# FedEst: A Federated K-Means Based Load Balancing for Channel Estimation in Cell-Free Massive MIMO Networks

Karidja Christelle Adje Dominique, Oussama Habachi, Gerard Chalhoub, Asma Ben Letaifa, Majed Haddad

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Karidja Christelle Adje Dominique, Oussama Habachi, Gerard Chalhoub, Asma Ben Letaifa, Majed Haddad. FedEst: A Federated K-Means Based Load Balancing for Channel Estimation in Cell-Free Massive MIMO Networks. International Wireless Communications & Mobile Computing Conference (IWCMC 2025), May 2025, Abu Dabi, United Arab Emirates. hal-05004825

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FedEst: A Federated K-Means Based Load Balancing for Channel Estimation in Cell-Free Massive MIMO Networks

Karidja Dominique Christelle Adje*†, Oussama Habachi†, Gerard Chalhoub†, Asma Ben Letaifa*, and Majed Haddad‡

*LR11TIC05 Mediatron University of Carthage, SUPCOM, Tunisia

†LIMOS Université Clermont Auvergne, France

‡LIA Avignon University, France

**Abstract**—In the next generation of wireless communication systems, Cell-Free massive Multiple-Input-Multiple-Output (CF-MIMO) is emerging as a promising solution to address the challenges posed by traditional cellular networks, including interference management and resource allocation. The dynamic nature of CF-MIMO requires efficient load management between the Access Points (APs) and the Central Processing Unit (CPU) to ensure optimal performance, reduced latency, and effective resource utilization. This paper investigates the load balancing between APs and CPUs in CF-MIMO, focusing on the optimal distribution of computational resources for channel estimation. We explore the interaction between APs, which role is to provide connectivity to users, and the CPU that handles processing tasks, including channel estimation, data encoding/decoding, and user scheduling. We propose a Federated K-means framework (FedEst) that takes into account factors such as traffic load, user mobility, computational power, and network topology. Simulation results demonstrate that the proposed framework not only improves system throughput and efficiency but also enhances user experience in terms of latency and reliability. This work contributes to the development of more efficient, scalable, and robust cell-free network architectures capable of supporting the growing demands of next-generation wireless technologies.

**Index Terms**—CF-mMIMO, Federated KMeans, load balancing, user mobility

## I. INTRODUCTION

The proliferation of wireless users and services, namely with the integration of Internet of Things (IoT) in the fifth generation of wireless communications (5G), introduced significant challenges for traditional cellular networks, especially in terms of scalability and meeting the ever-growing Quality of Service (QoS) requirements. To address these issues, Cell-Free (CF) networks have emerged as a promising approach, gaining increasing attention as a potential solution to tackle the aforementioned challenges [1], [2]. In this architecture, Access-Points (APs) with multiple antennas are geographically distributed and connected to a Central Processing Unit (CPU) responsible of the coordination between them. To serve a given User Equipment (UE), a suitable subset of APs is selected to fulfill the QoS requirements [2]. Using a larger number of antennas enhances channel predictability and reduces susceptibility to random variations [3]. However, a key challenge with

this promising architecture is the need to estimate or process the large number of channels across multiple users. Several studies have addressed this challenge by proposing different strategies for channel estimation. For instance, in [4] and [5], channel estimation is performed entirely at the CPU, allowing for centralized processing and coordination, which can improve overall network efficiency. On the other hand, authors of [6] proposed a distributed approach where channel estimation is carried out by the APs, reducing the computational burden on the CPU and leveraging the spatial diversity offered by the APs. In [7], the authors derived the achievable communication rates of the active primary user and passive secondary user while the CSI estimation of the active and passive channels is performed based on two-phase uplink-training at the APs. Both approaches have their advantages and limitations, with the centralized method offering better coordination but facing scalability issues, while the distributed method improves scalability but may suffer from coordination challenges, as it has been shown in [8]. Indeed, estimating all the channels directly at the APs may result in performance drop, as the APs lack a global view of the network load and sufficient resources. Although the CPU has a global view of the network and greater resources, estimating all the channels at CPU level may cause delay increase for dense scenarios. One way to alleviate this bottleneck is to distribute the channel estimation between the CPU and the APs. Furthermore, leveraging user mobility patterns can help structure the estimation process, determine the channels to be estimated locally and those at the CPU, ensuring that computational resources are allocated dynamically based on network conditions. This complexity balancing is closely related to the QoS in terms of achievable sum-rate and delay. Optimizing the processing delay has been largely investigated in the literature. For example, authors in [3] focused on reducing the time required for power allocation in a CF system using a DNN approach, where the training has been performed offline. Similarly, DNN has been used in [9], [10] and [11] for channel estimation in order to reduce processing delay and computational cost.

Federated Learning (FL) techniques are well known to be adapted for decentralized decision making, and well suited
for large-scale networks since they enable training a Machine Learning (ML) model without sharing data between different entities [12]. FL has been applied in CF networks to take advantage of its benefits. For example, Banerjee et al. used in [13] a FL approach to coordinate APs in a CF network by enabling them to share the weights of their neural networks through an aggregated global model. This global model harmonizes their decisions, improves the overall network efficiency, and reduces conflicts and interference among APs.

K-means is a widely used unsupervised ML algorithm that partitions data into distinct clusters, minimizing the variance within each cluster. In the context of CF networks, K-means has been applied to group users based on their channel conditions or spatial location. This allows the system to optimize resource allocation, improve the efficiency of channel estimation and reduce the computational burden. K-means can be applied in a federated approach where clustering results of multiple decision makers are aggregated to achieve a common goal. Garst et al. [14] and Kumar et al. [15] explore the application of FL with clustering algorithms, particularly with K-means. In typical federated K-means clustering, each agent sends the centroids of its clusters to the server. Then, at the server level, these centroids are federated or aggregated and brought back to the agents to adjust the K-means model for another cycle, until convergence to an optimal model adapted to the problem. Federated K-means, in particular, is well suited for clustering UEs in a way that optimally balances the workload between the CPU and APs. By grouping users with similar mobility patterns, we can reduce redundant computations and enhance estimation efficiency.

In this paper, we focus on the channel estimation in CF networks and we investigate how this can be achieved in a collaboration between CPU and APs. In the proposed federated approach, we consider that APs perform a K-means clustering to group users based on their channel variation level. The APs decide then which clusters of users to process locally and which ones will be delegated to the CPU to achieve global channel estimation. Thereafter, an aggregated QoS feedback is sent back to the APs to adjust their K-means-based decisions for the next time coherence interval.

The remainder of this paper is structured as follows. Section II introduces our system model, and Section III presents the proposed FedEst framework. Section IV presents simulation results to illustrate the pertinence of the proposed solution, and Section V concludes the paper and gives some directions for future works.

## II. SYSTEM MODEL

We consider a CF massive MIMO network consisting of N APs, each equipped with M antennas, and a set K of K single-antenna UEs, where N × M > K. We adopt Time Division Duplexing (TDD) mode, which ensures channel reciprocity

between the uplink and downlink within a given coherence time interval [16]. The channel between UE k and AP n, denoted as $h_{n,m}^k$, follows a complex Gaussian distribution $CN(0, \beta_{n,m}^k)$, where $\beta_{n,m}^k$ combines Path Loss (PL) and the long-term fading coefficients. The path loss model and long-term fading coefficient used in this study are derived from the WINNER report [17], ensuring a realistic representation of propagation conditions.

To perform resource allocation, modulation, and decoding, channel estimation must be completed beforehand. Indeed, pilot transmission, channel estimation, and data transmission must all occur within the coherence time interval, denoted by $\tau_c$. Thus, each UE is assigned a pilot sequence of length K, such that $K < \tau_c$, which is transmitted to the APs for channel estimation using techniques such as Minimum Mean Square Error (MMSE). To avoid interference, pilot sequences from different UEs must be orthogonal. Specifically, for a UE k assigned the pilot $\psi_k$ (with $E[|\psi_k|^2] = 1$), the orthogonality condition is $\psi_k^H \psi_{k'} = 0$ for $k \neq k'$, and $\psi_k^H \psi_{k'} = 1$ for $k = k'$. However, due to the constraints imposed by the coherence time $\tau_c$, the number of available pilot sequences is often smaller than the number of UEs, forcing some UEs to reuse identical pilot sequences, which can lead to pilot contamination. Thus, the signal received at antenna m of AP n is a superposition of orthogonal pilots coming from all the UEs:

$$y_{n,m} = \sum_{k \in K} p_p^{1/2} h_{n,m}^k \psi_k + \tau \quad (1)$$

where $p_p$ is the pilot power. The pilot sequence of UE k is denoted by $\psi_k$, and the pilot contamination vector is referred to as $\tau$. To decode the desired signal from UE k, the AP performs conjugate operations on the superposition of received pilots:

$$y_{n,m}^k = y_{n,m} \psi_k^H = \sum_{k' \in K} p_p^{1/2} h_{n,m}^{k'} \psi_{k'} \psi_k^H + \psi_k^H w \quad (2)$$

An appropriate estimator is then applied to obtain the estimated channel $\hat{h}_{n,m}^k$. Estimating the channel for each UE requires a delay that must fit within the coherence time. Therefore, the channel estimation process needs to be optimized in order to satisfy the coherence time interval, especially in dense scenarios. However, this process places an overload on the CPU, which is usually responsible for estimating all the channels in the system and transmitting them to the APs. This increases the channel estimation delay, ultimately affecting service quality. To efficiently distribute the load between the APs and the CPU in the channel estimation process, we propose an approach based on Federated K-means in the next section.

## III. FEDEST: FEDERATED K-MEANS BASED CHANNEL ESTIMATION

In this section, we introduce the proposed FedEst framework, which enables APs and the CPU to collaborate effectively to perform channel estimation within a specified delay constraint.
We consider that the APs refer to the K-means to group users into clusters based on their mobility profiles. Thereafter, every AP decides to estimate the channels of low mobility clusters locally and delegates high mobility clusters to the CPU. This latter federates the APs to achieve a load balancing between APs and CPU. In what follows, we describe the proposed federated K-means approach.

### 1) Step 1 - Clustering phase

The APs use K-means clustering to group the UEs based on the variation in the magnitude of their estimated channels between two coherence time intervals. This approach aims to capture the variation in pathloss between UEs and APs.

### 2) Step 2 - Offloading

Once the UEs are grouped by their mobility profiles, each AP decides which UEs to offload for channel estimation to the CPU. The rationale is as follows: UEs with low mobility variation have their channels estimated locally at the AP, while those with high mobility variation are estimated by the CPU. In fact, UEs with high mobility profiles require a centralized view of their situation, whereas those with low mobility profiles would be rather managed locally. Since offloading decisions affect both the APs' load and the CPU, the APs initially offload half of their UEs to the CPU and adjust this based on the CPU's processing delay feedback.

### 3) Step 3 - Channels estimation

In this step, the CPU and APs estimate the channels for their respective users. The APs then wait for the estimated channels from the CPU. By the end of this phase, each AP has local information (the channel estimation delay at the AP) and global information (the channel estimation delay at the CPU).

### 4) Step 4 - Federation of APs

Once the APs receive the channel estimation at the CPU, they can assess the CPU load and decide how to adjust the number of UEs to offload in the next coherence interval. Each AP uses data from the previous cycle to optimally distribute the load with the CPU, minimizing the maximum delay between local and CPU channel estimations. We propose a dynamic adjustment mechanism to determine the optimal number of channels to be processed locally by each AP, based on its relative delay with the CPU.

Let $d_a^{t-1}$ denotes the channel estimation delay of the AP a and $d_{CPU}^{t-1}$ represents the delay at CPU, both at time coherence interval $t-1$. The delay gap, which indicates the relative delay difference, is computed as:

$$d_{\text{gap}} = \frac{s \cdot |d_a^{t-1} - d_{\text{CPU}}^{t-1}|}{\max(d_{\text{AP}}^{t-1}, d_{\text{CPU}}^{t-1})}$$

This delay gap quantifies the discrepancy in delay between the AP and the CPU, scaled by a smoothing factor $s$. Let us denote by $C_a^t$ the number of users to offload to CPU by AP a. Then, we subsequently adjust the number of offloaded users as follows:

* If the delay at AP a is greater than the global CPU delay ($d_a^{t-1} > d_{CPU}^{t-1}$), the number of users whose channels have to be offloaded is increased proportionally to the delay gap when the initial channel count $C_a^{t-1}$ is large (i.e., more than half the users):

$$C_a^t = \min(C_a^{t-1}(1 + d_{\text{gap}}), U_a)$$

where $U_a$ represents the total number of users connected at AP a. If $C_a^{t-1}$ is small, the number of users to be estimated locally is reduced proportionally:

$$C_a^t = \min(U_a - (U_a - C_a^{t-1})(1 - d_{\text{gap}}), U_a)$$

* If the delay at AP a is less than the global CPU delay ($d_a^{t-1} < d_{CPU}^{t-1}$), the number of users to be offloaded is reduced when $C_a^{t-1}$ is large, and the number of users to be estimated locally is increased when $C_a^{t-1}$ is small:

$$C_a^t = \max(C_a^{t-1}(1 - d_{\text{gap}}), 0)$$

if $C_a^{t-1}$ is large, or

$$C_a^t = \max(U_a - (U_a - C_a^{t-1})(1 + d_{\text{gap}}), 0)$$

if $C_a^{t-1}$ is small. This ensures that more channels are processed locally when the AP's delay is lower than that of the CPU.

In summary, the optimal number of channels allocated locally to each AP is dynamically adjusted based on the relative delay between the AP and the CPU. The error percentage plays a critical role in determining how the channel count is scaled, either increasing or decreasing the local processing based on the relative delays. The proposed Federated K-means channel estimation is summarized in Algorithm 1.

## IV. SIMULATION RESULTS

In order to validate the proposed FedEst framework, we consider a cell-free massive MIMO system consisting of one CPU, multiple APs, and a set of users, each of whom is covered by several APs simultaneously. Users select their set of serving APs based on the received signal strength. Each AP must estimate the channels between itself and the connected users to effectively allocate resources and meet the users' QoS requirements. This section examines two scenarios: a homogeneous scenario where all APs share the same characteristics, and a heterogeneous scenario where the APs have varying capabilities. In both scenarios, we compare FedEst technique with local and offloaded channel estimation methods, as well as threshold-based techniques.
**Algorithm 1** Channel Estimation and Offloading for APs and CPU

1: **Input:** Set of UEs $U = \{U_1, U_2, ..., U_n\}$, channel magnitude variation $C = \{C_1, C_2, ..., C_n\}$, number of clusters $k$, initial offloading fraction $\alpha = 0.5$

2: **Output:** Channel estimations $H$

3: **for** for every time coherence interval **do**

4: **Step 1: Clustering Phase**

5: Apply K-means clustering to group the UEs based on channel magnitude variations

6: **Clusters** = KMeans($C$, $k$)

7: **Step 2: Offloading Phase**

8: **for** each AP **a** **do**

9: $U_a^o = \emptyset$

10: **for** each UE $u$ in its set of users $U_a$ **do**

11: **if** $frac|U_a^o||U_a| < \alpha$ **then**

12: $U_a^o = U_a^o \cup \{u\}$

13: **end if**

14: **end for**

15: **end for**

16: **Step 3: Channel Estimation Phase**

17: CPU estimate the channels for $\cup U_a^o$

18: **for** each AP **a** **do**

19: AP **a** estimate the channels for $U_a \setminus U_a^o$

20: **end for**

21: CPU send $H(U_a^o)$ for AP **a**

22: **Step 4: Federation of APs Phase**

23: **for** each AP **a** **do**

24: Adjust offloading decisions based on CPU's processing delay feedback

25: **if** CPU delay is high **then**

26: Increase fraction of UEs offloaded to CPU

27: **else**

28: Decrease fraction of UEs offloaded to CPU

29: **end if**

30: **end for**

31: **end for**

A. Homogeneous scenario

In this section, we consider a scenario with 10 APs, each equipped with 64 antennas and capable of processing 561 channels/ms, along with a CPU providing a total capacity of 7816 channels/ms. To evaluate the impact of load on performance, we start with 10 users, increasing by 5 every 10 ms, during 70 cycles (the time coherence interval). We consider two mobility profiles: a high mobility scenario, in which the channel estimation must fit within a 1 ms coherence interval, and a moderate/low mobility scenario, in which the coherence interval is 2 ms.

As shown in Figure 1, using the FedEst framework, the APs and the CPU are able to estimate the channels in a distributed manner while remaining within the coherence interval for up to 20 users. This is achieved by dynamically adjusting the load

at both the CPU and APs, as seen in Figure 2. As shown in Figure 3, the ratio of the number of channels to estimate at the CPU as well as at the APs evolves similarly with the number of users in the system.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Channel estimation delay for CPU and APs.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Channel estimation load for CPU and APs.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: CPU and AP Load depending on the number of users.</figcaption></figure>

Let us now compare the proposed technique with the benchmarks considered from the literature. As shown in Figures 4 and 6, FedEst Framework, through efficient load balancing, dynamically ensures fairness between the CPU and the APs,
resulting in a better overall delay. In fact, FedEst can handle more than 20 users (resp. 40 users) in the high mobility scenario (resp. moderate/low mobility scenario), while the other techniques handle at most 15 users (resp. 35 users), as either the APs or the CPU fail to complete the estimation within the coherence interval.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Channel estimation delay for CPU: FedEst vs benchmark.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Average channel estimation delay for APs: FedEst vs benchmark.</figcaption></figure>

Specifically, when the CPU processes all channels, the delay exceeds 1 ms if there are more than 10 users (resp. 30 users) at 50 ms. Similarly, when the APs process all channels locally, they are not able to handle more than 10 users (resp. 20 users), since the channel estimation takes longer than 1 ms (resp. 2 ms). When using a fixed threshold, either the APs fail to handle 20 users (resp. 30 users) when using a threshold of 50% APs - 50% CPU, or the CPU fails to handle 35 users when using a fixed threshold of 20% APs - 80% CPU.

## B. Heterogeneous scenario

In this section, we consider a cell-free massive MIMO network composed of 10 APs having different capabilities: 4 low-capacity APs (32 antennas), 4 medium-capacity APs (64 antennas), and 2 high-capacity APs (128 antennas). The goal is to assess whether the proposed FedEst framework remains

<figure><img src="image_7.png" /><figcaption>Fig. 6: Real channel estimation delay in homogeneous scenario: FedEst vs benchmark.</figcaption></figure>

effective in a network with heterogeneous APs. We consider that there is 10 users at the beginning of the simulation, and that the number of users increases by 10 every 50 ms for 150 cycle.

As we can see in Figure 7, FedEst is able to efficiently balance the load between APs having different capabilities and CPU in order to achieve, in a decentralized manner, a common goal, that is all the channels across the network are estimated within the coherence time interval. Indeed, as we can see, the APs and the CPU converge to a close channel estimation delay that does not exceed the coherence interval for 20 users in the system. This collaborative estimation results in different loads at the CPU and the APs depending on the number of users (channels to estimate) as shown in Figure 8. As it is obvious, we can observe in Figure 9 that this dynamic balancing between APs and CPU results in a reduced overall channel estimation delay enabling the system to scale up and handle more users for the same time coherence interval.

## V. CONCLUSION

In this work, we addressed the challenge of channel estimation delays in CF-mMIMO networks. These networks can better manage interference and resource allocation using distributed APs with multiple antennas connected to a CPU which has the role to coordinate these APs. Each UE can be served by a subset of APs in order to answer its QoS requirements. By using more antennas per UE, CF-mMIMO networks enhance channel quality and overall performance. One of the main challenges in these networks is load balancing the channel estimation process between APs and the CPU. To tackle this issue, we proposed a distributed approach that balances the channel estimation load between the CPU and the APs. The proposed FedEst framework leverages a Federated K-means approach to minimize overall estimation delay by classifying users based on their mobility profiles. Simulation results demonstrate that our approach significantly reduces channel
<figure><img src="image_8.png" /><figcaption>Fig. 7: Channel estimation delay for CPU and APs in heterogeneous scenario.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8: Channel estimation load for CPU and APs in heterogeneous scenario.</figcaption></figure>

estimation delays while supporting a larger number of users compared to other techniques from the literature, for both homogeneous and heterogeneous network topologies. In our future work, we will tackle the challenge of optimizing the selection of subset of APs that serve each UE. Indeed, this aspect will help enhance the channel quality for UE by serving them using the APs that are able to provide the best QoS available.

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