cellular network over a limited local area network. However, the deployment of UDSC in HetNets will result in a higher number of Unnecessary Handovers (UHOs), leading to a substantial increase in signaling overhead within the system and a decrease in the overall quality of service. Consequently, the HO management strategy in UDSC deployed HetNets will play a crucial role in mitigating UHOs and Radio Link Failures (RLFs), thereby ensuring the overall quality of the network. In HO management, as the UE moves from the coverage area of the serving cell to that of the target cell, Handover Control Parameters (HCPs), such as the Time-To-Trigger (TTT) and Handover Margin (HOM), significantly influence HO performance. The precise configuration of HCPs is crucial in minimizing UHOs and RLFs [8, 9]. Signal level fluctuation, interference, UE velocity, cell load, and other system parameters significantly influence the settings of HCPs, aiming to achieve a balanced approach in mitigating both UHOs and RLFs. Despite the static setting of HCPs [9, 10], which may be suboptimal for HetNets, the self-configuration and self-optimization of HCPs are key factors in self-organizing networks [11, 12]. Numerous studies have explored the configuration and optimization of HCPs using various methodologies, ranging from UE positioning [13] and consideration of UE speed and HO types [14] to the application of diverse Machine Learning (ML) approaches. These methodologies have been investigated across various network configurations and system metric settings, including real-world network environments [15].

To attain optimal system performance, it is essential to carefully adjust the HCPs. This involves considering various system parameters from both network and UE perspectives, including signal level fluctuations, cell load, and UE speed variations. Furthermore, deploying ML techniques for these objectives demands comprehensive offline training due to the complexity of the parameters involved before online deployment. This is because an inappropriate setting online may lead to a degradation in network performance.

In this study, we propose a method based on an optimization algorithm and ML that focuses on the adjustment, optimization, and prediction of HCPs, including HOM and TTT. A comprehensive dataset containing information about Reference Signal Received Power (RSRP), Signal to Interference plus Noise Ratio (SINR), Cell load, UE speed scenarios, and associated HOM and TTT values was obtained. Additionally, Key Performance Indicators (KPIs) including, RLF and UHO, are also associated with the aforementioned parameters in the dataset. The data are collected for each UE speed scenario, for each UE, and at each measurement time.

1.1 Related Work and Motivation

Various ML approaches have been proposed in the literature for optimizing and dynamically setting both HOM and TTT, considering a range of system metrics and KPIs. Some studies have specifically used Fuzzy Logic Controller (FLC) to optimize HCPs, with a focus on enhancing parameters such as HOM and TTT. The authors of both [16] and [17] introduced a similar approach employing FLC within the context of 5G and beyond networks. This methodology uses inputs such as RSRP, Reference Signal Received Quality (RSRQ), and UE velocity to configure HOM and TTT automatically. In [16], the primary aim of this method is to address challenges related to Handover Rate (HOR) and HOPP. However, while the study does not explicitly provide the specific FLC rules for determining HOM and TTT, these rules are delineated in [17] by the authors, along with additional KPIs such as HOF, Handover Latency (HOL), and Handover Interruption Time (HOIT). In [18], the authors presented an HO decision approach employing FLC within a Long Term Evolution (LTE)/5G Ultra-Dense Network (UDN) setting. This method dynamically adapts both HOM and TTT based on SINR and UE velocity. Evaluation of its performance included metrics like HOR, HOPP, and overall system throughput. In [19], the authors proposed an approach that combines FLC with weight functions of the parameters to optimize HOM and TTT. In this approach, the input parameters of the FLC include SINR, cell load, and UE velocity. The performance of the system in this approach was evaluated using KPIs such as Handover Failure (HOF), Handover Ping-Pong (HOPP), and RLF. The study considered a maximum UE speed of 160 km/h. The study in [20] introduced an algorithm within a 4G/5G network scenario that integrates FLC into weight functions to enable adaptive adjustments to both HOM and TTT levels. The system performance evaluation included metrics such as HOPP, RLF, HOL, and outage probability.

Additionally, Q-learning, a type of reinforcement learning (RL), has been employed in certain studies for similar optimization tasks regarding HCPs. Notably, research efforts have explored the application of Q-learning algorithms to dynamically adjust parameters such as HOM and TTT in various environments. In [21], the authors presented an algorithm for an LTE network based on Q-learning. Various sets of HOM and TTT are selected to optimize performance. By observing parameters such as HOR, system throughput, and system delay and assigning weights to each, the reward function is derived. Ultimately, the set of HOM and TTT yielding optimal performance is identified for specific UE speeds. However, this study overlooks the consideration of additional metrics to evaluate the algorithm’s performance. In addition, the algorithm only considers UE speeds up to a maximum of 120 km/h. The authors in [22] introduced a method using the Q-learning algorithm to collectively estimate HCPs within the LTE for railways (LTE-R) system. HCPs were classified according to events based on UE measurement report, with HO threshold and offset for A2 and A4 events and HOM and TTT for A3 event. They examined HCPs at various speeds, including high-speed trains. However, the evaluation of the method’s performance was limited to assessing the HO success rate and system throughput, which may not provide a comprehensive evaluation of the proposed approach. In [23], the authors introduced an algorithm using Q-learning within a dynamic topology comprising 12 cells to optimize HOM, TTT, and cell individual offset (CIO), considering RLF and HOPP based on prior offline knowledge. The learning range for TTT and CIO is limited to 0 millisecond (ms) to 480 ms and − 4 dB to 4 dB, respectively. Additionally, the system’s performance is evaluated using KPIs such as RLF and HOPP, considering UE speeds of 5 km/h and 30 km/h, HO performance time, and CIO steps.

Moreover, researchers have merged FLC with Q-learning, giving rise to what is termed fuzzy Q-learning, aimed at enhancing HCPs. This integration uses the strengths of FLC alongside the adaptive learning capabilities of Q-learning, resulting in the development of effective hybrid methods. In [24], the authors introduced an approach based on fuzzy Q-learning in an LTE network. This approach aims to reduce the probabilities of HOF, HOPP, and call dropping ratio (CDR). The proposed platform outputs HOM and TTT while considering parameters such as adaptive HOM, HOF, HOPP, and CDR, and assigns weights to each KPI. The system’s performance is evaluated on the basis of HOF, HOPP, and CDR, as well as overall KPI, too-early HO, and UE satisfaction, with a maximum UE speed of 120 km/h. The authors in [25] proposed an optimization algorithm based on fuzzy Q-learning within an LTE network. The goal of the algorithm is to dynamically adjust the HOM to optimize load balancing and HO performance in the system. The FLC adjusts the HOM based on metrics such as HOR, call blocking ratio (CBR), and CDR, while the Q-learning platform provides rewards based on the level of CDR to further improve performance. The performance of the KPIs was evaluated by varying the optimization steps of load and HOM under different scenarios, including high mobility, high load, and combinations of both. However, the algorithm’s evaluation is limited by considering a maximum UE speed of 50 km/h, which may not fully demonstrate its effectiveness at higher speeds. In [26], the authors introduced a fuzzy Q-learning-based algorithm to dynamically adjust the HOM in a 5G HetNet. The objective of the algorithm is to optimize HOR and CDR without initially specifying FLC rules. Instead, the rules are injected into the FLC platform by a Q-learning agent, with HOR and CDR serving as inputs to dynamically adjust HOM. The performance of the system was evaluated in terms of HOR and CDR, considering UE speeds of 10 and 60 km/h, with TTT set to 400 and 200 ms, respectively. The authors in [27] suggested an algorithm based on fuzzy Q-learning to minimize the effects of RLF and HOPP in an LTE network. This approach dynamically adjusts the HOM using FLC, considering the current HOM and RLF conditions. Q-learning determines the actions based on the rewards derived from the RLF and HOPP rates. UEs are categorized into real-time (e.g., voice and video conference services) and non-real-time (e.g., messaging and email), as well as fast and slow, based on their traffic usage and speed. This categorization is essential because of differences in HOPP and RLF occurrences between real-time and non-real-time UEs, and UE speeds. The TTT is set to 256 and 160 ms for non-real-time and real-time UEs, respectively, across all speed scenarios. However, the study has some limitations, notably the consideration of HOM by a cell, in which the UEs engaged to that cell may experience different speeds and extreme variations in the received signal level. Additionally, setting TTT statically can result in HOPP and RLF occurrences. Although UE speeds are mentioned to be a maximum of 350 km/h, which is the highest speed considered in this context and has not been implemented outside of an LTE-R environment, specific evaluations regarding this aspect were not conducted.

ML techniques are also used for predicting prior data, in addition to classification, which is then applied to the system to perform necessary actions. In addition, these techniques can be particularly useful for determining HCPs which may then facilitate HO decisions. The authors of [28] proposed an ML framework aimed at maximizing SINR in an LTE network. The framework encompasses various ML techniques, including linear regression, Deep Neural Network (DNN), Categorical Boosting (CatBoost), eXtreme Gradient Boosting (XGBoost), and K-Nearest Neighbor (KNN). Genetic Algorithm (GA) is employed to collectively select the set of HOM and CIO values to achieve the maximum SINR. The HOM and CIO values were chosen within the ranges of 0 to 10 dB and − 10 to 10 dB, respectively. The evaluation of ML predictions was conducted in terms of Root Mean Square Error (RMSE), with CatBoost exhibiting superior performance compared to other techniques. The system is further evaluated on the basis of SINR levels and convergence time.

Among other ML techniques, Neural Networks (NN) are also employed for optimization problems. Various NN techniques have contributed to the optimization of cellular networks. The authors in [29] proposed a method that combines Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with a combination of Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) in an Ultra-Dense Network (UDN) environment. TOPSIS selects the optimal target BS based on RSRP, SINR, and cell load, while a Q-network, jointly using CNN and RNN, optimizes HO. The values of HOM and TTT are determined by a Q-learning agent that interacts with the environment. The system’s performance was evaluated using KPIs such as UE throughput, HOF, HOPP, and HO delay, considering various UE and BS densities. The method assigns equal importance weights to HOF and HOPP to reward the action, with the claim that HOF leads to RLF, despite RLF significantly impacting quality of service (QoS) more than HOPP. However, the UE speeds considered in this study may not accurately represent real-world scenarios, which could affect the optimality of the proposed method. In [30], the authors proposed a method to classify prior UE measured data into RLF and HOPP based on SINR levels using a DNN. This method identifies RLF by considering the worst SINR and sets the HOM value to zero accordingly. Additionally, the TTT is set to 80 ms. The dataset was collected through simulations with time slots of 10 ms length. The method considers SINR variations 200 ms prior, which are then used to predict SINR variations in the subsequent 200 ms, as claimed by the authors. The duration for completing the HO measurement and preparation phases was set to 200 ms. When RLF occurs in any time slot, a timer is initiated for 1 s (s), equivalent to 100 time slots, and counts down. For instance, if RLF occurs in time slot x, the 119 previous time slots leading up to time slot x are classified as RLF, indicating that HO should have been triggered in time slot 119 before the occurrence of RLF. The remaining time slots are classified as HOPP. However, it is worth noting that the accuracy of this method may be compromised because of its classification approach, which relies solely on the SINR level and employs a binary classification approach for HO decisions. Additionally, there may be room for improvement in the dataset acquisition process, as setting a fixed HOM value might not capture all details. Moreover, after classification, optimizing both HOM and TTT may require further refinement.

Multi-Layer Perceptron (MLP), a type of Artificial Neural Network (ANN), is widely recognized as a popular technique for classification and prediction. The authors in [31] proposed a data-driven HO optimization method based on MLP, which predicts the relationship between the weighted average of various mobility problem ratios and HCPs, such as HOM and TTT, in an LTE network environment. The aim of this method is to mitigate the weighted mobility problem ratios. The HO problems considered in their study include too-late HO, too-early HO, HO to the wrong cell, HOPP, and UHO. To identify HO problems, the authors introduce counters such as the time interval since the last HO, a threshold value to identify the time closeness between the current and previous HO events, RLF occurrence for the current link, new target cell Identity (ID), and previous serving cell ID, which indicate the similarity of the new target cell ID and the previous serving cell ID. The system’s performance was evaluated considering each mobility problem and their total ratio with various transmission power settings, such as 15, 20, and 43 dBm, over a fixed UE speed. Similarly, the authors in [32] presented a similar approach as [31] with a minor difference in that they ignored only one mobility problem: HOPP. Additionally, the performance was evaluated with transmission power settings, such as 15, 23, 30, and 40 dBm. However, applying MLP for KPI function estimation and HCP optimization requires a diverse training dataset. Moreover, using an online training approach and applying the estimation process in live networks may be inappropriate and risky.

1.2 Contributions

In our proposed method, we have developed two algorithms: one optimizes the HOM and TTT to create an optimized dataset, while the other is responsible for HO decision-making. By considering the KPIs and various parameters, our approach fine-tunes the HOM and TTT for each UE, resulting in an optimized dataset. This dataset is then fed into an MLP model to predict HOM and TTT based on the system inputs. The contributions of our study can be summarized as follows:

  • Development of an optimization algorithm for optimizing HCPs such as HOM and TTT based on received signal levels, UE speed categories ranging from 5 to 220 km/h, and cell load to obtain an optimized dataset.

  • Development of an algorithm that facilitates an efficient HO decision-making process in a UDSC HetNet by integrating an MLP model for HOM and TTT predictions. The reason for choosing MLP in our algorithm is its capability to effectively handle the nonlinear relationships among the parameters within the dataset.

  • Mitigation of the effects of RLF and UHO to a remarkable level compared with other methods and confirmation of a balance between RLF and HOPP occurrence probabilities.

The remainder of the paper is organized as follows. Section 2 provides background information on HO. Then, Sect. 3 introduces the KPI of HO performance. Section 4 presents the proposed system model, gives an overview of MLP, explains the data generation process, and describes the proposed method and algorithms. Furthermore, the simulation results are presented in terms of KPIs in Sect. 5. Finally, Sect. 6 concludes the paper.

2 Background Information

2.1 Handover Margin

The HOM, also known as the hysteresis margin, is a parameter used to define the threshold difference in the received signal strength between the source and target BSs. Depending on the system configuration, this difference can be indicated by either RSRP or SINR. The HOM typically ranges from 0 to 16 dB, with varying differences between the actual values. The setting of the HOM significantly impacts HO performance, where suboptimal configurations may lead to early or late HOs, resulting in more UHOs or RLFs depending on the UE’s speed. For example, increasing the HOM value decreases the number of HORs and HOPPs but increases the probability of RLFs. Conversely, decreasing the HOM value increases the number of HORs and HOPPs while decreasing the occurrence of RLFs.

2.2 Time-to-Trigger

TTT is an essential parameter used to control the HO process. It represents the time interval during which the network recognizes the need for an HO after specific conditions are met. The standard interval defined by 3GPP falls within the range [0, 40, 64, 80, 100, 128, 160, 256, 320, 480, 512, 640, 1024, 1280, 2560, and 5120] ms [33]. Similar to the HOM, the configuration of TTT plays a crucial role in HO performance. High TTT settings may reduce the number of UHOs but could increase the occurrence of RLFs. Conversely, low TTT settings may lead to a high number of UHOs but reduce RLF occurrence. Consequently, the optimal configuration of both the HOM and TTT parameters leads to the optimization of the HO process, ensuring the consistent performance of the network and improving overall network performance and QoS.

2.3 Handover Decision

HO decisions in the network rely on factors like signal strength, quality, and user mobility, determined by sophisticated algorithms that consider network resources and user needs. Following adjustments to HCPs, the HO decision is made based on certain conditions. These conditions involve ensuring that the target BS’s signal strength surpasses that of the serving BS, plus the HOM, within a certain TTT period to prevent connectivity issues. In this study, we consider the A3 event [34] to determine HO triggering.

$$\begin{aligned} RSRP_{target} \ge RSRP_{serving} + HOM, \end{aligned}$$
(1)

where \(RSRP_{serving}\) and \(RSRP_{target}\) denote the RSRP values of the current serving cell and target cell, respectively.

3 Key Performance Indicators

3.1 Handover Rate

This metric, also known as HO probability, quantifies the frequency of HOs experienced by a UE during its movement within the network coverage. High HORs can severely disrupt network operations and user satisfaction by consuming excessive network resources and generating increased signaling traffic. These disruptions can manifest as call drops, diminished call quality, and heightened latency, thereby further reducing the overall network capacity and efficiency. Additionally, HOPP contributes to high HORs. To address these concerns, optimizing HCPs that directly influence UE HOs is crucial. It is important to note that in UDSC-deployed HetNets, controlling HOR becomes challenging, particularly at high speeds where cell coverage is limited, leading to more frequent HOs between BSs along the UE’s trajectory.

3.2 Handover Ping-Pong

HOPP describes a wireless network scenario characterized by frequent and repetitive HOs between two cells or BSs within a short period [35]. It is a critical performance metric reflecting the UHO. HOPP occurrences often arise from fluctuations in signal levels and improper configuration settings of HCPs in both automatic and manual setups. Specifically, setting HCPs to minimum values in either configuration mode triggers early HOs, thereby increasing the likelihood of HOPP. This phenomenon significantly worsens network QoS, wastes network resources, and results in excessive power consumption.

3.3 Handover Failure

An unsuccessful HO from the serving BS to the target BS is referred to as the HOF. In other words, HOF typically occurs when the UE is unable to establish a connection with the target cell or experiences a connection failure due to various factors. These factors encompass interference, imbalanced load between BSs, coverage deficiencies resulting in abrupt decreases in received power levels, and insufficient implementation of mobility management strategies. In HetNets, inappropriate setting of HCPs leads to HOFs, which in turn increases the probability of RLF. Depending on the HCPs settings, various scenarios in HO occur, namely, too-early HO, too-late HO, and HO to the wrong cell. Each of these scenarios affects the probability of the HOF. Furthermore, HOPP also contributes to HOF occurrences.

3.4 Radio Link Failure

RLF, an important metric for evaluating network performance, pertains to the potential disruption of the radio link between the UE and the BS during a call due to various triggering factors. This interruption occurs when an HO is initiated to a specific BS, but the downlink SINR from that BS falls below a predetermined threshold within a specified time frame. Increasing HCPs to their maximum values can induce RLF, particularly affecting UEs at cell edges or moving at high speeds, leading to delayed HOs. A high rate of RLF can result in the wastage of network resources and a decrease in the overall QoS of the network. Therefore, it is essential to set HCPs optimally to minimize the frequency of RLF and avoid inefficient utilization of network resources.

3.5 Handover Latency

HOL is a crucial parameter for system performance, especially in 5G and beyond networks, where some applications require ultra-low latency to function smoothly. HOL is the total duration between the command received from the serving BS and the completion of the HO to the target BS.

3.6 Handover Interruption Time

HOIT refers to the time during HO when a pause occurs in the exchange of UE data between the serving and target cells. In other words, during an HO from a serving cell to a target cell, there is a specific period during which the mobile user cannot send or receive data. Various factors influence this pause, including different HO conditions and received signal conditions. To optimize network utilization, this pause should be minimized as much as possible.

4 System Architecture

This section provides an in-depth exploration of the system model and simulation parameters, offers a general overview of MLP, the data generation process, and explains the proposed method and algorithm for HO decision-making.

4.1 System Model and Simulation Setup

In this study, we investigate a UDSC HetNet architecture comprising densely deployed millimeter wave (mmWave) BSs integrated into an LTE-Advanced (LTE-A) system. This architecture consists of seven LTE-A BSs, each with three sectors, alongside an ultra-dense array of 5G BSs. The LTE-A BSs are strategically positioned at the center of the macro cells (MCs) to cover the surrounding area with three sectors. Meanwhile, the 5G BSs are positioned at the center of the SCs, propagating signals in all directions. SCs and UEs are uniformly distributed throughout the area and within the coverage areas of each MCs, respectively. The UDSC HetNet is simulated in MATLAB to model the architecture and interactions within the network. The mobility of UEs is defined by two key factors: their directional orientation and velocity. UEs move concurrently, following the trajectories determined by their initial positions. Throughout the simulation, UEs positioned along the positive x-axis exhibit a leftward trajectory, whereas those situated along the negative x-axis exhibit a rightward trajectory. This movement pattern is due to the unlimited number of simulation steps, allowing UEs to traverse the simulation environment without constraints. The considered system model is shown in Fig. 1, which depicts one sector of the MC consisting of a dense number of SCs in an urban area.

Fig. 1
figure 1

System model of the UDSC HetNet, illustrating the deployment of MBSs and an ultra-dense number of SBSs

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4.2 Multi-Layer Perceptron (MLP)

MLP is a type of ANN characterized by several layers. It comprises an input layer, a hidden layer, and an output layer, each serving specific functions within the network. The input layer receives the input signals, whereas the output layer is responsible for different tasks, including prediction or regression. Situated between the input and output layers, the hidden layers form a series of interconnected nodes through which data flows in a forward direction, resembling a feed-forward network. Using the backpropagation learning technique, the MLP trains its nodes, enabling it to effectively handle nonlinear distinctions and approximate continuous functions [36, 37]. A general representation of MLP is illustrated in Fig. 2.

Fig. 2
figure 2

General representation of MLP scheme

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The calculations performed by each neuron/node in the hidden and output layers are as follows:

For each neuron \(h_j\) in the hidden layer:

$$\begin{aligned} h_j = \phi \bigg (\sum _{i=1}^{n} w_{ji} x_{i} + b_{j}\bigg ), \end{aligned}$$
(2)

where \(\phi (.)\) is the activation function (ReLu, Sigmoid), n represents the total number of inputs, \(x_{i}\) denotes the \(i^{th}\) input, \(w_{ji}\) represents the weight connecting \(x_{i}\) to \(h_{j}\), and \(b_{j}\) is the bias for the hidden neuron \(h_{j}\), which contributes to the learning process by helping to determine an appropriate threshold for the function.

For each neuron \(y_{k}\) in the output layer:

$$\begin{aligned} y_{k} = \psi \bigg (\sum _{j=1}^{m} v_{kj} h_{j} + c_{k}\bigg ), \end{aligned}$$
(3)

where \(\psi (.)\) is the activation function (ReLu, Sigmoid) for the output layer, m represents the total number of neurons in the hidden layer, \(v_{kj}\) illustrates the weight connecting \(h_{j}\) to the output \(y_{k}\), and \(c_{k}\) is the bias term for the output \(y_{k}\).

The activation function takes each element of \(h_{j}\) or \(y_{k}\) as its input. For example, the sigmoid activation function for \(y_{k}\) will be expressed as follows:

$$\begin{aligned} \psi (y_{k}) = \frac{1}{1+exp(-y_{k})}. \end{aligned}$$
(4)

4.3 Data Generation

Learning the behavior of mobile networks can be challenging, particularly in UDSC-deployed HetNets, where numerous interconnected parameters influence KPIs. As a result, it is often impractical to directly observe and adjust these parameters to achieve optimized KPIs, especially in live networks where improper adjustments can lead to network underperformance. To provide an alternative for data gathering, simulators present viable options that can help us overcome the challenges in live networks.

In this study, we simulated a UDSC-deployed HetNet environment in MATLAB and developed a script comprising various algorithms to generate data. The script monitors the environment and computes the parameters required to achieve predefined KPIs as the UE moves through each step. Subsequently, it organizes all the data in a table, with columns representing UE speed, RSRP, SINR, cell load, HOM, TTT, and the associated KPIs. The table has a dimension of 140,000 rows and 10 columns. In our study, we considered HOM and TTT as outputs because they directly impact UHO and RLF, while treating parameters such as UE speed, RSRP, SINR, and cell load as inputs to our model. It is noteworthy that the simulation was conducted multiple times, and data were selected from the algorithm that produced the best results. The set of generated data, excluding the associated KPIs, is shown in Fig. 3.

Fig. 3
figure 3

Representation of generated data across iteration

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4.4 Proposed Method and Algorithm

Besides the other HCPs like CIO and HO hysteresis, HOM and TTT play a significant role in HO decision-making, especially in UDSC HetNets. The configuration of both HOM and TTT determines the impact of the algorithm on network performance. In particular, optimizing the configuration of HOM and TTT becomes more critical in UDSC deployed HetNets. The proposed method is depicted in Fig. 4.

Fig. 4
figure 4

Illustration of the proposed method

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Initially, a comprehensive dataset is generated, which capture relevant network parameters and KPIs. This dataset is iteratively evaluated to identify critical performance bottlenecks, and HCPs such as HOM and TTT are optimized on the basis of the identified deficiencies, as illustrated in Algorithm 1. In this algorithm, the adjustments of HCPs are made according to the identified sets, as demonstrated in Table 1.

Table 1 Defined sets for HCPs used in the proposed method
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Algorithm 1
figure a

Algorithm for HCP optimization

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As shown in Table 1, each set includes three elements for the HOM and two elements for the TTT. The optimized values for both HOM and TTT are selected based on the cell load, as illustrated by the flowchart in Fig. 5. In this figure, HOM(1), HOM(2), and HOM(3) represent low, average, and high values of the set, respectively, whereas TTT(1) and TTT(2) denote short and long periods of the set.

Fig. 5
figure 5

Flowchart depicting the algorithm for the HCP optimization process considering load

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The values for HOM and TTT are adjusted from the sets described in Table 1 based on three cell load categories: low (less than \(40\%\)), medium (less than \(80\%\)), and high (more than \(80\%\)). This iterative process continues until an optimized dataset reflecting enhanced network performance is achieved. The dataset is then used to train the MLP model located in the HO decision-making algorithm illustrated in Fig. 6.

Fig. 6
figure 6

Flowchart illustrating the HO decision-making algorithm

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Subsequently, the trained MLP model is applied to predict the optimal values for HOM and TTT. Using input parameters such as UE speed, RSRP, SINR, and cell load, the MLP model with 10 neurons in its hidden layer accurately predicts HCP values for each UE. This enables efficient parameter adjustment for enhanced network performance based on real-time data.

The prediction performance of the MLP model is evaluated in terms of RMSE, which is depicted in Eq. 5, and compared with that of linear regression illustrated in Fig. 7.

$$\begin{aligned} RMSE = \sqrt{\sum _{i=1}^{n_{size}}\frac{(y_i^t-y_i^p)^2}{n_{size}}}, \end{aligned}$$
(5)

where \(y^t\), \(y^p\), and \(n_{size}\) are actual target values, predicted values, and sample size (number of observations), respectively.

Fig. 7
figure 7

Prediction performance of MLP with comparison to linear regression using RMSE

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In addition, Fig. 8 depicts MLP performance in mean squared error (MSE) over epochs, offering insights into its convergence behavior and effectiveness throughout training.

Fig. 8
figure 8

Performance of MLP in terms of MSE versus number of epochs

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5 Performance Evaluation

The performance of the proposed data-driven MLP-based HO method (MHO) was evaluated using KPIs, such as HOR, HOPP, HOF, RLF, HOL, and HOIT, detailed in Sect. 3. A comparison was made with a traditional A3 event, linear regression, and a fuzzy logic-based algorithm [18], denoted as A3, LinReg, and FL, respectively. Simulation parameters adhere to established standards and reputable literature [38,39,40], as detailed in Table 2.

Table 2 Simulation Parameters for LTE-A and 5 G
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5.1 Handover Rate

HOR measures the frequency at which UEs transition between different cells in the network. This metric is influenced by factors such as UE mobility, network configuration, and signal conditions, making it a crucial metric influencing the UHO and overall network stability and performance. The average HOR is depicted in Fig. 9. Figure 9a illustrates the average HOR for all UEs under different UE speed scenarios. As it shows, with higher UE speeds, there is a corresponding rise in the HOR. This phenomenon primarily results from the UEs transitioning between multiple cells. Figure 9b illustrates the average HOR across the entire system for the proposed method and the comparison methods. Figure 9c shows the average HOR for all UEs plotted against simulation time. The initial peak in this plot is attributed to the surge in HO requests during the initial stages of network operation. At this stage, the UEs are transitioning to suitable cells that offer optimal cell load and signal quality.

Fig. 9
figure 9

Average HOR: a overall UEs versus different UE speed scenarios, b overall system, c overall UEs and UE speeds versus time

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Our proposed method consistently performed well across various UE speeds, effectively managing the increasing number of HOs associated with higher speeds. This highlights the robustness and adaptability of our method, which is important for maintaining seamless connectivity and UE experience under dynamic network conditions. Moreover, our method outperforms the methods under consideration. Its performance is approximately \(76.6\%\) better than that of A3, \(43.9\%\) better than that of LinReg, and \(65.4\%\) better than that of FL in terms of HOR.

5.2 Handover Ping-Pong

HOPP refers to frequent and repetitive HOs between two cells or BSs within a short period, often due to signal fluctuations and improper HCP settings. This phenomenon degrades network QoS, wastes resources, and increases power consumption. The average HOPP probability is illustrated in Fig. 10.

Fig. 10
figure 10

Average HOPP probability: a of overall UEs versus various speed scenarios b of overall the system c of overall UEs versus simulation time

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The average HOPP probability across all UEs is illustrated in Fig. 10a against various UE speeds. Here, A3 demonstrates fluctuating HOPP probabilities at different UE speeds. FL exhibits the lowest HOPP probability within the speed range of 5 to 50 km/h but shows an increase in HOPP probability for higher UE speeds. LinReg shows a stable HOPP across different UE speeds. In contrast, the proposed method demonstrates a decrease in the HOPP probability across different UE speeds from low to high, which is more logically consistent. Figure 10b displays the average HOPP probability across the entire system. As illustrated, the performance evaluation of the proposed method demonstrates its superiority over the comparison methods. In Fig. 10c, the average HOPP probability is depicted across all UEs and simulation time intervals. The results indicate that the proposed method consistently exhibits the lowest HOPP probability throughout the entire simulation duration, in contrast to the other methods.

Overall, with an HOPP probability of 0.022786, the proposed method exhibits a significant enhancement in performance compared with A3, LinReg, and FL. Specifically, the proposed method showcases approximately \(79.8\%\) improvement over A3, \(50.6\%\) improvement over LinReg, and \(65\%\) improvement over FL in terms of HOPP probability.

5.3 Handover Failure

HOF refers to the probability that an HO process fails, resulting in disruptions to UE connectivity. Figure 11 shows the average HOF probability.

Fig. 11
figure 11

Average HOF probability: a of overall UEs versus various UE speed scenarios (b) of overall system for all methods (c) of overall UEs versus simulation time

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In Fig. 11a, the average HOF probability is illustrated across the overall UEs versus various UE speed scenarios. In Figs. 11b and 11c, the average HOF probability for the overall system and the average HOF probability across all UEs over the simulation time are illustrated, respectively.

The results indicate that the proposed method outperforms the other considered methods. The evaluation reveals that our method, with an HOF probability of 0.0016429, demonstrates enhancements over A3, LinReg, and FL. Specifically, it achieves approximately \(90.9\%\) improvement over A3, \(22\%\) improvement over LinReg, and \(71.2\%\) improvement over FL in terms of HOF probability.

5.4 Radio Link Failure

RLF is an important metric that assesses the reliability of radio connections between UEs and BSs within a network environment. It measures the frequency and impact of disruptions in communication due to varying SINR levels and configurations of HCPs. The average probability of RLF across all UEs at various UE speeds is shown in Fig. 12a. The variability in RLF occurrences is attributed to fluctuations in SINR levels and the settings of HCPs corresponding to different UE speeds. In Figs. 12b and 12c, the average RLF probability across the entire system and the average RLF probability over the simulation time are illustrated, respectively. The proposed method outperforms the A3 and FL methods but exhibits a slightly inferior performance against LinReg.

Fig. 12
figure 12

Average RLF probability: a of overall UEs versus various UE speeds (b) across the system for different methods (c) of overall UEs versus simulation time

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In summary, compared to A3, the proposed method demonstrates an enhancement of approximately \(74.8\%\) in reducing the RLF probability, while compared to FL, the improvement amounts to approximately \(42.4\%\). However, it shows a \(0.3\%\) underperformance compared with LinReg. It is noteworthy that when configuring HCPs, it is essential to find a balance between RLF, HOR, and HOPP. Given the superior performance of our method observed in previous subsections, we consider the performance of our method to be optimal in terms of mitigating RLF.

5.5 Handover Latency

HOL measures the time taken for UEs to complete the HO process between different cells or BSs. It directly impacts the QoS experienced by UEs and the overall efficiency of network operations. As depicted in Fig. 13, the proposed method demonstrates better performance than the alternative methods in terms of HOL. With an HOL of 4.65 ms, it significantly outperforms A3, which records an HOL of 20.30, LinReg with 8.26, and FL with 13.53. This highlights the superiority of the proposed method, surpassing A3 by approximately \(77\%\), LinReg by approximately \(43.7\%\), and FL by approximately \(65.6\%\) in terms of HOL.

Fig. 13
figure 13

Average HOL overall the system

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5.6 Handover Interruption Time

HOIT measures the duration of communication disruption when UEs switch between cells or BSs in a wireless network. Minimizing this interruption is crucial for maintaining seamless connectivity and optimizing user experience. The average HOIT across the system for the proposed and comparison methods is illustrated in Fig. 14.

Fig. 14
figure 14

Average HOIT across the system

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Notably, A3 exhibits the highest HOIT, underscoring the direct correlation between HOIT and HOR. With an HOIT of 1.6396, the proposed method surpasses A3, which records an HOIT of 6.9939, LinReg, with an HOIT of 2.9221, and FL, with an HOIT of 4.7518. This translates to the proposed method outperforming A3 by approximately \(76.6\%\), LinReg by approximately \(43.9\%\), and FL by approximately \(65.5\%\) in terms of HOIT.

6 Conclusion

In this study, we proposed a method consisting of an optimization algorithm to obtain an optimized dataset by optimizing HCPs such as HOM and TTT in a prior dataset based on associated KPIs and an HO decision-making algorithm that uses MLP. The MLP model predicts the HOM and TTT based on the obtained optimized dataset by inputting parameters such as UE speed, RSRP, SINR, and cell load. Adjusting proper values for both HOM and TTT leads to optimal system performance, as addressed in our proposed method. Our approach offers significant enhancements in terms of HOR, HOPP, HOF, RLF, HOL, and HOIT compared with other methods in the literature. The proposed method demonstrates substantial performance improvements across key metrics when compared to A3, LinReg, and FL. In terms of HOR, it outperforms A3 by 76.6\(\%\), LinReg by 43.9\(\%\), and FL by 65.4\(\%\). For HOPP, it achieves enhancements of 79.8\(\%\) over A3, 50.6\(\%\) over LinReg, and 65\(\%\) over FL. Regarding HOF, the method shows improvements of 90.9\(\%\), 22\(\%\), and 71.2\(\%\) compared to A3, LinReg, and FL, respectively.

In terms of RLF, the proposed method reduces RLF by 74.8\(\%\) compared to A3 and 42.4\(\%\) compared to FL, while achieving near-equal performance with LinReg. For HOL, it surpasses A3, LinReg, and FL by 77\(\%\), 43.7\(\%\), and 65.6\(\%\), respectively. Lastly, for HOIT, it achieves performance gains of 76.6\(\%\), 43.9\(\%\), and 65.5\(\%\) over A3, LinReg, and FL, respectively.

These results highlight the ability of the proposed method to achieve a balance between RLF and UHO by minimizing the average RLF probability to 0.0046 and the average HOPP probability to 0.023. The improvements are attributed to the combined use of the optimization algorithm and the HO decision-making algorithm. By customizing HCPs for each UE independently and incorporating multiple parameters, the proposed method ensures enhanced performance in ultra-dense network environments.

However, the method underperforms slightly compared to LinReg in terms of RLF probability, where LinReg achieves the best result. The RLF probability of the proposed method is only 0.3\(\%\) higher than that of LinReg, indicating a potential area for further refinement. Additionally, the reliance on generating a customized dataset for each network adds complexity to real-world implementation, which presents a limitation for live network deployments.

Future work will aim to address these challenges by incorporating a broader range of metrics and scenarios into the validation process. This will enhance the robustness and applicability of the proposed method to diverse network environments, improving its potential for real-world deployment.