Unlicensed Spectrum Access and Performance Analysis for NR-U/WiGig Coexistence in UAV Communication Systems

Abstract

Unmanned aerial vehicles (UAVs) are extensively employed in pursuit, rescue missions, and agricultural applications. These operations necessitate substantial data and video transmission, requiring significant spectral resources. The unlicensed millimeter wave (mmWave) spectrum, especially in the 60 GHz frequency band, offers promising potential for UAV communications. However, WiGig users are the incumbent users of the 60 GHz unlicensed spectrum. Therefore, to ensure fair coexistence between UAV-based new radio-unlicensed (NR-U) users and WiGig users, unlicensed spectrum-sharing strategies need to be meticulously designed. Due to the beam directionality of the NR-U system, traditional listen-before-talk (LBT) spectrum sensing strategies are no longer effective in NR-U/WiGig systems. To address this, we propose a new cooperative unlicensed spectrum sensing strategy based on mmWave beamforming direction. In this strategy, UAV and WiGig users cooperatively sense the unlicensed spectrum and jointly decide on the access strategy. Our analysis shows that the proposed strategy effectively resolves the hidden and exposed node problems associated with traditional LBT strategies. Furthermore, we consider the sensitivity of mmWave to obstacles and analyze the effects of these obstacles on the spectrum-sharing sensing scheme. We examine the unlicensed spectrum access probability and network throughput under blockage scenarios. Simulation results indicate that although obstacles can attenuate the signal, they positively impact unlicensed spectrum sensing. The presence of obstacles can increase spectrum access probability by about 60% and improve system capacity by about 70%.

1. Introduction

UAVs are widely employed in various fields, such as emergency search and rescue operations [1], agricultural irrigation [2], and urban infrastructure development [3], due to their easy deployment and flexible scheduling. As UAVs take on more complex tasks, the demand for data transmission rates increases, leading to growing spectrum needs. Unlicensed spectrum sharing is an effective solution to address these urgent spectrum demands. The unlicensed millimeter wave spectrum, particularly the 60 GHz frequency band, holds significant potential for UAV communications [4,5]. It provides high-bandwidth, low-interference communication capabilities, making it suitable for various UAV applications. For example, the 60 GHz unlicensed millimeter wave band can support high-definition video and image transmission due to its high bandwidth. Its high-speed data transmission for short distances makes it ideal for applications like surveillance and patrolling. The Low latency and low interference also make it suitable for real-time control and navigation of UAVs. Moreover, the new radio unlicensed (NR-U), part of the 5G standard, supports communication over unlicensed bands, including the 60 GHz band, enhancing the flexibility and performance of UAV communication.

The global unlicensed spectrum available includes the 2.4 GHz, 5 GHz, and 60 GHz bands. In the 60 GHz unlicensed band, Europe has released 9 GHz of available spectrum, which is ten times that of the unlicensed spectrum below 6 GHz. The United States has released 14 GHz of unlicensed bandwidth [6], which is sixteen times that of the unlicensed spectrum below 6 GHz. As confirmed by the 3rd Generation Partnership Project (3GPP), the 60 GHz band is an attractive candidate because it is currently not very crowded and can provide a large amount of continuous bandwidth [7,8]. From the perspective of 3GPP standardization, NR-U (New Radio-unlicensed) operating below 7 GHz has already been standardized by 3GPP, while the spectrum access standard for NR-U operating in the millimeter-wave bands will be addressed in subsequent releases, namely NR Rel-17 and above.

However, there are already some Radio Access Technologies (RATs) operating in these bands, such as 802.11b/g/n working at 2.4 GHz, 802.11n/ac working at 5 GHz, and 802.11ad/ay (also known as WiGig) operating in the 60 GHz band. One of the most critical issues allowing cellular networks or NR-U to operate in unlicensed spectrum is to ensure fair and harmonious coexistence with other systems operating in the unlicensed bands [9,10].

For fair coexistence, any wireless access terminal that wants to use unlicensed spectrum (for example, a 5G network using unlicensed spectrum) must be designed according to the requirements and standards of the respective bands [10,11]. Therefore, duty cycle mechanisms and the Listen Before Talk (LBT) access mechanism have been proposed to solve the coexistence problem. In the 5 GHz and 60 GHz bands, the standard stipulates that Europe and Japan use the Listen Before Talk (LBT) mechanism [11]. To comply with the regulations (referred to as Collision Avoidance Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) in IEEE 802.11 versions), LAA, MulteFire, Wi-Fi, and WiGig all adopt the LBT mechanism [12,13].

LBT is a spectrum-sharing mechanism where devices sense the spectrum usage situation through this mechanism before accessing the unlicensed spectrum. It determines the channel’s busyness or idleness by comparing the received interference with an energy detection threshold. However, compared to LTE-U/Wi-Fi coexistence, NR-U/Wi-Fi coexistence cannot adopt the traditional LBT spectrum sensing mechanism, because the 5G NR-U network using unlicensed spectrum employs beamforming transmission, which changes the interference layout and thus alters the coexistence framework of unlicensed spectrum. In the beamforming-based transmission for NR-U/Wi-Fi coexistence, the traditional LBT technology leads to more severe exposed and hidden node problems [14,15]. For example, the use of omnidirectional LBT makes the exposed node problem more prominent, as verified in WiGig systems [10]. If the directionality of directional transmission is known, using directional LBT can improve spatial reuse, but it leads to a more severe hidden node problem [16]. Therefore, there is a trade-off between omnidirectional LBT and directional LBT [17]. To achieve this, two distributed LBT-based spectrum sensing strategies have been proposed: Pair LBT [17] and LBT switching [18].

1.1. Related Works

Beam-based transmission presents unique challenges in channel detection due to the limitations of Listen-Before-Talk (LBT) mechanisms. Previous studies have explored various methods to address the issue of undetectable interference at the transmitter. For instance, Ref. [19] discussed the receiver-assisted LBT as a more effective mechanism for interference assessment. The work [20] introduced a speak-before-listening (SBR) mechanism and Ref. [21] proposed the Listen-Before-Receive (LBR) strategy. Building on this, Ref. [22] presented a closed-loop LBT mechanism and Ref. [23] combined directional LBT-LBR with millimeter-wave beam training to reduce complexity. Additionally, existing receiver-assisted LBT strategies typically employ a fixed energy detection threshold [10,12,13,23], leading to a trade-off between spectrum efficiency and interference management. Therefore, it is necessary to optimize the receiver’s energy detection threshold to ensure fair coexistence between NR-U and Wi-Fi systems [9,24]. Traditional optimization-based coexistence approaches in unlicensed mmWave bands can be found in [10,25,26]. An underlying assumption of these methods, however, is that they know the topology or scheduling knowledge of other networks, which is usually unavailable in practice. Thus, the work in [27] adopted an efficient 3D radio environment map (REM) construction scheme based on sparse Bayesian learning (SBL) to recover the accurate REM with limited and optimized sampling data. Recently, DRL based spectrum sharing strategies have been introduced into the cognitive radio field due to their abilities to fit well in unknown environments [28,29,30,31,32,33]. However, past works are all proposed for spectrum sharing in sub-7 GHz bands. Thus, the work [5] attempted to exploit the DRL technique to tackle the NR-U/WiGig coexistence issue in unlicensed mmWave bands. Furthermore, the work [34] has proposed a Deep Q-learning Network (DQN) based scheme to achieve the fair coexistence of NR-U network with the existing WiGig network in unlicensed mmWave bands. Through the use of a centrally coordinated multi-point (CoMP) server that manages the operations of NR-U access points, a joint beamforming coordination and user selection approach is proposed to enable the fair coexistence between multi-operator NR-U networks and a WiGig network [35]. The authors in [5] studied the NR-U/WiGig coexistence in unlicensed mmWave bands, with the goal of maximizing the NR-U data rate while satisfying all UE’s QoS requirements. The proposed scheme in [5], however, cannot trade off different goals. Furthermore, online learning-based codebook optimization algorithms in [28] have shown their efficiency in NR-U even without prior network knowledge, but the impact of the codebook selection on WiGig was not considered. Thus, the work in [36] focuses on the codebook selection for the NR-U/WiGig coexistence in unlicensed mmWave bands.

In unlicensed millimeter-wave bands, data communication is extremely sensitive to obstacles in the environment. Obstacles can cause significant blocking effects, leading to communication interruptions. However, obstacles can play a positive role in spectrum sensing access because they can block interference, allowing different wireless access systems to achieve fair and harmonious coexistence. Obstacles can also increase spectrum access opportunities and improve system capacity. However, although the impact of obstacles on path loss has been studied in the literature [37,38,39], the impact of obstacles on access to unlicensed spectrum has not yet been studied. Such research is of great significance for access to millimeter-wave unlicensed spectrum based on beam transmission.

1.2. Motivations and Contributions

From the above discussion, in beam-based NR-U systems, to achieve coexistence with various wireless access technologies, a new and effective spectrum sensing access needs to be designed. Motivated by this, we propose a new and effective spectrum sensing strategy, i.e., collaborative spectrum sensing of the cellular user (CU) (we use UE to denote this type of user in this article to distinct the WiGig user.) and WiGig user (WUE), which addresses the problems of missed detection and false alarms in traditional LBT, as well as the spectrum access issues in special scenarios. We also analyze the influence of blockage on the spectrum access for the NR-U/WiGig coexistence systems. The contributions of our study are concluded as follows:

(1) A new and effective collaborative spectrum sensing strategy for the NR-U/WiGig coexistence is proposed, which solves the hidden and exposed node problems and spectrum sensing issues in special scenarios. The optimal transmit power for the gNB and WiGig as well as the optimal sensing detection threshold are obtained by maximizing the system sum rate using the Dinkelbach method.

(2) The effects of blockage on the spectrum sensing and system capacity are analyzed. The spectrum access probability and system sum rate with blockage are derived and compared with that of LoS links.

(3) The numeric simulations are performed to verify the theoretic analysis. The results show the proposed spectrum access strategy has the maximal sum rate with the optimal detection threshold and has the lower complexity although it has the relatively lower sum rate. At the same time, the NR-U/WiGig coexistence system with blockage has a higher spectrum access probability and sum rate compared to that without blockage scenarios.

The rest of the paper is organized as follows: In Section 2, we describe the system model of the mmWave cellular network coexisting with WiGig. In Section 3, we design a frame structure for the unlicensed mmWave spectrum sharing. To maximize the sum rate of cellular users as well as reduce the interference to WiGig networks, the unlicensed spectrum sharing problem is formulated in Section 4 and the Dinkelbach-based algorithm is designed to solve this problem. In Section 5, we evaluate the unlicensed spectrum sensing with blockages and analyze their impact on sensing performance. Simulation results are given in Section 6 and conclusions are drawn in Section 7.

2. Problem Description and Motivations

The traditional LBT (Listen Before Talk) technology no longer works in the beamforming-based NR-U/WiGig coexistence systems, which is mainly reflected in the following aspects:

(a) One of the significant characteristics of millimeter wave communication is beam-based transmission, which allows for beam steering to facilitate spectrum sharing between coexistence systems (it is important to recognize that UAVs are versatile within a coexistence system, capable of being gNBs, STAs, WiGigs, or WUEs. This versatility stems from the UAVs’ dual functionality as both mobile base stations and users. Consequently, in the system model outlined herein, the designations gNB (BS1), STA (UE1), WiGig (BS2), and WUE (UE2) correspond to the base stations and users of the NR-U and WiGIG systems, respectively. The specific node functioning as the UAV is not predefined, allowing for adaptability based on varying scenario requirements and communication needs. Therefore, to maintain general applicability across diverse scenarios, no particular node is explicitly identified as the UAV). Traditional spectrum sensing techniques such as Listen-Before-Talk (LBT), which rely on omnidirectional or directional sensing of interference by the base station, are no longer effective in millimeter-wave communications. As illustrated in Figure 1 with co-location scenario of WUE and STA users, conventional LBT spectrum sensing would conclude that the coexistence systems cannot operate concurrently. This is due to the WUE detecting interference from the gNB. However, in millimeter-wave communications, the directional capabilities of beams can be utilized to avoid mutual interference, thereby enabling simultaneous transmission. Consequently, the traditional LBT technique is rendered ineffective in this scenario.

(b) Additionally, traditional LBT can lead to false alarms and missed detection issues, as exemplified in Figure 2. In Figure 2a, the traditional LBT technique would cause the WiGig base station to omnidirectionally detect interference from the gNB base station. To avoid conflict, the WiGig base station would cease signal transmission. However, in reality, due to the directional nature of beams, the coexistence systems could communicate simultaneously, resulting in a false alarm. In Figure 2b, the WiGig base station employs directional sensing and does not detect the signal sent by the gNB base station. Consequently, the WiGig base station proceeds with its signal transmission, which causes substantial interference to the users, leading to a missed detection issue.

(c) Finally, when the gNB base station, STA, WiGig base station, and WUE are essentially aligned in a straight line, the traditional LBT technique completely fails, as shown in Figure 3. In Figure 3, the six scenarios from top to bottom in the left side of Figure 3 demonstrate that the STA and WUE users do not interfere with each other due to the opposite directions of transmission, allowing for concurrent transmission. In contrast, the six scenarios from top to bottom in the right side of Figure 3 cannot coexist due to mutual interference. According to traditional LBT spectrum sensing technology where the WiGig base station detects interference, none of the scenarios in Figure 3 can achieve concurrent transmission, leading to resource wastage and sensing failure.

Based on the above descriptions and analysis, it is evident that traditional LBT technology has its limitations in millimeter-wave communications. Therefore, this paper studies the spectrum-sharing access protocols suitable for beam-based communication, aiming to improve and supplement the traditional LBT technology.

3. Proposed the Spectrum Access Strategy for NR-U/Wi-Fi Coexistence Systems

The collaboration-based unlicensed spectrum sensing technology for the NR-U/WiGig system is proposed in this section. This strategy consists of two main steps:

(1) Beam Scanning Alignment: Before UE and WUE carry out LBT, beam scanning is performed to align the optimal beams of the base station and users, which has been studied in many documents [40,41,42]. Although some literature combines LBT with beam scanning, the results do not avoid the problem of false alarms [23]. Conducting LBT before beam scanning may reduce the complexity during the beam scanning phase. However, it is at the cost of losing sensing accuracy in the LBT phase, which also causes subsequent conflicts between STA and WUE users and degrades system performance. Therefore, in this study, beam scanning is conducted first to acquire the communication direction of the base station, and then LBT is carried out. It is worth noting that maintaining beam alignment can be difficult in dynamic environments where users or obstacles are moving. However, online learning-based code-book optimization algorithms are adaptable to highly dynamic systems and show their efficiency in NR-U even without prior network knowledge [36,43].

(2) LBT Spectrum Sensing in Optimal Communication Directions: The precondition for establishing NR-U communication is that the communication can be normally maintained with very low interference from the WiGig system. At the same time, to ensure the communication quality of the WiGig user (WUE), the interference from the gNB to the WUE must also be sufficiently small. Hence, both gNB and WiGig users need to conduct LBT spectrum sensing, respectively.

The proposed spectrum sensing protocol flowchart is shown in Figure 4.

In the protocol flowchart, base stations and users carry out beam scanning alignment. Then, the base station sends a Reference Signal (RTS) to request spectrum sensing toward the user direction. If simultaneous RTS messages come from multiple devices, the multiple users adopt Markov chain-based contention window back-off mechanism or priority-based access to avoid conflict. Users perform energy detection based on the signal received from the base station direction. If it is greater than the threshold value, there is interference in that direction and the spectrum sensing result is busy. Otherwise, the result is idle. Since both UE (STA) and WUE perform spectrum sensing simultaneously, there are four possible sensing results: WUE-idle, UE-idle; WUE-busy, UE-busy; WUE-idle, UE-busy; WUE-busy, UE-idle.

Situation 1: UE-idle, WUE-idle. In this case, the UE and WUE users do not interfere with each other, as in the scenarios in Figure 1 and Figure 2a, and left side of Figure 3. The directional nature of the beams in millimeter-wave communication allows both users to transmit simultaneously on the same frequency without interfering with each other. Under this condition, both users transmit data at normal power.

Situation 2: UE-busy, WUE-busy. In this situation, both UE and WUE users receive interference from each other, as in scenarios 2–5 in the right side of Figure 3. Here, the UE and WUE users have two options: one is for the UE to transmit data at normal power and the WUE to not transmit data, ensuring the priority and reception quality of UE; the other option is for the UE to increase the transmission power while the WUE decreases it. Although this option improves spectral efficiency, the communication quality of WUE is not guaranteed.

Situation 3: UE-idle, WUE-busy. In this situation, the UE is unaffected by the WUE’s communication, but the WUE is affected by the UE’s communication, as in the first scenario in the right side of Figure 3. Here, the UE and WUE users also have two choices: one is for the UE to transmit data at normal power and the WUE not to transmit, meaning the WUE does not send when interfered with; the other choice is for the UE to transmit normally while the WUE increases the transmission power to resist the interference from the UE’s communication. This option can improve spectral efficiency while the communication quality of the WUE can also be ensured, with the UE being completely undisturbed.

Situation 4: UE-busy, WUE-idle. In this situation, the UE is interfered with by the WUE’s communication, but the WUE is not affected by the UE’s communication, as in the sixth scenario in the right side of Figure 3. Here, the system also has two options: one is for the UE to transmit data at normal power and the WUE not to communicate, ensuring the priority and communication quality of the UE; the other option is for the UE to increase the transmission power and the WUE to decrease it, which reduces the interference experienced by the UE and improves communication quality, but may affect the WUE’s communication.

Based on the proposed collaborative spectrum sensing protocol for NR-U/WiGig coexistence systems, the frame structure for gNB and WiGig are shown in Figure 5, which illustrates our proposed CO-BT-LBT scheme and represents an original contribution of this paper.

To verify the effectiveness of the proposed collaborative spectrum sensing strategy, we compare the complexity of the proposed strategy with the existing main spectrum access strategies as shown in

Table 1. The complexity of channel access schemes.

Channel Access Mode	Numeric Complexity
IDL-BT [23]	$K_1+M_1+3K_2{M}_2$
JOL-BT [23]	$K_1+M_1+K_2{M}_2+K_{2}M$
CO-BT-LBT	$K_2{M}_2+2$

.

Table 1 compares the complexity of various channel access schemes. The parameter $K_1$ and $M_1$ are the required beam pair links (BPL) in Tx monitoring and BPL in Rx monitoring, respectively. The parameter $K_2$ is the subset of $K_1$ monitoring beams with energy below the threshold. The parameter $M_2$ is the subset of the $M_1$ receiver monitoring beams with energy below the threshold. Besides, independent beam training performs $k_2=M_2$ BPL before RTS/CTS sending. Next, the transmitter sends RTS in $M_2$ beams, and the receiver performs an entire beam sweeping in $K_2$ beams at the same time. After $K_2$ times of beam sweeping, the receiver sorts the receiving beams in descending order according to the reference signal receiving power (RSRP). The largest M beams in RSRP are then chosen to constitute a temporary beam set $R{R}_{temp}$.

It can be found that the joint directional LBT and beam training (JOL-BT) reduces more than 1/3 beam pair link (BPL) numbers than that of the independent directional LBT and beam training channel access mechanism (IDL-BT). It is shown that by increasing the number of antennae, the performance of the proposed mechanism can be remarkably improved. Moreover, the proposed collaborative beam training and LBT channel access scheme (CO-BT-LBT) has the lowest complexity.

4. Mathematical Formulation of the Proposed Solution

In the proposed collaborative spectrum sensing strategy, the false alarm and miss detection can be solved for the co-location scenario of UE and WUE, where any three points of gNB, UE, WiGig and WUE are in a straight line. For the scenario of gNB, UE, WiGig and WUE are all in a straight line, the proposed spectrum sensing strategy can accurately sense the channel state (idle or busy) with the perfect beamforming. However, for the imperfect beamforming with the strong side lobes, the scenarios where the gNB and WiGig systems can access the unlicensed spectrum simultaneously become infeasible, and vice versa. The detailed analysis is as follows:

When the directions of two communication links are opposite, the mutual interference can be avoided and thus, the coexistence system can be achieved. However, when the side-lobe gains are high, the two communication links may interfere with each other, potentially preventing simultaneous access to the unlicensed spectrum. In this case, the signal-interference-noise-ratio (SINR) of UE and WUE are deduced as

$${\mathrm{SINR}}_{ue}={\displaystyle \frac{P_1{H}_{bs,ue}{G}_{t,bs,m}{G}_{r,ue,m}}{P_2{H}_{wg,1}{G}_{t,wg,s}{G}_{r,ue,m}+{\sigma }^2}}={\displaystyle \frac{P_1\alpha }{P_2\beta +{\sigma }^2}}$$

(1)

and

$${\mathrm{SINR}}_{wue}={\displaystyle \frac{P_2{H}_{wg,2}{G}_{t,wg,m}{G}_{r,wue,m}}{P_1{H}_{bs,wue}{G}_{t,bs,s}{G}_{r,wue,m}+{\sigma }^2}}={\displaystyle \frac{P_2\beta }{P_1\mu +{\sigma }^2}}$$

(2)

where $\alpha =H_{bs,ue}{G}_{t,bs,m}{G}_{r,ue,m}$, $\beta =H_{wg,1}{G}_{t,wg,s}{G}_{r,ue,m}$, $\gamma =H_{wg,2}{G}_{t,wg,m}{G}_{r,wue,m}$ and $\mu =H_{bs,wue}{G}_{t,bs,s}{G}_{r,wue,m}$. The parameters $P_1$ and $P_2$ denote the transmit power of the gNB and WiGig, respectively. The channel parameters $H_{bs,ue},H_{wg,ue},H_{wg,wue}$ and $H_{bs,wue}$ represent the channel power gain from the gNB to the UE and WUE, and the channel power gain from the WiGig to the UE and WUE, respectively. The parameter $G_{x,y,z}$ is the beamforming gain, $x\in \left\{t,r\right\}$ denoting the transmitter or the receiver, $y\in \left\{bs,wg,ue,wue\right\}$ denoting the gNB, WiGig, UE and WUE, and $z\in \left\{m,s\right\}$ denoting the main lobe or the side lobe.

At the transmitter or receiver, the antenna gain can be calculated as [44]

$$G_{x,y,m}=10{log}_{10}N+G_{ele}.$$

(3)

where $G_{ele}$ denotes the independent power gain of each antenna, which is different from the parameters $G_{x,y,z}$ and N is the number of antennas.

The antenna gain loss in the direction of angle $\varphi$ compared to the expected direction to the user u can be expressed as [44]

$$G_{u,loss}^{\left(k\right)}\left(\varphi \right)=min\left\{12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2,30\right\}.$$

(4)

During the LBT process, the interference received by the WUE from gNB is expressed as

$$I={\displaystyle \frac{P_{t,ue1}}{PL\left(d\right)}}+G_{tx,ue1}+G_{rx,ue2}-G_{ue2,loss}^{\left(k\right)}\left(\varphi \right)\left[\mathrm{dB}\right],$$

(5)

where $PL\left(d\right)$ is the path loss when the transmission distance is d.

In scenarios with strong side lobes that cause mutual interference, the problem of maximizing the system sum rate when gNB and WiGig can simultaneously communicate with users can be formulated as:

$$\begin{array}{c}\mathbf{P}:\underset{P_1,P_2,I_1^{th},I_2^{th}}{max}{log}_2\left(1+{\displaystyle \frac{P_1\alpha }{P_2\beta +{\sigma }^2}}\right)+{log}_2\left(1+{\displaystyle \frac{P_2\gamma }{P_1\mu +{\sigma }^2}}\right)\hfill \\ s.t.\hfill \\ C1:P_2\beta \le I_1^{th}\hfill \\ C2:P_1\mu \le I_2^{th}\hfill \\ C3:0\le P_1\le P_{max}\hfill \\ C4:0\le P_2\le P_{max}\hfill \\ C5:0\le I_1^{th}\le P_{max}\hfill \\ C6:0\le I_2^{th}\le P_{max}.\hfill \end{array}$$

(6)

From the above problem, we can see that P is nonconvex due to the fraction-form objective function. The first constraint guarantees the interference received by the WUE is below the threshold. The second constraint guarantees the interference received by the UE is below the threshold. The constraints $C1$ and $C2$ guarantee the cellular and WiGig systems can access the unlicensed spectrum simultaneously. The third and fourth constraints ensure that the transmission power of the base stations, gNB, and WiGig is within the maximum transmission power. The fifth and sixth constraints indicate that the interference tolerance of UE and WUE is also limited to the maximum transmission power. To solve this problem, we need to transform it to a standard convex problem first and then adopt the classical optimization tool CVX to obtain the optimal transmit power.

By applying the Dinkelbach method to convert the fraction form into the rational expression [45,46,47,48], P can be transformed into

$$\begin{array}{c}\mathbf{P-D}:\underset{P_1,P_2,I_1^{th},I_2^{th},q}{max}\left(P_2\beta +{\sigma }^2+P_1\alpha \right)-q\left(P_1\mu +{\sigma }^2+P_2\gamma \right)\hfill \\ s.t.\hfill \\ C1:P_2\beta \le I_1^{th}\hfill \\ C2:P_1\mu \le I_2^{th}\hfill \\ C3:0\le P_1\le P_{max}\hfill \\ C4:0\le P_2\le P_{max}\hfill \\ C5:0\le I_1^{th}\le P_{max}\hfill \\ C6:0\le I_2^{th}\le P_{max}.\hfill \end{array}$$

(7)

The equivalence of (6) and (7) is obtained by the following theorem.

The optimal $q^{*}$ can be obtained as $q^{*}={\displaystyle \frac{P_2\beta +{\sigma }^2+P_1\alpha }{P_1\mu +{\sigma }^2+P_2\gamma }}$ if and only if

$$\begin{array}{cc}\hfill F\left(q^{*}\right)& =F(q^{*},P_1^{*},P_2^{*},I_1^{th,*},I_2^{th,*})\hfill \\ \hfill & =\underset{P_1,P_2,I_1^{th},I_2^{th}}{max}\left(P_2\beta +{\sigma }^2+P_1\alpha \right)\hfill \\ \hfill & -q^{*}\left(P_1\mu +{\sigma }^2+P_2\gamma \right)=0.\hfill \end{array}$$

(8)

Proof. 

see Appendix A.    □

From (7), we can see that the objective function and constraints are all linear functions of variables $P_1$, $P_2$, $I_1^{th}$ and $I_2^{th}$. The problem (7) is convex and can be solved by CVX. Then by iterating variable q, we can obtain the final optimal solution. For a given q in (7), the optimal transmit power can be obtained by CVX. The proposed Dinkelbach iterative algorithm is summarized in Algorithm 1.

Algorithm 1 Dinkelbach-based Iterative Power Allocation Algorithm

1: Initialize the related parameters $P_1$, $P_2$, ${I_1}^{\mathrm{th}}$ and ${I_2}^{\mathrm{th}}$.  2: Set maximal transmit power $P_{\max }$, channel parameters $\alpha$, $\beta$, $\gamma$, $\sigma$, and $\mu$, the convergence tolerance $ϵ$.  3: while not converged do   4:   Solve P-D by CVX tool.  5:   Update q by $q_{\mathrm{new}}={\displaystyle \frac{P_2\beta +{\sigma }^2+P_1\alpha }{P_1\mu +{\sigma }^2+P_2\gamma }}$.  6:   if $|q_{\mathrm{new}}-q|\le ϵ$ then  7:    Converge  8:   else  9:    $q=q_{\mathrm{new}}$ 10:   end if  11: end while  12: Obtain the optimal power allocation $P_1^{*}$, $P_2^{*}$, $I_1^{\mathrm{th},*}$, $I_2^{\mathrm{th},*}$, and $q^{*}$.

To show the convergence of the proposed algorithm, we find that $P_1\mu +{\sigma }^2+P_2\gamma \ge 0$, $f\left(q\right)$ is monotonic decreasing function of q. Define $q^{*}=\underset{P_1,P_2,I_1^{th},I_2^{th}}{max}\left\{{\displaystyle \frac{P_2\beta +{\sigma }^2+P_1\alpha }{P_1\mu +{\sigma }^2+P_2\gamma }}\right\}={\displaystyle \frac{P_2^{*}\beta +{\sigma }^2+P_1^{*}\alpha }{P_1^{*}\mu +{\sigma }^2+P_2^{*}\gamma }}$, we have $f\left(q^{*}\right)=P_2^{*}\beta +{\sigma }^2+P_1^{*}\alpha -q^{*}\left(P_1^{*}\mu +{\sigma }^2+P_2^{*}\gamma \right)=0$. So, $q_n$ and $q_{n+1}$ denoting the nth and $(n+1)$th iteration parameters satisfy $q_n\le q^{*}$, $q_{n+1}\le q^{*}$ and accordingly, $f\left(q_n\right)\ge f\left(q^{*}\right)=0$, $f\left(q_{n+1}\right)\ge f\left(q^{*}\right)=0$. Substituting $q_{n+1}={\displaystyle \frac{P_2^{\left(n\right)}\beta +{\sigma }^2+P_1^{\left(n\right)}\alpha }{P_1^{\left(n\right)}\mu +{\sigma }^2+P_2^{\left(n\right)}\gamma }}$, where $(P_1^{\left(n\right)},P_2^{\left(n\right)},I_1^{\left(n\right)},I_2^{\left(n\right)})$ represents the optimal power allocation in the nth iteration into $f\left(q_{n+1}\right)$, it is easy to obtain $f\left(q_n\right)=\left(P_1\mu +{\sigma }^2+P_2\gamma \right)(q_{n+1}-q_n)\ge 0$ and thus $q_{n+1}\ge q_n$. Increasing the value of q with the iteration number, $f\left(q\right)$ will finally be reduced and finally be equal to zero after sufficient iterations and optimal $q^{*}$ can be deduced by $f\left(q^{*}\right)=0$. Therefore, it is clear to conclude that the proposed algorithm is convergent and stops at an optimal solution.

The arithmetic cost of the Dinkelbach approach is in the order of $O(log(nM\left)\right)$, where n is a number of variables and $M=\underset{i\in \{1,2,\dots \}}{max}(c_i,d_i,1)$ with $c_i$’s being the coefficients of numerator and $d_i$’s being the coefficients of the denominator in the optimization fraction-form function.

When the side lobe of gNB interferes with the WUE and the side lobe of WiGig has no interference with the UE, the WUE can access the spectrum and the sum-rate maximization problem is formulated as

$$\begin{array}{c}\mathbf{P-1}:\underset{P_1,P_2,I_2^{th}}{max}F(P_1,P_2,I_1^{th},I_2^{th})={log}_2\left(1+{\displaystyle \frac{P_1\alpha }{{\sigma }^2}}\right)+{log}_2\left(1+{\displaystyle \frac{P_2\gamma }{P_1\mu +{\sigma }^2}}\right)\hfill \\ s.t.\hfill \\ 0\le P_1\mu \le I_2^{th},\hfill \\ 0\le P_1\le P_{max},\hfill \\ 0\le P_2\le P_{max},\hfill \\ 0\le I_2^{th}\le P_{max}.\hfill \end{array}$$

(9)

In the P-1, the first-order derivatives of objective function with respect to $P_1$ and $P_2$ are ${\displaystyle \frac{\partial F}{\partial P_1}}={\displaystyle \frac{P_2\gamma \alpha }{\left({\sigma }^2+P_1\alpha \right)P_2\gamma lg2}}-{\displaystyle \frac{P_2\gamma \alpha }{\left(P_1\alpha +{\sigma }^2\right)\left(P_2\gamma +P_1\alpha +{\sigma }^2\right)lg2}}>0$ and ${\displaystyle \frac{\partial F}{\partial P_2}}={\displaystyle \frac{\gamma }{\left(P_1\mu +{\sigma }^2+P_2\gamma \right)ln2}}>0$, respectively. Thus, the objective function is the increasing function with respect to $P_1$ and $P_2$. The optimal transmit power of gNB and WiGig is $P_1=min\left({\displaystyle \frac{I_2^{th}}{\mu }},P_{max}\right)$ and $P_2=P_{max}$.

When the interference received by the UE or WUE is above the threshold, the two communications cannot occur simultaneously and the NR-U system cannot access the spectrum to protect the incumbent user in the unlicensed spectrum. The sum-rate maximization problem can be formulated as $\underset{P_1,P_2,I_2^{th}}{max}{log}_2\left(1+{\displaystyle \frac{P_1\alpha }{{\sigma }^2}}\right)$ conditioned on $I_2^{th}\le min\left(P_1\mu ,P_{max}\right)$ or $I_1^{th}\le min\left(P_2\beta ,P_{max}\right)$. As we can see the objective function is increasing function with respect to $P_1$, the optimal transmit power for $P_1$ in this situation is as follows: when $P_1\mu \le P_{max}$, $P_1^{opt}={\displaystyle \frac{P_{max}}{\mu }}$; when $P_1\mu \ge P_{max}$, $P_1^{opt}=P_{max}$. Due to the gNB being unable to access the unlicensed spectrum, the transmit power $P_2$ does not exist.

When the directions of two communications are the same, which causes mutual interference for the coexistence systems, the two communications cannot occur simultaneously. However, when the interference is below the threshold, UE and WUE can also both access the unlicensed spectrum. The situation and analysis are similar to the case in which the directions of the two communications are opposite. We omit it here for brevity.

5. Spectrum Access Analysis for the Communication with Blockage

Assuming the main lobe gain of gNB is $G_{B,M}$, the beamwidth of the main lobe is ${\theta }_{B,M}$, and the sidelobe gain is $G_{B,S}$, with a beam width of sidelobe ${\theta }_{B,S}$. The primary user’s receive beam has a main lobe gain of $G_{U,M}$, and sidelobe gain $G_{U,S}$. Similarly, WiGig’s transmit beam main lobe gain is $G_{W,M}$, with a main lobe width of ${\theta }_{W,M}$ and a sidelobe gain of $G_{W,S}$, and a sidelobe width of ${\theta }_{W,S}$, the WUE’s receive beam main lobe gain $G_{WU,M}$ and sidelobe gain $G_{WU,S}$.

Based on a uniform random 2-D distribution assumption of all the nodes, the probabilities that this node lies in the mainbeam and sidebeam directions of NR-U gNB are given by $P_{B,M}={\displaystyle \frac{{\theta }_{W,M}}{2\pi }}$ with $G_B=G_{B,M}$ and $P_{B,S}=1-P_{B,M}$ with $G_B=G_{B,S}$.

The pathloss of LOS and NLOS is, respectively, expressed as

$$\begin{array}{c}P{L}_{LOS}\left(d\right)=32.4+17.3{log}_{10}d+20{log}_{10}{f}_c=A·d^{1.73},\hfill \\ P{L}_{NLOS}\left(d\right)=32.4+31.9{log}_{10}d+20{log}_{10}{f}_c=A·d^{3.19}.\hfill \end{array}$$

(10)

Considering the existence of blockage, we adopt the 3GPP indoor LOS probability model as follows [44]

$$p_{LOS}\left(d_{2D}\right)=\left\{\begin{array}{c}1,{\mathrm{d}}_{2D}\le 5m\hfill \\ exp\left(-{\displaystyle \frac{d_{2D}-5}{70.8}}\right),5m<{\mathrm{d}}_{2D}\le 49m\hfill \\ exp\left(-{\displaystyle \frac{d_{2D}-49}{211.7}}\right),{\mathrm{d}}_{2D}>49m.\hfill \end{array}\right.$$

(11)

Therefore, the average path loss is

$$\begin{array}{cc}\hfill PL\left(d_{2D}\right)& =p_{LOS}\left(d_{2D}\right)P{L}_{LOS}\left(d_{2D}\right)\hfill \\ \hfill & +\left(1-p_{LOS}\left(d_{2D}\right)\right)P{L}_{NLOS}\left(d_{2D}\right).\hfill \end{array}$$

(12)

When gNB, UE, WiGig, and WUE are in the same line and the two communications are in the same directions, according to the proposed spectrum sensing strategy, WUE can detect the interference from the gNB and thus, the two communications cannot occur simultaneously. However, when there are blocks between the two communications as shown in Figure 6, the interference is greatly reduced and the two communications can occur at the same time. To evaluate the maximum interference received by the WUE, we assume the interference received by the mainbeam of the WUE. In this situation, the interference is expressed as

$$\begin{array}{c}I=P_{B,M}{p}_{NLOS}{I}_{B,M}\hfill \\ =P_{B,M}{p}_{NLOS}\left({\displaystyle \frac{P_{B,t}H}{{PL}_{NLOS}}}+G_{B,M}+G_{U,M}\right)\hfill \\ ={\displaystyle \frac{{\theta }_{W,M}\left[1-exp\left(-\frac{d-5}{70.8}\right)\right]}{2\pi }}\left\{{\displaystyle \frac{P_{B,t}}{A·d^{3.19}}}+10{log}_{10}{N}_B+2G_{ele}+10{log}_{10}{N}_{wue}\right\}.\hfill \end{array}$$

(13)

Thus, the probability of unlicensed spectrum access, which is defined as the probability of interference below the threshold, is calculated as

$$\begin{array}{c}P=Pr\left(I<I_{th}\right)\hfill \\ \begin{array}{c}=Pr\left\{H<{\displaystyle \frac{A·d^{3.19}}{P_{B,t}}}\left.\left[{\displaystyle \frac{I_{th}2\pi }{{\theta }_{W,M}\left[1-exp\left(-\frac{d-5}{70.8}\right)\right]}}-10{log}_{10}{N}_B-2G_{ele}-10{log}_{10}{N}_{wue}\right]\right\}\right.\hfill \end{array}\hfill \\ =1-{\mathrm{e}}^{-{\displaystyle \frac{\frac{A·d^{3.19}}{P_{B,t}}\left[\frac{I_{th}2\pi }{{\theta }_{W,M}\left[1-exp\left(-\frac{d-5}{70.8}\right)\right]}-10{log}_{10}{N}_B-2G_{ele}-10{log}_{10}{N}_{wue}\right]}{2{\sigma }^2}}}.\hfill \end{array}$$

(14)

Proof. 

see Appendix B.   □

Compared with the coexistence system situation without the blockage, WUE will receive stronger interference, which is expressed as

$$\begin{array}{c}I=P_{B,M}{p}_{LOS}{I}_{B,M}\hfill \\ =P_{B,M}{p}_{LOS}\left({\displaystyle \frac{P_{B,t}H}{P{L}_{LOS}}}+G_{B,M}+G_{U,M}\right)\hfill \\ ={\displaystyle \frac{{\theta }_{W,M}exp\left(-\frac{d-5}{70.8}\right)}{2\pi }}\left[{\displaystyle \frac{P_{B,t}}{A·d^{1.73}}}+10{log}_{10}\left(N_B{N}_{wue}\right)+2G_{ele}\right].\hfill \end{array}$$

(15)

According to the definition of access probability, the access probability is derived as

$$\begin{array}{c}P=Pr\left(I<I_{th}\right)\hfill \\ \begin{array}{c}=Pr\left\{H<{\displaystyle \frac{A·d^{1.73}}{P_{B,t}}}\left[{\displaystyle \frac{I_{th}2\pi }{{\theta }_{W,M}exp\left(-\frac{d-5}{70.8}\right)}}-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}\right]\right\}\hfill \end{array}\hfill \\ =1-e^{-{\displaystyle \frac{A·d^{1.73}}{2{\sigma }^2{P}_{B,t}}}\left[{\displaystyle \frac{I_{th}2\pi }{{\theta }_{W,M}exp\left(-\frac{d-5}{70.8}\right)}}-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}\right]}.\hfill \end{array}$$

(16)

When the WUE is not in the mainbeam of gNB, according to the proposed strategy and under the perfect beam without the sidebeam, the two communications can occur simultaneously. However, there is a sidebeam in the antenna pattern in reality and thus, the two communications possibly cannot occur simultaneously in this situation. Then, the interference is deduced as

$$\begin{array}{c}\begin{array}{c}I=P_{B,S}{p}_{LOS}{I}_{B,S}\hfill \\ =P_{B,S}{p}_{LOS}\left[{\displaystyle \frac{P_{B,t}H}{P{L}_{LOS}}}+G_{B,M}-G_{B.loss}\left(\varphi \right)+G_{U,M}\right]\hfill \end{array}\hfill \\ =\left(1-{\displaystyle \frac{{\theta }_{W,M}}{2\pi }}\right)exp\left(-{\displaystyle \frac{d_{2D}-5}{70.8}}\right)\left[{\displaystyle \frac{P_{B,t}H}{A·d^{1.73}}}+10{log}_{10}\left(N_B{N}_{wue}\right)+2G_{ele}-12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right].\hfill \end{array}$$

(17)

The unlicensed spectrum access probability is

$$\begin{array}{c}P=Pr\left(I<I_{th}\right)\hfill \\ \begin{array}{c}=Pr\left\{H<{\displaystyle \frac{A·d^{1.73}}{P_{B,t}}}\left[{\displaystyle \frac{I_{th}}{\left(1-\frac{{\theta }_{W,M}}{2\pi }\right)exp\left(-\frac{d_{2D}-5}{70.8}\right)}}\right.\right.\hfill \\ \left.\left.-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}+12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right]\right\}\hfill \end{array}\hfill \\ =1-exp\left\{-{\displaystyle \frac{A·d^{1.73}}{2{\sigma }^2{P}_{B,t}}}\left[{\displaystyle \frac{I_{th}}{\left(1-\frac{{\theta }_{W,M}}{2\pi }\right)exp\left(-\frac{d_{2D}-5}{70.8}\right)}}\right.\right.\hfill \\ \left.\left.-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}+12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right]\right\}.\hfill \end{array}$$

(18)

Compared with the coexistence situation with the blockage, the received interference of WUE is calculated as

$$\begin{array}{c}\begin{array}{c}\begin{array}{c}I=P_{B,S}{p}_{NLOS}{I}_{B,S}\hfill \\ =P_{B,S}{p}_{NLOS}\left[{\displaystyle \frac{P_{B,t}H}{P{L}_{NLOS}}}+G_{B,M}-G_{B.loss}\left(\varphi \right)+G_{U,M}\right]\hfill \end{array}\hfill \\ =\left(1-{\displaystyle \frac{{\theta }_{W,M}}{2\pi }}\right)\left[1-exp\left(-{\displaystyle \frac{d_{2D}-5}{70.8}}\right)\right]\left\{{\displaystyle \frac{P_{B,t}H}{A·d^{3.19}}}+10{log}_{10}\left(N_B{N}_{wue}\right)\right.\hfill \end{array}\hfill \\ \left.+2G_{ele}-12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right\}.\hfill \end{array}$$

(19)

The unlicensed spectrum access probability can then be derived as

$$\begin{array}{c}P=Pr\left(I<I_{th}\right)\hfill \\ \begin{array}{c}=Pr\left\{H<{\displaystyle \frac{A·d^{3.19}}{P_{B,t}}}\left[{\displaystyle \frac{I_{th}}{\left(1-\frac{{\theta }_{W,M}}{2\pi }\right)\left[1-exp\left(-\frac{d_{2D}-5}{70.8}\right)\right]}}\right.\right.\hfill \\ \left.\left.-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}+12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right]\right\}\hfill \end{array}\hfill \\ \begin{array}{c}=1-exp\left\{-{\displaystyle \frac{A·d^{3.19}}{2{\sigma }^2{P}_{B,t}}}\left[{\displaystyle \frac{I_{th}}{\left(1-\frac{{\theta }_{W,M}}{2\pi }\right)\left[1-exp\left(-\frac{d_{2D}-5}{70.8}\right)\right]}}\right.\right.\hfill \\ \left.\left.-10{log}_{10}\left(N_B{N}_{wue}\right)-2G_{ele}+12{\left({\displaystyle \frac{36\varphi }{13\pi }}\right)}^2\right]\right\}.\hfill \end{array}\hfill \end{array}$$

(20)

The above analysis compares four unlicensed spectrum access scenarios: WiGig communication within gNB main lobe with obstacles between the two communicating systems, WiGig communication within gNB main lobe without obstacles between the communicating systems, WiGig communication within gNB sidelobe with obstacles between the communicating systems, and WiGig communication within gNB sidelobe without obstacles between the communicating systems. The interference and spectrum access probabilities are obtained, respectively, in the four scenarios. The comparison results are shown in the following simulation section.

6. Simulation Results and Analysis

6.1. Parameter Settings

We consider an NR-U and a Wi-Fi coexistence network with a uniform linear array (ULA) antenna at the gNB and WiGig AP. The simulation scenario is shown in Figure 7. The simulation results are obtained by the software tool MATLAB and the parameters setting is summarized in

Table 2. Simulation Parameters.

Notation	Parameter Definition	Value	Unit
$N_t$	The number of transmit antennas at gNB and WiGig	64	-
$N_r$	The number of receive antennas at UE and WUE	16	-
$G_{ele}$	The Tx antenna gain of each antenna	8	dB
B	Total bandwidth	2.16	GHz
$f_c$	The center frequency	60	GHz
$d_1$	The distance between gNB and WiGig	15	m
$d_2$	The distance between gNB and UE	6	m
$d_3$	The distance between WiGig and WUE	1	m
$d_4$	The distance between gNB and WUE	20	m
$d_5$	The distance between WiGig and UE	20	m
$N_0$	The power spectrum density of the noise	−174	dBm/Hz

. The number of antennas at gNB and WiGig is $N_t=64$ and the number of receive antennas at UE and WUE is $N_r=16$. The Tx antenna gain of each antenna is set as $G_{ele}=8$ dB [44] for the ULA antenna.

We consider one unlicensed mmWave channel with 2.16 GHz around 60 GHz [11,44]. Maximum number of shared unlicensed channels is set by one. The power density of the AWGN is −174 dBm/Hz [44].

6.2. The Performance of the Proposed Unlicensed Spectrum Access Strategy

Table 3. Performance Comparison of the three spectrum-sharing strategies.

Situation	Performance
	Access Probability	Sum Rate	Complexity
Situation 1	JOL-BT = IDL-BT > CO-BT-LBT	JOL-BT = IDL-BT = CO-BT-LBT	IDL-BT > JOL-BT > CO-BT-LBT
Situation 2	JOL-BT > IDL-BT > CO-BT-LBT	JOL-BT > IDL-BT = CO-BT-LBT	IDL-BT > JOL-BT > CO-BT-LBT
Situation 3	JOL-BT > IDL-BT > CO-BT-LBT	JOL-BT = IDL-BT ≈ CO-BT-LBT	IDL-BT > JOL-BT > CO-BT-LBT
Situation 4	JOL-BT > IDL-BT > CO-BT-LBT	JOL-BT = IDL-BT ≈ CO-BT-LBT	IDL-BT > JOL-BT > CO-BT-LBT

concludes the results for access probability and sum rate, comparing the three spectrum-sharing strategies across the four situations. Situation 1 denotes that there is no mutual interference between gNB and WiGig systems. In this situation, the three strategies achieve the same access opportunities, i.e., both systems can simultaneously access the unlicensed spectrum and thus, have the same sum rate. In situation 2, there is mutual interference between gNB and WiGig systems. For JOL-BT, communication always occurs between the transmitter and receiver no matter whether the interference is strong in the communication direction. The transmitter and receiver can jointly select the other direction with weaker interference to communicate. Therefore, communication exists all the time and the access probability and sum rate are higher than the other two strategies. In the IDL-BT scheme, the transmitter and receiver independently execute the LBT process first. Then, the transmitter and receiver establish a communication link in the direction with less interference even if this link is not the optimal communication link. In situation 3, the gNB system interferes with the WiGig system but the WiGig system has no interference on the gNB system and situation 4 is opposed. In these two situations, the JOL-BT can still access the spectrum and communicate even if there is interference. So, the access probability and sum rate are the biggest. However, according to the other two schemes, only one system can access the unlicensed spectrum. Therefore, the sum rate of IDL-BT and CO-BT-LBT is lower than that of JOL-BT. Although the access probability and sum rate of the proposed unlicensed spectrum access strategy is no higher than the other two strategies, the proposed spectrum access strategy can solve the false alarm and miss detection problem in the beamforming direction-based millimeter communication with the lower complexity.

In Figure 8, the received power at UE of the proposed spectrum access strategy is compared with the existing spectrum access strategies, i.e., JOL-BT spectrum access strategy and IDL-BT spectrum access strategy. It needs to be pointed out that there is no power control algorithm in this figure. We focus on beam scanning and spectrum sensing. Different spectrum access strategies have different access probabilities and may select different transmit and receive beam pairs to communicate, which are closely related to the received power. From the figure, we can see that the received power under the JOL-BT is the highest. The received power of the proposed spectrum access strategy is relatively lower. That is because, in the JOL-BT scheme, communication always occurs between the transmitter and receiver no matter whether the interference is strong in the communication direction. The transmitter and receiver can jointly select the other direction with weaker interference to communicate. Therefore, the communication exists all the time. In IDL-BT, the transmitter and receiver independently execute the LBT process first. Then, the transmitter and receiver establish a communication link in the direction with less interference. This strategy involves establishing a communication link as long as there is a direction with interference below the threshold even if this link is not the last link. In our proposed spectrum access strategy, beam training is first performed to select the optimal communication link. Then the LBT process is conducted on the selected communication link to detect the interference. If the interference is above the threshold, the communication is interrupted and otherwise, communication is established. Therefore, communication only occurs if there is no interference or very little interference in the communication direction. That is the reason why the received power at the user is relatively lower than the JOL-BT and IDL-BT strategies. However, the complexity of our proposed access strategy is also lower than the other two strategies and the proposed spectrum access strategy can solve the false alarm and miss detection problem in the beamforming direction-based millimeter communication.

Figure 9 shows the sum rate varying with the average SNR under different detection thresholds. We can see that the sum rate with the optimal threshold obtained by the Dinkelbach algorithm achieves the maximal sum rate. The sum rate with the lower threshold has the lowest sum rate. That is because, under the lower interference detection threshold, the channel is detected busy in most cases. Thus, the UE can not access the channel and the two communications can not occur simultaneously, which results in the lowest sum rate. Also, we see that the half of maximal transmit power, which is the cut-off point [23], is not optimal and this case cannot obtain the maximal sum rate.

Figure 10 compares the access probability versus transmit power under different interference thresholds. As we can see, when the interference threshold increases, the access probability rises too. This is because when the interference threshold increases, the UE can tolerate more interference and according to the energy detection criterion, the UE has a higher probability to access the spectrum. However, the higher the interference threshold becomes, the rate of UE is lower due to the lower SINR. From Figure 10, we can also see that the spectrum access probability decreases with the larger transmit power due to that the larger transmit power brings the higher interference to the UE and thus the lower access probability.

Figure 11 compares the spectrum access probability under different situations, i.e., WUE in the main lobe of gNB with LoS link, WUE in the main lobe of gNB with blockage, in the side lobe of gNB with LoS link and in the side lobe of gNB with blockage. From the figure, we can see the access probability of a situation where WUE is in the main lobe of gNB with blockage, is the highest. This is because the probability of WUE falling in the mainbeam of gNB is larger than that of WUE falling in the sidebeam of gNB. The interference of WUE received from the gNB with blockage is lower than that without blockage. The access probability of a situation with WUE in the side lobe of gNB and having an LoS link is the lowest. That is because the probability of WUE falling within the sidebeam is lower than other situations and the interference received by the WUE from the gNB without blockage is higher. Thus, the channel is detected busy by the WUE and to protect the incumbent user, the UE cannot access the unlicensed spectrum.

Figure 12 describes the system sum rate under different situations. As we can see, conditioned on UE and WUE simultaneously transmitting signals, the sum rate of WUE in the side lobe of gNB with blockage is the highest. That is because this case results in the lowest interference received by the WUE from the gNB. In this situation, the WUE has the highest SINR and access probability. According to Shannon capacity $C=p_{a}B{log}_2\left(1+\mathrm{SINR}\right)$ where $p_a$ is the access probability and $\mathrm{SINR}$ is the signal-interference-noise-ratio, the system has the highest sum rate. The WUE in the main lobe of gNB without blockage receives the highest interference and the lowest SINR. Thus, the coexisting system has the lowest sum rate. For the cases of WUE in the main lobe of gNB with blockage and WUE in the side lobe of gNB without blockage, the WUE receives about equal interference, which indicates that the main lobe gain of gNB with blockage is reduced to equal to the small side lobe gain of gNB without blockage. Moreover, when WUE is in the main lobe of gNB with blockage, it can access the unlicensed spectrum with high access probability due to the lower interference. This case can achieve a sum rate of about 2.43 bits/s/Hz higher than WUE in the same beam lobe of gNB but with no blockage.

Figure 13 shows the relationship between the access probability and the sum rate of the coexistence system. As we can see the access probability changes with the system throughput proportionally overall. However, the sum rate of the situation of WUE in the sidebeam of gNB with blockage is the highest and the sum rate of the situation of WUE in the mainbeam of gNB without blockage is the lowest. The reason is easy to see. The WUE in the sidebeam of gNB with blockage has the highest access probability and the lowest interference due to the blockage and thus the highest sum rate. The WUE in the mainbeam of gNB without blockage has the highest interference and lowest SINR compared to the four situations mentioned in Figure 13.

Figure 14 presents the trend of the sum rate with the main lobe beamwidth ${\theta }_{B,W}$. As we can see, when the main lobe beamwidth ${\theta }_{B,W}$ increases, the sum rate of the situation of WUE in the mainbeam without blockage decreases. This is because when the main lobe beamwidth ${\theta }_{B,W}$ of gNB increases, the probability of UE accessing the unlicensed spectrum decreases due to the higher probability of interfering with the WUE, and thus, the sum rate of the coexistence system decreases. In other cases, the trend of the system sum rate changing with the main lobe bandwidth is not significant. This is because an increase in the main lobe bandwidth results in a higher probability of the WUE falling within the main lobe, but the increased main lobe bandwidth also reduces the interference caused to the WUE. The advantages and disadvantages offset each other, resulting in minimal overall change in the sum rate.

7. Conclusions

This study introduces a novel cooperative spectrum sensing strategy for NR-U/WiGig coexistence in UAV communication systems. This method enhances traditional LBT approaches by exploiting beam directionality and effectively mitigates the challenges of hidden and exposed nodes of traditional LBT technology, improving spectrum sharing fairness and efficiency. Our analysis also shows that environmental obstacles, despite attenuating signals, boost system capacity by about 70% by increasing access probabilities by about 60%. Simulation results validate the effectiveness of our strategy in improving spectrum access and performance, even amid physical obstructions. This research advances unlicensed spectrum-sharing techniques, ensuring equitable and optimal utilization of millimeter wave bands in future UAV communication networks.