Joint User Association and Transmission Scheduling in Integrated mmWave Access and Terahertz Backhaul Networks

We consider a cellular network composed of one MBS, $L$ SBSs, and $K$ uniformly distributed UEs in a two dimensional space $\mathbb{R}^{2}$, as shown in Fig. 1. The MBS serves UEs within its coverage area over wireless links and is connected to the core network through wired fiber. Each SBS acts as an IAB node, then an access link refers to a link between a UE and an SBS. A backhaul link refers to a link between an SBS and the MBS. It is assumed that all UEs are connected to the MBS through a two-hop link, that is, the traffic of UEs is first routed to an SBS through the access link, and then forwarded to the MBS through the backhaul link. Furthermore, access traffic and backhaul traffic are carried over different frequency bands. Access links are assumed to operate in the mmWave frequency bands, and backhaul links are assumed to operate in the terahertz frequency bands to support ultra-high data rate transmission. As a result, there is no interference between the simultaneous transmissions of access links and backhaul links. It is assumed that all BSs and UEs are equipped with antenna arrays to compensate for the large path loss at these high frequencies.

In this system, time is partitioned into non-overlapping superframes. Each superframe is divided into a scheduling phase and a transmission phase, and each phase consists of multiple slots, which is illustrated in Fig. 2. Specifically, it is assumed that the scheduling phase of an access frame and a backhaul frame have the same duration, denoted by $t_{s}$, and the transmission phases of the two consist of $N$ and $M$ equal length slots, respectively. The duration of each slot is denoted by $\Delta$, then the duration of an access superframe is ${t_{A}}={t_{s}}+N\Delta$, and the duration of a backhaul superframe is ${t_{B}}={t_{s}}+M\Delta$.

Let $\mathcal{B}$ denote the set of SBSs, as $\mathcal{B}=\left\{{{b_{1}},{b_{2}},\ldots,{b_{L}}}\right\}$, where $b_{l},l\in\mathcal{L}$ is the $l$th SBS and $\mathcal{L}=\left\{{1,2,\ldots,L}\right\}$. Let $\mathcal{U}$ denote the set of UEs, as $\mathcal{U}=\left\{{{u_{1}},{u_{2}},\ldots,{u_{K}}}\right\}$, where $u_{k},k\in\mathcal{K}$ is the $k$th UE and $\mathcal{K}=\left\{{1,2,\ldots,K}\right\}$. The MBS is denoted by $b_{0}$.

For an access link with $b_{l}$ as the transmitter (TX) and $u_{k}$ as the receiver (RX), we denote the antenna gain of $b_{l}$ by ${G_{tx}}\left({{\theta_{lk}}}\right)$, and the antenna gain of $u_{k}$ by ${G_{rx}}\left({{\theta_{lk}}}\right)$, where ${\theta_{lk}}$ is the off-axis angle. Accordingly, the received power at $u_{k}$ from $b_{l}$, denoted by $P_{{b_{l}},{u_{k}}}^{A}$, is given by

where $\beta\propto{\left({{\lambda\mathord{\left/{\vphantom{\lambda{4\pi}}}\right.\kern-1.2pt}{4\pi}}}\right)^{2}}$ is a constant coefficient, $\lambda$ is the wavelength, $P_{t}^{A}$ is the transmit power of access links, $d_{lk}$ is the distance between $u_{k}$ and $b_{l}$, and $\alpha$ is the path loss exponent. Since the directional transmission reduces the inter-link interference, the downlink data rate of $u_{k}$ from $b_{l}$, denoted by $R_{{b_{l}},{u_{k}}}^{A}$, can be achieved as

where $\eta\in\left({0,1}\right)$ is the efficiency of the TX, $W_{A}$ is the bandwidth of access links, and $N_{0}$ is the noise power spectral density.

Similarly, we denote $P_{t}^{B}$ as the transmit power of backhaul links, and $W_{B}$ as the bandwidth of backhaul links. Then the data rate of the backhaul link from ${b_{0}}$ to ${b_{l}}$ associated with $u_{k}$, denoted by $R_{{b_{0}},{b_{lk}}}^{B}$, is given by

where ${G_{tx}}\left({{\phi_{0l}}}\right)$ and ${G_{rx}}\left({{\phi_{0l}}}\right)$ are the antenna gains of TX and RX, respectively, $\phi_{0l}$ is the off-axis angle, and $\rho\left({{b_{0}},{b_{l}}}\right)$ denotes the path loss from ${b_{0}}$ to ${b_{l}}$.

In the considered IAB-enabled networks, SBSs act as relays between UEs and the MBS. After a UE initiates a communication request, it first associates with an SBS before establishing an access link. Multiple UEs may connect to different SBSs according to the user association policy. For the $u_{k},\forall k\in\mathcal{K}$, the binary user-association vector is defined as ${{\bf{x}}_{b,{u_{k}}}}=\left({{x_{{b_{1}},{u_{k}}}},{x_{{b_{2}},{u_{k}}}},\ldots,{x_{{b_{L}},{u_{k}}}}}\right)$, where

Assume that each UE can only associate with one SBS at time $t$, that is,

After user association, the SBS and the MBS will schedule the access link and the backhaul link respectively. A binary scheduling variable is given by

Let $a_{{}_{{b_{0}},{b_{lk}}}}^{B}$ denote whether data from $u_{k}$ associated with the SBS $b_{l}$ is scheduled in the backhaul scheduling phase,

We assume that the MBS and SBSs operate under half-duplex constraints. If two different UEs $u_{i}$ and $u_{j}$ are both associated with the same SBS $b_{l}$, the potential access links $(b_{l},u_{i})$ and $(b_{l},u_{j})$ cannot be scheduled to transmit at the same time, i.e.,

Similarly, backhaul links can only be transmitted sequentially,

We denote the number of slots allocated to the access link $(b_{l},u_{i})$ and the backhaul link $(b_{0},b_{lk})$ by $T_{{b_{l}},{u_{k}}}^{A}$ and $T_{{b_{0}},{b_{lk}}}^{B}$, respectively. Since the number of transmission slots is limited and each slot can only be occupied by one link, we have

Consequently, the throughput achieved by UE $u_{k}$ on the access link, denoted by $C_{{u_{k}}}^{A}$, can be expressed as

The throughput achieved by UE $u_{k}$ on the backhaul link, denote by $C_{{u_{k}}}^{B}$, can be expressed as

In an IAB network, a user can be successfully served only if the achievable throughput of the access link and the backhaul link meet the user’s minimum QoS requirements ${\Omega_{{u_{k}}}}$, that is, $C_{{u_{k}}}^{A}\geq{\Omega_{{u_{k}}}}$ and $C_{{u_{k}}}^{B}\geq{\Omega_{{u_{k}}}}$. The user who meets the above conditions is called a served user. A binary variable $I_{u_{k}}$ is defined to indicate whether $u_{k}$ is a served user, which is given by

From the perspective of improving user experience, the optimization problem is formulated as

where constraints (15b), (15d), and (15e) define the user association variable and two transmission scheduling variables, respectively. Constraint (15c) ensures that the UE can only associate with one SBS at any time. Constraint (15f) and (15g) indicate that the MBS and SBSs operate in the half-duplex mode. Constraint (15h) and (15i) guarantee that the number of scheduled slots does not exceed the number of transmission slots per frame. Since the problem is a non-linear integer optimization problem, it is challenging to design the optimal joint user association and transmission scheduling scheme. In the next section, we will propose a heuristic algorithm to obtain a suboptimal solution to this problem.

Assume that there are 8 SBSs and no more than 500 UEs uniformly distributed in a 100 $\times$ 100 $m^{2}$ area. Considering that the user experience rate will reach 1 Gbps or even higher in the near future [26], it is assumed that the QoS requirements of each user are uniformly distributed between $\left[{2,5}\right]$ Gbps. We take the average value of 50 executions of the algorithm as the final result. The topology of the network, the locations of the SBSs, the locations of UEs, and the QoS requirements of users are varied in each simulation.

The realistic directional antenna model is adopted for mmWave access links [27]. The directional antenna gain, denoted by $G(\theta)$, is given by

where $\theta$ is the off-axis angle, $\theta_{-3dB}$ is the angle of the half-power beamwidth, and $\theta_{ml}$ is the main lobe width and satisfies ${\theta_{ml}}=2.6\cdot{\theta_{-3dB}}$. The maximum antenna gain $G_{0}$ is computed as ${G_{0}}=10\lg{\left({{{1.6162}\mathord{\left/{\vphantom{{1.6162}{\sin\left({{{{\theta_{-3dB}}}\mathord{\left/{\vphantom{{{\theta_{-3dB}}}2}}\right.\kern-1.2pt}2}}\right)}}}\right.\kern-1.2pt}{\sin\left({{{{\theta_{-3dB}}}\mathord{\left/{\vphantom{{{\theta_{-3dB}}}2}}\right.\kern-1.2pt}2}}\right)}}}\right)^{2}}$. The side lobe gain $G_{sl}$ can be expressed as ${G_{sl}}=-0.4111\cdot\ln\left({{\theta_{-3dB}}}\right)-10.579$.

The ITU-R Recommendation F.699-7 narrow beam antenna model is adopted for terahertz backhaul links [28]. The antenna gain relative to an isotropic antenna, denoted by $G\left(\phi\right)$, is given by

where $\phi$ is the off-axis angle, $G_{\max}$ is the maximum antenna gain, $D$ is antenna diameter and $\lambda$ is wavelength. $G_{1}$ is the gain of the first side-lobe and is obtained by ${G_{1}}=2+15\lg\left({{D\mathord{\left/{\vphantom{D\lambda}}\right.\kern-1.2pt}\lambda}}\right)$. In the simulation, Cassegrain antennas are deployed on the MBS and SBSs, with ${G_{\max}}=47\ dBi$ and ${D\mathord{\left/{\vphantom{D\lambda}}\right.\kern-1.2pt}\lambda}=152$. Parameters ${\phi_{m}}$ and $\phi_{r}$ can be calculated by ${\phi_{m}}={{20\lambda}\mathord{\left/{\vphantom{{20\lambda}D}}\right.\kern-1.2pt}D}\sqrt{{G_{\max}}-{G_{1}}}$ and ${\phi_{r}}=15.85{\left({{D\mathord{\left/{\vphantom{D\lambda}}\right.\kern-1.2pt}\lambda}}\right)^{-0.6}}$ respectively.

Since the terahertz backhaul link suffers from high molecular absorption loss, the path loss in the terahertz band is defined as the product of the spreading loss and the molecular absorption loss, which is given by [15, 29]

where $c$ is the speed of light, $f_{B}$ is the operating frequency at the backhaul link, $d_{0l}$ is the distance between $b_{0}$ and $b_{l}$, and $k(f_{B})$ is the medium absorption coefficient. In (23), $\left(c/4\pi f_{B}d_{0l}\right)^{2}$ refers to the spreading loss, and $e^{-k(f_{B})d_{0l}}$ stands for the molecular absorption loss, that is, the energy attenuation of electromagnetic waves caused by molecular absorption. Specifically, at pressure $p$ and temperature $T$, $k(f_{B})$ can be further computed by $k(f_{B})=\frac{p}{p_{STP}}\frac{T_{STP}}{T}\sum_{i,g}Q^{i,g}\sigma^{i,g}(f_{B})$, where $p_{STP}$ and $T_{STP}$ are the standard pressure and temperature, respectively, $Q^{i,g}$ is the molecular volumetric density of the isotopologue $i$ of gas $g$, and $\sigma^{i,g}(f_{B})$ is the absorption cross section for the isotopologue $i$ of gas $g$ at the frequency $f_{B}$. Parameters $Q^{i,g}$ and $\sigma^{i,g}(f_{B})$ can be obtained from the HITRAN (high resolution transmission molecular absorption) database [30].

In order to verify the effectiveness of the proposed algorithm in transmission scheduling, the algorithm is compared with the following baseline algorithms.

• •

  Integrated access and backhaul with maximum signal-to-noise (IAB-MSNR): The algorithm takes the SNR as the association criterion, that is, each UE is associated with the SBS providing the maximum SNR [31]. The backhaul scheduling is the same as the proposed algorithm, but the number of access transmission slots allocated to users is not updated.

• •

  Random and integrated access and backhaul (RIAB): UEs will randomly connect to an SBS with this algorithm. In the backhaul scheduling phase, if the total number of slots required by the associated UEs is greater than the actual number of backhaul transmission slots $M$, the associted UEs are randomly eliminated.

The proposed algorithm is referred to as the IAB-MQR algorithm in this algorithm.

The results of the number of served UEs and system throughput of the three algorithms under different user numbers are shown in Fig. 3 and Fig. 4, respectively. The transmit power of access links and backhaul links are both 1,000 mW, and the number of access transmission slots and the number of backhaul transmission slots are both 2,000. In Fig. 3, as the number of UEs is increased, the number of served UEs of the proposed IAB-MQR algorithm is steadily rising, while the numbers of served users of the other two algorithms remain almost the same. Since the IAB-MQR algorithm takes into account the limited system resources, it preferentially selects and schedules the UEs with fewer required slots to serve more UEs, while the other two algorithms can only serve fewer UEs with limited resources. This also shows that the proposed algorithm can guarantee the service of more users and respond to a large number of bursty user requests under the condition of limited resources. When the number of system UEs is 500, the number of served UEs of the IAB-MQR algorithm is $35.5\%$ and $42.9\%$ higher than that of the IAB-MSNR algorithm and the RIAB algorithm, respectively.

In Fig. 4, as the number of system users grows up, the system throughput of the IAB-MQR algorithm fluctuates slightly around 543 Gbps, which shows the advantages of the proposed algorithm in improving network throughput. The IAB-MSNR algorithm selects UEs with the strongest SNR for association and transmission scheduling. UEs with high QoS requirements and low access rates occupy system resources for a long time, resulting in access failure of other UEs. Futhermore, the algorithm does not reallocate the slot resources of access links after backhaul scheduling, and the access transmission slots are not fully utilized. Similarly, the RIAB algorithm may have more UEs occupying system resources all the time than the IAB-MSNR algorithm, and the performance of this algorithm is the worst.

Fig. 5 and Fig. 6 show the number of served UEs and system throughput with various access transmission slots, respectively. We set the transmit power of both access links and backhaul links to 1,000 mW, the number of backhaul transmission slots to 2,000, and the number of users to 500. The proposed algorithm is superior to the other two algorithms in terms of the number of served UEs and system throughput. With the increase of access transmission slots, the number of served UEs and system throughput of the three algorithms also increase, and the growth rate slows down. When there are fewer access transmission slots, there are fewer schedulable access links in the access phase, that is, fewer associated UEs, resulting in a portion of unused backhaul transmission slot resources and fewer schedulable backhaul links. As the number of access transmission slots goes up, so does the number of scheduled backhaul links and therefore the number of served UEs and system throughput. After the number of access transmission slots reaches 2,000, the number of served UEs of the proposed IAB-MQR algorithm remains stable. This is because under the constraints of backhaul slots, the scheduled backhaul links are also limited. It is worth noting that the system throughput of the proposed IAB-MQR algorithm still increases slightly after the number of access transmission slots reaches 2,000. The reason is that the algorithm updates the number of access slots allocated to UEs according to (20) after the completion of backhaul scheduling, which makes full use of the access slot resources and further improves the actual throughput of access links. Because the system throughput satisfies $C=\sum\nolimits_{\mathcal{U}}{\left({{x_{{b_{l}},{u_{k}}}}\cdot\min\left({C_{{u_{k}}}^{A},C_{{u_{k}}}^{B}}\right)}\right)}$, the system throughput also increases slightly.

Fig. 7 and Fig. 8 plot the performance comparison of the three schemes under different backhaul transmission slots, where the transmit power of access links and backhaul links is 1,000 mW, the number of access transmission slots is 2,000, and the number of users is 500. The proposed algorithm serves the most users and achieves the highest throughput. When the number of backhaul transmission slots is small, the QoS requirements of most users cannot be satisfied and thus there are fewer backhaul links that can be scheduled. In this case, the number of backhaul transmission slots is the main factor limiting the performance of the algorithm. Regarding system throughput, the IAB-MQR algorithm reallocates transmission slots of access links after backhaul scheduling, hence users achieves higher throughput on access links. However, the actual throughput depends on the minimum throughput achieved by the access link and the backhaul link, the throughput of the IAB-MQR algorithm is also limited by the finite backhaul transmission slots. In addition, when the number of backhaul transmission slots is 2,000, the performance of the proposed algorithm is not further improved, while the values of the other two algorithms are 1,500 and 1,000, respectively. This difference also shows the advantages of the proposed algorithm in resource allocation.

From Fig. 5 to Fig. 8, it can be seen that setting the appropriate number of access transmission slots and backhaul transmission slots helps improve the overall performance of the network while making full use of system resources.

The number of served UEs and system throught with varying transmit power of access links are shown in Fig. 9 and Fig. 10 with $P_{T}^{B}=1,000$ mW, $N=3,000$, $M=2,000$ and $K=500$. The proposed algorithm outperforms the other algorithms with respect to these two performance metrics. When the access transmission power is 1,400 mW, the number of served users of the IAB-MQR algorithm is still $33.4\%$ and $40.2\%$ higher than that of the IAB-MSNR algorithm and the RIAB algorithm, respectively. Particularly, when the access transmit power exceeds 800 mW, the number of served UEs of the proposed IAB-MQR algorithm remains nearly stable, and the system throughput still increases slightly. Higher access transmission power helps to improve the transmission rate of access links. Therefore, with the same number of access transmission slots, the access link can achieve a greater throughput at higher access transmission power. On the other hand, when the backhaul resources are consistent, the performance of the IAB-MQR algorithm is basically the same under the following two simulation settings: (i) the access transmit power is 800 mW, and the number of access transmission slots is 3,000, (ii) the access transmit power is 1,000 mW, and the number of access transmission slots is 2,000. This also shows that appropriately increasing the number of access transmission slots can reduce the requirements for access transmit power.

Fig. 11 and Fig. 12 plot the results of the three algorithms under different transmit power of backhaul links with $P_{T}^{A}=800$ mW, $N=3,000$, $M=1,500$, and $K=500$. When the backhaul transmit power exceeds 2,000 mW, the number of served users of the IAB-MQR algorithm is almost constant, and its system throughput still goes up. Compared with Fig. 9 and Fig. 10, the curves of IAB-MSNR algorithm and RIAB algorithm are relatively flat in general. These two algorithms do not update the number of access slots of associated UEs after the backhaul scheduling. According to (12) and (16), the actual throughput of access links of the two algorithms is only slightly greater than the QoS requirements of users. Even if the transmit power of the backhaul link is increased, the actual throughput of the system cannot be increased.