# Uncoordinated RIS-Aided Uplink IoT Cell-Free Massive MIMO-NOMA Systems

Mohamad Ousseily, Joumana Farah, Matthieu Crussière, Joseph Doumit, Charbel Abdel Nour, Eric Pierre Simon

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Mohamad Ousseily, Joumana Farah, Matthieu Crussière, Joseph Doumit, Charbel Abdel Nour, et al. Uncoordinated RIS-Aided Uplink IoT Cell-Free Massive MIMO-NOMA Systems. IEEE Open Journal of the Communications Society, In press, 10.1109/OJCOMS.2025.3623368. [hal-05329424](https://HAL Id: hal-05329424)

https://cnrs.hal.science/hal-05329424v1

Submitted on 24 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Received XX Month, XXXX; revised XX Month, XXXX; accepted XX Month, XXXX; Date of publication XX Month, XXXX; date of current version 11 January, 2024.

Digital Object Identifier 10.1109/OJCOMS.2024.011100

# Uncoordinated RIS-aided Uplink IoT
Cell-Free Massive MIMO-NOMA
Systems

Mohamad Ousseily<fnref n="1" />, Joumana Farah<fnref n="1" /> (Senior Member, IEEE), Matthieu

Crussière<fnref n="1" /> (Member, IEEE), Joseph Doumit<fnref n="2" /> (Member, IEEE), Charbel Abdel Nour<fnref n="2" /> (Senior Member, IEEE), and Eric Pierre Simon<fnref n="3" />.

CORRESPONDING AUTHOR: M. Ousseily (e-mail: mohamad.ousseily@insa-rennes.fr).

This work was supported by the ANR under the France 2030 program, grant "NF-PERSEUS: ANR-22-PEFT-0004".

**ABSTRACT** Cell-free massive MIMO (CF-MIMO) has emerged as a promising architecture for beyond 5G networks, offering enhanced coverage and spectral efficiency through distributed antenna arrays. This paper proposes a novel framework integrating reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA) in CF-MIMO for uplink grant-free internet of things (IoT) scenarios. In such scenarios, devices transmit without prior coordination with a central unit, which increases the risk of multi-user interference. NOMA is thus introduced to address this challenge through successive interference cancellation (SIC). IoT devices autonomously select subbands using the multi-armed bandit (MAB) framework. Based on the devices subband choices, RIS angles are configured so as to satisfy the quality-of-service (QoS) requirements of all devices while leveraging NOMA SIC ordering. The resulting optimization problem becomes infeasible in many practical scenarios. To address these cases, we introduce: (1) a classification approach to proactively identify certain infeasible constraints, and (2) an iterative constraint relaxation method to improve the likelihood of finding feasible solutions. Additionally, a dynamic SIC reordering strategy is proposed to further enhance system performance. An enhanced upper confidence bound (UCB) algorithm is also introduced where, upon convergence, devices maintain their subband choices to minimize unnecessary explorations and optimizations. Simulation results demonstrate that our framework achieves higher success rates while reducing the required optimizations compared to baseline approaches.

**INDEX TERMS** Cell-free massive MIMO, Reconfigurable intelligent surfaces, Non-orthogonal multiple access, Grant-free access, Resource allocation.

## I. INTRODUCTION

THE integration of the internet of things (IoT) in cellular networks presents significant challenges for wireless communication systems. While the IoT represents an ever-expanding ecosystem of intelligent devices requiring seamless connectivity without human intervention [1], conventional cellular architectures rely on base stations (BSs) that coordinate communications using massive multiple-input multiple-output (MIMO) within fixed cell boundaries [2]. Large-scale IoT deployments exacerbate cellular networks

weaknesses, most notably the severe inter-cell interference encountered by cell-edge users, making it difficult to meet quality-of-service (QoS) requirements in dense environments [3].

Cell-free massive MIMO (CF-MIMO) networks have emerged as a promising solution to overcome the inter-cell interference limitation by eliminating cell boundaries [4]. A large number of access points (APs) coordinate through fronthaul links connected to central processing units (CPUs) to jointly serve users, mitigating interference and improving

<footnote n="1">¹Univ Rennes, INSA Rennes, CNRS, IETR-UMR 6164, F-35000 Rennes, France.</footnote>

<footnote n="2">²IMT Atlantique, Lab-STICC, UMR CNRS 6285, F-29238 Brest, France.</footnote>

<footnote n="3">³Université de Lille, CNRS, UMR 8520 - IEMN, F-59000 Lille, France.</footnote>
network performance through macro-diversity [5]. Unlike coordinated multipoint (CoMP)—which employs fixed, dis-joint cooperation clusters among neighboring base stations to jointly serve users within cellular boundaries [6]—cell-free massive MIMO eliminates traditional cell structures, implementing fully user-centric cooperation where distributed APs coherently serve each user across shared time-frequency resources [7]. This evolution positions CF-mMIMO as a cluster-free extension of CoMP’s joint-processing principles [7]. Despite these advantages, CF-mMIMO networks face practical challenges related to deployment cost, power consumption, and the complexity of coordinated resource allocation, especially as the number of APs and users grows [4], [8]. To address these challenges while maintaining uniform coverage, reconfigurable intelligent surfaces (RIS) have emerged as a cost-effective and energy-efficient solution. A RIS consists of passive reflecting elements dynamically configured to adjust reflection coefficients, intelligently manipulating the wireless propagation environment without requiring high-power radio frequency chains [9]. The integration of RIS in CF-mMIMO systems has demonstrated significant performance gains, where studies such as [10] have shown that optimized RIS phase configurations can substantially enhance overall system-level performance, thereby validating the potential of RIS-assisted cell-free network architectures.

The massive connectivity requirement of IoT systems can also be fulfilled through advanced multiple access techniques such as non-orthogonal multiple access (NOMA) [11]–[15]. NOMA boosts spectral efficiency and user fairness by simultaneously serving multiple users using the same resources. Specifically, power-domain NOMA exploits differences in received signal powers through successive interference cancellation (SIC) at the receiver [16]. However, the practical implementation of SIC in IoT networks faces challenges due to hardware imperfections, channel estimation errors, and the low-cost nature of IoT devices, which can lead to imperfect SIC and residual interference [17]. While such imperfections can be mitigated through careful system design and optimization, they represent an important practical consideration for real-world deployments. These implementation challenges, combined with the increasing density of IoT devices, introduce technical challenges in interference management, latency reduction, and efficient resource utilization. While CF-mMIMO and NOMA individually address aspects of these challenges, their integration in uncoordinated uplink IoT scenarios remains under-explored. This study proposes a new framework that leverages NOMA and CF-mMIMO in an uplink IoT network with uncoordinated transmissions. Such networks [18] allow devices to transmit without prior network coordination, significantly reducing signaling overhead and communication latency. Despite these benefits, the lack of coordination introduces challenges related to collisions and multi-user interference, which the proposed framework aims to effectively address.

## A. RELATED WORKS

A few previous works have studied uplink RIS-aided CF-mMIMO systems, primarily optimizing system performance through power control and RIS configuration. For instance, [19] optimize power control and RIS configuration to maximize the sum-rate. The authors in [20] maximize the minimum signal-to-interference-plus-noise ratio (SINR) by optimizing RIS phase shifts and power allocation through an alternating maximization algorithm, considering imperfect CSI and discrete RIS phase shifts. Genetic algorithms are employed in [21] to optimize RIS phase shifts for both sum-rate and max-min rate maximization. In [22], power control, precoding, and RIS phase optimization are addressed for downlink RIS-aided CF-mMIMO systems serving IoT networks. However, these studies assume that all resource allocation and optimization tasks are performed in a centralized manner at the CPU level, which precludes their applicability in an uncoordinated context. Besides, none of these mentioned works considered NOMA transmission.

RIS-assisted uplink NOMA has been explored in several works. The study in [23] optimizes signal detection, transmit power, and RIS phases while considering group-based SIC. In [24], semidefinite programming and majorization-minimization methods are used to optimize the sum-rate in RIS-assisted uplink NOMA with single-input single-output (SISO) transmissions. Energy efficiency optimization in RIS-enhanced cell-free NOMA networks using hybrid deep deterministic policy gradient (DDPG)-based algorithms is investigated in [25]. Active RIS configurations have also been studied in [26], which proposes an uplink design for URLLC jamming mitigation that uses a surrogate optimization and a deep-learning model to optimize the amplitude and phase coefficients. However, all of these studies only consider grant-based scenarios and do not address subband allocation or grant-free access optimization.

Previous research has utilized reinforcement learning, particularly multi-armed bandit (MAB) algorithms, for uncoordinated resource allocation and power control in uplink NOMA systems. Works such as [27] and [28] leverage the upper confidence bound (UCB) algorithm for joint channel selection and power allocation, while [29] investigates self-organizing networks with autonomous uplink transmission organization. The UCB framework is extended to CF-mMIMO-NOMA for subband and power selection by IoT devices in [15]. Nevertheless, these studies have not integrated RIS.

In contrast, this work addresses resource allocation for grant-free uplink RIS-aided CF-mMIMO-NOMA with minimal signaling overhead. Devices independently select sub-bands using the UCB algorithm based only on local information and feedback from the CPU. We propose a multi-stage process, beginning with initial SIC ordering, followed by RIS optimization, dynamic SIC reordering, and a reward distribution mechanism for refined decision-making. Our approach uniquely addresses the subband allocation challenge
in this integrated scenario, a topic largely overlooked by prior research in the CF-mMIMO-NOMA context.

## B. MOTIVATIONS, CONTRIBUTIONS AND PAPER ORGANIZATION

To the best of our knowledge, no previous works have considered the subband allocation problem in an uncoordinated uplink RIS-aided CF-mMIMO-NOMA system. In this paper, we propose a novel framework for joint subband allocation and RIS phase optimization in a grant-free RIS-aided CF-mMIMO-NOMA network. The main contributions of this study can be summarized as follows.

* Subband allocation to devices is determined while simultaneously optimizing the RIS phases in such a way to satisfy the devices QoS requirements. The study considers the case of IoT devices with low-cost transmitters that cannot perform complex power control, and therefore transmit at constant power. Instead of an explicit power control, the proposed framework relies on RIS phase optimization and linear receive combining to optimize the received signal powers implicitly and reshape multi-user interference. This approach enables SIC under constant device power, thereby supporting NOMA multiplexing while satisfying all devices' QoS requirements. Given the complexity of this joint optimization problem, we decompose it into two interconnected subproblems: subband allocation and RIS phase optimization. The subband allocation problem is addressed using the UCB algorithm within the MAB framework, leveraging the grant-free nature of the network.

* To improve the devices success rate over the time horizon, we propose an enhanced UCB decision function. Moreover, since in a grant-free system it is sufficient to guarantee the QoS constraints of IoT devices, the latter are invited to retain their subband selections once the system reaches convergence (in terms of QoS satisfaction), thereby significantly reducing system complexity.

* To further accelerate convergence and avoid unnecessary computations, we propose a classification method of the devices that can be applied prior to addressing the RIS optimization problem. In this technique, the maximum achievable rate is pre-computed for each device on every subband at the start of the time horizon by solving independent optimization problems conducted in parallel. This strategy allows an early elimination of some of the infeasible constraints in the optimization problem.

* Leveraging the characteristics of MIMO-NOMA networks, we introduce a dynamic SIC reordering approach, which allows lower-order devices to achieve QoS despite the outage of higher-order devices. It relies on a backtracking SIC process in order to retry the decoding of signals of devices in outage. This adaptive method enhances overall system performance compared

to traditional sequential SIC methods that are ended after the first decoding failure.

* We propose a sequential constraint removal technique in the RIS optimization procedure, where potentially infeasible constraints are gradually removed from the optimization problem. This technique accelerates system convergence and increases the percentage of devices successfully reaching their target QoS in each timeslot.

The remainder of this paper is organized as follows. Section II presents the system model for uplink uncoordinated RIS-aided CF-mMIMO-NOMA systems, including the relevant channel models, the uplink NOMA system, and the problem formulation. Section III details the proposed framework for the joint optimization of subband allocation and RIS phase configuration. The device classification and the SIC reordering procedures are also described in this section. In section IV, a comprehensive analysis of the proposed framework performance is presented. Finally, section V concludes the paper with key findings and future research directions.

## C. NOTATIONS

Boldface lowercase letters, $\mathbf{x}$, and uppercase letters, $\mathbf{X}$, denote column vectors and matrices, respectively. The transpose and conjugate transpose of a matrix are denoted by $\mathbf{X}^T$ and $\mathbf{X}^H$, respectively. $\mathbb{E}\{\mathbf{x}\}$ is the expected value of the random vector $\mathbf{x}$. $|\mathbf{a}|$ is the absolute value of a complex number, and $\|\mathbf{a}\|$ is the $\ell_2$-norm of vector $\mathbf{a}$. The identity matrix of size $N \times N$ is denoted by $\mathbf{I}_N$, and the zero matrix of size $M \times N$ is denoted by $\mathbf{0}_{M \times N}$. The cardinality of a set $\mathcal{A}$ is $|\mathcal{A}|$. $a \mod b$ returns the remainder when $a$ is divided by $b$. The floor function $\lceil n \rceil$ returns the largest integer less than or equal to $n$. The Hadamard product of matrices is denoted by $\circ$.

## II. SYSTEM MODEL

We consider an uplink RIS-aided CF-mMIMO-NOMA network where $L$ APs, each equipped with $N$ antennas, and $J$ RISs, each with $S$ reflective elements, serve $K$ single-antenna IoT devices. The devices are stationary over a horizon $T$ and any change in their activity starts a new horizon. Since dense IoT traffic consists of short, latency-sensitive packets, we consider a grant-free access scheme. Let $\mathcal{K} = \{1, \dots, K\}$ be the set of active devices and $\mathcal{C} = \{1, \dots, C\}$ the set of available subbands. In every timeslot $t \in [1, T]$, each device $k \in \mathcal{K}$ transmits on one subband $c \in \mathcal{C}$. We adopt the block fading channel model in [4], where each block corresponds to a timeslot consisting of $\tau = \tau_p + \tau_u$ instants. In this context, $\tau_p$ instants are used for pilot transmission, while the remaining $\tau_u$ instants are utilized for uplink data transmission. We assume that all APs are connected to the CPU through an ideal fronthaul providing error-free links with unlimited capacityNote that fronthaul links are naturally constrained in practice. The proposed framework can also be extended to scenarios with
limited-bandwidth fronthaul, which remains an interesting direction for future research. [3].

This work relies on a centralized operation of the network, where each AP acts as a relay that forwards its received signals to the CPU where all the processing and calculations are carried out [4]. We assume that the CPU has sufficient computational resources, consistent with a cloud-computing setup, thereby making centralized optimization feasible. In order to achieve system scalability and reduce the excessive computational complexity and signaling overhead associated with the centralized operation, the dynamic cooperation clustering (DCC) framework from [4] is adopted. In DCC, each device is served by a subset of APs that are determined offline, prior to the communication phase, by an AP selection technique such as the one introduced in [30]. This selection relies on the large-scale fading (LSF) parameters of the devices-AP links for decision-making. The device-AP correspondence is independent from the subband used for transmission. AP selection is described by block-diagonal matrices $D_k = \text{diag}\{D_{k1}, \dots, D_{kL}\}$, where $D_{kl} = I_N$ if AP $l$ serves device $k$, and $D_{kl} = 0_{N \times N}$ otherwise. At the beginning of each timeslot $t$, the CPU receives the pilot signals from all APs and estimates the transmission channel of each device over all subbands. Hence, pilot contamination can arise leading to channel estimation errors and decoding failures. However, pilot contamination is controlled by limiting every AP to at most $\tau_p$ served devices. The competitive AP selection mechanism of [30], combined with efficient pilot allocation, enforces this limit and prevents strong pilot contamination.

## A. CHANNEL MODEL

Environmental obstacles within the communication area can obstruct line-of-sight (LoS) links between devices and APs. Hence, the direct devices-APs links, denoted by $H_c^d \in \mathbb{C}^{K \times NL}$, are modeled by Rayleigh fading, as in [31], [32]. $H_c^d = [\mathbf{h}_{1,c}^d, \mathbf{h}_{2,c}^d, \dots, \mathbf{h}_{K,c}^d]^T$, where $\mathbf{h}_{k,c}^d \in \mathbb{C}^{NL \times 1}$ is given by $\mathbf{h}_{k,c}^d = [\mathbf{h}_{k,1,c}^{dT}, \mathbf{h}_{k,2,c}^{dT}, \dots, \mathbf{h}_{k,L,c}^{dT}]^T$. $\tilde{\mathbf{h}}_{k,l}^d \in \mathbb{C}^{N \times 1}$ is the channel between device $k$ and AP $l$ on subband $c$. Hereafter, we focus on one subband and omit the index $c$ and the slot index $t$ (since channels are static over $T$). $\mathbf{h}_{k,l}^d = \sqrt{\gamma_{k,l}} \tilde{\mathbf{h}}_{k,l}^d$, where $\gamma_{k,l}$ is the LSF coefficient, and $\tilde{\mathbf{h}}_{k,l}^d \in \mathbb{C}^{N \times 1}$ is the non-line-of-sight (NLoS) channel vector of the direct AP-device link, whose entries are independent and identically distributed (i.i.d.) complex Gaussian random variables, i.e., $\tilde{\mathbf{h}}_{k,l}^d \sim CN(0, I_N)$.

Multiple RISs are deployed across the network area to support device communication and improve signal quality. Due to severe attenuation, we consider only the first signal reflected by the RIS and ignore subsequent reflections [33]. While practical RIS deployments face hardware impairments such as phase-control errors and transceiver distortions that can degrade performance [34]–[37], this work adopts the widely used impairment-free RIS model with unit-modulus phase shifts. Therefore, the RIS phase shift matrix $\Theta$ is

denoted by $\Theta = \text{diag}\{\theta_1^T, \theta_2^T, \dots, \theta_J^T\} \in \mathbb{C}^{JS \times JS}$, $\theta_j = [e^{j\theta_{j,1}}, e^{j\theta_{j,2}}, \dots, e^{j\theta_{j,s}}]^T \in \mathbb{C}^{S \times 1}$, where $\theta_{j,s} \in [0, 2\pi)$ is the phase shift of the $s$th reflective element in the $j$th RIS. The total channel from $K$ devices to $L$ APs is given by $H^{\text{tot}} = H + H^d$, where $H = G\Theta Z \in \mathbb{C}^{K \times NL}$ represents the RIS-cascaded channels from devices to APs reflected by RISs. $G \in \mathbb{C}^{K \times JS}$ and $Z \in \mathbb{C}^{JS \times NL}$ denote the devices-RISs and RISs-APs channels, respectively.

Considering that APs and RISs are typically installed at elevated positions above the ground, and that RISs are often mounted on the exterior walls of tall buildings, it is highly likely that LoS links are present between devices and RISs, as well as between RISs and APs [21]. The general Rician fading model is used to model the RIS-cascaded channels [31], [32]:

$$G = [g_1, g_2, \dots, g_K]^T, g_k^T = [g_{k,1}^T, g_{k,2}^T, \dots, g_{k,J}^T], \quad (1)$$

$$Z = [Z_1, Z_2, \dots, Z_J]^T, Z_j^T = [Z_{j,1}, Z_{j,2}, \dots, Z_{j,L}], \quad (2)$$

$$Z_{j,l} = [z_{j,l,1}, \dots, z_{j,l,N}], \quad (3)$$

$$g_{k,j} = \sqrt{\alpha_{k,j}} \left( \sqrt{\frac{\varepsilon_{k,j}}{\varepsilon_{k,j}+1}} \bar{g}_{k,j} + \sqrt{\frac{1}{\varepsilon_{k,j}+1}} \tilde{g}_{k,j} \right), \quad (4)$$

$$Z_{j,l} = \sqrt{\beta_{j,l}} \left( \sqrt{\frac{\delta_{j,l}}{\delta_{j,l}+1}} \bar{Z}_{j,l} + \sqrt{\frac{1}{\delta_{j,l}+1}} \tilde{Z}_{j,l} \right), \quad (5)$$

for $1 \le j \le J$, $k \in K$, $1 \le l \le L$. $\alpha_{k,j}$ and $\beta_{j,l}$ are the LSF coefficients of device-RIS and RIS-AP links respectively. $\varepsilon_{k,j}$ and $\delta_{j,l}$ are the Rician factors. $\bar{g}_{k,j} \in \mathbb{C}^{S \times 1}$, $\bar{Z}_{j,l} \in \mathbb{C}^{S \times N}$ and $z_{j,l,n} \in \mathbb{C}^{S \times 1}$ are the deterministic LoS components [21] of the links between device $k$ and RIS $j$, and between RIS $j$ and AP $l$ respectively. Besides, $\tilde{g}_{k,j} \in \mathbb{C}^{S \times 1}$ and $\tilde{Z}_{j,l} \in \mathbb{C}^{S \times N}$ denote the NLoS channel components whose elements are i.i.d. variables following a $CN(0, 1)$ distribution. Moreover, the LoS components are modeled using the uniform square planar array (USPA) [38]. Therefore, $\bar{g}_{k,j}$ and $\bar{Z}_{j,l}$ can be represented by:

$\bar{g}_{k,j} = a_S(\varphi_{k,j}^a, \varphi_{k,j}^e)$, $\bar{Z}_{j,l} = a_N(\phi_{j,l}^a, \phi_{j,l}^e)a_S^H(\varphi_{j,l}^a, \varphi_{j,l}^e)$, where $a_X(\omega^a, \omega^e) \in \mathbb{C}^{X \times 1}$ is the array response vector. Based on [21], the $x$th entry of $a_X(\omega^a, \omega^e)$ is defined by:

$$[a_X(\omega^a, \omega^e)]_x = \exp \left\{ j2\pi \frac{b}{\lambda} \left( \lfloor (x-1)/\sqrt{X} \rfloor \sin \omega^a \sin \omega^e + ((x-1) \mod \sqrt{X} \cos \omega^e) \right) \right\}. \quad (6)$$

$b = \lambda/2$ is the array element spacing, with $\lambda$ the carrier wavelength. $\varphi_{k,j}^a$ and $\varphi_{k,j}^e$ are the azimuth and elevation angles of arrival (AoA) at RIS $j$ from device $k$. The corresponding azimuth and elevation angles of departure (AoD) from RIS $j$ to AP $l$ are $\varphi_{j,l}^a$ and $\varphi_{j,l}^e$, and the azimuth/elevation AoA at AP $l$ from RIS $j$ are $\phi_{j,l}^a$ and $\phi_{j,l}^e$.

In this work, only the total channels between any device $k$ and any AP $l$, including the direct channel $\mathbf{h}_{k,l}^d$ and the RIS-cascaded channel $g_{k,j} \circ z_{j,l,n}$, need to be estimated. This avoids the need for estimating the individual channels to or from a RIS, such as $\tilde{g}_{k,j}$ and $\tilde{Z}_{j,l}$, which is hard to implement in practice. The channel estimation can be performed using
the method in [39]. It is usually realized using a fixed RIS configuration. The estimation is performed by the CPU at the beginning of each timeslot *t*, during the pilot transmission period $\tau_p$, based on the received pilot signals from all APs. In the sequel, the proposed framework is first described for the case of perfect channel estimation. Then, in section IV, results are also provided for the case of an imperfect channel estimation.

## B. NOMA UPLINK TRANSMISSION

Let $\mathcal{K}_c(t) \subset \mathcal{K}$ be the set of devices transmitting over subband *c* at timeslot *t*. $\mathbf{h}_{k,c}^{\text{tot}} = \mathbf{Z}_c^T \Theta \mathbf{g}_{k,c} + \mathbf{h}_{k,c}^d$ is the total channel of device *k* over subband *c*, where $\mathbf{Z}_c$ is the channel matrix $\mathbf{Z}$ defined in II-A for subband *c*. $\mathbf{g}_{k,c}$ is the link between device *k* and the RISs over *c*. In fact, $\mathbf{h}_{k,c}^{\text{tot}}$ also depends on the timeslot index *t* since $\Theta$ changes with *t*. However, to simplify notations, the timeslot index is dropped in all channel, signal, SINR, and rate variables. The collective $NL \times 1$ received signal vector at the CPU from all APs on subband *c* is:

$$y_c = \sum_{k \in \mathcal{K}_c(t)} \sqrt{p_k} \mathbf{h}_{k,c}^{\text{tot}} x_{k,c} + \mathbf{n}_c, \quad (7)$$

where $x_{k,c} \in \mathbb{C}$ is the transmit symbol of device *k* over subband *c*, with $\mathbb{E}\{|x_{k,c}|^2\} = 1$, and $p_k$ the transmit power of device *k*. $\mathbf{n}_c \sim \mathcal{CN}(0, \sigma^2 \mathbf{I}_{NL})$ denotes the receiver additive white Gaussian noise (AWGN) vector on subband *c*.

Considering a grant-free system, and knowing that IoT devices most often have limited power variation capabilities, we assume that devices transmit with an equal constant power $p_k = p$, $\forall k \in \mathcal{K}$. In other words, no power control is applied in the uncoordinated context. However, as will be explained afterwards, the NOMA received powers at the CPU level are implicitly optimized by guaranteeing the requested QoS of each device through RIS phase optimization. Based on the estimated channels on all subbands, the CPU applies receive combining on the received signals at each subband. The low-complexity maximum-ratio combining (MRC) [5] is applied to maximize the device received signal-to-noise-ratio (SNR), by multiplying its received signal by the conjugate transpose of the combining vector $\mathbf{v}_{k,c} = \mathbf{h}_{k,c}^{\text{tot}}$. Note that the MRC scheme does not handle the inter-user interference, and more advanced combining schemes could have been used, such as regularized zero forcing (RZF) or minimum mean squared error (MMSE) [4]. However, such schemes require the inversion of channel matrices which size scales with the number of devices, APs and antennas, and that must be performed on each subband. Besides, the inclusion of RIS phase parameters in these matrix inversions significantly complicates the implementation of the RIS configuration problem. Consequently, we rely on RIS phase optimization, together with linear receive combining, to implicitly optimize received powers and reshape the interference among devices so that the resulting SINRs can satisfy the QoS requirements needed for SIC decoding. After signal detection, the received

signal from device *k*, transmitting over subband *c*, becomes:

$$\begin{aligned} \hat{y}_{k,c} = & \sqrt{p} \mathbf{v}_{k,c}^{H} \mathbf{D}_{k} \mathbf{h}_{k,c}^{\text{tot}} x_{k,c} \\ & + \sum_{\substack{k' \in \mathcal{K}_c(t) \\ k' \neq k}} \sqrt{p} \mathbf{v}_{k,c}^{H} \mathbf{D}_{k} \mathbf{h}_{k',c}^{\text{tot}} x_{k',c} + \mathbf{v}_{k,c}^{H} \mathbf{D}_{k} \mathbf{n}_{c}. \end{aligned} \quad (8)$$

According to (8), the achievable SINR and rate of device *k* transmitting on subband *c* are given respectively by:

$$\Gamma_k = \frac{p_k |\mathbf{v}_{k,c}^H \mathbf{D}_k \mathbf{h}_{k,c}^{\text{tot}}|^2}{\sum_{\substack{k' \in \mathcal{K}_c(t) \\ k' \neq k}} p_{k'} |\mathbf{v}_{k,c}^H \mathbf{D}_k \mathbf{h}_{k',c}^{\text{tot}}|^2 + \sigma^2 \|\mathbf{D}_k \mathbf{v}_{k,c}\|^2}, \quad (9)$$

$$R_k = \frac{\tau - \tau_p}{\tau} B \log_2(1 + \Gamma_k), \quad (10)$$

with *B* the subband bandwidth. Note that (9) will subsequently be modified to include the specific SIC scheme in NOMA.

In uplink NOMA, SIC is usually performed on each subband in the descending order of the devices total channel gain $\|\mathbf{D}_k \mathbf{h}_{k,c}^{\text{tot}}\|^2$ [40]. The SIC success is conditioned by the SINR levels of the received signals. More specifically, if the achievable SINR $\Gamma_k$ of device *k* is larger than or equal to a required SINR $\Gamma_k^{\text{req}}$, the CPU can successfully apply SIC to recover $x_{k,c}$ and subtract it from the total received signal, before attempting to decode the next device signal. $\Gamma_k^{\text{req}}$ is directly related to the requested rate (QoS) of device *k* by: $R_k^{\text{req}} = \frac{\tau - \tau_p}{\tau} B \log_2(1 + \Gamma_k^{\text{req}})$. In this work, SIC is supposed to be perfectly implemented without error propagation. However, to mitigate error propagation and limit the receiver complexity in practical SIC implementations, we assume that the number of SIC operations that the CPU can perform on each subband is limited to a maximum of $M_{\text{SIC}}$. Let $\mathcal{K}_c^{\text{SIC}}(t)$ be the set of devices transmitting on subband *c* whose signals have been removed by SIC at a certain stage of the SIC process. $\mathcal{K}_c^{\text{SIC}}(t)$ is initialized to an empty set, and a device index is added after each SIC operation on *c*. Accordingly, (9) is rewritten to include the SIC scheme as follows:

$$\Gamma_k = \frac{p_k |\mathbf{v}_{k,c}^H \mathbf{D}_k \mathbf{h}_{k,c}^{\text{tot}}|^2}{\sum_{p_{k'}} |\mathbf{v}_{k,c}^H \mathbf{D}_k \mathbf{h}_{k',c}^{\text{tot}}|^2 + \sigma^2 \|\mathbf{D}_k \mathbf{v}_{k,c}\|^2}. \quad (11)$$

In this framework, when $|\mathcal{K}_c(t)| > M_{\text{SIC}}$, the signals of the remaining devices in $\mathcal{K}_c(t) \setminus \mathcal{K}_c^{\text{SIC}}(t)$ undergo a "normal" decoding (without SIC, i.e., without signal subtraction) in the presence of the respective interference of non removed devices. Such decoding can be either successful or not, depending on the interference mitigation performed by the joint effect of RIS configuration and MIMO combining at the CPU.

## C. PROBLEM FORMULATION

The proposed framework aims to serve the devices on the available subbands while meeting their requested rates. For
this purpose, the following optimization problem is formu-
lated at each timeslot $t$:

$$
\underset{\Theta(t), \Psi(t)}{\text{Maximize}} \quad \sum_{k=1}^{K} \eta_k(t), \qquad (12a)
$$

$$
\text{subject to} \quad \theta_{j,s}(t) \in [0, 2\pi), \quad 1 \le j \le J, \quad 1 \le s \le S, \tag{12b}
$$

$$
\psi_{k,c}(t) \in \{0,1\}, k \in \mathcal{K}, c \in \mathcal{C}, \quad (12c)
$$

$$
\sum_{c \in \mathcal{C}} \psi_{k,c}(t) = 1, k \in \mathcal{K}. \quad (12d)
$$

$\Theta(t)$ represents the RIS phases determined at timeslot $t$, while $\eta_k(t) \in \{0,1\}$ is the success indicator of device $k$ at timeslot $t$, defined as $\eta_k(t) = 1$ if $\Gamma_k \ge \Gamma_k^{\text{req}}$, and 0 otherwise. $\Psi(t) \in \{0,1\}^{K \times C}$ contains the device-subband assignments, defined in (12c), such that $\psi_{k,c}(t) = 1$ if device $k$ transmits on subband $c$ at timeslot $t$, and 0 otherwise. In problem (12), (12b) represents the constraint on the RIS elements phases, while constraint (12d) ensures that each device transmits its data on only one subband.

In a practical IoT system, devices have a predetermined
amount of data to transmit at each timeslot. Because of the
uncoordinated characteristic of the grant-free system, they
are unaware of their achievable rate before transmission.
Indeed, the devices proceed to the transmission of their
data at the beginning of the uplink phase of each timeslot,
without having to wait for the scheduling outcome from
the CPU, as is done in grant-based systems. Therefore,
the devices are assumed to always transmit their data at
their requested rate, regardless of their actual achievable rate
(which depends on channel conditions and interferences) and
the RIS configuration. For these reasons, any solution that
satisfies the constraints of problem (12), while satisfying the
devices requested rates, is acceptable. Therefore, (12) can
be turned into a constraint satisfaction problem (CSP) [41],
with no particular objective function, as:

$$
\underset{\Theta(t), \Psi(t)}{\text{Maximize}} \quad 1, \qquad (13a)
$$

$$
\text{subject to} \quad \theta_{j,s}(t) \in [0, 2\pi), \quad 1 \le j \le J, \quad 1 \le s \le S, \tag{13b}
$$

$$
\Gamma_k(t) \ge \Gamma_k^{\text{req}}, \quad k \in \mathcal{K}, \qquad (13c)
$$

$$
\psi_{k,c}(t) \in \{0,1\}, \qquad (13d)
$$

$$
\sum_{c \in \mathcal{C}} \psi_{k,c}(t) = 1, k \in \mathcal{K}. \quad (13e)
$$

The feasibility of (13) is highly dependent on the ratio
between the number of devices and subbands, as well as
the QoS required by devices. Therefore, the current study
will focus on crowded scenarios with a limited number
of subbands, where constraints (13c) become particularly
challenging.

Problem (13) is a mixed-integer and non-convex optimization
problem due to the integer variables $\Psi(t)$ and the non-
convex nature of the SINR constraints in (13c) with respect
to the variables $\Theta(t)$, as can be seen in (11). Hence, it is

difficult to obtain a closed-form solution for this problem.
Therefore, we propose a new framework to solve (13). This
framework relies on an MAB system to perform subband
allocation in a distributed uncoordinated way, with the goal
of minimizing the interference caused by having too many
devices transmitting on the same subband. Indeed, this would
hinder the feasibility of the RIS configuration problem. The
latter is solved based on the devices subband choices, and
depends on the SIC ordering scheme. It is formulated as
follows:

$$
\underset{\Theta(t)}{\text{Maximize}} \quad 1, \qquad (14a)
$$

$$
\text{subject to} \quad (13b), (13c). \qquad (14b)
$$

As will be detailed afterwards, problem (14) will be solved
using an iterative procedure that relies on the interior point
method [42], [43].

III. DESCRIPTION OF THE OPTIMIZATION FRAMEWORK

In this section, we describe the proposed framework, sum-
marized in Algorithm 1, including the subband allocation
and RIS configuration procedures. To improve problem
feasibility and system performance, this section introduces
five enhancements: an enhanced UCB algorithm, a device
classification technique, a constraint removal procedure, a
dynamic SIC reordering method, and a stay mechanism.

A. SUBBAND ALLOCATION STRATEGY

To manage the uncoordinated transmissions of devices, the
subband allocation problem is solved using the UCB tech-
nique within the MAB framework [27]. In this work, the
UCB algorithm is chosen for its ability to balance exploration
and exploitation, ensuring an efficient resource allocation
even with limited feedback. Although one might consider
using deep reinforcement learning (DRL) techniques [44],
either centralized (at the CPU level) or multi-agent (at the
devices level), to solve this problem, a centralized DRL
approach at the CPU level is not viable in the context
of this study. This is due to the large action space of
size K × C resulting from the subband selection, coupled
with the grant-free system assumption that precludes CPU-
based resource allocation. Furthermore, devices are generally
assumed to have limited computational capabilities, making
it challenging for each device to train its own neural network.
Additionally, since devices are not expected to exchange
information about their states and rewards, the efficiency of a
multi-agent DRL approach is further diminished. Moreover,
each device independently selects a subband without cooper-
ation, making UCB’s independence from external decision-
making interactions particularly appropriate.

We begin with a high-level general description of the
proposed UCB algorithm, which incorporates an enhanced
decision function that includes the success indicator, as
well as a stay mechanism, where all devices retain their
subband choices once the system converges. This section
describes the UCB algorithm without the proposed device
classification procedure, which will be introduced in section III-B. Therefore, in the current section, the sets $\bar{\mathcal{K}}^{\text{block}}$ (the non-blocking devices that can achieve their required QoS on at least one subband) and $\mathcal{K}^{\text{inc}}(t)$ (devices whose QoS constraints are included in (14) at timeslot $t$) used in Algorithm 1, and that will be defined in III-B, are taken as: $\bar{\mathcal{K}}^{\text{block}} = \mathcal{K}^{\text{inc}}(t) = \mathcal{K}$. In this framework, the system is considered to have converged when all devices in $\bar{\mathcal{K}}^{\text{block}}$ achieve their required rate for the remainder of the time horizon.

In the MAB framework, each player (i.e., device) $k$ has an action profile $\mathcal{A}_k$ (set of arms), where $\mathcal{A}_k$ consists of the $\mathcal{C}$ available subbands, i.e., $\mathcal{A}_k = \mathcal{C}$. At each timeslot $t$, based on the devices subband choices, the CPU calculates and forwards, to every device, its achievable rate on its chosen subband, calculated according to the optimized RIS phases. Consequently, the reward transmitted by the CPU to a device $k$ that chose an action $a_k$ at timeslot $t$ is expressed by:

$$U_k(a_k, t) = \eta_k(t) \times R_k(t), \quad k \in \mathcal{K}, \quad (15)$$

where $R_k(t)$ is the achievable rate of $k$ at timeslot $t$. Note that this rate is only used as a reward indicator, while devices actually transmit at constant rate, as previously explained. It is worth mentioning that the reward calculation itself is simple, incurs negligible computational complexity at the CPU, and is performed after the devices signals have been decoded.

To perform subband selection, each device evaluates a decision function to determine its optimal action $a_k^*(t)$, which corresponds to the most suitable subband at timeslot $t$ as follows:

$$a_k^*(t) = \underset{a_k \in \mathcal{A}_k}{\operatorname{argmax}} \left( \nu_1 \frac{Q_k(a_k, t) + \sqrt{\frac{\log(t)}{n_k(a_k, t)}}}{R_k^{\text{req}} + \sqrt{\log(T)/T}} + \nu_2 \frac{\zeta_k(a_k, t)}{T} \right), \quad (16)$$

where $\nu_1$ and $\nu_2$ are two positive weights with $\nu_1 + \nu_2 = 1$. $Q_k(a_k, t)$ represents the mean reward for device $k$ when choosing action $a_k$, averaged from timeslot 1 to $t-1$. $n_k(a_k, t)$ is the number of times device $k$ performs action $a_k$ up to timeslot $t-1$. $\zeta_k(a_k, t) \in \mathbb{N}$ is introduced in (16) to represent the number of times device $k$ succeeded in achieving its requested QoS upon choosing action $a_k$ between timeslots 1 and $t-1$. This modification is a change to the classical UCB, where the decision function is defined as:

$$a_k^*(t) = \underset{a_k \in \mathcal{A}_k}{\operatorname{argmax}} \left( Q_k(a_k, t) + \sqrt{\frac{\log(t)}{n_k(a_k, t)}} \right). \quad (17)$$

The importance of adding $\zeta_k(a_k, t)$ in our framework stems from the fact that devices that achieve their target often have very close values of $Q_k(a_k, t)$ on multiple subbands and keep changing their choices during the upcoming timeslots. These multiple changes tend to delay system convergence (in case the global problem is feasible) and/or to reduce

the number of succeeded devices (in case the problem does not have a solution that can satisfy all devices). Adding $\zeta_k(a_k, t)$ to the decision function in (16) reduces the search space of the subband allocation problem in an efficient way, by encouraging the succeeded devices to maintain their subbands, while failed devices continue their explorations until possibly reaching a satisfying choice. Note that the two terms in (16) have been normalized, while $\nu_1$ and $\nu_2$ allow an appropriate balance between the UCB exploration and exploitation phases. Increasing $\nu_2$ tends to encourage the succeeded devices to maintain their subband choices, but at the cost of eventually preventing the success of other devices. Therefore, a compromise on the choice of $\nu_1$ and $\nu_2$ has to be determined.

After each device selects a subband for transmission (steps 4-6 in Algorithm 1), the CPU sorts the devices on each subband in a decreasing order of their total channel gains (step 10). Then, the RIS phase optimization problem (14) is solved at the CPU level (step 11), using the procedure that will be detailed in III-C. Upon convergence of the UCB process (steps 26-27), the CPU sends a quasi-infinite reward signal to all devices through APs to ensure that they maintain their subband choices for the remainder of the time horizon. This mechanism, called the stay mechanism, prevents unnecessary additional explorations and optimizations. Therefore, $Q_k(a_k^*, t+1)$ is calculated as follows:

$$Q_k(a_k^*, t+1) = \begin{cases} +\infty, & k \in \mathcal{K}, \text{ system converged,} \\ \frac{s_k(a_k^*, t+1)}{n_k(a_k^*, t+1)}, & k \in \mathcal{K}, \text{ otherwise,} \end{cases} \quad (18)$$

with $s_k(a_k^*, t+1) = s_k(a_k^*, t) + U_k(a_k^*, t)$ the sum of the rewards for each device $k$ from timeslot 1 to $t$.

To justify the stay mechanism, suppose that the system has succeeded in serving the devices in $\bar{\mathcal{K}}^{\text{block}}$ during a period of $T^{\text{cv}}$ successive timeslots. During $T^{\text{cv}}$, each device $k$ performs the same action $a_k$, receiving an identical reward $U_k(a_k, t)$ throughout this period ($U_k(a_k, t) = U_k(a_k, t+1) = \dots = U_k(a_k, t+T^{\text{cv}}-1)$). Consequently, the mean reward $Q_k(a_k, t)$ (calculated in step 37) remains constant over $T^{\text{cv}}$. However, the exploration term for device $k$, corresponding to its chosen action $a_k$, given by $\sqrt{\frac{\log(t)}{n_k(a_k, t)}}$, decreases after each timeslot in $T^{\text{cv}}$, since $\sqrt{\frac{\log(i+1)}{n_k(a_k, i)+1}} < \sqrt{\frac{\log(i)}{n_k(a_k, i)}}$. Conversely, the exploration term for alternative actions $a_k'$ of device $k$ increases during $T^{\text{cv}}$, as $\sqrt{\frac{\log(i+1)}{n_k(a_k, i)}} > \sqrt{\frac{\log(i)}{n_k(a_k, i)}}$. At timeslot $t+T^{\text{cv}}$, the value of the decision function in (16) for action $a_k'$ can become higher than that for action $a_k$, which may lead the device $k$ to change its action. Without the infinite reward mechanism upon convergence, this behavior can potentially trigger a cascade of action changes among many devices. Such changes would lead to system instability and unnecessary RIS optimization cycles, despite the fact that the existing configuration already satisfies the QoS requirements for devices in $\bar{\mathcal{K}}^{\text{block}}$. Indeed, recall that problem (13) aims at maximizing the number of satisfied
<figure><img src="image_2.png" /><figcaption>FIGURE 1. Illustration of group classification of devices.</figcaption></figure>

devices, and does not focus on maximizing their achieved rates. Therefore, if after convergence, some devices keep changing their subband choices to achieve higher rewards, they may hinder the satisfaction constraint of other devices. Note that the stay mechanism forces the devices to maintain their choices as the system converges, while the variable $\zeta_k(a_k, t)$ is used to accelerate the convergence by reducing the search space of devices.

In steps 31-38, at the end of the current timeslot, each device $k$ updates the UCB parameters ($Q_k(a_k^*, t+1)$, $\zeta_k(a_k^*, t+1)$, $n_k(a_k^*, t+1)$) associated with each action, using the reward calculated in step 29. These updated parameters are then used for subband selection in the next timeslot.

## B. DEVICE CLASSIFICATION PROCEDURE

In order to accelerate system convergence and further decrease the number of unnecessary optimizations, while maintaining a high success rate, we introduce a device classification procedure in the proposed framework. Indeed, it was noticed that some devices may not achieve their requested SINR even in the absence of inter-user interference, due to poor channel conditions, regardless of the RIS configuration. Therefore, each device $k$ is classified based on its maximum achievable SNR on every subband $c$. The SNR of $k$ over subband $c$ is:

$$ \mu_{k,c} = \frac{p_k \left\| \mathbf{D}_k \left( \mathbf{Z}_c^T \mathbf{\Theta}_{k,c} \mathbf{g}_{k,c} + \mathbf{h}_{k,c}^d \right) \right\|^2}{\sigma^2}. \quad (19) $$

To determine $\mu_{k,c}^{\max}$, the maximum achievable SNR of $k$ on subband $c$, the following optimization problem needs to be solved separately for every pair $(k, c)$, $k \in \mathcal{K}, c \in \mathcal{C}$:

$$ \mu_{k,c}^{\max} = \max_{\Theta_{k,c}} \mu_{k,c}, \quad (20a) $$

$$ \theta_{j,s}(t) \in [0, 2\pi), \quad 1 \le j \le J, \quad 1 \le s \le S. \quad (20b) $$

The devices are then classified into three separate sets:

* Servable devices: devices having the possibility to achieve their target QoS over all subbands:

$$ \mathcal{K}^{\text{serv}} = \{ k \in \mathcal{K} \mid \forall c \in \mathcal{C}, \mu_{k,c}^{\max} \ge \Gamma_k^{\text{req}} \}. $$

## Algorithm 1 Proposed Framework

1: Initialization: $\Theta(0) = \mathbf{I}_{JS}$; $Q_k(a_k, t) = 0$; $\zeta_k(a_k, 0) = 0$; $\eta_k(0) = 0$; $s_k(a_k, 0) = 0$; $k \in \mathcal{K}$, $a_k \in \mathcal{A}_k$.

2: Constitute the sets $\mathcal{K}^{\text{serv}}$, $\mathcal{K}^{\text{crit}}$ and $\mathcal{K}^{\text{block}}$, as described in III-B.
Device classification (III-B)

3: **for** $t=1$ **to** $T$ **do**

4: **for** $k=1$ **to** $K$ **do**

Enhanced UCB (III-A)

5: $a_k^*(t) = \underset{a_k \in \mathcal{A}_k}{\operatorname{argmax}} \left( \nu_1 \frac{Q_k(a_k, t) + \sqrt{\frac{\log(t)}{n_k(a_k, t)}}}{R_k^{\text{req}} + \sqrt{\log(T)/T}} + \nu_2 \frac{\zeta_k(a_k, t)}{T} \right)$

6: **end for**

7: **if** $\psi_{k,c}(t) \neq \psi_{k,c}(t-1)$, $\forall k, c$ **then**

8: **//The subband choices have changed, need to optimize.**

9: Calculate $\mathbf{H}^{\text{tot}}(t)$ using $\Theta(t-1)$.

10: Order the devices on each subband in descending order of $\|\mathbf{D}_k \mathbf{h}_{k,c}^{\text{tot}}(t)\|^2$.

11: Optimize RIS: solve (14) for devices in $\mathcal{K}^{\text{inc}}(t)$.

Dynamic SIC reordering (Algorithm 2)

12: Use Algorithm 2 to calculate $\mathbf{\Gamma}$ and reorder devices.

13: $\mathcal{K}^{\text{rem}}(t) = \{\}$;

14: **for** $\delta=1$ **to** $\Delta$ **do**

15: **if** $\sum_{k \in \{\mathcal{K}^{\text{inc}}(t) \setminus \mathcal{K}^{\text{rem}}(t)\}} (\Gamma_k < \Gamma_k^{\text{req}}) < 1$ **then**

16: **Break;**
**//All constraints are satisfied.**

17: **end if**

18: Remove the SINR constraint of a device $k$, as presented in III-C;

19: $\mathcal{K}^{\text{rem}}(t) = \mathcal{K}^{\text{rem}}(t) \cup \{k\}$;

20: Optimize RIS: solve (14) for devices in $\mathcal{K}^{\text{inc}}(t) \setminus \mathcal{K}^{\text{rem}}(t)$;

21: Use Algorithm 2 to calculate $\mathbf{\Gamma}$ and reorder devices.
Dynamic SIC reordering (Algorithm 2)

22: **end for** RIS phase optimization and constraint removal process (III-C)

23: **end if**

24: Calculate $R_k$ using (10) $\forall k$;

25: $\eta_k(t) = \begin{cases} 1 & \text{if } \Gamma_k \ge \Gamma_k^{\text{req}}, k \in \mathcal{K}, \\ 0 & \text{otherwise.} \end{cases}$

26: **if** $\sum_{k=1}^{K} \eta_k(t) == |\bar{\mathcal{K}}^{\text{block}}|$ **then**

27: $U_k(a_k^*, t) = +\infty$, $k \in \mathcal{K}$;
**//The devices are informed to maintain their choices.**

28: **else**

29: $U_k(a_k^*, t) = \eta_k(t) \times R_k, \forall k$;

30: **end if**

31: **for** $k=1$ **to** $K$ **do**

32: **if** $\eta_k(t) == 1$ **then**

33: $\zeta_k(a_k^*, t+1) = \zeta_k(a_k^*, t) + 1$;

34: **end if**

35: $s_k(a_k^*, t+1) = s_k(a_k^*, t) + U_k(a_k^*, t)$

36: $n_k(a_k^*, t+1) = n_k(a_k^*, t) + 1$

37: $Q_k(a_k^*, t+1) = \frac{s_k(a_k^*, t+1)}{n_k(a_k^*, t+1)}$

38: **end for**

39: **end for**
* Critical devices: devices that can achieve their target over some of the subbands only:

$$ \mathcal{K}^{\text{crit}} = \left\{ \begin{array}{l} k \in \mathcal{K} \mid \exists c \in \mathcal{C}, \mu_{k,c}^{\max} \ge \Gamma_k^{\text{req}} \\ \qquad \wedge \exists c' \in \mathcal{C}, \mu_{k,c'}^{\max} < \Gamma_k^{\text{req}} \end{array} \right\}. $$

* Blocking devices: for such devices, the maximum achievable SNR across all subbands is less than the required:

$$ \mathcal{K}^{\text{block}} = \{k \in \mathcal{K} \mid \forall c \in \mathcal{C}, \mu_{k,c}^{\max} < \Gamma_k^{\text{req}}\}. $$

Note that the expression "blocking devices" stems from the fact that these devices prevent the system from converging in the time horizon, since their SINR constraints make the problem (14) infeasible. A critical device ends up to be either blocking or servable depending on its subband choice. Let:

$$ \mathcal{K}^{\text{crit-serv}}(t) = \{k \in \mathcal{K}^{\text{crit}} \mid \exists c \in \mathcal{C}, \psi_{k,c}(t) = 1 \wedge \mu_{k,c}^{\max} \ge \Gamma_k^{\text{req}}\} $$

the subset of devices from $\mathcal{K}^{\text{crit}}$ that choose a subband on which they can achieve their target at timeslot $t$. Note that $\mathcal{K}^{\text{serv}}$, $\mathcal{K}^{\text{crit}}$ and $\mathcal{K}^{\text{block}}$ are not function of the timeslot index, since they do not depend on the choices of the devices, and the propagation channels (devices-AP, devices-RIS and RIS-AP) remain static throughout the horizon. Consequently, the global set of devices that have the capability to achieve their requested rate over their chosen subbands at timeslot $t$ is: $\mathcal{K}^{\text{inc}}(t) = \mathcal{K}^{\text{serv}} \cup \mathcal{K}^{\text{crit-serv}}(t)$. The constraints of the devices in $\mathcal{K}^{\text{inc}}(t)$ will therefore be included in the RIS optimization problem. The main sets used in the classification procedure are illustrated in Fig. 1.

To determine these sets, a maximum of $K \times C$ independent optimizations need to be performed. In fact, the direct link between devices and APs is sometimes sufficient to guarantee the required QoS for some devices, especially at low requested rates. The corresponding subset of such $(k, c)$ pairs can be determined by relying only on the direct link through a straightforward verification of the SNR level using (19). This can reduce the number of needed optimizations to a number lower than $K \times C$, in case of favorable direct link conditions. Then, the remaining independent optimizations are executed in parallel and solved only once per time horizon, after the channel estimation phase of timeslot 1. Problem (20a) is solved for the remaining $(k, c)$ pairs using the interior point algorithm. Based on the device classification outcome, the infeasible constraints at timeslot $t$ corresponding to the devices in $\bar{\mathcal{K}}^{\text{inc}}(t)$ (the complement of $\mathcal{K}^{\text{inc}}(t)$) are removed from the RIS phases configuration problem (14). In other words, only the constraints of the devices in $\mathcal{K}^{\text{inc}}(t)$ are included in the problem formulation. The devices in $\bar{\mathcal{K}}^{\text{inc}}(t)$ will receive a zero reward at the end of the current timeslot. This strategy has two advantages: on the one hand, it avoids useless RIS optimizations that are unsuccessful because of the devices that cannot be served on their chosen subbands. On the other hand, it can accelerate system convergence by increasing the probability of reaching a feasible solution for (13) at earlier timeslots As

a result, when the classification procedure is applied within the framework, (13c) becomes:

$$ \Gamma_k(t) \ge \Gamma_k^{\text{req}}, k \in \mathcal{K}^{\text{inc}}(t). $$

### C. RIS PHASE OPTIMIZATION PROCEDURE

Solving the RIS phase optimization problem (14) requires appropriate ordering for decoding device signals on each subband. The formulation of SINR constraints (13c) of devices in $\mathcal{K}^{\text{inc}}(t)$ depends on the specific SIC ordering on each subband. For this purpose, for each subband $c$, devices in $\mathcal{K}_c(t)$ are first sorted in descending order of their total channel gain (step 10 in Algorithm 1). To ensure optimization efficiency, on each subband $c$, devices belonging to $\mathcal{K}_c(t) \setminus \mathcal{K}^{\text{inc}}(t)$, i.e, corresponding to infeasible constraints at timeslot $t$ (based on the classification procedure in III-B), are moved to the latest ordering levels. This step aims at avoiding SIC attempts for blocking devices at $t$. The device ordering remains unchanged during the RIS phase optimization process. In other words, the optimization aims to satisfy QoS requirements of devices in the given SIC ordering. To reduce unnecessary optimizations and decrease computational complexity, RIS phase optimization is skipped if subband choices at timeslot $t$ remain the same as those at $t-1$ (step 7). This situation may occur during the exploration phase (due to device choices) or after system convergence, when devices maintain their choices until the end of the time horizon. In such cases, the phases obtained at $t-1$ are reused for all calculations in $t$.

On each subband $c$, if a solution exists for (14), the ordering strategy ensures that the system performs $\min(M_{\text{SIC}}, |\mathcal{K}_c(t) \cap \mathcal{K}^{\text{inc}}(t)|)$ SIC operations, followed by a normal decoding (with no SIC) for the remaining devices. The system is considered to have converged when all devices in $\bar{\mathcal{K}}^{\text{block}}$ achieve their required rates for the remainder of the time horizon. Problem (14) is solved using the interior point algorithm. Note that while our framework does not introduce a specific RIS optimization algorithm, it is designed to be flexible, allowing the integration of any suitable algorithm for RIS phase optimization. This work is rather focused on proposing a complete solution for the studied context.

After completing the RIS phase optimization (step 11 or 20), the SINR values for all devices in $\mathcal{K}$ are computed and stored in the $K \times 1$ vector $\Gamma$ (step 12 or 21). During the calculation of $\Gamma$, a new SIC ordering is obtained using Algorithm 2, which will be detailed in Section III-D. In the case of an optimization failure, this new decoding order is used as an input to the first optimization repeat in step 20 (the optimization repeat will be explained later in this section). An optimization failure is defined as the inability to satisfy one or more devices in $\mathcal{K}^{\text{inc}}(t)$, which typically occurs due to an inappropriate subband selection by the devices. In this case, the problem is gradually relaxed by sequentially removing the device constraints that are the most likely to have caused the optimization failure, aiming to
improve the success rate. This iterative approach is repeated until the problem solution meets the QoS of the remaining non removed devices or reaches a predetermined number of iterations Δ (steps 14-22). Let $K^{\text{rem}}(t) \subset K^{\text{inc}}(t)$ be the set of devices whose constraints are removed during the sequential optimization procedure at timeslot $t$, initialized to an empty set. The constraint removal process is summarized by the following steps:

(a) Identify the subband with the highest number of failed constraints for devices in $K^{\text{inc}}(t)$. This subband is likely to have infeasible constraints due to high interference from numerous devices. If multiple such subbands are identified, randomly select one of them.

(b) For the identified subband, remove the constraint of the failed device $k \in K^{\text{inc}}(t)$ with the weakest channel gain. $K^{\text{rem}}(t)$ is updated such that $K^{\text{rem}}(t) = K^{\text{rem}}(t) \cup \{k\}$.

(c) Perform the optimization again by solving (14) for the devices in $K^{\text{inc}}(t) \setminus K^{\text{rem}}(t)$.

(d) Repeat steps (a) to (c) until the relaxed problem satisfies all remaining constraints or until Δ iterations are reached.

This approach achieves QoS satisfaction for a larger number of devices by removing potentially infeasible constraints that are not identified during device classification (due to the presence of interference).

Afterwards, the rewards are calculated by the CPU according to (15) (step 29), and transmitted to devices through APs. Combined to the effect of introducing $\zeta_k(a_k, t)$ in (16), this approach generally accelerates system convergence and further reduces the likelihood of optimization failure due to subband congestion in subsequent timeslots. This congestion occurs when no problem relaxation is applied, since failed devices (which have received zero rewards) keep changing their choices inefficiently in subsequent timeslots.

## D. DYNAMIC SIC REORDERING PROCEDURE

Before describing the proposed SIC reordering procedure, we start by explaining its importance in the uplink MIMO-NOMA context by highlighting the difference in SIC feasibility towards the SISO case. For this purpose, consider the context of one single-antenna receiver $l$ and $K$ transmitters requesting a common rate $R^{\text{req}} = \frac{\tau - \tau_p}{\tau} B \log_2(1 + \Gamma^{\text{req}})$. Let $h_{k,l}$ the channel between device $k$ and $l$. The uplink devices are ordered in descending order of $p_k|h_{k,l}|^2$: $p_1|h_{1,l}|^2 > p_2|h_{2,l}|^2 > \dots > p_K|h_{K,l}|^2$. Consider that the receiver succeeds in decoding the signals of the first $k-1$ devices (i.e., $\Gamma_i \ge \Gamma^{\text{req}}$, $i = 1, \dots, k-1$), then the SINR for decoding the signal of the next device $k$ is:

$$ \Gamma_k = \frac{p_k|h_{k,l}|^2}{\sum_{i=k+1}^{K} p_i|h_{i,l}|^2 + \sigma^2}. $$

Suppose that device $k$ fails to achieve its requested QoS ($\Gamma_k < \Gamma^{\text{req}}$) and hence its signal is not removed by SIC. The

## Algorithm 2 SIC Reordering and SINR calculation

1: **Input:** $K_c \forall c$. //Initial devices ordering on each subband.

2: **for** $c = 1$ **to** $C$ **do**

3: $K_c^{\text{SIC}} = []$; //Array of removed devices by SIC.
$K_c^{\text{n-SIC}} = K_c$; //Array of non-removed devices by SIC.
$m = 0$; //Number of performed SIC.

4: **V = true;**

5: **while** V **do**

6: $i = 0$; //Number of calculated SINRs.

7: **for** $k$ **in** $K_c^{\text{n-SIC}}$ **do**

8: Calculate $\Gamma_k$ based on $G, \Theta, Z, H^d, D_k, K_c^{\text{n-SIC}}$ using (11);

9: $i = i + 1$;

10: **if** $\Gamma_k \ge \Gamma_k^{\text{req}}$ **and** $m < M_{\text{SIC}}$ **and** $k \in K_c^{\text{inc}}$ **then**

11: Perform SIC for device $k$;

12: $m = m + 1$;

13: $K_c^{\text{SIC}} = [K_c^{\text{SIC}}, k]$;

14: $K_c^{\text{n-SIC}} = K_c^{\text{n-SIC}} \setminus k$;

15: **end if**

16: **if** $i == |K_c^{\text{n-SIC}}|$ **then**

17: **V = false;**

//The final SINR has been calculated for all devices.

18: **end if**

19: **end for**

20: **end while**

21: $K_c = [K_c^{\text{SIC}}, K_c^{\text{n-SIC}}]$;

22: **end for**

23: **Output:** $\Gamma, K_c \forall c$. //Output SINRs and the new devices ordering on each subband.

SINR of the subsequent device $k+1$ is:

$$ \Gamma_{k+1} = \frac{p_{k+1}|h_{k+1,l}|^2}{p_k|h_{k,l}|^2 + \sum_{i=k+2}^{K} p_i|h_{i,l}|^2 + \sigma^2}. $$

Knowing that

$$ p_{k+1}|h_{k+1,l}|^2 < p_k|h_{k,l}|^2 $$

and

$$ p_k|h_{k,l}|^2 + \sum_{i=k+2}^{K} p_i|h_{i,l}|^2 > \sum_{i=k+1}^{K} p_i|h_{i,l}|^2, $$

this leads to: $\Gamma_{k+1} < \Gamma^{\text{req}}$. As a result, in uplink SISO, if the receiver fails to decode the signal of a device, then it will surely fail to decode the signals of all the subsequent device signals on the same subband.

In contrast, this proof does not hold in MIMO systems, because of the presence of the combining vector $v_{k,c}$ in the SINR expression of $k$ (11). As a result, it is possible for other devices transmitting over the same subband as the unsatisfied device $k$ to still achieve their requested SINR, regardless of their position in the SIC decoding order. Another contributing factor to the necessity of revisiting the
decoding order is that this ordering can be suboptimal since, at timeslot $t$, devices are ordered based on the total channels calculated using the RIS phases obtained at timeslot $t-1$. When the phases are optimized at $t$ based on the new devices choices, the actual ordering of the devices might change. For this reason, the SINR calculations in steps 12 and 21 of Algorithm 1 are performed using the most recently obtained $\Theta(t)$ and the SIC decoding order generated dynamically in Algorithm 2. This leads to the possibility of succeeding in the decoding of a device's signal at order $i$ despite the failure of one or more previous decodings at lower orders.

Accordingly, in this framework, when a device $k$ fails to achieve its requested QoS, rather than stopping the SIC process in the corresponding subband $c$, the SINR of subsequent devices in $K_c(t) \setminus K_c^{\text{SIC}}(t)$ continues to be computed using (11) (where $K_c^{\text{SIC}}(t)$ is defined in section II-B). If a subsequent device $k'$ succeeds in achieving its SINR requirement and the maximum number of SIC operations $M_{\text{SIC}}$ has not been reached yet, the signal of $k'$ is removed by SIC. $k'$ is then inserted before $k$ in the decoding order. After this removal, the algorithm backtracks to recalculate the SINR of previously failing devices, starting from $k$. This backward recalculation therefore leads to a dynamic reordering of SIC operations, which often increases the number of successful decodings (either in SIC or normal decoding) on all subbands. This process is summarized in Algorithm 2, where the timeslot index $t$ was removed for clarity. In addition, Fig. 2 presents a flow chart illustrating the process of Algorithm 2.

As an example, consider the case where $M_{\text{SIC}} = 4$ and six devices have chosen subband $c$, with $K_c(t) = (1, 2, 3, 4, 5, 6)$ ordered by decreasing channel gain. Assume that device 1 and 4 achieve their required QoS, while 2 and 3 do not. The signals $s_1$ and $s_4$ are sequentially removed by SIC, in the order of $s_1$ followed by $s_4$. The SINR calculation is repeated starting from $s_2$ (with the corresponding interference terms that take into account the dynamic SIC process, i.e. the removal of $s_1$ and $s_4$) followed by $s_3$, etc. The latter might succeed due to the removal of $s_4$, while it could have failed without it. Indeed, suppose that the decoding of $s_2$ fails again while the decoding of $s_3$ succeeds. The algorithm now backtracks to the decoding of $s_2$ which now succeeds, thereby reaching the maximum number of SIC operations $M_{\text{SIC}}$. Subsequently, the signals of the remaining devices will be normally decoded without SIC (i.e. their SINRs are calculated by taking into consideration the interference of each others), which can result in SINR values higher than $\Gamma_k^{\text{req}}$ due to the additionally removed signals by the dynamic SIC process. Therefore, the final decoding order on $c$ is $K_c(t) = (1, 4, 3, 2, 5, 6)$, with $K_c^{\text{SIC}}(t) = (1, 4, 3, 2)$. Consequently, this dynamic reordering process often increases the number of successful decodings (either in SIC or normal decoding) on all subbands, leading to a higher number of satisfied devices and eventually an earlier system

<figure><img src="image_3.png" /><figcaption>FIGURE 2. Flow chart of Algorithm 2 over one subband.</figcaption></figure>

convergence. An illustration of this example is shown in Fig. 3.

E. COMPLEXITY ANALYSIS

We begin by analyzing the complexity of the RIS optimization problem (14). Following [45], each iteration of the interior-point method requires factorizing a Karush-Kuhn-Tucker (KKT) system of size $N^{\text{Var}} + N^{\text{Const}}$, where $N^{\text{Var}} = JS$ is the number of variables and $N^{\text{Const}} = |K_c^{\text{inc}}(t)|$ is the number of constraints. This factorization costs about $\frac{1}{3}(JS + |K_c^{\text{inc}}(t)|)^3$ flops per iteration. Simple bound constraints and function evaluations are neglected since they add negligible cost compared to the KKT factorization cost. Thus, the overall complexity scales as $O(itr^{\text{opt}}(t)(JS + |K_c^{\text{inc}}(t)|)^3)$, where $itr^{\text{opt}}(t)$ is the total number of solver iterations across optimization repeats in timeslot $t$. It should be reminded that optimization is not necessarily executed at every timeslot due to the proposed enhancements.

As for the classification problem (20) complexity, it scales as $O(itr^{\text{class}} J^3 S^3)$, where $itr^{\text{class}}$ is the number of solver iterations. Its function evaluations are also neglected since they involve only simple SNR computations. Classification is performed once at the beginning of the time horizon, with at most $K \times C$ optimizations in parallel.

For the dynamic SIC reordering algorithm (Figs. 2–3), the device order is not recomputed at each backtracking step; instead, the final order is obtained once after all SINR
<figure><img src="image_4.png" /><figcaption>FIGURE 3. Illustration of a SIC reordering example.</figcaption></figure>

calculations have been completed. The number of SINR computations on subband c can reach, in the worst case (where the last $M_{SIC}$ devices on a subband c successfully perform SIC), $M_{SIC}(|Kc(t)| - \frac{M_{SIC}-1}{2})$. We consider that the complexity of normal decoding can be neglected since SINR calculations can be parallelized after all allowed SIC operations are performed. Hence, the worst-case complexity per subband is $O((M_{SIC}|Kc(t)| - M_{SIC}^2)C^{SINR})$, where $C^{SINR}$ is the average cost of one SINR calculation. In practice, the maximum number of allowed SIC operations is small, and, after early UCB exploration, the number of devices per subband is limited, mitigating error propagation and keeping the complexity manageable. The computational complexity of the three main algorithmic components are summarized in Table 1.

Finally, when the number of devices grows to hundreds or thousands, scalability can be maintained by serving each group of devices with a subset of RISs based on LSF channel parameters, or/and by grouping devices by type (e.g., temperature sensors, cameras, etc.), with each group restricted to organizing their transmissions over a separate subset of subbands, using the same approach used in this paper. Note that increasing the number of devices would also require a proportional increase in the number of available subbands.

<table><caption>TABLE 1. Complexity of the three main algorithmic components.</caption><thead><tr><td>Technique</td><td>Complexity</td></tr></thead><tbody><tr><td>RIS phase optimization</td><td>O(itr<sup>opt</sup>(t) (JS + |K<sup>inc</sup>(t)|)<sup>3</sup>)</td></tr><tr><td>Device classification</td><td>O(itr<sup>class</sup> J<sup>3</sup>S<sup>3</sup>)</td></tr><tr><td>Dynamic SIC reordering</td><td>O((M<sub>SIC</sub>|K<sub>c</sub>(t)| - M<sub>SIC</sub><sup>2</sup>) C<sup>SINR</sup>)</td></tr></tbody></table>

## IV. SIMULATION RESULTS

This section presents a detailed system-level performance analysis of the proposed framework obtained through numerical simulations. Starting with the deployment model, inspired by [21], we consider an example of a network spread over an area of 250 m × 250 m, having the topology presented in Fig. 4. The area is partitioned into four regions, arranged from top to bottom as follows: RISs, devices, vegetation (to illustrate obstacles), and APs. This positioning model is only chosen as an illustrative example, while the proposed framework is flexible and applicable to various network topologies, supporting diverse AP and RIS deployment scenarios. The devices are randomly deployed using a uniform distribution over their area, where the direct link between devices and APs is weakened due to the presence of the vegetation.

Unless otherwise specified, we consider $L = 10$ APs each equipped with $N = 4$ antennas, serving $K = 25$ devices. To enhance the network coverage, $J = 4$ RISs, each with $S = 16$ reflective elements, are deployed. Moreover, the time horizon consists of $T = 150$ timeslots of duration 1 ms each. The RIS phases are updated once per 1 ms slot. This choice is well supported by hardware reports, as PIN-diode RIS prototypes achieve switching frequencies up to 5 MHz ($\approx 0.2$ µs per state change) [46], which is several thousand times faster than the considered slot duration. We consider $C = 5$ available subbands, each with bandwidth $B = 312$ KHz. Devices transmit at power $p_k = 20$ dBm. Without loss of generality, and to simplify the results analysis, all devices are assumed to request a common rate: $R_k^{req} = R^{req}, \forall k$. The noise power is $\sigma^2 = -104$ dBm. The LSF coefficients $\gamma_{k,l}, \alpha_{k,j}$ and $\beta_{j,l}$ capture the effects of path loss and shadow fading as follows: $\gamma_{k,l} = 10^{-3}(d_{k,l}^{-\gamma_{pl}})10^{-\frac{\sigma_{sh}\kappa_{k,l}}{10}}, \alpha_{k,j} = 10^{-3}(d_{k,j}^{-\alpha_{pl}})10^{-\frac{\sigma_{sh}\kappa_{k,j}}{10}}, \beta_{j,l} = 10^{-3}(d_{j,l}^{-\beta_{pl}})10^{-\frac{\sigma_{sh}\kappa_{j,l}}{10}},$ where $d_{k,l}, d_{k,j},$ and $d_{j,l}$ respectively represent the distances between device $k$ and AP $l$, device $k$ and RIS $j$, RIS $j$ and AP $l$. $\gamma_{pl} = 4, \alpha_{pl} = 2$, and $\beta_{pl} = 2.5$ are the path-loss exponents [21]. $10^{-\frac{\sigma_{sh}\kappa_{k,l}}{10}}$ represents the shadow fading with standard deviation $\sigma_{sh} = 8$ dB, and $\kappa_{k,l}, \kappa_{k,j}, \kappa_{j,l} \sim N(0, 1)$. Other system parameters are specified in Table 2. The results are obtained by averaging 2000 independent simulation setups.

In order to assess the performance improvement obtained by each additional procedure in the proposed framework, multiple variants of the latter are analyzed. They are defined as follows:

(A) Full proposal: All the proposed enhancements described in section III are included (Algorithm 1).
<table><caption>TABLE 2. System Parameters</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>UCB parameters</td><td>ν<sub>1</sub> = 0.3, ν<sub>2</sub> = 0.7</td></tr><tr><td>Rician factors</td><td>ε<sub>k,j</sub> = 10, δ<sub>j,l</sub> = 1 ∀k, l, j</td></tr><tr><td>Maximum SIC operations per subband</td><td>M<sub>SIC</sub> = 4, except for Fig. 8 where M<sub>SIC</sub> = 4 to 7</td></tr><tr><td>Timeslot partitioning</td><td>τ = 200, τ<sub>p</sub> = 10</td></tr><tr><td>Maximum number of optimization repeats</td><td>Δ = 2</td></tr><tr><td>ξ<sub>k</sub>, p<sub>k</sub>, P<sup>static</sup><sub>k</sub></td><td>0.3, 20 dBm, 10 mW</td></tr><tr><td>P<sup>static</sup><sub>l</sub>, P<sup>antenna</sup><sub>l</sub></td><td>100 mW, 50 mW</td></tr><tr><td>P<sup>ft</sup><sub>l</sub></td><td>0.25 mW/Mbps</td></tr><tr><td>P<sup>element</sup></td><td>10 mW</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>FIGURE 4. RIS-aided CF-mMIMO network configuration.</figcaption></figure>

(B) Full proposal w/o Class: Devices are not classified prior to the optimization and subsequent steps. All the devices QoS constraints are taken into consideration in (14).

(C) Full proposal w/o SIC reorder: In this version, SINRs are calculated using (11) without applying the dynamic SIC reordering procedure of Algorithm 2. The SIC process at each subband is ended at the first failure of a device satisfaction. Other device signals are normally decoded (i.e. by taking into consideration the remaining interferences of signals not removed by SIC).

(D) Full proposal w/o ReOpt: In this variant, at each timeslot only one optimization is performed. Hence, the constraint removal process is not applied.

(E) Full proposal w/o Stay: Here, devices are not invited to maintain their subband choices upon system convergence. Recall that system convergence is achieved when all devices in the set $\bar{K}^{block}$ achieve their required rate for the remainder of the time horizon.

(F) Full proposal w/o Enhanced UCB: In this version of the framework, the additional term $\zeta_k(a_k, t)$ in (16) is not used in the UCB process, thereby reverting to the classical UCB decision function defined in (17).

(G) Classical UCB: The basic UCB algorithm (based on (17)) is applied without any of the proposed enhancements.

(H) Full proposal w/o RIS: A RIS-free network is considered with the same configuration as Fig. 4, where the channels only include the direct links between devices and APs.

(I) Full proposal w/o SIC: In this variant, all enhancements are taken into consideration, except that SIC is not applied at the receiver. On each subband, the decoding of each device's signal is attempted in the presence of the interference from all other devices on the same subband.

(J) Full proposal with Rand Angles: No RIS optimization is conducted. Instead, the RISs are configured with randomly chosen angles.

(K) Full proposal with Rand Access: In this version, the UCB algorithm is not applied; each device randomly chooses one subband for transmission at each timeslot.

Fig. 5 compares the performance of various versions of the proposed framework, presenting the percentage of successful transmissions (PST) over the time horizon $T$. The PST accounts for the number of satisfied devices in each timeslot, divided by $K$ and averaged over simulation setups. Framework (A) significantly outperforms other variants, achieving a 97% final PST compared to 93.6% for framework (B) without device classification. The difference is most noticeable in the later part of the horizon, as framework (A) achieves earlier system convergence, while (B) shows continued exploration of infeasible device constraints. When all enhancements are used with classical UCB, framework (F) remains significantly below framework (A) during the earlier part of the horizon, with the largest gap of 14.3% at timeslot 40. However, framework (F) achieves a minor gain of 0.6% in final PST due to the chosen values of $\nu_1$ and $\nu_2$ balancing exploitation and exploration. The SIC reordering procedure significantly enhances PST across the entire horizon, with framework (A) gaining 7.5% over (C). The re-optimization procedure based on constraint removal shows clear enhancement in system performance, with a maximum PST difference of 9.1% around timeslot 37. Maintaining device choices upon convergence brings a gain reaching 1.2% at timeslot 96. This procedure will be further explored in the results of Table 4.

In Fig. 6, the performance of the complete framework is compared to several baseline variants. The results show that our framework (A) significantly outperforms the basic UCB with no enhancements (G) with a maximum gain in PST that reaches 32.4%, and a gain of 10.8% at the end of the time horizon. Moreover, the enhancements in (A) provide faster convergence compared to (G), as (A) attains substantially higher PST within only a few timeslots. This accelerated convergence reduces the computational load by lowering the number of optimization runs and, consequently, the CPU power consumption. In early timeslots, the framework
<figure><img src="image_6.png" /><figcaption>FIGURE 5. Average PST over the time horizon for different versions of the framework, for $R^{\text{req}} = 1.75$ Mbps.</figcaption></figure>

enhancements are beneficial even in a RIS-free network, since variant (H) achieves a gain of up to 13.7% w.r.t. (G). However, the PST of (H) saturates early at around 68.8%, while due to RIS implementation in (G), a PST of 86% is reached by the end of the time horizon. Since this study relies on the RIS to mitigate inter-user interference, using random angles for the RIS leads to loss of interference mitigation. Some random angle configurations can increase interference, further degrading system performance. This explains why (H) outperforms (J) over the entire horizon, achieving a performance gain of up to 25.8%. Implementing the framework without SIC (variant (I)) results in significantly lower PST compared to most other variants, primarily due to unmitigated interference in the absence of SIC. The lowest PST occurs when devices select subbands randomly (without the MAB framework), even when other enhancements are applied (framework (K)). In this variant, the PST remains consistently low, fluctuating around 22%.

Fig. 7 illustrates the PST of the complete framework (A) over the time horizon, for varying values of the number of RISs, *J*. The results show how increasing *J* enhances the PST, achieving 98% at the end of the time horizon with 6 RISs compared to 81.8% with 1 RIS. However, as *J* increases from 1 to 6, the PST improvement becomes less pronounced starting from *J* = 4, with gains that reach 12.2% and 5.3% when *J* is raised from 2 to 4, and from 4 to 6, respectively. The largest PST improvement, 10.2%, occurs between 1 and 2 RISs. In the network under consideration, using *J* = 4 RISs provides a sufficient balance between system performance and complexity, where at the end of the horizon the PST gain between *J* = 6 and 4 is 0.5%.

The influence of the maximum number of SIC operations per subband, $M_{\text{SIC}}$, is analyzed in Fig. 8 with different values of *K*. The results show how the average PST increases significantly with $M_{\text{SIC}}$, especially for large numbers of devices. In the complete framework (A), the average PST

<figure><img src="image_7.png" /><figcaption>FIGURE 6. Average PST over the time horizon for different versions of the framework, for $R^{\text{req}} = 1.75$ Mbps.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 7. Average PST for different values of the number of RISs using (A)-Full proposal, for $R^{\text{req}} = 1.75$ Mbps.</figcaption></figure>

increases by 3.2%, 16.7%, and 21.6% for *k* = 30, 35 and 40, respectively, when $M_{\text{SIC}}$ is raised from 4 to 7. The benefits of increasing $M_{\text{SIC}}$ are more pronounced at *K* = 35 and 40, compared to *K* = 30, since at UCB convergence, the average number of devices per subband typically tends to 7 or 8 when *K* = 35 or 40. Integrating dynamic SIC reordering with high $M_{\text{SIC}}$ becomes particularly beneficial in such situations, as higher SIC operations are needed in crowded areas, at the expense of increased decoding complexity. This behavior also occurs when increasing the requested rate for a fixed *K*. When comparing frameworks (A) and (C), the SIC reordering procedure is especially effective at network saturation. It improves the likelihood of devices achieving target rates by leveraging a decoding reordering strategy that reduces interference through SIC. Framework (A) surpasses (C) in average PST, with improvements of up to 1.7%, 5%, and 11.7% for *K* = 30, 35, and 40, respectively.
<figure><img src="image_9.png" /><figcaption>FIGURE 8. Average PST in terms of $M_{SIC}$ for frameworks (A)-Full proposal and (C)-Full proposal w/o SIC reorder, with $K = 30, 35$ or $40$, $R^{req} = 1.4$ Mbps.</figcaption></figure>

<table><caption>TABLE 3. Average PST and percentage of timeslots with no optimization in terms of $J$ for (A)-Full proposal, with $R^{req} = 1.75$ Mbps.</caption><thead><tr><td></td><td>PST</td><td>% timeslots with no optimization</td></tr></thead><tbody><tr><td>$J = 1$</td><td>69.5</td><td>31.5</td></tr><tr><td>$J = 2$</td><td>77.3</td><td>54.8</td></tr><tr><td>$J = 4$</td><td>84.3</td><td>72</td></tr><tr><td>$J = 6$</td><td>85.4</td><td>75.8</td></tr></tbody></table>

In order to analyze the receiver complexity for different system parameters, we observe the percentage of timeslots where no RIS optimization is required. Recall that the RIS phase optimization is skipped if the subband choices at timeslot $t$ remain unchanged from those at $t-1$. Table 3 illustrates how this percentage rises with the number of RISs. Specifically, at $J = 1$ and 2, optimization is unnecessary in 31.5% and 54.8% of the timeslots, respectively, while at $J = 4$ and 6, the percentage increases to 72% and 75.8% respectively. In fact, the increase of $J$ enlarges the subset of subbands on which each device is servable, as well as the search space in the RIS optimization problem in (14). This enlargement increases the chances of earlier system convergence and decreases the number of useless RIS optimization processes. This advantage comes with a simultaneous increase in the average PST that increases from 69.5% for $J = 1$ to 85.4% for $J = 6$, which is in accordance with the results of Fig. 7.

Table 4 compares frameworks (A), (B), and (E) under varying requested rates, illustrating the impact of the classification procedure and the stay mechanism on the average PST and the percentage of timeslots without optimization. At low and medium rates ($R^{req} = 1.5$ and 1.6 Mbps), the average PST gain of framework (A) vs. (B) is limited. However, framework (B) performs optimization in 5.1% and 6.9%

<table><caption>TABLE 4. Average PST and % of timeslots with no optimization vs. $R^{req}$.</caption><thead><tr><th rowspan="3">Framework</th><th colspan="3">PST</th><th colspan="3">% timeslots<br>with no optimization</th></tr><tr><th colspan="3">$R^{req}$ [Mbps]</th><th colspan="3">$R^{req}$ [Mbps]</th></tr><tr><th>1.5</th><th>1.6</th><th>1.75</th><th>1.5</th><th>1.6</th><th>1.75</th></tr></thead><tbody><tr><td>(A)</td><td>97.1</td><td>93.6</td><td>82.2</td><td>91.9</td><td>85.8</td><td>68.7</td></tr><tr><td>(B)</td><td>96.6</td><td>92.5</td><td>79</td><td>86.8</td><td>78.9</td><td>57.7</td></tr><tr><td>(E)</td><td>97</td><td>93.5</td><td>81.5</td><td>86.7</td><td>78.6</td><td>57.9</td></tr></tbody></table>

<table><caption>TABLE 5. Average timeslot index at which 75% of the simulation setups reached convergence for different frameworks, at $R^{req} = 1.75$ Mbps.</caption><thead><tr><td>Framework</td><td>Average timeslot number</td></tr></thead><tbody><tr><td>(A)</td><td>30.4</td></tr><tr><td>(B)</td><td>37.9</td></tr><tr><td>(C)</td><td>34.7</td></tr><tr><td>(D)</td><td>35.8</td></tr><tr><td>(E)</td><td>34.6</td></tr><tr><td>(F)</td><td>36</td></tr></tbody></table>

more timeslots compared to (A). At a high requested rate (1.75 Mbps), the PST difference increases slightly to 3.2%. Notably, RIS optimization in framework (A) is not performed in 11% more timeslots than in (B). This varying performance gain stems from the differing impact of requested rates on device classification. At low rates, device constraints are rarely classified as infeasible. Conversely, at high requested rates, constraints in problem (12b) are more likely to be removed by the classification process, leading to higher PST and more timeslots without optimization in framework (A) w.r.t. (B). When comparing frameworks (A) and (E), framework (E) performs significantly more optimizations, while the average PST difference remains negligible. From low to high requested rates, optimization in (A) is skipped in 5.2%, 7.2%, and 10.8% more timeslots than in (E). This difference arises from changes in subband choices that occur in (E) after convergence, triggering a cascade of action changes and resulting in higher percentage of timeslots requiring optimization. Our study emphasizes crowded systems with moderate to high requested rates, where solution finding becomes challenging, underscoring the importance of efficient resource allocation. While optimized for heavy loads, the framework also accommodates low-rate traffic and, maintains high success for small packets, thereby verifying its ability to support the coexistence of different services. It is also worth noting that the proposed framework typically converges within a few tens of milliseconds, and that no more than two optimization repeats were required in our experiments. Combined with the bounded number of SIC operations, this ensures that the overall optimization delay remains compatible with the low-latency objectives of grant-free IoT access.

To further assess system performance in terms of convergence, Table 5 reports the average timeslot index at which
75% of the simulation setups reach convergence (i.e., all devices in $\bar{\mathcal{K}}^{\text{block}}$ achieve their required rate for the remainder of the time horizon). Framework (A) reaches convergence for 75% of the simulation setups in 30.4 timeslots on average, which is 19.8%, 12.4%, 15.1%, 12.1%, and 15.6% fewer than required by frameworks (B), (C), (D), (E), and (F), respectively. The largest difference is observed with respect to framework (B), in which optimization is always performed to satisfy all K devices, a requirement that may be infeasible. Overall, these results highlight the importance of the proposed enhancements in accelerating convergence, thereby reducing computational complexity and CPU power consumption by avoiding unnecessary optimizations.

<figure><img src="image_10.png" /><figcaption>(a) Average EE w.r.t. K, with $R_k^{\text{req}} = 1.6$ Mbps and $L = 10$ APs.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(b) Average EE w.r.t. L, with $R_k^{\text{req}} = 2$ Mbps and $K = 25$.</figcaption></figure>

<caption>FIGURE 9. Average EE in terms of (a) the number of devices K and (b) the number of APs L, for $M_{\text{SIC}} = 5$, $C = 5$ subbands, and $J = 4$ RISs.</caption>

In order to assess the energy efficiency (EE) of the proposed framework under different system configurations, Figs. 9a and 9b compare the average EE of frameworks (A), (B), (C), (G), and (H) as a function of the number of devices and APs, respectively. The power consumption model and

corresponding EE formulation are defined based on [21] and [47], considering the power consumption of devices, RISs, APs, and fronthaul links. The total power is given by:

$$P^{\text{total}} = \sum_{k=1}^{K} P_{k}^{\text{total}} + P_{\text{RIS}}^{\text{total}} + \sum_{l=1}^{L} P_{l}^{\text{total}} + P^{\text{fronthaul}}. \quad (21)$$

The different terms in (21) are defined as follows:

* device power: $P_k^{\text{total}} = \frac{1}{\xi_k} p_k + P_k^{\text{static}}$,

* RISs power: $P_{\text{RIS}}^{\text{total}} = J S P^{\text{element}}$,

* AP power: $P_l^{\text{total}} = U(\sum_{k=1}^{K} \partial_{k,l}) N P_l^{\text{antenna}} + P_l^{\text{static}}$,

* fronthaul power: $P^{\text{fronthaul}} = \sum_{l=1}^{L} \sum_{k=1}^{K} \partial_{k,l} P_l^{\text{ft}} R_k^{\text{req}}$.

$p_k$ is the transmit power of device k, $\xi_k$ (with $0 < \xi_k \le 1$) is the amplifier efficiency, $P_k^{\text{static}}$ is the device's static power, $P^{\text{element}}$ is the RIS element power consumption, $\partial_{k,l}$ equals 1 if AP l serves device k and 0 otherwise. $U(x)$ denotes the unit step function which equals 1 if $x > 0$ and 0 otherwise, $P_l^{\text{antenna}}$ is the internal power consumed by each antenna of AP l, $P_l^{\text{static}}$ is the static power of AP l, and $P_l^{\text{ft}}$ is the traffic-dependent fronthaul power.

When a device fails to achieve its requested rate, i.e., the CPU fails to decode its signal, its effective rate is set to zero. The EE at timeslot t is then defined as:

$$EE(t) = \frac{\sum_{k=1}^{K} \eta_k(t) R_k^{\text{req}}}{P^{\text{total}}(t)}. \quad (22)$$

Note that, for a fixed AP selection matrix $D_k$, $k \in \mathcal{K}$ (which is the case in this work), and since the requested rates appear in the numerator and denominator of (22), the EE depends only on the values of $\eta_k(t)$. It should also be noted that guaranteeing the devices target rates inherently leads to a higher network power consumption, unless AP selection and/or sleep strategies are jointly optimized. However, this last aspect falls outside the scope of the current study. Nevertheless, the following results show how our proposed solutions can enhance the EE for a given range of the network load as a positive return effect of the PST improvement.

Fig. 9a shows that framework (A) consistently achieves higher EE compared to all other frameworks due to its superior PST. As the number of devices increases from 20 to 25, EE rises because most devices meet their requested rates. However, at $K = 30$ and $K = 35$, EE drops significantly as the increased interference reduces PST. This reduction lowers the numerator of (22), while the denominator also increases. Notably, the enhancements incorporated in framework (A) yield clear benefits: it achieves 33.2% more EE than (G) at $K = 35$ and 19.3% more EE than (C) at $K = 30$. Furthermore, framework (A) outperforms (B) in crowded systems by relaxing constraints through the device classification procedure, which further improves PST and EE.

In Fig. 9b, the average EE is analyzed as a function of the number of APs L at high requested rates. Increasing L helps mitigate system congestion, although it also increases
<table><caption>TABLE 6. Average relative CPU power increase due to applied enhancements vs. K and C, for $R^{\text{req}} = 1.75$ Mbps, $M_{\text{SIC}} = 4$.</caption><thead><tr><th></th><th>K = 15<br>C = 3</th><th>K = 25<br>C = 5</th><th>K = 35<br>C = 7</th></tr></thead><tbody><tr><td>$\frac{\Delta P^{\text{CPU}}}{P^{\text{CPU}}_{(\text{A})}} = \frac{P^{\text{CPU}}_{(\text{A})} - P^{\text{CPU}}_{(\text{D})}}{P^{\text{CPU}}_{(\text{A})}}$</td><td>7.3%</td><td>11.1%</td><td>18.3%</td></tr><tr><td>$\frac{\Delta P^{\text{CPU}}}{P^{\text{CPU}}_{(\text{A})}} = \frac{P^{\text{CPU}}_{(\text{A})} - P^{\text{CPU}}_{(\text{C})}}{P^{\text{CPU}}_{(\text{A})}}$</td><td>0.7%</td><td>2.9%</td><td>7.4%</td></tr></tbody></table>

power consumption. Framework (A) maintains the highest EE across all values of L. At L = 10, the gap between (A) and (B) is the most pronounced due to the critical role of device classification in crowded systems. As L increases to 25, the advantage diminishes because the SNR becomes sufficiently high due to the added APs, making instances of devices being non-servable rather rare. For all frameworks, EE increases from L = 10 to L = 15 as the benefits of additional successful transmissions outweigh the extra power cost. Beyond L = 15, further AP additions yield diminishing returns, as increased power consumption outweighs the marginal gains in the PST.

In order to further assess the impact of the dynamic SIC reordering and constraint removal enhancements, we analyze the increase in CPU power consumption when each of these enhancements is applied. The CPU power consumption required by the optimization (problem (14)) and SIC tasks, at timeslot t, is expressed as $P^{\text{CPU}}(t) = P_{\text{Opt}}^{\text{CPU}}(t) + P_{\text{SIC}}^{\text{CPU}}(t)$, where $P_{\text{Opt}}^{\text{CPU}}(t)$ is the power consumed by the CPU for the optimization task, and $P_{\text{SIC}}^{\text{CPU}}(t)$ is the power consumed for SIC at timeslot t. Inspired by [48], $P_{\text{Opt}}^{\text{CPU}}(t)$ is calculated as

$$P_{\text{Opt}}^{\text{CPU}}(t) = P^{\text{CPU-idle}} + \frac{C_{\text{GPP}}(t)}{\eta^{\text{CPU}}}, \quad (23)$$

where $C_{\text{GPP}}(t)$ is the total processing utilization in giga operations per second (GOPS) at timeslot t, and $\eta^{\text{CPU}}$ is the processing efficiency (in GOPS/W). According to the complexity analysis (section III-E), one iteration of the interior-point method costs $\frac{1}{3}(JS + |K^{\text{inc}}(t)|)^3$ flops. Therefore, $C_{\text{GPP}}(t)$ is given by

$$C_{\text{GPP}}(t) =itr^{\text{opt}}(t)\frac{\frac{1}{3}(JS + K^{\text{inc}}(t))^{3}}{\Delta_{t} \times 10^{9}},$$

where $\Delta_t$ is the timeslot duration (1 ms). Moreover, following [49], the total power of the SIC operations is calculated as

$$P_{\text{SIC}}^{\text{CPU}}(t) = \kappa^{\text{SIC}} \sum_{c=1}^{C} |K_{c}^{\text{SIC}}(t)|, \quad (24)$$

where $\kappa^{\text{SIC}}$ is the average power consumed per SIC iteration during the SIC process at the receiver. We consider $P^{\text{CPU-idle}} = 1$ W, $\eta^{\text{CPU}} = 2.434$ GOPS/W, and $\kappa^{\text{SIC}} = 0.5$ W.

Table 6 reports the average relative increase in CPU power consumption, defined as $\frac{\Delta P^{\text{CPU}}}{P^{\text{CPU}}_{(\text{A})}} = \frac{P^{\text{CPU}}_{(\text{A})} - P^{\text{CPU}}_{(\text{D})}}{P^{\text{CPU}}_{(\text{A})}}$, for framework (A) with respect to (D) and (C), averaged over all timeslots and simulation setups, where (fr) denotes the framework ((D) or (C)). Table 6 is obtained while fixing the $K/C$ ratio

such that $K/C = M_{\text{SIC}} + 1$. The constraint removal process in framework (A) incurs an increase of 7.3%, 11.1%, and 18.3% in CPU power consumption for $(K, C) = (15, 3)$, (25, 5), and (35, 7), respectively. It should be reminded that optimization is not always repeated (see Section III-C and Algorithm 1), and no further optimization is performed once system convergence is reached. On the other hand, applying dynamic SIC reordering generally increases the number of SIC operations in order to enhance the success rate. This results in an average increase in CPU power consumption of 0.7%, 2.9%, and 7.4% for $(K, C) = (15, 3)$, (25, 5), and (35, 7), respectively. This power increase remains reasonable, especially when considering the achieved significant performance gains.

We now proceed to analyze the system robustness with respect to channel estimation errors, using the model from [50] and [51]. The estimated channel for each link is expressed as: $\hat{\mathbf{H}}_c^d = \mathbf{H}_c^d + \mathbf{E}_c^d$, $\hat{\mathbf{G}}_c = \mathbf{G}_c + \mathbf{E}_c^g$, $\hat{\mathbf{Z}}_c = \mathbf{Z}_c + \mathbf{E}_c^z$. Here, $\mathbf{E}_c^d \in \mathbb{C}^{K \times NL}$, $\mathbf{E}_c^g \in \mathbb{C}^{K \times JS}$, and $\mathbf{E}_c^z \in \mathbb{C}^{JS \times NL}$ represent the channel estimation errors for the direct (device-AP) links, device-RIS links, and RIS-AP links at subband c, respectively. Their entries are given by: $e_{k,l,n,c}^d \sim \mathcal{CN}(0, \epsilon_0^2|h_{k,l,n,c}^d|^2)$, $e_{k,j,s,c}^g \sim \mathcal{CN}(0, \epsilon_0^2|g_{k,j,s,c}|^2)$, $e_{j,s,l,n,c}^z \sim \mathcal{CN}(0, \epsilon_0^2|z_{j,s,l,n,c}|^2)$, where $\epsilon_0 \ge 0$ denotes a factor quantifying the channel estimation error magnitude. System robustness is investigated by increasing $\epsilon_0$. With channel estimation errors, the true channels are not accessible to the CPU. However, we assume that the CPU can determine whether it has successfully decoded the signal of each device. Therefore, the success indicator $\eta_k$ is calculated based on (11) using true channels $\hat{\mathbf{h}}_{k,c}^{\text{tot}}$ and estimated combining vectors $\hat{\mathbf{v}}_{k,c}$. The rewards are calculated by the CPU based on (11) by considering the estimated channels $\hat{\mathbf{h}}_{k,c}^{\text{tot}}$ and the estimated combining vectors $\hat{\mathbf{v}}_{k,c}$.

<figure><img src="image_12.png" /><figcaption>FIGURE 10. Average PST w.r.t. $\epsilon_0$, with $K = 25$, $R_k^{\text{req}} = 1.6$ Mbps, $L = 10$, $C = 5$, and $M_{\text{SIC}} = 4$.</figcaption></figure>
Fig. 10 illustrates the evolution of the average PST for frameworks (A), (C), and (G) as the estimation error factor $\epsilon_0$ varies. The PST of (A) starts at 92.6% and declines to 9.8% at $\epsilon_0 = 0.9$, demonstrating the impact of channel estimation errors. However, the proposed enhancements improve robustness, with (A) surpassing (C) and (G) by up to 6.8% and 11.5%, respectively. As channel estimation error increases, the SIC ordering is determined based on inaccurate channel information, leading to erroneous ordering that approaches randomness at very high $\epsilon_0$ values. This error is mitigated by the dynamic SIC ordering technique in framework (A), and normal decoding when devices with higher ordering level fail to achieve target rates. Another effect is that RIS phase optimization is performed based on channel estimates that deviate significantly from true channels, particularly at high $\epsilon_0$ values. Moreover, at $\epsilon_0 = 0.9$, framework (C) approaches (A) because dynamic SIC ordering fails to compensate for mismatches caused by incorrectly optimized RIS angles, reduced SNR due to large discrepancy between combining vectors and true channels, and UCB rewards calculated based on these mismatches. Nevertheless, with effective pilot allocation strategies such as [30], $\epsilon_0$ remains relatively small, especially when combined with the cell-free MIMO-OFDM (orthogonal frequency division multiplexing) scheme from [52] that minimizes pilot contamination.

## V. CONCLUSION

In this paper, we proposed a novel framework for resource allocation in uncoordinated uplink RIS-aided CF-mMIMO-NOMA networks, addressing QoS requirements through two challenging problems: subband allocation using the MAB framework and RIS configuration for uncoordinated CF-mMIMO-NOMA. Key contributions include a proactive device classification technique, dynamic SIC reordering procedure, and several UCB algorithm enhancements. Extensive simulation results validate the framework effectiveness, demonstrating improved success rate and reduced necessary optimizations compared to previous approaches. The results show that the enhancements also improve robustness to channel estimation errors. Future work will explore joint RIS phase optimization and AP selection techniques. This study can be extended to scenarios involving dynamic device activity, where devices alternate between transmitting data and entering inactive states.

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