Dynamic Topology Reconfiguration for Energy-Efficient Operation in 5G NR IAB Systems

Abstract

The utilization of high millimeter wave (mmWave, 30–100 GHz) in 5G New Radio (NR) systems and sub-terahertz (sub-THz, 100–300 GHz) in future 6G requires dense deployments of base stations (BSs) to provide uninterrupted connectivity to the users. 3GPP Integrated Access and Backhaul (IAB) deployments that utilize wireless relay nodes offer cost-efficient densification options for these systems. However, the infrastructure that is often scaled and deployed for busy-hour traffic conditions is not used efficiently during periods when traffic demands are lower, resulting in excessive power consumption. In this work, we consider the IAB roadside deployment option and demonstrate that the deployment designed to meet traffic demands during busy-hour traffic conditions can be efficiently controlled to provide large power savings during other times of the day. To demonstrate the feasibility of the solution, we will utilize the tools of stochastic geometry and queuing theory. Our numerical results show that the dynamic switching of IAB nodes may lead to power savings of up to 40% depending on the traffic and deployment specifics. The proposed methodology also allows us to maintain the specified upper bound on the transit delay and improve the utilization of active IAB nodes.

1. Introduction

The utilization of high-frequency bands, such as millimeter wave (mmWave, 30–70 GHz) and sub-THz (sub-THz, 100–300 GHz), in 5G/6G cellular systems is virtually the only option to meet the growing needs of user traffic demands [1,2]. These bands, which provide hundreds of megahertz of consecutive bandwidth at the air interface, can potentially enable future applications characterized by extreme rate requirements at the air interface [3].

However, radio access network (RAN) densification incurs significant capital expenditures (CAPEXs) for network operators. To reduce the costs of infrastructure deployment, services such as enhanced mobile broadband (eMBB) and massive machine-type communications (mMTCs) are expected to be delivered in a multi-hop manner using technologies such as Integrated Access and Backhaul (IAB) and DECT-2020 New Radio (NR) [4,5]. The former is based on the utilization of reduced-function relay nodes, called IAB nodes, that are centrally controlled by the base station (BS), called the IAB donor. Such systems form a wireless network in the last mile by efficiently utilizing the radio resources available to the network operator [6,7]. In an urban environment, IAB systems can be installed along roads and avenues to provide uninterrupted coverage to end users [8].

RANs are conventionally planned for busy-hour (BH) traffic conditions [9]. In an urban environment, this conventionally corresponds to the time periods during the morning and evening [10]. However, during other times of day, such as the afternoon or night, the system resources are over-provisioned, and the BSs remain active even when there is less traffic demand (up to 15% and 88% for afternoon and night time, respectively [11]). In dense RAN deployments, the BS can be temporarily turned off to save power [12], whereas the associated users can be handed over to nearby BSs for service. Section 2 reviews the related work in this area. However, the support of these mechanisms requires additional features to be introduced to the 5G NR and future 6G systems, allowing for forced handovers of users, support of BS-side sleeping modes, and dynamic reconfiguration of BS states.

In IAB deployments, some relay nodes can also be turned off to save the power consumed by the network. Furthermore, as the segment of the RAN consisting of several IAB nodes is fully and centrally controlled by the IAB donor, topology reconfiguration is inherently supported by the network starting from the 3GPP Release 17, implying that the ecosystem for infrastructure-based power saving is available for the network operator [8]. However, differently from conventional BS-based deployments, there are no studies addressing infrastructure-side power savings in IAB systems; see Section 2 for details.

The aim of this study is to assess the potential infrastructure-based power savings in 5G NR IAB deployments with half-duplex constraints. To this aim, we consider one of the most useful urban deployments, roadside IAB deployment along streets and avenues, and utilize the tools of stochastic geometry and queuing theory to propose a model of IAB network operation. We then utilize this model to determine the optimal configuration of the IAB network for BH conditions. Finally, we estimate the power savings achieved during the other times of the day by switching off redundant IAB nodes. The proposed framework can be used to analyze multi-hop technologies operating under half-duplex constraints.

The main contributions of our study are

• A mathematical model for optimal topology inference in chain-like topologies along avenues/highways for IAB systems with half-duplex constraints;
• A methodology for dynamically switching IAB nodes on/off in the considered deployment allowing for energy to be saved while still meeting variable traffic demands during the day;
• Numerical results illustrating that the application of the proposed methodology allows for a reduction in the averaged energy consumption of up to 40% depending on the traffic parameters and deployment configuration.

The remainder of this paper is organized as follows: We begin with related work in Section 2. In Section 3, we formulate the system model. The proposed approach is introduced and mathematically analyzed in Section 4. The numerical results are presented in Section 5. Finally, conclusions are drawn in the last section.

2. Related Work

The network densification trend has recently spawned a wave of research on infrastructure-based power savings. In [13], methods to reduce energy consumption in cellular networks by dynamically switching BSs on and off based on the traffic load were explored. The authors developed a mathematical model that accounts for RAN traffic variability and the density of BSs, and ran simulations to show that energy savings of up to 80% can be achieved during low-traffic conditions without compromising service quality. The proposed strategies are adaptable to traffic fluctuations and are generally simple enough for real-world implementation.

The study in [14] proposes a novel energy-efficient strategy for Software-Defined Networks (SDNs) that dynamically changes the network topology based on traffic conditions while ensuring system reliability. The proposed approach relies on a mathematical model that integrates energy consumption with reliability constraints to determine which BS, routers, and links can be safely turned off during low-traffic conditions. The computer simulations show that the proposed approach significantly reduces energy use without compromising network performance or availability. The reported energy savings enabled by the proposed approach were 2.07 and 4.63 times greater for the two considered topologies. The solution is scalable and leverages the centralized control capabilities of the SDN architecture.

The authors of [15] presented a dynamic energy-saving strategy for cellular networks by selectively switching BSs on and off based on user traffic demands. Unlike previous approaches, the authors explicitly accounted for the energy costs associated with turning BSs on and off, referred to as ”switching” costs. They formulated the Minimum Energy Cost Problem (MECP) and proposed a two-step solution combining per-time-slot optimization and a minimum-cost flow algorithm to minimize the overall energy usage. The simulation results show that the proposed method achieves significant energy savings while maintaining service quality and efficiently handling switching overhead.

In [16], a joint optimization framework was proposed to improve the energy efficiency in cellular networks by dynamically managing BS operations and user associations. The authors introduced a cost function that balances energy consumption and user delay, allowing flexible trade-offs. They developed distributed algorithms for energy-aware user association and heuristic greedy algorithms for BS activation/deactivation. Simulation results demonstrated that the proposed approach can reduce energy consumption by up to 70–80% while maintaining acceptable service performance, making it practical for green and scalable network deployments.

The authors in [17] proposed a spectrum-efficient switching BS off and on mechanism aimed at reducing energy consumption in cellular networks while maintaining quality of service (QoS) parameters and spectrum efficiency. The approach dynamically identifies underutilized BSs during low-traffic periods and switches them off while reallocating their radio resources to neighboring active BSs to sustain user service quality. By integrating both spectrum efficiency and QoS considerations, the method offers a balanced and scalable solution for energy-efficient and high-performance green cellular network operations.

Next, we present several studies focused on energy saving in IAB networks. The authors of [18] proposed an optimization model aimed at maximizing energy efficiency (EE), which is the ratio of the total user data rate to the network’s total energy consumption. Simulation results show that the proposed algorithm achieves a 36.1% increase in EE compared with networks with fixed or single-point connections. In [19], a polar-domain channel estimation method is proposed for near-field XL-MIMO in low-SNR scenarios, reducing the estimation error by approximately 35% compared to conventional approaches.

The study [20] proposes joint optimization of energy consumption in IAB networks using an Open RAN architecture. The developed model minimizes network energy expenditure through dynamic node activation/deactivation and optimal traffic allocation while maintaining the required quality of service. Simulations showed a reduction in energy consumption of up to 47% compared with the baseline schemes without degrading the network performance. In [21], an intelligent approach to managing 5G+ IAB mobile networks was proposed, employing a Zero-Touch Management architecture for autonomous network optimization. The model demonstrates potential for reducing energy consumption and improving network efficiency without compromising service quality.

The article [22] presents a method to improve IAB network energy efficiency using renewable energy sources and dynamic sleeping of small base stations. The developed a heuristic algorithm, Heuristic Backhauling and Dynamic Sleeping, reduced the total network energy consumption by more than 40% compared to traditional schemes, and decreased the computation time from 16 h to 0.03 h while maintaining user QoS. In [23], the use of IAB technology in millimeter-wave (mmWave) 5G RANs was investigated, showing that with the optimal configuration of IAB nodes, the spectral efficiency can be increased by approximately 30%, while the energy efficiency improves by approximately 25% compared to conventional architectures without IAB. Finally, ref. [24] proposes the IEDS method, which combines edge computing and energy harvesting for mmWave backhauling in heterogeneous networks. Simulations showed a 20–30% reduction in energy consumption compared to conventional schemes while maintaining QoS.

The abovementioned review of selected studies highlights that the problem has been well investigated in the context of conventional BS-based deployment, where each BS has wired connectivity to the core network. For 5G NR deployments, infrastructure-related energy conservation techniques have been deeply investigated. However, to the best of our knowledge, no studies have assessed infrastructure-related power savings in IAB deployments, where the backhaul links add additional constraints on the inter-site distance when meeting BH traffic demands.

3. System Model

In this section, we introduce the system model. We begin by describing the considered deployment. Then, we proceed to specify the radio part, including the propagation and antenna models. Next, we introduce the resource-allocation principles in half-duplex IAB systems. Finally, the metrics of interest are introduced.

3.1. Deployment

We consider a typical urban deployment for IAB systems, where IAB donors and IAB nodes are deployed along the streets and avenues, as shown in Figure 1, on lampposts or the sides of buildings. Each chain consists of N IAB nodes, where N may vary depending on the BH traffic conditions. The heights of the IAB nodes and donor are assumed to be the same, $h_A$. The carrier frequency is 28 GHz, whereas the bandwidth supported by the system is W. The IAB donor and nodes are assumed to operate using the modulation and coding schemes (MCSs) defined for 5G NR [25].

We also assume that pedestrians and vehicles follow one-dimensional Poisson point processes (PPPs) with densities ${\rho }_P$ and ${\rho }_V$, respectively, for each of the sidewalks, ${\nu }_P$, and road lanes, ${\nu }_V$.

3.2. Radio Part Models

At IAB donor/nodes and user equipment (UE), we assume planar antenna arrays with gains $G_B$ and $G_U$, respectively. Following [26,27], we used a cone antenna model, where the width of the beam coincides with the half-power beamwidth (HPBW) of the radiation pattern. The mean gain over HPBW is given by [28]

$$\begin{array}{c}\hfill G={\displaystyle \frac{1}{{\theta }_{3db}^{+}-{\theta }_{3db}^{-}}}{\int }_{{\theta }_{3db}^{-}}^{{\theta }_{3db}^{+}}{\displaystyle \frac{sin(N_{(·)}\pi cos\left(\theta \right)/2)}{sin(\pi cos(\theta )/2)}}d\theta ,\end{array}$$

(1)

where $N_{(·)}$ is the number of antenna elements in the appropriate plane, ${\theta }_{3db}^{+}$ and ${\theta }_{3db}^{-}$ are the upper and lower 3 dB angles, respectively, and the HPBW ${\alpha }_A$ is approximated by $102°/N_{(·)}$ [28].

We also consider the 3GPP-standardized Urban Micro (UMi) path loss model [29]. In linear scale, the UMi path loss can be written as

$$\begin{array}{c}\hfill L\left(y\right)={10}^{2{log}_{10}{f}_c+3.24+I_B}{y}^{\zeta },\end{array}$$

(2)

where y is the three-dimensional (3D) distance between the BS and UE, $f_c$ is the carrier frequency, and $\zeta =2.1$ is the path loss exponent for the line-of-sight (LoS) state. Note that we also utilized a constant attenuation factor of 15 dB related to the penetration through the car body [30], leading to $I_B=1.5$ in (2).

3.3. Resources, Half-Duplex Constraint, and Traffic Demands

As in-band IAB deployments may suffer from cross-link interference, 3GPP Release 16 [31] proposed multiple half-duplex multiplexing schemes that primarily adopt Time-Division Multiplexing (TDM) for wireless resource allocation. Such multiplexing schemes (or patterns) comprise repeated time phases, where each phase may be dedicated to either the DL or UL transmission. Within a UL phase, an IAB node may only provide access to associated UEs, whereas in the DL phase, a transit node has a few options:

• Upload backhaul data from parent and child nodes;
• Transmit access data only to associated UEs;
• Transmit access data to associated UEs and backhaul data to parent and child nodes while blocking their access transmissions.

The mix and duration of different phases can be flexible depending on the scenario, access/backhaul link performance, load, etc. [32].

We now specify the traffic arrival patterns at both the session and packet levels. In our environment, we considered both vehicles and pedestrians generating traffic. In addition to the BH conditions characterized by traffic jams and the highest pedestrian density, we also considered normal and night conditions. The time-varying traffic arriving pattern at the session level during the 24 h time span is regulated by the relative load provided in [11]. The parameters for these conditions related to road traffic and assumed pedestrian densities are provided in Table 1 in Section 5.

The mean traffic load in packets per second is modeled as

$$\begin{array}{c}\hfill L_n\left(t\right)={\displaystyle \frac{{\mu }_t{I}_n}{2{\lambda }_F}}\sum _{\tau \in \{P,V\}}{\nu }_{\tau }{\rho }_{\tau }{\gamma }_{\tau },\end{array}$$

(3)

where ${\mu }_t$ is the fraction of the busiest hour load at time t, ${\gamma }_{\tau }$ is the coefficient that reflects the degree of user involvement and technology penetration, ${\lambda }_F$ is the packet inter-arrival time, and $I_n$ is the coverage radius of IAB nodes that will be determined in (4).

To investigate the impact of traffic load variability, we first assume that the peak daily load is as shown in (3) with coefficient ${\gamma }_{\tau }=1$. Then, we calculate the relative coefficients ${\gamma }_{\tau }$ for each hour $\tau$ of the 24-h time span using the statistics provided in [11]. Packet user traffic is assumed to follow 3GPP’s ftp3 traffic model [33]. Accordingly, a batch of size $l_p=0.5$ Mbyte is generated every ${\lambda }_F=30$ ms.

3.4. Metrics of Interest

When dealing with multi-hop communication systems, the critical performance metric of interest is latency [34,35]. In the following, we first utilize the upper bound on the mean latency to determine the optimal deployment for BH traffic conditions. Then, we propose a methodology that allows the IAB nodes to be switched for other times of the day while still preserving the upper bound on the mean latency. The ultimate metric of interest is the average energy savings throughout the day.

We note that in this paper, we are concerned with infrastructure-related energy conservation. Thus, the constraints relevant to transmission-related energy conservation mechanisms, such as discontinuous reception (DRX), radio resource management (RRM) relaxation, and wake-up signal (WuS), are not applicable to our study. Although additional signaling is needed to enable turning on/off of IAB nodes as we highlighted in the text, the rest of the transmission-related mechanisms operate at smaller timescales as compared to the system we consider.

4. The Proposed Methodology

In this section, we present our energy-saving methodology. We begin by formulating the packet service model of a single IAB node. Then, by utilizing it, we formalize an optimization problem for determining the optimal topology that satisfies the mean latency constraints for the BH conditions. Finally, we modified the proposed optimization problem for non-BH conditions by providing the number of IAB nodes that need to be active for a given traffic condition.

4.1. Model of a Single IAB Node

We begin by determining the coverage radius $r_n$ of the n-th IAB node with MCS index $m_n$ using the signal-to-interference-plus-noise ratio (SINR)-based approach proposed in [36] as

$$\begin{array}{c}\hfill r\left(m_n\right)=\sqrt{{\left({\displaystyle \frac{P{G}_B{G}_U}{{10}^{2lg\left(f\right)+\zeta }(N_0{B}_W+M_I)s_{m_n}}}\right)}^{2/\zeta }-{(h_A-h_B)}^2},\end{array}$$

(4)

where P is the IAB-node-emitted power, $G_B$ and $G_U$ are the mmWave BS and UE gains, respectively, f and $B_M$ are the operational frequency and bandwidth, $\zeta$ is the path loss exponent, $M_I$ is the interference margin, $N_0$ is the thermal noise, $B_W$ is the bandwidth, $s_{m_n}$ is the SINR associated with the $m_n$-th MCS index of the n-th node [25], and $h_B$ is the height of the UE.

Then, it is possible to evaluate the inter-site distances between consecutive nodes n and $n+1$ as the minimum of their coverage radii $I_n=min\left(r\left(m_n\right),r\left(m_{n+1}\right)\right)$. Having obtained the coverage radius of a node and UE densities and assuming that only half of the area is served by a single node, one can evaluate the traffic load served by IAB nodes using (3).

To investigate the performance metrics of the IAB transit node, we employ the queuing theory apparatus and consider the node as an infinite-buffer discrete-time queue with bulk service $Ge{o}^X/Ge{o}^Y/1/\infty$. The batches of packets arrive at the system at the beginning of the slot with probability a. Packets arrive in batches of no more than $A=L_n/\gamma$ packets and are served in batches of no more than B packets, which is limited by the operational bandwidth B and availability of the radio resource in the time domain accounting for half-duplex constraints and depends on the mean spectral efficiency within the service area of the node. We assume that resources are allocated for data transmission in the considered direction independently of probability b.

The introduced queuing system can be described by the discrete-time Markov chain (DTMC) $S_Q\left(t\right),t=0,1,\dots$, defined over the discrete state space $S_Q\left(t\right)\in \{0,1,\dots \}$ denoting the number of packets in the system immediately before the end of the t slot. The transition probabilities of DTMC $S_Q\left(t\right),t=1,2,\dots$ can be derived as the following:

$$\begin{array}{c}\hfill q_{ij}=\mathrm{P}\{S_Q\left(t\right)=j|S_Q(t-1)=i\}=\left\{\begin{array}{c}\overline{a}+{\displaystyle \sum _{k=1}^A}a{l}_{k}b{\displaystyle {\displaystyle \sum _{j=k}^B}}{h}_j,i=j=0,\hfill \\ a{l}_A\overline{b},i\ge 0,j=i+A,\hfill \\ \overline{a}\overline{b}+{\displaystyle \sum _{k=1}^A}a{l}_{k}b{h}_k,i\ge 1,j=i,\hfill \\ a{l}_{j-i}\overline{b}+{\displaystyle \sum _{k=1}^{A-j+i}}a{l}_{j-i+k}b{h}_k,0\le i<j<A+i,\hfill \\ \overline{a}b{H}_i+{\displaystyle \sum _{k=1}^{min(A,B-i)}}a{l}_{k}b{\displaystyle \sum _{j=i+k}^B}{h}_j,1\le i<B,j=0,\hfill \\ \overline{a}b{h}_{i-j}+{\displaystyle \sum _{k=1}^{min(A,B-i+j)}}a{l}_{k}b{h}_{i-j+k},0<j<i<j+B,\hfill \\ \overline{a}b{h}_B,j\ge 0,i=j+B,\hfill \\ 0,\mathrm{otherwise}.\hfill \end{array}\right.\end{array}$$

(5)

Using the transition probabilities defined in (5), the stationary probability distribution of the system states

$$\begin{array}{c}\hfill p_i=\underset{t\to \infty }{lim}P\{S_Q\left(t\right)=i\},i\ge 0,\end{array}$$

(6)

can be obtained as shown below:

$$\begin{array}{cc}\hfill p_0& {\displaystyle =p_0\left({\displaystyle \overline{a}+\sum _{k=1}^{A}a{l}_{k}b{\displaystyle \sum _{j=k}^B}{h}_j}\right)+\sum _{i=1}^B{p}_i\left({\displaystyle \overline{a}b{\displaystyle \sum _{j=i}^B}{h}_j+\sum _{k=1}^{min(A,B-i)}a{l}_{k}b\sum _{j=i+k}^B{h}_j}\right),}\hfill \\ \hfill p_i& {\displaystyle =\sum _{m=max(0,i-A)}^{i-1}{p}_m\left({\displaystyle a{l}_{i-m}\overline{b}+\sum _{k=1}^{A-i+m}a{l}_{i-m+k}b{h}_k}\right)+}\hfill \\ \hfill & {\displaystyle + p_i\left({\displaystyle \overline{a}\overline{b}+\sum _{k=1}^{A}a{l}_{k}b{h}_k}\right)+\sum _{m=i+1}^{B+i}{p}_m\left({\displaystyle \overline{a}b{h}_{m-i}+\sum _{k=1}^{min(A,B-m+i)}a{l}_{k}b{h}_{m-i+k}}\right),i\ge 1.}\hfill \end{array}$$

(7)

This leads to the probability-generating function (PGF) of steady-state probabilities that can be derived as

$$P\left(z\right)={\displaystyle \frac{{\displaystyle \sum _{i=0}^{B-1}{p}_i\left({\displaystyle \overline{a}b\sum _{j=i+1}^B{h}_j+\sum _{k=1}^{min(A,B-i)}a{l}_{k}b\sum _{j=i+k+1}^B{h}_j}\right)-\sum _{i=1}^B\frac{1}{z^i}{C}_i\sum _{k=0}^{i-1}{p}_k{z}^k}}{{\displaystyle 1-\left({\displaystyle \overline{a}\overline{b}+\sum _{k=1}^{A}a{l}_{k}b{h}_k}\right)-a\overline{b}L\left(z\right)-ab\sum _{i=1}^{A-1}{z}^i\sum _{k=i+1}^A{l}_k{h}_{k-i}-\sum _{i=1}^B\frac{1}{z^i}{C}_i}}},$$

(8)

where

$$L\left(z\right)=\sum _{i=1}^A{l}_i{z}^i,\{l_i,i=1,\dots ,A\},\{h_i,i=1,\dots ,B\},$$

(9)

are the probability mass function (PMF) of the batch length for the arrival and served batches, and

$${\displaystyle C_i=\overline{a}b{h}_i+\sum _{k=1}^{min(A,B-i)}a{l}_{k}b{h}_{i+k}}.$$

Applying Rouché’s theorem, we define the system of linear equations (SLE)

$$\left\{\begin{array}{c}{\displaystyle \sum _{i=0}^{B-1}{p}_i\left({\displaystyle \overline{a}b\sum _{j=i+1}^B{h}_j+\sum _{k=1}^{min(A,B-i)}a{l}_{k}b\sum _{j=i+k+1}^B{h}_j}\right)-\sum _{i=1}^B\frac{1}{z_j^i}{C}_i\sum _{k=0}^{i-1}{p}_k{z}_j^k=0,}\hfill \\ P\left(1\right)=1,\hfill \end{array}\right.$$

(10)

where $z_j$, $j=1,\dots ,B-1$, are the roots of the denominator of the PGF $P\left(z\right)$ such that $|z_j|<1$. By solving this SLE, we can obtain the steady-state probability distribution $\{p_i,i=0,1,\dots \}$ of the number of packets in the system.

Then, the mean delay, $E\left[D\right]$, in the system can be found as

$$E\left[D\right]=\mathrm{\Delta }\sum _{i=0}^{\infty }{p}_i⌈{\displaystyle \frac{i+a{\sum }_{i=1}^{A}i{l}_i}{b{\sum }_{i=1}^{B}i{h}_i}}⌉,$$

(11)

while the mean fraction of resources utilized, $E\left[U\right]$, can be defined by

$$E\left[U\right]=\sum _{i=0}^{\infty }{p}_{i}min\left({\displaystyle \frac{i+a{\sum }_{i=1}^{A}i{l}_i}{b{\sum }_{i=1}^{B}i{h}_i}},1\right).$$

(12)

4.2. BH-Optimized Topology

By utilizing the specified model, we can now solve the inverse task numerically to provide the optimal deployment configuration in terms of the number of nodes in a chain with the highest possible MCS scheme utilized at the backhaul, satisfying the mean latency constraint.

Let us denote the set of all possible MCS configurations of an IAB-node chain as ${\mathcal{M}}_{\mathcal{N}}=\{$$\mathbf{M}$$=\left(m_1,\dots ,m_N\right):0\le m_i\le 15\}$, where $m_i=0$ represents the IAB nodes in the off mode with $i=1,\dots ,N$. Thus, the optimization problem of extending the IAB-chain coverage can be formalized as follows:

$$\begin{array}{cc}\hfill & \underset{\begin{array}{c}N>0,\\ \mathbf{M}\in {\mathcal{M}}_{\mathcal{N}}\end{array}}{max}\sum _{n=1}^{N}I\left(m_n\right),\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& \sum _{n=1}^{N}I\left(m_n\right)E_n\left[D\right]{\widehat{L}}_n<{\delta }_{max},\hfill \end{array}$$

(13)

where ${\widehat{L}}_n=\underset{0\le t<24}{max}{L}_n\left(t\right)$ is the traffic load at the busiest hour arriving at the n-th node.

Note that the problem (13) can be classified as a mixed-integer programming (MIP) problem that is known to be NP-hard. However, as the integer variable is the number of nodes, which is usually well below 10, it can be efficiently solved using conventional branch-and-cut or branch-and-bound methods; see, for example, ref. [37]. The overall methodology utilized in our paper to optimize IAB network topology is illustrated in Figure 2. Note that the coverage length evaluation is a much simpler operation than the delay estimation. Therefore, it can be used as the primary criterion when assessing candidate topologies. This allows for a significant reduction in the computational complexity, which is characterized by $O\left(2^N\right)$ as each additional node within the IAB chain that can be switched off, and doubles the number of possible topologies.

The derived topologies are illustrated in Section 5.

4.3. Power Savings for Non-BH Conditions

The results provided in the previous section allow us to utilize the following simple method for infrastructure-based power savings in IAB systems. Specifically, as the utilization of the optimal topology meeting the mean latency constraints requires careful tuning of not only the number of IAB nodes in a chain but also the minimal MCS utilized at the backhaul, some of the IAB nodes can be turned off for different times of day. The same framework can be used to assess the number of IAB nodes that can be turned off in the network.

We denote the inter-site distance under MCS configuration $\mathbf{M}$ between the n-th node and the nearest active child node K such that $m_K>0$ as

$${\pi }_n(\mathbf{M},\widehat{\mathbf{M}})=\sum _{j=n}^{K-1}{I}_j\left(\widehat{\mathbf{M}}\right).$$

(14)

Then, we arrive at determining the optimization problem for topology reconfiguration as minimization of active IAB nodes at time t, which takes the following form:

$$\begin{array}{cc}\hfill & \underset{\mathbf{M}\in \mathcal{M}}{min}{\displaystyle \sum _{n=1}^N}I\left(m_n\right),\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& \left\{\begin{array}{c}{\displaystyle \sum _{n=1}^N}I\left(m_n\right)E_n\left[D\right]\left(L\left(t\right)\right)<{\partial }_{max},\hfill \\ r\left(m_n\right)>{\pi }_n\left(\mathbf{M},\widehat{\mathbf{M}}\right),n=1,\dots ,N:m_n>0,\hfill \end{array}\right.\hfill \end{array}$$

(15)

where $\widehat{\mathbf{M}}$ is the initial configuration at the BH obtained in (13), and $I\left(x\right)$ is the indicator function such that $I\left(x\right)=1$ when $x>0$ and $I\left(0\right)=0$.

Note that the resulting problem in (15) is conceptually similar to that in (13) with the same limited state space. Thus, branch-and-cut or branch-and-bound methods can also be utilized to solve it efficiently.

5. Numerical Results

In this section, we present our numerical results. We begin by reviewing the considered scenarios and system parameters. We then report the results for the BH-optimized topology. Finally, the energy savings are characterized and discussed.

5.1. Scenario and Parameters

The default system parameters are listed in Table 1. Specifically, we note that the input parameters for the considered numerical examples are based on the session arrival dynamics during the full day reported in [11]. These data were utilized to compute the session arrival rates during the daytime using the 3GPP-standardized ftp3 packet arrival model [33].

Table 1. The default system parameters.

Parameter	Description	Value
$B_W$	Operational bandwidth	400 MHz
$M_I$	Interference margin	3 dBm
$h_A$	IAB-node height	10 m
$h_B$	UE height	1.5 m
P	IAB-node-emitted power	33 dBm
N	Number of IAB nodes	3
$\mathbf{M}$	Initial MCS configuration of IAB nodes	{6, 9, 7}
$N_0$	Thermal noise	−174 dBm
$G_B$	BS antenna gain	11.58 dBi
$G_U$	UE antenna gain	0.43 dBi
${\alpha }_A$	Half-power beamwidth	12.25°
$\zeta$	Path loss exponent	2.1
$N_l$	Number of traffic lanes	4
${\lambda }_F$	Packet inter-arrival time	30 ms
$\mathrm{\Delta }$	Slot duration	1 ms
b	Probability of batch service in a slot	0.25
${\gamma }_V$	User involvement rate	0.1
${\gamma }_P$	Technology penetration rate	0.1
$l_p$	Packet size	1 Mb
${\rho }_V$	Vehicle density	25 unit/km
${\rho }_P$	Pedestrian density	35 unit/km
${\delta }_{\max }$	Transit delay limit	30 ms

Table 1. The default system parameters.

Parameter	Description	Value
$B_W$	Operational bandwidth	400 MHz
$M_I$	Interference margin	3 dBm
$h_A$	IAB-node height	10 m
$h_B$	UE height	1.5 m
P	IAB-node-emitted power	33 dBm
N	Number of IAB nodes	3
$\mathbf{M}$	Initial MCS configuration of IAB nodes	{6, 9, 7}
$N_0$	Thermal noise	−174 dBm
$G_B$	BS antenna gain	11.58 dBi
$G_U$	UE antenna gain	0.43 dBi
${\alpha }_A$	Half-power beamwidth	12.25°
$\zeta$	Path loss exponent	2.1
$N_l$	Number of traffic lanes	4
${\lambda }_F$	Packet inter-arrival time	30 ms
$\mathrm{\Delta }$	Slot duration	1 ms
b	Probability of batch service in a slot	0.25
${\gamma }_V$	User involvement rate	0.1
${\gamma }_P$	Technology penetration rate	0.1
$l_p$	Packet size	1 Mb
${\rho }_V$	Vehicle density	25 unit/km
${\rho }_P$	Pedestrian density	35 unit/km
${\delta }_{\max }$	Transit delay limit	30 ms

The initial IAB topology deployment is computed such that it allows the indicated density of vehicle and pedestrian users to be served during the BH traffic conditions, and it consists of four nodes (IAB donor and three IAB nodes) with IAB nodes covering a distance of 1591 m and utilizing MCSs $\widehat{\mathbf{M}}=\{7,9,6\}$ with spectral efficiency $\mathbf{S}=\{1.4766,2.4063,1.1758\}$ bit/s/Hz for the backhaul between them; see Figure 3. That is, in what follows, we will show the gain in energy conservation achieved via topology reconstruction for each hour during the day, as shown in Figure 3, and also report the associated performance metrics, including the total delay and IAB-node utilization coefficient. The optimal topologies and associated power savings were estimated such that the transit delay in the IAB chain never exceeded 30 ms.

We specifically note that in practical conditions, 5G NR IAB mmWave systems can be either signal-to-noise ratio (SNR)- or traffic-limited even under the 3GPP-standardized traffic models considered in our study. This implies that the distances between IAB nodes in BH traffic conditions need to account for these two factors.

5.2. BH-Optimized Topology

The metrics associated with the BH-optimized topology are shown in Figure 4. First, we see that the distances covered by a single hop are different because of the use of different MCS at the backhaul links. This is due to the border effects from both ends of the IAB chain. Second, as the number of nodes increased, better coverage was provided. However, this trend was nonlinear. This is explained by traffic dynamics, as delays are accumulated along the chain. Recalling that we set the maximum allowed delay to 30 ms, we observe that the chain is effectively limited to four nodes. Increasing this bound further, say to 50 ms, would allow the creation of longer chains. However, as one may deduce, in practice, the number of IAB nodes in a chain is limited to just 4–6.

5.3. Characterization of Energy Savings

We proceed with Figure 5 showing the overall amount of traffic generated by users (left-hand-side y-axis) and the number of active nodes in a chain needed to serve it (right-hand-side y-axis) as a function of the time of day. By analyzing the presented data, it can be observed that all nodes are only needed during the busiest hours, for example, 11.00–15.00 and around 21.00. During the night between 1.00 and 7.00, the traffic load decreases drastically, and in this case, enabling just the IAB donor and a single node is sufficient. During the rest of the time, the IAB donor and two IAB nodes are utilized. The overall relative power saving amounts to 36.11% throughout the day. Note that these gains are expected to be even larger on weekends, when less traffic is usually generated by users.

Recalling the results shown in Figure 5, we observe that the actual traffic may fluctuate during different times of the day while the optimal number of utilized IAB nodes may remain the same, e.g., IAB donor and two IAB nodes for 16.00–20.00 time frame. Thus, it is important to investigate the impact of the load and number of utilized IAB nodes during different times of the day on the delay and utilization coefficient. To this end, Figure 6 shows the total transit delay (right-hand-side y-axis) as a function of the time of day, complementing it with traffic fluctuations (left-hand-side y-axis). One critical observation is that the transit delay and traffic load are tightly correlated, even when some nodes are switched off. In general, benefiting from power savings also increases the transit delay of packets; thus, there is a natural trade-off between energy savings and delay. However, the proposed approach allows us to estimate the optimal number of nodes such that the upper bound on the transit delay is preserved.

Finally, we assessed the utilization of nodes as a function of time of day. These results are shown in Figure 7, where the utilization of only active IAB nodes is shown. As one may observe, logically, in the majority of configurations, the last parent node is the most loaded. Notably, the utilization fell below 50% only during the lowest load conditions at night. Thus, the proposed procedure also allows the utilization of IAB nodes at a relatively high level, maximizing the use of available system resources.

6. Conclusions

Modern cellular system deployments are characterized by high power consumption and associated carbon emissions [38,39]. To reduce both factors, components can be dynamically switched off and on when the traffic demands are lower than those during the BH conditions. To this end, we propose a simple approach that allows us to determine the optimal number of IAB nodes in the chain that need to be active at any time of the day to serve a given time-varying traffic pattern.

Our numerical results illustrate that the dynamic adaptation of the IAB topology results in energy consumption gains of up to 40%, depending on the traffic and deployment conditions. Although most of these gains occur during the night, energy is also saved during the daytime because of the difference in the amount of traffic generated during different hours. At the same time, the proposed approach allows the IAB-chain transit delay to be upper-bounded. As a side effect, it also improves the resource utilization of the active IAB nodes.