Resource Scheduling in MU-MIMO and NOMA Enabled Integrated Access and Backhaul Networks

The integrated access and backhaul (IAB) architecture utilizes wireless backhaul to facilitate the expansion of fifth-generation (5G) New Radio (NR) networks. In an IAB network, intermediate base stations (or say IAB nodes) can be connected in a multi-hop fashion. However, optimizing resource scheduling in such a network remains a critical challenge. In this work, we present a novel method that integrates multi-user multiple-input and multiple-output (MU-MIMO) and non-orthogonal multiple access (NOMA) technologies into IAB networks. The designed two-phase algorithm has the following features: 1) support for multi-path routing and efficient resource utilization through the combined use of MU-MIMO and NOMA, 2) a novel route decision phase that selects optimal paths by considering load balancing among IAB nodes, and 3) a dynamic link scheduling phase that allocates transmission power and schedules links to maximize network capacity. Simulation results demonstrate that the proposed solution achieves significant improvements in throughput, fairness, and latency compared to existing methods.

SECTION I. Introduction

The fifth generation (5G) New Radio (NR) technology is designed to provide higher data rates to meet users’ demands for modern network services, such as live streaming and virtual reality. According to the specifications, 5G NR operates in high-frequency bands, resulting in significant signal attenuation. Consequently, the coverage area of 5G NR base stations (BS) is reduced, necessitating the deployment of more BSs to ensure service quality. To facilitate this deployment, the 3GPP organization has introduced the integrated access and backhaul (IAB) network architecture [1], which utilizes multi-hop wireless backhaul to replace traditional wired fiber backhaul. This approach not only reduces deployment costs but also allows for easier network expansion.

In general, an IAB network consists of one IAB donor and several IAB nodes. The IAB donor is composed of a Central Unit (CU) and a Distributed Unit (DU). The CU connects to the core network and manages higher-layer protocols. The DU functions similarly to a base station (BS), which schedules network resources and managing mobile terminals (MTs) to access the network. On the other hand, an IAB node contains both a DU unit and an MT unit. Therefore, an IAB node operates in either DU mode or MT mode. In MT mode, the IAB node acts as user equipment (UE), receiving data from its parent node (either the IAB donor or another IAB node). In an IAB network, data is transmitted in a multi-hop fashion. When an IAB node in MT mode receives data from its parent node, it can switch to DU mode to relay the data to its child IAB nodes. However, IAB nodes typically operate in a half-duplex manner. According to the 3GPP specification, network time is divided into Transmission Time Intervals (TTIs). This means that an IAB node can only be in DU mode or MT mode during a given TTI, but not both simultaneously. As discussed in [2], [3], [4], [5], [6], [7], [8], [9], the scheduling of IAB nodes must be done carefully to optimize data transmission and minimize packet delay.

We consider a network architecture that supports multi-path routing, where the IAB donor can establish multiple paths to disseminate downstream data to IAB nodes. This work adopts multi-user multiple-input and multiple-output (MU-MIMO) and non-orthogonal multiple access (NOMA) technologies to enable simultaneous data transmissions. On the transmitter side, MU-MIMO leverages spatial diversity to transmit signals to multiple receivers simultaneously [2], maximizing resource utilization and enhancing network throughput. On the receiver side, NOMA allows an IAB node to receive superimposed signals from multiple parent nodes and decode them efficiently using successive interference cancelation (SIC), improving spectral efficiency and network capacity in multi-path scenarios. By integrating NOMA and MU-MIMO, this work addresses the challenges of multi-path routing and resource scheduling in such IAB networks.

In the network, UEs are connected to IAB nodes. We assume that IAB nodes are capable of collecting downstream data requirements from UEs and subsequently reporting the corresponding expected data rate requirements to the IAB donor. The objective of this work is to meet IAB nodes’ data rate requirements. In this paper, we propose a two-phase scheme. First, in each TTI, the route decision phase identifies IAB nodes that are not satisfied with their data rates. It then determines routing paths to disseminate the buffered data of these selected IAB nodes. Next, the link scheduling phase decides whether to schedule a link, taking into account the amount of buffered data and the power allocation for that link. Specifically, a link will be scheduled if it can facilitate the consumption of more data without negatively affecting existing (or previously selected) links. Simulation results demonstrate that the proposed scheme significantly improves network throughput. Besides, the designed approach ensures that more IAB nodes can fulfill their data rate requirements, achieving better performance than previous methods. Our contributions are summarized as follows:

• This is the first work to integrate MU-MIMO and NOMA technologies into IAB networks. By leveraging the strengths of these two technologies, the proposed method enhances spectral efficiency and enables effective support for multi-path routing.

• We define a system model that accurately represents the network scenario and effectively captures the complexities of IAB networks. The corresponding optimization problem is formulated to prioritize achieving the downstream data rate requirements of IAB nodes.

• A two-phase method is developed to tackle the challenges of resource scheduling and routing in IAB networks. The first phase makes routing decisions by balancing loads across IAB nodes to optimize data transmission paths. The second phase schedules links and allocates transmission power to efficiently utilize available resources and improve network capacity.

• Simulations demonstrate that the proposed scheme can achieve higher network throughput, reduced latency, and improved fairness compared to existing methods. Furthermore, the designed approach enables most IAB nodes to meet their data rate requirements.

The remainder of this paper is organized as follows. In Sections II and III review some previous works and MU-MIMO/NOMA technologies, respectively. Then, Section IV presents our network model, and Section V describes the designed scheme. Next, Section VI shows the simulation results. Finally, Section VII concludes this paper.

SECTION II. Related Work

The authors in [10], [11] introduce IAB network prototyping and field measurements. The work [10] introduces a layer 2 protocol (which integrates channel estimation and phase noise compensation) validated by real testing. Reference [11] introduces a dual-link architecture to enhance coverage, handover, and bandwidth efficiency for IAB in subway tunnel scenarios. However, these works [10], [11] do not consider the resource scheduling issues. References [2], [3], [4] discuss resource scheduling strategies for IAB networks. The authors in [2] focus on arranging traffic flow for IAB nodes equipped with MU-MIMO capability. Reference [3] presents a semi-centralized resource allocation strategy that takes into account fairness, spectral efficiency, and buffer status of IAB nodes. Additionally, [4] introduces slot reservation methods to maintain the quality of service for UEs. However, the schemes designed in [2], [3], [4] primarily focus on link scheduling strategies for IAB networks.

The works [5], [6], [7], [8], [9] design schemes for IAB networks that allow IAB nodes to have multiple parents, i.e., a network structure is connected by a multi-path Directed Acyclic Graph (DAG) topology. The authors in [5] focus on resource allocation to maximize network throughput based on local channel state information from IAB nodes. Reference [6] proposes a reinforcement learning-based strategy for topology construction, considering both spectral efficiency and network load. The scheme developed in [7] allocates resources to IAB nodes while taking their data rate requirements into account. While the works [5], [6], [7] consider IAB networks with multi-path capability, they do not address routing selection or link scheduling. Reference [8] introduces a link activation and routing strategy based on deep reinforcement learning techniques. The study in [9] aims to minimize total resource usage during the relaying process, but its designed scheme requires high computational complexity and only supports Guaranteed Bit Rate (GBR) traffic. Although [8] and [9] support multi-path routing or scheduling in IAB networks, they do not incorporate NOMA in their proposed network scenarios.

References [12], [13], [14], [15], [16] investigate the application of NOMA technology in multi-hop networks. The work in [12] introduces a joint power allocation and user association scheme aimed at maximizing network throughput while satisfying the quality of service (QoS) requirements of UEs. Reference [13] integrates NOMA and beamforming technologies in user-centric ultra-dense networks, focusing on user association, resource allocation, and power assignment to maximize energy efficiency. The authors in [14] address power and resource allocation for networks that include both Orthogonal Multiple Access (OMA) and NOMA UEs. Reference [15] proposes a task offloading strategy that minimizes transmission latency and energy consumption in a NOMA-enabled network. The work in [16] focuses on balancing user fairness in NOMA-enabled millimeter wave ultra-dense networks. While these [12], [13], [14], [15], [16] utilize NOMA technology in multi-hop networks, the proposed schemes do not address routing selection. Additionally, [17], [18] enhance spectral efficiency by simultaneously employing Downlink NOMA (DL-NOMA) and Uplink NOMA (UL-NOMA) in dual-hop network scenarios. In [17], the authors propose a power allocation method to maximize throughput, while [18] designs a relay node selection strategy for maximizing network throughput. However, both [17] and [18] are limited to dual-hop networks, restricting the scope of their findings.

Table 1 summarizes the discussions above. To the best of our knowledge, this is the first work to integrate MU-MIMO and NOMA technologies into IAB networks. The proposed approach takes into account load balancing among IAB nodes connected by a DAG topology. To fully leverage the benefits of MU-MIMO and NOMA, the designed scheme meticulously schedules the links of IAB nodes and the power levels of transmitters.

TABLE 1 Comparisons With Previous Works

SECTION III. MU-MIMO and NOMA Technologies in an IAB Network

We use Fig. 1 to demonstrate the advantages of using MU-MIMO and NOMA in an IAB network. In this example, $n_{0}$ aims to deliver downstream data to $n_{3}$ . In Fig. 1, $t_{i}$ represents the order of link activation when disseminating data. We assume that the capacities of links $(n_{0},n_{1})$ , $(n_{1},n_{2})$ , and $(n_{2},n_{3})$ are 1 unit, and the capacities of links $(n_{0},n_{2})$ and $(n_{1},n_{3})$ are 0.8 units. Moreover, according to the analysis in [19], average link capacities can increase up to 70% when using NOMA. In this example, we assume that the average link capacity gain is only 50%. So, for example, when NOMA is used between $(n_{1}, n_{3})$ and $(n_{2}, n_{3})$ , the link capacity of these two links will be $((1+0.8)/2)\times 1.5 = 1.35$ units.

FIGURE 1.

The time slot usage performance of different relay technologies.

In Fig. 1(a)–(c), links do not adopt MU-MIMO and NOMA, and each node can have one active link per time slot. First, Fig. 1(a) employs the spectral efficiency (SE) first routing strategy. By prioritizing SE, each link in the routing path can achieve higher capacity, but it requires more hops to reach $n_{3}$ . In this example, the capacity bottleneck on the routing path is $\min (1,1,1) = 1$ unit, resulting in $n_{0}$ taking 3 time slots to relay data to $n_{3}$ . Therefore, the average link capacity of Fig. 1(a) will be $1/3 = 0.33$ units. Next, Fig. 1(b) adopts the hop count (HC) first routing strategy. Again, the capacity bottleneck on the routing path is $\min (1,0.8) = 0.8$ units, and $n_{0}$ takes 2 time slots to relay data to the destination. The average link capacity of Fig. 1(b) is $0.8/2 = 0.4$ units. Finally, Fig. 1(c) employs a multi-path routing scheme. With this strategy, links $(n_{1}, n_{3})$ and $(n_{0}, n_{2})$ can be scheduled simultaneously, allowing $n_{0}$ to disseminate data to $n_{3}$ via these two paths. The capacity bottleneck on both routing paths is 0.8 units, and $n_{0}$ takes 3 time slots to relay the data. The average link capacity of Fig. 1(c) is $(0.8 + 0.8)/3 = 0.53$ units. Comparing Fig. 1(a) and Fig. 1(b), it is evident that the multi-path strategy can indeed enhance network performance.

Fig. 1(d)-(e) consider multi-path routing. Fig. 1(d) indicates scheduling results when using only MU-MIMO. We can see that the bottleneck of the network is $n_{3}$ , which can receive $1 + 0.8$ units of data. In this example, it takes 3 time slots to send 1.8 units of data, and thus the average link capacity is $1.8/3 = 0.6$ units. Finally, in Fig. 1(e), both MU-MIMO and NOMA are adopted. With this setting, $n_{3}$ utilizes NOMA to receive 1.35 units of data in two time slots, resulting in an average link capacity of $1.35/2 = 0.675$ units.

Fig. 2 further illustrates the relationship between NOMA gain (ranging from 0.4 to 0.7) and average link capacity. Unlike other methods, which remain unaffected by changes in NOMA gain, the proposed concept of combining MU-MIMO with NOMA shows a consistent increase in link capacity as the gain increases. Different NOMA gains can be interpreted as representing various network conditions, and the results demonstrate that integrating MU-MIMO and NOMA effectively enhances link capacity across diverse scenarios.

FIGURE 2.

Relationship between NOMA gain and average link capacity.

SECTION IV. System Models

In the network, there is an IAB donor $n_{0}$ and $\hat {m}$ IAB nodes, which are denoted by $N = \{n_{0}, n_{1}, {\dots }, n_{\hat {m}}\}$ . We assume that the links between nodes in N are line-of-sight (LoS) connections (which can be achievable by positioning all IAB donor and IAB nodes at fixed locations with appropriate heights [20], [21]). Let L be the set of backhaul links in the network, where $(n_{i}, n_{j}) \in L$ represents the link between $n_{i}$ and $n_{j}$ . UEs can connect to either the IAB donor or an IAB node to access the network. We assume that IAB nodes and UEs operate in different frequency bands, and IAB nodes operate in half-duplex mode. The IAB donor and IAB nodes employ MU-MIMO technology, enabling an IAB node to emit signals to its child IAB nodes simultaneously.

According to the 3GPP standard [22], IAB networks utilize the Backhaul Adaptation Protocol (BAP) to facilitate multi-hop routing [23]. Under the BAP, the IAB donor determines the routing paths for packets. When establishing the network, the network operator can decide the routes, which are differentiated by BAP path IDs, with a network supporting a maximum of 256 routes. We assume that the network contains $\hat {k}$ routes. Let $R^{k}$ represent a route with ID k, where the set $R^{k}$ contains a sequence of IAB nodes. For example, in Fig. 3, we have $R^{1} = [n_{0}, n_{1}, n_{4}]$ and $R^{2} = [n_{0}, n_{2}, n_{4}]$ . The destination node may also be an intermediate node within a BAP route. For instance, in Fig. 3, a packet destined for IAB node $n_{1}$ can use route $R^{1}$ . In this work, we use $R^{k}(n_{i})$ to denote the subsequence of $R^{k}$ , representing the routing path from the IAB donor to IAB node $n_{i}$ . Additionally, if an IAB node $n_{i}$ does not exist in $R^{k}$ , the corresponding $R^{k}(n_{i})$ will be empty.

FIGURE 3.

The network scenario.

In a TTI t, the network decides the mode (i.e., DU or MT) for IAB nodes. When an IAB node $n_{i}$ is set to DU mode in t, it will use the entire TTI t to disseminate data. Let $n_{j}$ be one of the child IAB nodes of $n_{i}$ . When $n_{i}$ is in DU mode at t and the link $(n_{i}, n_{j})$ is scheduled, we set $e^{t}_{i,j} = 1$ ; otherwise, $e^{t}_{i,j} = 0$ . Thus, the link scheduling results for all backhaul links at TTI t can be modeled as

$$\begin{equation*} {E}^{t} = \{e^{t}_{i,j}, {\dots }\}, \quad \forall (n_{i},n_{j}) \in L.\end{equation*}$$ Moreover, when $e^{t}_{i,j} = 1$ , the receiving power of IAB node $n_{j}$ will be $$\begin{equation*} \alpha ^{t}_{i,j}p_{max}h_{i,j},\end{equation*}$$ where $\alpha ^{t}_{i,j} \in [{0,1}]$ represents the power allocation by $n_{i}$ to link $(n_{i}, n_{j})$ at TTI t, $p_{max}$ is the maximum transmit power of $n_{i}$ , and $h_{i,j}$ is the channel coefficient for the link $(n_{i}, n_{j})$ . When $n_{i}$ is in DU mode, it can disseminate data to several child IAB nodes, which means the power allocation of $n_{i}$ is divided among its child links. According to the configuration in [2], IAB nodes are set up with a range of possible power allocations. Additionally, to ensure that the total transmit power does not exceed $p_{max}$ , the power allocation of $n_{i}$ at TTI t must satisfy the following equation: $$\begin{equation*} \sum _{(n_{i},n_{j})\in L}\alpha ^{t}_{i,j}\leq 1.\end{equation*}$$ This condition ensures that the cumulative power allocated to all child links remains within the node’s maximum power capacity.

In this work, we define $I(n_{x})$ as the set of IAB nodes that can receive the signal from IAB node $n_{x}$ . In other words, when $n_{x}$ emits signals, the IAB nodes in $I(n_{x})$ can either receive the signal or perceive it as interference. Furthermore, an IAB node $n_{j}$ may belong to multiple sets $I(n_{x})$ for all $n_{x} \in N$ . Consequently, at a TTI t, $n_{j}$ may receive signals from different links. Let ${\mathcal {S}}^{t}(n_{j})$ be the set of links whose signals are received by $n_{j}$ at TTI t. When a link $(n_{x}, n_{y}) \in {\mathcal {S}}^{t}(n_{j})$ , $n_{j}$ can receive the signal of link $(n_{x}, n_{y})$ with power $\alpha ^{t}_{x,y} p_{max} h_{x,j}$ . It is important to note that when calculating the received power of link $(n_{x}, n_{y})$ at $n_{j}$ , we must consider the channel coefficient between $n_{x}$ and $n_{j}$ , denoted as $h_{x,j}$ . Using SIC technology, an IAB node can eliminate signals with stronger received power than its target signal. Consequently, signals with weaker received power than the target signal are regarded as interference. Let $\bar {{\mathcal {S}}}^{t}(n_{i}, n_{j}) \subseteq {\mathcal {S}}^{t}(n_{j})$ represent the links that have weaker received power than that of link $(n_{i}, n_{j})$ observed at $n_{j}$ . Therefore, when decoding the signal of link $(n_{i}, n_{j})$ , the observed signal-to-interference ratio (SINR), say $\mathrm {SINR}^{t}(n_{i}, n_{j})$ , can be defined as the following Eq. (1).

$$\begin{equation*} \mathrm {SINR}^{t}(n_{i}, n_{j}) = \frac {e^{t}_{i,j}\alpha ^{t}_{i,j}p_{max}h_{i,j}}{\sum _{(n_{x},n_{y})\in \bar {{\mathcal {S}}}^{t}(n_{i}, n_{j})} e^{t}_{x,y}\alpha ^{t}_{x,y}p_{max}h_{x,j} + z_{0}} \tag {1}\end{equation*}$$ In Eq. (1), $z_{0}$ is the thermal noise. Based on Eq. (1), we can use Shannon’s formula to derive the capacity with B bandwidth by Eq. (2). $$\begin{equation*} C^{t}_{i,j} = B\log _{2} (1 + \mathrm {SINR}^{t}(n_{i}, n_{j})) \tag {2}\end{equation*}$$

In this work, each IAB node $n_{i}$ has expected data rate requirements denoted as $D(n_{i})$ , which can be determined based on UEs served by $n_{i}$ . Let $\bar {U}^{t}(n_{i})$ represent the average data rate of IAB node $n_{i}$ observed at TTI t. Using $D(n_{i})$ and $\bar {U}^{t}(n_{i})$ , we define the achieved ratio at time t as follows:

$$\begin{equation*} {\mathcal {A}}(n_{i}) = \frac {\bar {U}^{t}(n_{i})}{D(n_{i})}.\end{equation*}$$ In TTI t, the IAB donor determines the routing strategy, link activation ${E}^{t}$ , and power allocation $\alpha ^{t}_{i,j}$ for links $(n_{i},n_{j}) \in L$ based on $D(n_{i})$ for all $n_{i} \in N$ . The objective of the IAB donor’s decision-making process is to maximize the minimum achieved ratio among all IAB nodes observed at time t, i.e., $$\begin{equation*} \max \{\!\min _{\forall n_{i}\in {N}} {\mathcal {A}}(n_{i}) \}. \tag {3}\end{equation*}$$ Based on Eq. (3), the decision of the IAB donor is to preserve the balance between the fairness and the requirements of IAB nodes.

Note that as mentioned above, the connections between IAB donor and IAB nodes are assumed to be LoS, and thus the link quality remains relatively stable. To deal with time-variant link conditions, IAB nodes periodically measure signal quality from their parent IAB nodes and report the measurement results to the IAB donor. The proposed algorithm in Section V can then make decisions based on the updated link conditions.

SECTION V. The Proposed Scheme

In each TTI t, the IAB donor executes the designed algorithm, which consists of a route decision phase and a link scheduling phase. Before showing the details of these phases, we first define three parameters, $c(n_{i}, n_{j})$ , $\varepsilon (n_{i}, n_{j})$ , and $r(n_{i}, n_{j})$ for link $(n_{i}, n_{j})$ : In our scheme, the IAB donor first collects the maximum capacity of each link in the network. Let $c(n_{i}, n_{j})$ denote the maximum capacity of link $(n_{i}, n_{j})$ . Moreover, in the IAB network, downlink traffic from the Internet will be relayed starting from the IAB donor. The IAB donor controls the loads of IAB nodes, specifically managing the amount of data transmitted to them in each TTI. In our design, the IAB donor records the accumulated traffic loads assigned to each link. For a link $(n_{i}, n_{j})$ , the load assigned to that link is defined as $\varepsilon (n_{i}, n_{j})$ . Based on the definitions of $c(n_{i}, n_{j})$ and $\varepsilon (n_{i}, n_{j})$ , these two variables must satisfy the inequality that $\varepsilon (n_{i}, n_{j}) \leq c(n_{i}, n_{j})$ . Additionally, the IAB donor can determine the remaining capacity of link $(n_{i}, n_{j})$ , which is given by $r(n_{i}, n_{j}) = c(n_{i}, n_{j}) - \varepsilon (n_{i}, n_{j})$ .

A. The Route Decision Phase

The detailed procedures are outlined in Algorithm 1. In line 1, there is a sort_and_extract function that selects q IAB nodes (from N) with the least achieved ratios and stores them in a list $N^{q}$ . For each node $n_{i} \in N^{q}$ , the IAB donor will determine its routing path and update the corresponding link loads in the following steps. Line 2 traverses all IAB nodes in $N^{q}$ . For a given IAB node $n_{i}$ , the IAB donor will find a route for it using lines 3-12. In lines 3-4, the algorithm initializes two variables to record the remaining capacity of the found routes, denoted as $\hat {r}$ , and the decided route, denoted as $\hat {R}$ . Next, in the loop at line 5, the algorithm examines all possible BAP paths in the network. In line 6, the algorithm checks whether the path $R^{k}$ contains the IAB node $n_{i}$ . If this condition is satisfied, line 7 identifies the minimum remaining capacity of the links along the sub-path $R^{k}(n_{i})$ . Then, in line 8, if the recorded value of temp_r is greater than $\hat {r}$ , it indicates that the sub-path $R^{k}(n_{i})$ can facilitate the relay of more downlink data to $n_{i}$ . Consequently, lines 9-10 will update the information for the identified sub-path $R^{k}(n_{i})$ . After traversing all BAP paths, the decided route for $n_{i}$ will be stored in $\hat {R}$ . Finally, the loop in line 11 will update the loads, $\varepsilon ()$ , for the links recorded in $\hat {R}$ .

Algorithm 1: The Route Decision Phase

1

$N^{q}=\mathrm {sort\_and\_extract}(N, q)$ ;

2

for $n_{i} \in N^{q}$ do

3

set $\hat {r} = - \infty$ ;

4

set $\hat {R} = \emptyset$ ;

5

for $R^{k} \in R$ do

6

if $R^{k}(n_{i}) \neq \emptyset$ then

7

set ${temp\_r} = \min ~\{ r(n_{x}, n_{y}) | (n_{x}, n_{y}) \in R^{k}(n_{i}) \}$ ;

8

if $\mathrm {temp\_r} \gt \hat {r}$ then

9

set $\hat {r} = {temp\_r}$ ;

10

set $\hat {R} = R^{k}(n_{i})$ ;

11

end

12

end

13

end

14

for $(n_{x}, n_{y}) \in \hat {R}$ do

15

update $\varepsilon (n_{x}, n_{y}) = \varepsilon (n_{x}, n_{y}) + \hat {r}$ ;

16

end

17

end

Let $\hat {l}$ be the number of links in the IAB network. The computational complexity of Algorithm 1 is analyzed below.

Theorem 1:

The computational complexity of Algorithm 1 is $O(\hat {m}\hat {k}\hat {l})$ .

Proof:

In the network, there are $\hat {m}$ IAB nodes. The computational complexity of sorting the $\hat {m}$ IAB nodes in line 1 is $O(\hat {m} \log {\hat {m}})$ . The loop in line 2 will be executed q times, where $q \leq \hat {m}$ . Recall that there are k paths in the network, so the loop in line 5 will be executed at most $\hat {k}$ times. Since there are $\hat {l}$ links in the network, line 7 requires a linear search with a complexity of $O(\hat {l})$ to find the minimum value. The computational complexity in lines 11-12 is also bounded by the number of paths in the network, yielding a complexity of $O(\hat {l})$ . Therefore, the computational complexity of the loop in line 2 is $O(\hat {m} \times (\hat {k} \times \hat {l} + \hat {l})) = O(\hat {m} \hat {k} \hat {l})$ . As a result, the overall computational complexity of Algorithm 1 is $O(\hat {m} \log {\hat {m}} + \hat {m} \hat {k} \hat {l}) = O(\hat {m} \hat {k} \hat {l})$ .◼

However, in real cases, the network operator may choose a small value for q, for example, $q=2$ . When q is large, it indicates that a receiver must decode signals from multiple transmitters simultaneously. Currently, a typical setting for NOMA involves decoding signals from two transmitters at the same time [24], [25]. Therefore, in practical scenarios, the computational complexity of Algorithm 1 can be effectively reduced to $O(\hat {k} \hat {l})$ .

B. The Link Scheduling Phase

Algorithm 2 outlines the procedures for deciding link scheduling and power allocation. In line 1, the algorithm sorts the links in L by their loads (i.e., $\varepsilon ())$ in decreasing order, and the sorted links are placed in a list Q. Then, line 2 sets all links as unscheduled for this TTI. Line 3 traverses all links according to the order determined in Q. In other words, links with greater remaining loads are checked first. After extracting a link $(n_{i}, n_{j})$ from Q, line 5 checks for conflicts using a check_if_conflict function, which will return “True” if one of the following two conditions is satisfied:

• For the transmitter $n_{i}$ , $n_{i}$ has been set as a receiver in this TTI.

• For the receiver $n_{j}$ , $n_{i}$ has been set as a transmitter in this TTI.

Recall that in this iteration, the procedure aims to determine if $n_{i}$ can serve as a transmitter. Line 7 calculates the current capacity surrounding $n_{i}$ . More specifically, if $n_{i}$ is a transmitter, this procedure considers the interfering neighbors of $n_{i}$ , denoted as $I(n_{i})$ . For each neighbor $n_{y}$ that is affected by $n_{i}$ , the procedure calculates its link capacity as $\sum _{\forall (n_{x},n_{y}) \in {\mathcal {S}}(n_{y})} C^{t}_{x,y}$ . Through the calculation in line 7, the algorithm can ascertain the current link capacity surrounding $n_{i}$ .

After line 7, the procedure evaluates whether to enable the link $(n_{i}, n_{j})$ . In lines 8-9, the algorithm sets temporary variables $\mathscr {I^{\prime }}(n_{i})$ and ${\mathcal {S}}^{\prime }(n_{y})$ , and then calculates a new power allocation for the enabled links starting from $n_{i}$ , specifically deciding $\alpha ^{\prime t}_{i, y}$ for all $n_{y} \in I^{\prime }(n_{i})$ . Line 10 employs an exhaustive search to derive new $\alpha$ values that optimize the $c^{\prime }$ value. Next, as indicated in line 11, if $c^{\prime } \gt c$ , this indicates that enabling link $(n_{i}, n_{j})$ can facilitate the transmission of more data during this TTI. Consequently, line 12 enables the link by setting $e^{t}_{i, j}$ to 1. Lines 13-15 then update ${\mathcal {I}}(n_{i})$ and ${\mathcal {S}}(n_{y})$ for each $n_{y} \in {\mathcal {I}}(n_{i})$ , along with the power allocation $\alpha$ values for $n_{i}$ . Finally, after traversing all links in Q, line 16 updates the $\varepsilon$ values for all enabled links in this TTI.

Algorithm 2: The Link Scheduling Phase

1

$Q = \mathrm {sorted}(\varepsilon (n_{i},n_{j})|\forall (n_{i},n_{j})\in L)$ ;

2

set $e^{t}_{i,j} = 0, \forall ({n_{i},n_{j}})\in L$ ;

3

while Q is not empty do

4

$({n_{i},n_{j}}) {=}$ dequeue$(Q)$ ;

5

if $\mathrm {check\_if\_conflict}(E^{t}, (n_{i},n_{j}))$ then

6

continue;

7

set $c = \sum _{n_{y}\in I(n_{i})} \left ({{ \sum _{\forall (n_{x},n_{y}) \in {\mathcal {S}}(n_{y})} C^{t}_{x,y}}}\right)$ ;

8

set $I^{\prime }(n_{i}) = I(n_{i}) \cup n_{j}$ ;

9

set $\mathscr {S^{\prime }}(n_{y}) = {\mathcal {S}}(n_{y}) \cup (n_{i}, n_{y})$ , $\forall n_{y} \in I^{\prime }(n_{i})$ ;

10

derive $\alpha ^{\prime }t_{i, y}~(\forall n_{y} \in I^{\prime }(n_{i}))$ to maximize $c^{\prime } = \sum _{n_{y}\in I^{\prime }(n_{i})} \left ({{ \sum _{\forall (n_{x},n_{y}) \in \mathscr {S^{\prime }}(n_{y})} C^{t}_{x,y}}}\right)$ ;

11

if $c^{\prime } \gt c$ then

12

set $e^{t}_{i,j} = 1$ ;

13

set $I(n_{i}) = I^{\prime }(n_{i})$ ;

14

set ${\mathscr {S}}(n_{y}) = \mathscr {S^{\prime }}(n_{y})$ , $\forall n_{y} \in I(n_{i})$ ;

15

set $\alpha ^{t}_{i, y} = \alpha ^{\prime }t_{i, y}$ , $\forall n_{y} \in I^{\prime }(n_{i})$ ;

16

set $\displaystyle \varepsilon (n_{i},n_{j}) = \varepsilon (n_{i},n_{j}) - e^{t}_{i,j}C^{t}_{i,j}$ , $\forall (n_{i},n_{j})\in L$ ;

In the following, we highlight the design considerations for line 10. According to our network model, the possible power allocations form a finite set, which limits the search space in line 10. In this work, we propose two constraints to enhance the search procedure:

• Constraint 1: Based on the current power allocation, for each IAB node $n_{y} \in I^{\prime }(n_{i})$ , we can derive a sequence representing the level of received power at $n_{y}$ , denoted as ${\mathcal {R}}(n_{y})$ , in decreasing order. The newly determined power allocation $\alpha ^{\prime t}_{i, y}$ (for all $n_{y} \in I^{\prime }(n_{i}))$ should maintain the same order for all sequences ${\mathcal {R}}(n_{y})$ (for all $n_{y} \in I^{\prime }(n_{i}))$ .

• Constraint 2: Let $P(n_{j})$ represent the set of parent nodes of $n_{j}$ . If the receiver $n_{j}$ has been scheduled (i.e., $\exists ~n_{a} \in P(n_{j})$ such that $e^{t}_{aj} = 1$ ), then the received power level on the newly added link should be minimized. This condition is expressed as

  $$\begin{equation*} \alpha ^{t^{\prime }}_{i, j} p_{max} h_{i,j} \lt \min _{n_{a} \in P(n_{j})}\{\alpha ^{t^{\prime }}_{a,j} p_{max} h_{a,j}\}.\end{equation*}$$

Next, we analyze the computational complexity of line 10, denoted as $O({\mathcal {C}})$ . Assuming that a transmitter can simultaneously disseminate signals to $\hat {c}$ receivers and has $\hat {p}$ adjustable power allocation values, the computational complexity will be $O(\hat {p}^{\hat {c}})$ . However, under typical network configurations, an IAB node will disseminate signals to no more than four child nodes [2], [3], [4]. Therefore, the computational complexity of finding an optimal power allocation is controllable. Moreover, we remark that the main objective of Algorithm 2 is to manage power allocation and schedule links. When integrating MU-MIMO and NOMA within IAB networks, power allocation across links is essential to optimize transmission efficiency while minimizing interference. An improper power allocation can result in insufficient SINR at the receiver, which diminishes the effectiveness of NOMA and reduces its capacity gains. By maximizing $c^{\prime }$ in line 10, the designed link schedule brings the benefit of mitigating interference at receivers, ensuring successful decoding of signals from multiple links and further improving network capacity.

Theorem 2:

The computational complexity of Algorithm 2 is $O(\hat {l}{\mathcal {C}})$ .

Proof:

In the network, there are $\hat {l}$ links, and thus the computational complexity of sorting $\hat {l}$ links in line 1 is $O(\hat {l} \log {\hat {l}})$ . Lines 2 and 16 assign values to $O(\hat {l})$ variables for all links. Then, the loop in line 3 will traverse at most $\hat {l}$ links. Within this loop, lines 9, 14, and 15 may perform operations on no more than $O(\hat {m})$ neighbors, but the computational complexity of the loop is dominated by line 10, which has a complexity of $O({\mathcal {C}})$ . Therefore, the computational complexity of the loop in line 3 is $O(\hat {l} {\mathcal {C}})$ . As a result, the overall computational complexity of Algorithm 2 is $O(\hat {l}{\mathcal {C}})$ .◼

Based on Theorem 1 and Theorem 2, the overall computational complexity of the proposed algorithm will be $O(\hat {l}(\hat {m}\hat {k} + {\mathcal {C}}))$ .

SECTION VI. Simulation Results

In this work, we implement a simulator using the Haskell programming language. In our simulation, there is one IAB donor and 15 IAB nodes, arranged in a $4\times 4$ grid. The IAB donor is positioned at the corner of the network, with a distance of 100 meters set between the IAB donor and the IAB nodes. In our simulator, the IAB donor can have multiple paths to reach each IAB node. Both the IAB donor and the IAB nodes can be scheduled to transmit/receive a maximum of two links in one TTI. For each link, the transmitter can support up to 275 radio bearers (RBs). Additional network settings are summarized in Table 2. Furthermore, each node is assigned a constant bit rate (CBR) traffic, with packet sizes fixed at 100 KB. In our simulation, we take the CBR data arrival rates as the expected data rate requirements of the IAB nodes.

TABLE 2 Network Configuration Table

We compare the proposed scheme (denoted by OUR) with the schemes presented in [4] (denoted by SSR), [3] (denoted by MRBA), and [9] (denoted by eReal). As mentioned in Section II, the IAB donor in SSR and MRBA disseminates downstream traffic to IAB nodes using a tree topology, while the IAB donor in eReal utilizes multiple paths to disseminate downstream data. Additionally, we implement two baseline methods, named MuMimo and TreePF, for comparison. The IAB nodes in MuMimo employ MU-MIMO technology to disseminate downstream data to multiple child IAB nodes, while TreePF utilizes a tree topology for routing and a proportional fairness (PF) strategy for link scheduling.

Fig. 4(a) presents the simulation results for the average throughput of IAB nodes. We observe that as the average data rate of the IAB nodes increases, the throughput of all methods reaches saturation. The OUR outperforms the other schemes by effectively leveraging MU-MIMO and NOMA technologies to achieve higher throughput. For instance, when the average data arrival rate is 24 Mbps, OUR achieves approximately 30% higher throughput compared to MRBA, SSR, TreePF, and eReal. Additionally, compared to MRBA, eReal, and SSR, the MuMimo method also demonstrates better throughput because each IAB node can enable multiple downstream links per TTI. In contrast, TreePF performs the worst, as it only employs the legacy strategy (i.e., tree topology and proportional fairness scheduling) to manage downstream data. Furthermore, as the data arrival rate increases, the performance of SSR deteriorates since it does not account for network saturation scenarios. Additionally, eReal prioritizes achieving fairness among IAB nodes over increasing overall network throughput. Consequently, the network throughput achieved using eReal can not be better than that of TreePF.

FIGURE 4.

Simulation results on (a) throughput, (b) achieved ratio, (c) fairness, (d) latency when varying the data arrival rate.

Fig. 4(b) shows the results of the achieved ratio. The findings indicate that OUR can maintain a high achieved ratio even when the average data arrival rate of IAB nodes is 24 Mbps, achieving an achieved ratio above 90%. This demonstrates that OUR effectively consumes downstream data for IAB nodes. As network loads increase, the achieved ratios of MRBA, eReal, SSR, and TreePF degrade rapidly because these schemes reach their capacity limits. In contrast, OUR and MuMimo can sustain higher network capacities to consume more data. Moreover, the MuMimo method enables an IAB node to transmit data to multiple child nodes simultaneously, but its achieved ratio performs 5-7% lower than other methods when the data arrival rate is under 20 Mbps. This is because MuMimo does not account for link load during scheduling, resulting in inefficient traffic consumption under light traffic conditions. In contrast, the proposed strategy prioritizes link scheduling based on load, effectively improving the achieved ratio across varying network loads.

Fig. 4(c) presents the fairness results. Fairness is measured using Jain’s fairness equation based on the received throughput among IAB nodes. We observe that OUR and eReal outperform the other schemes, with fairness values close to 0.98. Recall that when deciding routes, OUR identifies IAB nodes with lower achieved ratios, which helps preserve fairness among IAB nodes. Although eReal is specifically designed to achieve fairness, its throughput remains low, as mentioned earlier. Compared to eReal, MRBA relies on a tree topology for data transmission but achieves higher throughput by compromising some fairness. MuMimo can transmit data to multiple child IAB nodes simultaneously, but it fails to effectively ensure fairness among the nodes. We can see that when network load increases, the fairness of SSR declines quickly because some IAB nodes fail to obtain sufficient resources in this scenario.

Fig. 4(d) illustrates the average delay. It is evident that OUR significantly achieves lower delays, maintaining low-latency downstream data delivery in all cases. This result validates that the link scheduling in OUR can effectively consume buffered data quickly. Both MuMimo and TreePF utilize PF for radio resource allocation, resulting in better latency performance compared to the other three schemes. To achieve fairness, both eReal and MRBA evenly distribute available resources, which leads to higher latency. In contrast, SSR fails to efficiently allocate resources to IAB nodes under high network load, and thus the SSR strategy will result in higher transmission delays.

Finally, we remark that based on the above simulation results, two aspects demonstrate that the proposed scheme can effectively fulfill the data rate requirements of IAB nodes. Firstly, the achieved ratio is a direct indicator. Compared to other methods, the proposed scheme can achieve a higher achieved ratio, which directly supports that our scheme meets more IAB nodes’ data rate requirements. Secondly, improvements in overall throughput compared to other methods suggest an indirect benefit. A higher network throughput increases the chance of meeting individual IAB nodes’ data rate demands.

SECTION VII. Conclusion

This paper addresses the challenges of applying MU-MIMO and NOMA technologies within the IAB network to enhance throughput and fairness. For the IAB network scenario, we define a problem formulation that considers both the expected data requirements and the achieved data rates. We then develop a two-phase method, which includes a route selection phase and a link scheduling phase. The proposed method focuses on fully optimizing network capacities while maintaining fairness among IAB nodes. The simulation results demonstrate that the designed scheme effectively improves network throughput and achieves fairness. Furthermore, this work only optimizes the transmissions of downstream data. In the future, we have two directions. First, we can investigate resource allocation by jointly considering upstream and downstream data flows. Second, we plan to develop a distributed algorithm to support both route selection and link scheduling in IAB networks.