Multi-Target Sensing with Interference Analysis for the Multi-UAV-Enabled ISAC Network

Abstract

Integrated sensing and communication (ISAC) is recognized as a key technology in the multi-UAV-enabled 6G network. In this paper, we propose a simultaneous sensing and communication method for the multi-UAV network with multiple users and targets. Firstly, we investigate the ISAC channel model for the multiple users and targets, which can be determined by the physical parameters between the UAVs and the users or the targets. Then, we design the ISAC signal for the multi-UAV-enabled network and analyze the interference of the downlink signal for the multi-users and the echo signal for the multi-targets, respectively. On this basis, we further propose a multi-target sensing method with multi-UAV cooperation, where angle division multiple access (ADMA) is exploited to decrease the effect of the multi-user and multi-target interference. Finally, various simulation results are provided to verify the effectiveness of the proposed method.

1. Introduction

With the development of information technologies such as advanced computing, big data, artificial intelligence (AI), blockchain, etc., the next generation of mobile communication technology (6G) will make full use of low, medium, and high spectrum resources to realize the interconnection of everything and collaborative symbiosis [1,2,3,4]. The requirements for the higher information interaction and information collection capability in the future drive the expansion of 6G air interface functions from wireless transmission to wireless sensing [5,6], which makes the communication and sensing functions overlap in the spatiotemporal and frequency domains [7,8]. Integrated sensing and communication (ISAC) realizes the coordination of sensing and communication functions with software and hardware resource sharing and has become a hot signal processing technology for 6G [9,10,11].

UAV has strong mobility and flexible scheduling properties, and task execution efficiency can be further improved via multi-UAV collaboration. Therefore, UAV has become an important platform for the realization of 6G ISAC technology [12,13,14]. The combination of UAV and ISAC can effectively leverage their respective advantages while improving the communication and sensing performance for the multi-UAV-enabled 6G ISAC network [15,16,17,18,19,20,21,22]. On one hand, the integrated ISAC loads can be configured on UAV platform to replace the traditional discrete communication and sensing loads, which can effectively reduce the UAV loads and improve UAV endurance and flexibility. On the other hand, ISAC can realize the full communication coverage and the effective environment sensing by utilizing the flexible deployment of the UAV platform and the collaboration of the multiple UAVs [23,24,25].

The service scenario of the multi-UAV-enabled ISAC network is shown in Figure 1. The multi-UAV ISAC consists of two typical circumstances, namely, communication-aided sensing and sensing-aided communication. On one hand, the communication signal could help user to realize positioning, tracking, and imaging. On the other hand, the sensing results could help communication functions such as beamforming, networking, task deployment, and resource allocation.

The design and transmission of the ISAC signal are the basis of the multi-UAV-enabled 6G network [26,27,28,29]. Therefore, the authors of [30] proposed an integrated frame structure for the transmission of a UAV ISAC signal, which improves the efficiency of UAV sensing and communication. The authors of [31] improved radar target sensing accuracy through the extended Kalman filter (EKF). The authors of [32] proposed an effective ISAC method by utilizing UAV collaborative networking, which analyzed the average mutual interference and communication capacity of the system. The authors of [33] evaluated the interrupt probability of the communication terminal and the discovery probability of the sensing terminal by exploiting the communication-aided sensing method. The authors of [34] developed the channel estimation method for UAV communications with the mmWave large-scale antenna array, where the compressed sensing technology is exploited to reduce pilot overhead. The authors of [35] proposed a new space division multiple access technology for the ISAC network. The authors of [36] proposed a periodic-function-aided ISAC method, where the communication and sensing are performed in different time slots to reduce system overhead and complexity. The authors of [37] investigated the UAV networking design for ISAC to support low-altitude economy, which provides the solid research background of this work. The authors of [38] decomposed the ISAC signal into two parts, namely, the information transmission and target sensing, which improved the task efficiency through optimizing the UAV position and transmission power.

It can be seen that most of the existing works realize ISAC with traditional communication or radar sensing techniques, which might not be applicable for the future multi-UAV-enabled ISAC network with multiple users and targets. The theoretical frameworks for the communication and sensing belong to different branches; therefore, we need to design the proper ISAC framework for the multi-UAV-enabled ISAC network. Moreover, considering the dynamic change in UAV, the new ISAC channel model should be established for the multi-UAV-enabled ISAC network. In addition, the UAV movement and multi-dimension sensing information should be utilized to assist beamforming design, beam tracking, and dynamic target sensing.

In this paper, we consider a multi-UAV-enabled ISAC network where the multiple users and targets coexist, and propose a simultaneous multi-target sensing and multi-user communication method. Firstly, we investigate the channel model for the multi-user communications and multi-target sensing, which can all be determined by the physical parameters between the UAVs and the users, as well as the targets. Then, we propose an simultaneous sensing and communication scheme for the UAV ISAC BS. Specifically, we design the ISAC signal for the multi-UAV-enabled network with multiple users and targets, and analyze the downlink transmission signal for the multi-users and echo signal for multi-targets, respectively. Moreover, a multi-target sensing method is developed with multi-UAV corporation. Due to the coexistence of the multiple users and targets, the interference becomes the dominant factor in the ISAC performance. Therefore, angle division multiple access (ADMA) is exploited to decrease the effect of the multi-user and multi-target interference. Finally, we provide various simulation results to verify the effectiveness of the proposed simultaneous sensing and communication scheme for the multi-UAV-enabled ISAC network. The main contributions are listed as follows.

• We propose an simultaneous sensing and communications scheme for the UAV ISAC BS, and the spectral efficiency of the multi-UAV ISAC network can be greatly enhanced by UAV cooperation.
• We investigate the channel model for the multi-user communications and multi-target sensing, which can all be determined by the physical parameters between the UAVs and the users, as well as the targets.
• We propose a multi-target sensing method with multi-UAV cooperation, where ADMA is exploited to decrease the effect of the multi-user and multi-target interference.

The rest of the paper is organized as follows. The system model, including the sensing and communication channel model for the multiple users and multiple targets, is described in Section 2. The simultaneous sensing and communications scheme for the UAV ISAC BS is presented in Section 3. The multi-target sensing method for the ISAC network is presented in Section 4. The simulations are then displayed in Section 5. Practical limitations and considerations are presented in Section 6. Finally, conclusions are drawn in Section 7.

Notations: Vectors and matrices are denoted by boldface small and capital letters; the transpose, complex conjugate, Hermitian, inverse, and pseudo-inverse of the matrix $\mathbf{A}$ are denoted by ${\mathbf{A}}^T$, ${\mathbf{A}}^{\ast }$, ${\mathbf{A}}^H$, ${\mathbf{A}}^{-1}$ and ${\mathbf{A}}^{†}$, respectively; ⊙ represents the operation of dot product. A list of acronyms is listed in Abbreviations.

2. System Model

We consider a multi-UAV-enabled 6G ISAC network where Q UAVs serve as the aerial ISAC platforms to communicate with V users and detect K targets. The joint sensing and communications can be realized by multi-UAV cooperation. We denote the number of users and targets served by UAV q as $V_q$ and $K_q$. Moreover, each UAV is equipped with two parallel and closely placed uniform linear arrays (ULAs) composed of $N_t$ and $N_r$ antennas for transmitting and receiving signals. The multi-UAV-enabled ISAC network operates in the high frequency band, such as mmWave and Teraherz, and the antenna spacing is set as $d={\displaystyle \frac{\lambda }{2}}$, where $\lambda$ is the wavelength. The multi-UAV-enabled ISAC system is shown in Figure 2. We consider horizontal deployment of ULAs on UAVs, and the steering vectors (AoDs) will change at the same UAV location with different orientations. In this case, the effect of UAV movement and attitude variation can be integrated into the channel modeling. In this paper, we focus our attention on the multi-target sensing for the multi-UAV-enabled ISAC network; therefore, we neglect the effect of different orientations.

The UAV ISAC platform works in the orthogonal frequency division multiplexing (OFDM) modulation, and the bandwidth is denoted as $W=(M-1)\Delta f$, where M is the number of subcarriers, $\Delta f={\displaystyle \frac{B}{M}}$ is the subcarrier interval, and B is the bandwidth. Then, the symbol duration can be derived as $T_s={\displaystyle \frac{1}{\Delta f}}$, while the m-th subcarrier frequency can be expressed as $f_m=f_0+(m-1)\Delta f$, where $f_0$ is the carrier frequency.

The location of the UAV q at the n-th OFDM symbol is denoted as ${\mathbf{p}}_{q,n}^U=[x_{q,n}^U,y_{q,n}^U,h_{q,n}^U]$, while the locations of the user v and the target k are denoted as ${\mathbf{p}}_{v,n}^{US}=[x_{v,n}^{US},y_{v,n}^{US},0]$ and ${\mathbf{p}}_{k,n}^T=[x_{k,n}^T,y_{k,n}^T,0]$, respectively. Each UAV could adjust its location to serve the users and targets in the specific area, and the multiple UAVs fulfill the sensing and communication tasks cooperatively.

2.1. The Channel Model for the Multi-UAV-Enabled Communications

Denote the state of the v-th moving target at the n-th OFDM symbol time as $(r_n^{s,v},{\theta }_n^{s,v},{\mu }_n^{s,v})$, where $r_n^{s,k}$ is the distance between the UAV ISAC BS and user, ${\theta }_n^{s,v}$ is the angle of the departure (AOD), and ${\mu }_n^{c,v,q}$ is the radial velocity with respect to the UAV. The physical parameters of the UAV q can be derived as

$$\begin{array}{cc}\hfill & r_n^{s,v}=\sqrt{{\left|{\mathbf{p}}_{q,n}^U-{\mathbf{p}}_{v,n}^{US}\right|}^2},\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill & {\theta }_n^{s,v}=arcsin{\displaystyle \frac{\left|y_{q,n}^U-y_{v,n}^{US}\right|}{r_n^{s,v}}}.\hfill \end{array}$$

(2)

For UAV communications, there are fewer scattered objects in the air. Therefore, the LoS path is dominated, while the NLoS path can be neglected. Then, the channel between the v-th user and the q-th UAV ISAC BS on the n-th OFDM symbol at the m-th subcarrier is

$${\mathbf{h}}_{n,m}^{c,v,q}={\alpha }_{n,m}^{c,v,q}{e}^{j2\pi {\displaystyle \frac{{\mu }_n^{c,v,q}}{\lambda }}(n-1)T_s}{e}^{-j{\displaystyle \frac{2\pi f_m{r}_n^{c,v,q}}{c}}}\mathbf{a}\left({\theta }_n^{c,v,q}\right),$$

(3)

where ${\alpha }_{n,m}^{c,v,q}$ is the channel fading factor, c is the velocity of light, and $\mathbf{a}\left({\theta }_n^{c,v,q}\right)$ is the array steering vector, which is given by

$$\mathbf{a}\left({\theta }_n^{c,v,q}\right)={\left[1,e^{j2\pi f_0{\displaystyle \frac{dsin{\theta }_n^{c,v,q}}{c}}},\cdots ,e^{j2\pi f_0{\displaystyle \frac{(N_t-1)dsin{\theta }_n^{c,v,q}}{c}}}\right]}^T.$$

(4)

According to Equation (3), the channel model for the multi-UAV communications can be determined by the physical parameters, such as ${\theta }_n^{c,v,q}$, ${\mu }_n^{c,v,q}$, $r_n^{c,v,q}$, and ${\alpha }_{n,m}^{c,v,q}$.

2.2. The Channel Model for the Multi-UAV-Enabled Sensing

Denote the state of the k-th moving target at the n-th OFDM symbol as $(r_n^{s,k},{\theta }_n^{s,k},{\mu }_n^{s,k})$, where $r_n^{s,k}$ is the distance between the UAV ISAC BS and target, ${\theta }_n^{s,k}$ is the AOD, and ${\mu }_n^{s,k,q}$ is the radial velocity with respect to the UAV. Since the transmit and receive ULAs are parallel, the angle of the arrival (AOA) of the receive array is the same as the AOD. Then, the echo channel between the k-th moving target and the q-th UAV on the n-th OFDM symbol at the m-th subcarrier can be derived as

$$\begin{array}{cc}\hfill {\mathbf{H}}_{n,m}^{s,k,q}=& {\alpha }_{n,m}^{s,k,q}{e}^{j4\pi {\displaystyle \frac{{\mu }_t^{s,k,q}}{\lambda }}(n-1)T_s}{e}^{-j{\displaystyle \frac{4\pi f_m{r}_n^{s,k,q}}{c}}}\mathbf{a}\left({\theta }_n^{s,k,q}\right){\mathbf{b}}^T\left({\theta }_n^{s,k,q}\right),\hfill \end{array}$$

(5)

where $\mathbf{b}\left({\theta }_n^{s,k,q}\right)$ is the array steering vector, which is given by

$$\mathbf{b}\left({\theta }_n^{s,k,q}\right)={\left[1,e^{j2\pi f_0{\displaystyle \frac{dsin{\theta }_n^{s,k,q}}{c}}},\cdots ,e^{j2\pi f_0{\displaystyle \frac{(N_r-1)dsin{\theta }_n^{s,k,q}}{c}}}\right]}^T,$$

(6)

and ${\alpha }_{n,m}^{s,k,q}$ is the sensing channel fading factor.

According to Equation (5), the channel model for the multi-UAV sensing can be determined by the physical parameters, such as the ${\theta }_n^{s,k,q}$, ${\mu }_n^{s,k,q}$, $r_n^{s,k,q}$, and ${\alpha }_{n,m}^{s,v,q}$. As with the noncooperative target, we need to estimate ${\theta }_n^{s,k,q}$, ${\mu }_n^{s,k,q}$, and $r_n^{s,k,q}$ for the target sensing.

3. Multi-Target Sensing and Multi-User Communications with Interference Analysis

3.1. Downlink Transmission of the ISAC Signal

The essence of simultaneous sensing and communication is to realize position, tracking, and communications enhancement by fully exploiting the ISAC signals. The frame structure of the multi-UAV-enabled ISAC network is shown in Figure 3, where DL-CS represents the downlink ISAC signal transmission, UL-C represents the uplink communications, and UAV T and R represent the transmit and receive procedure of the UAV BS. Each UAV transmits the ISAC signal to realize the dual functions of the communications and sensing in the downlink. The users receive the ISAC signal in the downlink and transmit the signal to UAV BS in the uplink. The UAV ISAC BS receives the echo signal for sensing and receives the user signal for the uplink data transmission. It is worth mentioning that there is an guard interval between the echo signal and the UL signal to decrease the inteference between the sensing and communication.

Denote the n-th transmission symbol of the UAV q at the m-th subcarrier as ${\mathbf{x}}_{n,m}^q$, which can be denoted as

$$\begin{array}{cc}{\mathbf{x}}_{n,m}^q\hfill & ={\displaystyle \sum _{v=1}^{V_q}}{\displaystyle \frac{p_{n,m}^{c,v,q}}{\sqrt{N_t}}}{\mathbf{w}}_{n,m}^{c,v,q}{s}_{n,m}^{c,v,q}+{\displaystyle \sum _{k=1}^{K_q}}{\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}\hfill \\ \hfill & =[{\mathbf{w}}_{n,m}^{c,1,q},\dots ,{\mathbf{w}}_{n,m}^{c,V_q,q},{\mathbf{w}}_{n,m}^{s,1,q},\dots ,{\mathbf{w}}_{n,m}^{s,K_q,q}]{[s_{n,m}^{c,1,q},\dots ,s_{n,m}^{c,V_q,q},s_{n,m}^{s,1,q},\dots ,s_{n,m}^{s,K_q,q}]}^H\odot {\mathbf{p}}_{q,n,m}^{ISAC}\hfill \\ \hfill & ={\mathbf{W}}_{n,m}^q{\mathbf{S}}_{n,m}^q\odot {\mathbf{p}}_{q,n,m}^{ISAC},\hfill \end{array}$$

(7)

where ${\mathbf{w}}_{n,m}^{c,v,q}$ and $s_{n,m}^{c,v,q}$ are the beamforming vector and the symbol for the communications of the user v, while ${\mathbf{w}}_{n,m}^{s,k,q}n$ and $s_{n,m}^{s,k,q}$ are the beamforming vector and the symbol for the sensing of the target k. Moreover, ${\mathbf{W}}_{n,m}^q=[{\mathbf{w}}_{n,m}^{c,1,q},\dots ,{\mathbf{w}}_{n,m}^{c,V_q,q},{\mathbf{w}}_{n,m}^{s,1,q},\dots ,{\mathbf{w}}_{n,m}^{s,K_q,q}]$ is the integrated beamforming matrix, ${\mathbf{S}}_{n,m}^q={[s_{n,m}^{c,1,q},\dots ,s_{n,m}^{c,V_q,q},s_{n,m}^{s,1,q},\dots ,s_{n,m}^{s,K_q,q}]}^H$ is the symbol vector, and ${\mathbf{p}}_{n,m,q}^{ISAC}={[p_{n,m}^{c,1,q},\dots ,p_{n,m}^{c,V,q},p_{n,m}^{s,1,q},\dots ,p_{n,m}^{s,K,q}]}^H$ is the power allocation vector.

According to channel model (3) and the ISAC signal (7), the received signal of user v from the UAV q in the downlink can be derived as

$$\begin{array}{cc}\hfill y_{n,m}^{c,v,q}& ={\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{W}}_{n,m}^q{\mathbf{S}}_{n,m}^q\odot {\mathbf{p}}_{n,m,q}^{ISAC}+{\mathit{\omega }}_{n,m}^{c,v,q}\hfill \\ \hfill & ={\displaystyle \frac{p_{n,m}^{c,v,q}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v,q}{s}_{n,m}^{c,v,q}+\sum _{v^{\prime }=1(v^{\prime }\ne v)}^{V_q}{\displaystyle \frac{p_{n,m}^{c,v^{\prime },q}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v^{\prime },q}{s}_{n,m}^{c,v^{\prime },q}+\sum _{k=1}^{K_q}{\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}+{\mathit{\omega }}_{n,m}^{c,v,q},\hfill \end{array}$$

(8)

where ${\mathit{\omega }}_{n,m}^{c,v,q}$ is the zero-mean additive complex Gaussian white noise with variance ${{\sigma }_{n,m}^{c,v,q}}^2$. Moreover, ${\sum }_{v^{\prime }=1(v^{\prime }\ne v)}^{V_q}{\displaystyle \frac{p_{n,m}^{c,v,q^{\prime }}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v^{\prime },q}{s}_{n,m}^{c,v^{\prime },q}$ is the interference due to the coexistence of the multiple users, while ${\sum }_{k=1}^{K_q}{\displaystyle \frac{p_{n,m}^{s,k}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}$ is the sensing interference due to the coexistence of the sensing and communication function.

Under the configuration of the massive array antenna and the high frequency band, the UAV ISAC BS can generate a high directional beam towards both the users and the targets. According to the angle domain signal processing scheme, the beamforming vector for the user v can be expressed as ${\mathbf{w}}_{n,m}^{c,v,q}=\mathbf{a}\left({\theta }_n^{c,v,q}\right)$, while the beamforming vector for the target v can be expressed as ${\mathbf{w}}_{n,m}^{s,k,q}=\mathbf{a}\left({\theta }_n^{s,k,q}\right)$.

The signal to the interference plus noise ratio (SINR) for the user v can be derived as

$$\begin{array}{cc}\hfill & {\mathrm{SIN}\mathrm{R}}_{n,m}^{c,v,q}=\hfill \\ \hfill & {\displaystyle \frac{\mathbb{E}\left\{{\left|p_{n,m}^{c,v}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v}{s}_{n,m}^{c,v,q}\right|}^2\right\}}{\mathbb{E}\left\{{\left|{\sum }_{v^{\prime }=1(v^{\prime }\ne v)}^V{p}_{n,m}^{c,v^{\prime },q}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v^{\prime },q}{s}_{n,m}^{c,v^{\prime },q}\right|}^2\right\}+\mathbb{E}\left\{{\left|{\sum }_{k=1}^K{p}_{n,m}^{s,k,q}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}\right|}^2\right\}+{N_t{\sigma }_{n,m}^{c,v,q}}^2}}.\hfill \end{array}$$

(9)

Then, the downlink average achievable sum rate (AASR) can be derived as

$$\begin{array}{c}\hfill {\mathcal{R}}_{n,m}^{c,q}={\displaystyle \frac{1}{V_q}}\sum _{v=1}^{V_q}10\log \left(1+{\mathrm{SINR}}_{n,m}^{c,v,q}\right).\end{array}$$

(10)

According to Equation (9), the main interference for the downlink transmission is the multi-user interference and the multi-target interference. The interference from the user $v^{\prime }$ can be calculated as

$$\begin{array}{cc}\hfill {\displaystyle \frac{p_{n,m}^{c,v^{\prime },q}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v^{\prime },q}{s}_{n,m}^{c,v^{\prime },q}& ={\displaystyle \frac{p_{n,m}^{c,v^{\prime },q}{s}_{n,m}^{c,v^{\prime },q}}{\sqrt{N_t}}}\times \sum _{n=0}^{N_t-1}{e}^{{\displaystyle \frac{j2\pi n{f}_{0}d}{c}}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{c,v^{\prime },q})}\hfill \\ \hfill & ={\displaystyle \frac{\mathrm{Const}}{\sqrt{N_t}}}{\displaystyle \frac{sin\frac{\pi N_t{f}_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{c,v^{\prime },q})}{sin\frac{\pi f_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{c,v^{\prime },q})}}.\hfill \end{array}$$

(11)

When $N_t\to \infty$, the interference from the user $v^{\prime }$ would tend towards 0, and therefore, the multi-user interference can be neglected for the UAV ISAC system with a massive antenna array. However, when the value of $N_t$ is finite, the multi-user interference cannot be neglected for the UAV ISAC system. In particular, when the value of ${\theta }_n^{c,v,q}$ is close to the value of ${\theta }_n^{c,v^{\prime },q}$, there would be a large amount of interference.

Similar to the analysis of the multi-user interference, the multi-target interference can be derived as

$$\begin{array}{cc}\hfill {\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{h}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}& ={\displaystyle \frac{p_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}}{\sqrt{N_t}}}\times \sum _{n=0}^{N_t-1}{e}^{{\displaystyle \frac{j2\pi n{f}_{0}d}{c}}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{s,k,q})}\hfill \\ \hfill & ={\displaystyle \frac{\mathrm{Const}}{\sqrt{N_t}}}{\displaystyle \frac{sin\frac{\pi N_t{f}_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{s,k,q})}{sin\frac{\pi f_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{s,k,q})}}.\hfill \end{array}$$

(12)

When $N_t\to \infty$, the interference from the target k would tend towards 0, and therefore, the multi-target interference can be neglected for the UAV ISAC system with a massive antenna array. However, when the value of $N_t$ is finite, the multi-target interference cannot be neglected for the UAV ISAC system, and the interference is related to the AOD value of the target.

Different from the existing works [30,31,32,33], the ISAC signal in (7) is designed for multiple users and targets, and an explicit example is illustrated in Figure 4. There are three targets and three users in the network, and the AOD of the users and targets are $[15,61,75]$ degrees and $[5,32,60]$ degrees, respectively. The transmitted beams for the communication and sensing are shown in subfigures (a) and (b). Since the AOD of the second user is 61 degrees and close to the AOD of the third target (60 degrees), there will be a large amount of interference when the target and user are simultaneous in the same group, which is shown in subfigure (c). Therefore, the second user should be assigned to another UAV to decrease the interference. Then, the ISAC signal for the current UAV can be derived, which is shown in subfigure (d).

3.2. Echo Signal

The echo signal at the UAV ISAC BS can be derived as

$$\begin{array}{cc}\hfill {\mathbf{y}}_{n,m}^{s,k,q}& ={\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{W}}_{n,m}^q{\mathbf{S}}_{n,m}^q\odot {\mathbf{p}}_{n,m,q}^{ISAC}+{\mathit{\omega }}_{n,m}^{s,k,q}\hfill \\ \hfill & ={\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}+\sum _{k^{\prime }=1,k^{\prime }\neg k}^{K_q}{\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k}{s}_{n,m}^{s,k,q}\hfill \\ \hfill & +\sum _{v=1}^{V_q}{\displaystyle \frac{p_{n,m}^{c,v,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v,q}{s}_{n,m}^{c,v,q}+{\mathit{\omega }}_{n,m}^{s,k,q},\hfill \end{array}$$

(13)

where ${\mathit{\omega }}_{n,m}^{s,k}$ is the zero-mean additive complex Gaussian white noise with variance ${{\sigma }_{s,k}^{c,v}}^2$. Moreover, ${\sum }_{k^{\prime }=1,k^{\prime }\neg k}^K{\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k}{s}_{n,m}^{s,k,q}$ is the interference due to the multi-target sensing, while ${\sum }_{v=1}^V{\displaystyle \frac{p_{n,m}^{c,v,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v,q}{s}_{n,m}^{c,v,q}$ is the communication interference due to the coexistence of the sensing and communication function.

Similar to the traditional angle domain signal processing methods [37], the movement related parameters, namely, ${\theta }_n^{c,v,q}$, ${\mu }_n^{c,v,q}$ and $r_n^{c,v,q}$, can be derived by the movement state estimation, while the channel gain information can be estimated by a few pilots for the cooperative user. Therefore, the channel can be reconstructed with the estimated parameters, and then the communication interference ${\sum }_{v=1}^V{\displaystyle \frac{p_{n,m}^{c,v,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{c,v,q}{\mathbf{w}}_{n,m}^{c,v,q}{s}_{n,m}^{c,v,q}$ can be compensated, and the echo signal can be simplified as

$$\begin{array}{cc}\hfill {\mathbf{y}}_{n,m}^{s,k,q}=& {\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}+\sum _{k^{\prime }=1,k^{\prime }\ne k}^{K_q}{\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k}{s}_{n,m}^{s,k,q}+{\mathit{\omega }}_{n,m}^{s,k,q}.\hfill \end{array}$$

(14)

Denote the receive beamforming vector for the target k as

$$\begin{array}{c}\hfill {\mathbf{w}}_{n,m}^{r,s,k,q}={\left[1,e^{j2\pi f_0{\displaystyle \frac{dsin{\theta }_n^{s,k,q}}{c}}},\cdots ,e^{j2\pi f_0{\displaystyle \frac{(N_r-1)dsin{\theta }_n^{s,k,q}}{c}}}\right]}^T,\end{array}$$

(15)

where is ${\theta }_n^{s,k,q}$ is the AOA of the echo signal.

The equivalent echo signal can be represented as

$$\begin{array}{cc}\hfill {\widehat{y}}_{n,m}^{s,k,q}& ={\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t{N}_r}}}{{\mathbf{w}}_{n,m}^{r,s,k,q}}^H{\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}+\hfill \\ \hfill & \sum _{k^{\prime }=1,k^{\prime }\ne k}^{K_q}{\displaystyle \frac{p_{n,m}^{s,k^{\prime },q}}{\sqrt{N_t{N}_r}}}{{\mathbf{w}}_{n,m}^{r,s,k,q}}^H{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k^{\prime },q}{s}_{n,m}^{s,k^{\prime },q}+{\widehat{\mathit{\omega }}}_{n,m}^{s,k,q},\hfill \end{array}$$

(16)

where ${\widehat{\mathit{\omega }}}_{n,m}^{s,k,q}$ is the zero-mean additive complex Gaussian white noise with variance ${{\sigma }_{n,m}^{s,k,q}}^2$.

Then, SNR for sensing can be derived as

$$\begin{array}{c}\hfill {\mathrm{SIN}\mathrm{R}}_{n,m}^{s,k,q}={\displaystyle \frac{\mathbb{E}\left\{{\left|p_{n,m}^{s,k,q}{{\mathbf{w}}_{n,m}^{r,s,k,q}}^H{\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}\right|}^2\right\}}{\mathbb{E}\left\{{\left|{\sum }_{k^{\prime }=1,k^{\prime }\neg k}^K{p}_{n,m}^{s,k,q}{{\mathbf{w}}_{n,m}^{r,s,k^{\prime },q}}^H{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}\right|}^2\right\}+{N_r{N}_t{\sigma }_{n,m}^{s,k,q}}^2}}.\end{array}$$

(17)

For target detection, the output SINR is positively proportional to the detection probability with a fixed probability of false alarm, which is an important metric of target sensing and determines the detection ability, measurement accuracy, and tracking performance of sensing. Similar to the formation of the AASR for communications, the AASR for sensing can be derived as

$$\begin{array}{c}\hfill {\mathcal{R}}_{n,m}^{s,q}={\displaystyle \frac{1}{K_q}}\sum _{k=1}^{K_q}10\log \left(1+{\mathrm{SINR}}_{n,m}^{s,k,q}\right).\end{array}$$

(18)

According to Equation (16), the main interference for the downlink transmission is the multi-target interference. The sensing interference from target $k^{\prime }$ can be derived as

$$\begin{array}{c}\hfill {\displaystyle \frac{p_{n,m}^{s,k^{\prime },q}}{\sqrt{N_t{N}_r}}}{{\mathbf{w}}_{n,m}^{r,s,k,q}}^H{\mathbf{H}}_{n,m}^{s,k^{\prime },q}{\mathbf{w}}_{n,m}^{s,k^{\prime },q}{s}_{n,m}^{s,k^{\prime },q}={\displaystyle \frac{\mathrm{Const}}{\sqrt{N_t{N}_r}}}\mathcal{F}({\theta }_n^{s,k,q},{\theta }_n^{s,k^{\prime },q}),\end{array}$$

(19)

where $\mathcal{F}({\theta }_n^{s,k,q},{\theta }_n^{s,k^{\prime },q})$ is given by

$$\begin{array}{c}\hfill \mathcal{F}({\theta }_n^{s,k,q},{\theta }_n^{s,k^{\prime },q})={\displaystyle \frac{sin\frac{\pi N_t{f}_{0}d}{c}(sin{\theta }_n^{s,k,q}-sin{\theta }_n^{s,k^{\prime },q})}{sin\frac{\pi f_{0}d}{c}(sin{\theta }_n^{s,k,q}-sin{\theta }_n^{s,k^{\prime },q})}}{\displaystyle \frac{sin\frac{\pi N_r{f}_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{c,v^{\prime },q})}{sin\frac{\pi f_{0}d}{c}(sin{\theta }_n^{c,v,q}-sin{\theta }_n^{c,v^{\prime },q})}}.\end{array}$$

(20)

When $N_t\to \infty$ or $N_r\to \infty$, the interference from the target $k^{\prime }$ would tend towards 0, and the multi-target interference can be neglected for the UAV ISAC system with a massive antenna array. However, when the values of both $N_t$ and $N_r$ are finite, the multi-target interference cannot be neglected. In particular, when the value of ${\theta }_n^{s,k,q}$ is close to the value of ${\theta }_n^{s,k^{\prime },q}$, there will be a large amount of interference.

4. Multi-Target Sensing with Multi-UAV Cooperation

The massive antenna array could provide a large amount of spatial gain. However, according to Equation (19), when the directions of the users or targets are close to each other, there will be a lot of interference. In this case, the multiple UAVs can cooperatively sense the targets and communicate with the users. Specifically, the targets and users could be roughly allocated into several groups, and users and targets in the same group have different DOAs to decrease the interference.

We take UAV q as an example and denote the target and user set of UAV q and the whole target set as ${\mathcal{K}}_q$ and $\mathcal{K}$, respectively. Then, it holds that $\mathcal{K}={\mathcal{K}}_1\cup {\mathcal{K}}_2\cup \cdots \cup {\mathcal{K}}_Q$, ${\mathcal{K}}_i\cap {\mathcal{K}}_j=\varnothing$. Besides $\forall i,j\in {\mathcal{K}}_q$, there is $|{\theta }_n^{s\left(c\right),j,q}-{\theta }_n^{s\left(c\right),i,q}|\ge \delta \theta$. An explicit example is shown in Figure 5, where the blue beam is the communication beam and the red beam is the sensing beam. The proposed multi-target sensing method can be viewed as an extension of ADMA in the multi-UAV-enabled ISAC network. Under the ADMA sensing scheme, the sensing interference in Equation (16) would be small.

The prior value of ${\theta }_n^{s,k,q}$ can be derived from the traditional beam sweeping method [39,40,41,42]. Specifically, we denote the angle range of the target as ${\theta }_{min},{\theta }_{max}$, and the beam sweeping set can be expressed as

$$\begin{array}{c}\hfill {\theta }_i={\theta }_{min}+i\Delta ,i=0,1,\dots ,I-1,\end{array}$$

(21)

where $\Delta ={\displaystyle \frac{{\theta }_{max}-{\theta }_{min}}{I}}$ is the interval of the beam sweeping and I is the dimension of the beam sweeping set.

After beam sweeping, the echo signal power vector can be derived as

$$\begin{array}{c}\hfill {\mathbf{Y}}_{n,m}^{s,k,q}=[{\widehat{y}}_{n,m,1}^{s,k,q},\dots ,{\widehat{y}}_{n,m,I}^{s,k,q}].\end{array}$$

(22)

Moreover, according to Equation (16), the echo signal can be further expressed as

$$\begin{array}{c}\hfill {\widehat{y}}_{n,m}^{s,k,q}\approx {\alpha }_{n,m}^{s,k,q}{e}^{j4\pi {\displaystyle \frac{{\mu }_t^{s,k,q}}{\lambda }}(n-1)T_s}{e}^{-j{\displaystyle \frac{4\pi f_m{r}_n^{s,k,q}}{c}}}{s}_{n,m}^{s,k,q}+{\widehat{\mathit{\omega }}}_{n,m}^{s,k,q}.\end{array}$$

(23)

Then, the index of the maximum power in ${\mathbf{Y}}_{n,m}^{s,k,q}$ is the AOA estimation of the target. We stack ${\widehat{y}}_{n,m}^{s,k,q}$ to form the matrix ${\mathbf{Y}}^{s,k,q}\in {\mathcal{C}}^{N\times M}$, and it holds that

$$\begin{array}{cc}\hfill {\mathbf{Y}}^{s,k,q}=& {\alpha }_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}\left[\begin{array}{c}{e}^{j4\pi {\displaystyle \frac{{\mu }_t^{s,k,q}}{\lambda }}0T_s}\\ ⋮\\ e^{j4\pi {\displaystyle \frac{{\mu }_t^{s,k,q}}{\lambda }}(N-1)T_s}\end{array}\right]\left[e^{-j{\displaystyle \frac{4\pi f_0{r}_n^{s,k,q}}{c}}},\cdots ,e^{-j{\displaystyle \frac{4\pi f_M{r}_n^{s,k,q}}{c}}}\right]+{\mathbf{\Omega }}^{s,k,q},\hfill \end{array}$$

(24)

where ${\mathbf{\Omega }}^{s,k,q}$ is the noise stacked by ${\widehat{\mathit{\omega }}}_{n,m}^{s,k,q}$.

We can see that the target power is located in a small region in the Doppler and delay domain. Moreover, when $M\to \infty$ and $N\to \infty$, the Doppler–delay domain sensing signal ${\mathbf{F}}_N^H{\mathbf{Y}}^{s,k,q}{\mathbf{F}}_M^{★}$ is a sparse matrix, and the non-zero values are determined by the Doppler shift ${\mu }_t^{s,k,q}$ and the distance $r_n^{s,k,q}$, where ${\mathbf{F}}_N$ and ${\mathbf{F}}_M$ are the DFT matrix with dimensions $N\times N$ and $M\times M$ and the $(p,q)-th$ element is given by ${\left[{\mathbf{F}}_M\right]}_{p,q}\triangleq e^{-j{\displaystyle \frac{2\pi }{M}}pq}/\sqrt{M}$. However, when the values of M and N are finite in practice, the region of the non-zero values will be expanded due to the power leakage effect.

Denote

$$\begin{array}{c}\hfill {\mathbf{\Psi }}_M(\Delta {\mu }^{s,k,q})=\mathrm{diag}\left(1,e^{j\Delta {\mu }^{s,k,q}},\dots ,e^{j(M-1)\Delta {\mu }^{s,k,q}}\right),\end{array}$$

(25)

$$\begin{array}{c}\hfill {\mathbf{\Psi }}_N(\Delta r^{s,k,q})=\mathrm{diag}\left(1,e^{j\Delta r^{s,k,q}},\dots ,e^{j(N-1)\Delta r^{s,k,q}}\right),\end{array}$$

(26)

as the Doppler rotation matrix and the delay rotation matrix, respectively, where $\Delta {\mu }^{s,k,q}={\displaystyle \frac{2\pi }{M}}\left|{\displaystyle \frac{2M{T}_s{\mu }_t^{s,k,q}}{\lambda }}-\lceil {\displaystyle \frac{2M{T}_s{\mu }_t^{s,k,q}}{\lambda }}\rfloor \right|$ and $\Delta r^{s,k,q}={\displaystyle \frac{2\pi }{N}}\left|{\displaystyle \frac{2N\Delta f{r}_n^{s,k,q}}{c}}-\lceil {\displaystyle \frac{2N\Delta f{r}_n^{s,k,q}}{c}}\rfloor \right|$. Moreover, $\Delta {\mu }^{s,k,q}$ and $\Delta r^{s,k,q}$ can be derived by searching within the sections $[0,{\displaystyle \frac{2\pi }{M}})$ and $[0,{\displaystyle \frac{2\pi }{N}})$, respectively. Then, the Doppler–delay rotation can be exploited to focus the signal power on one entry, which is given by

$$\begin{array}{cc}\hfill {\mathbf{G}}^{s,k,q}& ={\mathbf{F}}_N^H{\mathbf{\Psi }}_M(\Delta {\mu }^{s,k,q}){\mathbf{Y}}^{s,k,q}{\mathbf{\Psi }}_N(\Delta r^{s,k,q}){\mathbf{F}}_M^{★}\hfill \\ \hfill & ={\alpha }_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}.\hfill \end{array}$$

(27)

According to the index of the maximum power in ${\mathbf{G}}^{s,k,q}$ and the Doppler–delay rotation parameters, we could derive the estimated value of the Doppler shift ${\mu }^{s,k,q}$ and the distance $r^{s,k,q}$ as

$$\begin{array}{c}\hfill {\widehat{\mu }}^{s,k,q}={\displaystyle \frac{2\pi m\lambda \pm M\Delta {\mu }^{s,k,q}\lambda }{4\pi M{T}_s}},\end{array}$$

(28)

$$\begin{array}{c}\hfill {\widehat{r}}^{s,k,q}={\displaystyle \frac{2\pi nc\pm Nc\Delta r^{s,k,q}}{4\pi N\Delta f}}.\end{array}$$

(29)

The concrete steps of the multi-target sensing are shown in the following algorithm (Algorithm 1). As with the high mobility, the parameter of the targets would vary frequently and the total overhead would increase. With the derived state in Equations (28) and (29) and ${\widehat{\theta }}_n^{s,k,q}$, the one-step prediction can be derived from the Kalman filter to decrease the training overhead. The proposed scheme incurs multi-faceted signaling overhead, primarily due to the beam acquisition, ongoing channel and target parameter estimation, and the necessary coordination between UAVs to manage interference.

(1) Beam Acquisition: The paper proposes a beam sweeping method where the UAV scans the angular range ${\theta }_{min},{\theta }_{max}$ in steps of $\Delta$ (Equation (21)). This process consumes time and spectral resources proportional to the number of beams in the sweeping codebook.

(2) UAV Coordination and Grouping: The multi-UAV cooperation scheme requires grouping users and targets such that their angles are separated by at least $\mathsf{\delta }$$\mathsf{\theta }$. This implies a need for inter-UAV communication to coordinate allocation of users/targets to specific UAVs $K_q,V_q$ and exchange of AOD information for interference management. This creates a backhaul signaling overhead between the UAVs, scaling with the number of UAVs Q and the dynamics of the environment.

(3) Parameter Estimation for Sensing: For sensing non-cooperative targets, the UAV must estimate parameters $\theta ,\mu ,r$. This is achieved by processing the echo of the dedicated sensing signal $s^{s,k,q}$. The resource cost here is the power and bandwidth allocated to these sensing streams, which could otherwise be used for communication.

Algorithm 1 Multi-Target Sensing with Multi-UAV Corporation

Step 1: Initialization: the multi-targets are allocated into different groups by the multi-UAV deployment and trajectory adjustment, and each group meets $\mathcal{K}={\mathcal{K}}_1\cup {\mathcal{K}}_2\cup \dots \cup {\mathcal{K}}_Q$, ${\mathcal{K}}_i\cap {\mathcal{K}}_j=\varnothing$, $\forall i,j\in {\mathcal{K}}_q$. Step 2: Beam sweeping: denote the beam sweeping set as ${\theta }_i={\theta }_{min}+i\Delta ,i=0,1,\dots ,I-1$, and meanwhile, design the transmit and receive beamforming vector with the directions of the beam sweeping. Step 3: Echo signal receive: the q-th UAV receives the echo signal as ${\mathbf{y}}_{n,m}^{s,k}={\displaystyle \frac{p_{n,m}^{s,k,q}}{\sqrt{N_t}}}{\mathbf{H}}_{n,m}^{s,k,q}{\mathbf{w}}_{n,m}^{s,k,q}{s}_{n,m}^{s,k,q}+{\mathit{\omega }}_{n,m}^{s,k,q}$. Step 4: The AOA of the target: according to the echo signal power vector ${\mathbf{Y}}_{n,m}^{s,k,q}=[{\widehat{y}}_{n,m,1}^{s,k,q},\dots ,{\widehat{y}}_{n,m,I}^{s,k,q}]$, derive the AOA set of the targets served by UAV q. Step 5: Sensing the Doppler and distance of each target: as with target k, derive the equivalent echo signal as ${\mathbf{Y}}^{s,k,q}$; then, the coarse estimation of the Doppler and distance can be derived from ${\mathbf{F}}_N^H{\mathbf{Y}}^{s,k,q}{\mathbf{F}}_M^{★}$. Step 6: Doppler and distance rotation: according to ${\mathbf{G}}^{s,k,q}$, ${\mathbf{\Psi }}_M(\Delta {\mu }^{s,k,q})$ and ${\mathbf{\Psi }}_N(\Delta r^{s,k,q})$ are designed to focus the signal power on one entry. Step 7: The estimated value of the Doppler shift and the distance can be derived as ${\widehat{\mu }}^{s,k,q}$ and ${\widehat{r}}^{s,k,q}$ according to Equations (28) and  (29).

5. Simulations and Results

In this section, we provide various simulation results to verify the effectiveness of the proposed method. We consider the multi-UAV-enabled 6G ISAC network, where $Q=3$ UAVs serve as the aerial ISAC platform to communicate with $V=9$ users and detect $K=9$ targets. The numbers of transmit and receive antennas are $N_t=128$ and $N_r=64$, respectively, and the carrier frequency is set as $f=60$ GHz with bandwidth $W=600$ MHz. The detailed parameter set can be seen in

Table 1. The parameter set.

Parameter	Q	V	K	Nt	Nr	f	W
value	3	9	9	128	64	60 GHz	600 MHz

.

Figure 6 shows the ISAC signal for the simultaneous sensing and communications. As is discussed in Section 3, the users and targets should be kept away from each other to decrease the user interference. We can see that when the guard interval is set to a larger value, the beam directions of the users and targets can be easily distinguished. Therefore, users and targets should be allocated into different groups to improve the spectral efficiency.

Figure 7 shows AASR of the proposed method, where C represents the communication and S represents the sensing, which can be viewed as the baseline comparison method of the proposed method. It can be seen that the sum rate becomes larger with the increase in SNR. Moreover, we can also find that both the communication interference and the sensing interference degrade the system performance. Therefore, when the guard interval is increased from $\delta \theta =1$ to $\delta \theta =10$, the performance of the sum rate becomes better. Moreover, due to the large spatial gain of the massive MIMO, the sum rate is also increased when the number of antennas becomes larger. The results verify that when $N_t\to \infty$, the interference from the target k would tend towards 0; therefore, the multi-target interference can be neglected for the UAV ISAC system with a massive antenna array. However, when the value of $N_t$ is finite, the multi-target interference cannot be neglected for the UAV ISAC system.

Figure 8 shows AASR for sensing. We can find that the AASR becomes larger with the increase in SNR. Moreover, the communication interference degrades the sensing performance. When the communication interference is compensated, the AASR for sensing becomes larger. Moreover, due to the large spatial gain of the massive MIMO, when antenna number becomes larger, the performance of the AASR is also increased, which verifies that when $N_t\to \infty$ or $N_r\to \infty$, the interference from the target $k^{\prime }$ would tend towards 0; therefore, the multi-target interference can be neglected for the UAV ISAC system with a massive antenna array. However, when the values of both $N_t$ and $N_r$ are finite, the multi-target interference cannot be neglected.

The results of target sensing after DFT are shown in Figure 9, while the parameter estimation results of the Doppler and delay are shown in Figure 10. We can find that there are three targets after DFT, which verifies the effectiveness of the proposed method. Then, the target parameters can be estimated by the Doppler–delay domain echo analysis. With the increase in SNR, MSE is decreased. Moreover, there are error floors for the estimation of the Doppler and delay that arise from the finite number of the subcarrier and time slot. Therefore, when the number of subcarriers becomes larger, the precision of the delay estimation becomes better. Additionally, the proposed method is superior to the benchmark, which further verifies the effectiveness of the proposed method.

6. Practical Considerations

The practical considerations of real-world scenarios and the necessary limitations for the proposal are listed as follows.

• Limited Endurance and Flight Time: Battery technology severely restricts UAV flight time (typically to under an hour for many commercial models). This necessitates frequent landings for battery swaps or recharging, interrupting communication services.
• Payload and Energy Constraints: UAVs have strict weight and power budgets. Carrying heavy communication equipment (e.g., large antennas, powerful transceivers) and the onboard computing systems drains the limited battery power even more rapidly.
• Dynamic and Unreliable Channel Conditions: Air-to-ground links are highly susceptible to environmental factors. Signal blockage, severe fading, Doppler shift due to UAV mobility, and weather conditions (rain, wind) can significantly degrade link quality and reliability.
• Mobility Management and Trajectory Optimization: Optimizing the UAV’s flight path for maximum coverage, energy efficiency, and service quality is a complex, NP-hard problem that requires real-time processing and is challenging in dynamic environments with moving users.
• Interference Management: In dense urban areas or when multiple UAVs are deployed, co-channel interference between UAV cells and with existing terrestrial networks becomes a major issue, reducing overall network capacity.
• Safety, Security, and Privacy Concerns: System failure leads to crashes. UAVs are vulnerable to jamming, spoofing, and physical capture, which can disrupt the entire network. UAVs equipped with cameras and sensors can raise significant privacy concerns among the public.
• Regulatory and Airspace Restrictions: Operating UAVs, especially Beyond Visual Line of Sight, is heavily regulated. Obtaining flight permits, adhering to altitude limits, and avoiding no-fly zones (e.g., near airports) adds complexity and limits deployment flexibility.
• Cost of Deployment and Operation: The total cost includes not just the UAVs themselves but also ground control stations, maintenance, backup systems, and skilled personnel for operation and monitoring, which can be prohibitive for large-scale or long-term use.
• Limited Backhaul Capacity: Providing a high-capacity, low-latency backhaul connection from the UAV to the core network is challenging. Satellite backhaul can be expensive and have high latency, while terrestrial links may not always be available.
• Integration with Existing Networks: Seamlessly integrating a dynamic, mobile UAV component into the static architecture of existing cellular (e.g., 5G) or dedicated networks requires new protocols, interfaces, and core network modifications.

7. Conclusions and Future Directions

In this paper, we proposed a multi-target sensing method for a multi-UAV-enabled ISAC network with multiple users and targets. Firstly, we investigated the ISAC channel model. Then, we designed the ISAC signal for multi-target sensing and multi-user communications, and analyzed the downlink signal for the multi-users and the echo signal with inteference for the multi-targets, respectively. On this basis, we designed the multi-target sensing method with ADMA-based multi-UAV cooperation, which effectively decreases the effect of the multi-user and multi-target interference. Finally, we provided various simulation results to verify the effectiveness of the proposed method. In the future work, it will be necessary to further design the ISAC transmission signal, channel modeling methods, parameter estimation methods, and collaborative transmission methods, etc., to achieve a deep integration of communication and sensing in UAV swarms. The integration of UAVs with ISAC is a cornerstone of next-generation wireless networks. While current research has established its feasibility, several challenging and promising directions remain open for future exploration, such as AI-driven and semantic-aware ISAC, advanced waveform and signal design, multi-UAV swarm coordination and scalability, and integrated sensing, communication, and computation co-design.