Rate maximization of low-altitude integrated sensing and communication systems with fluid antennas

1 Introduction

With the vision of sixth-generation (6G) wireless communication systems progressively materializing, there is growing urgency to meet escalating requirements, including enhanced data rates, reduced latency, expanded connectivity, and a broader range of application scenarios (Saad et al., 2019; Bazzi et al., 2025; Bazzi et al., 2026). Low-altitude communication has become particularly important in this scenario as many unmanned aerial vehicles (UAV) and mission-critical services operate close to the ground. Given this scope, it is essential to ensure reliable short-range links, rapid adaptation to changing propagation conditions, and robust interactions with ground infrastructure for achieving good performance and safety under various scenarios (Yuhong et al., 2025).

Due to their high mobility, flexible deployment, and ability to circumvent obstacles to establish Line-of-Sight (LoS) links, UAVs have attracted considerable interest in wireless communication and sensing applications (Xu et al., 2025). As integral elements of low -altitude communication systems (Xu et al., 2020), UAVs can effectively extend network coverage while improving system adaptability in challenging environments. Through the integration of sensing and communication (ISAC) (Bazzi and Chafii, 2023), UAVs that function as edge nodes enable a range of emerging applications, including environmental monitoring, intelligent transportation, and emergency rescue. Nevertheless, the efficient co-design of communication and sensing functionalities on dynamic UAV platforms within complex electromagnetic environments remains a significant challenge (Mozaffari et al., 2019).

Enhancing the performance of such as system requires research into novel antenna technologies. Fluid antennas (FAs), also known as fluid antenna systems (FASs), constitute an emerging technology that enables flexible positioning and configuration of antenna elements within a predefined space; this allows dynamic reconfiguration of the antenna array (Wong et al., 2021). Unlike traditional fixed-position antennas, FAs can adaptively adjust the activation positions of the antenna ports according to channel conditions and service requirements. These features enable superior beamforming gains, interference suppression capabilities, and spatial resolution, offering new opportunities to improve the ISAC system performance (Zhou et al., 2024).

However, the integration of FAs into low-altitude, UAV-assisted ISAC systems introduces additional design dimensions and complexities. In particular, it is essential to maximize the base-station-to-UAV (BS–UAV) transmission rate to guarantee timely communication while ensuring that adequate power is allocated to meet the sensing requirements of the system.

The objective of this work was to jointly design the beamforming and selection of activated ports for UAVs hovering at low altitudes while considering the sensing power constraint in a given direction. The main contributions of this study are as follows:

• We investigated a low-altitude ISAC system operated with UAVs employing FAs. In this system, the UAVs act as aerial base stations (BSs) to simultaneously provide communication services to a ground BS while sensing a ground target. Our objective was to maximize the downlink communication rate by jointly optimizing the activated port selection of the FAs on the UAVs and the communication beamforming vector, subject to sensing the beam-pattern gain constraints.
• A unified optimization framework that jointly captures both communication and sensing functionalities is developed. The resulting problem is inherently non-convex due to the coupling between discrete port selection decisions and continuous beamforming variables, which makes it difficult to solve directly. To tackle this issue, we design an iterative solution based on alternating optimization (AO), where the original problem is split into two subproblems. Specifically, with fixed port selection, the beamforming design is optimized via convex optimization techniques; conversely, with fixed beamforming, an efficient search-based method is proposed to determine the port activation without resorting to computationally intensive integer programming.
• Numerical simulations are conducted to verify the effectiveness of the proposed approach. The results demonstrate that the algorithm can effectively trade off communication performance and sensing requirements, while also highlighting the advantages of employing fluid antennas in enhancing ISAC system capabilities.

Notations: Throughout this work, we employ standard mathematical notations, where t r ( ⋅ ), ( ⋅ ) H, and ( ⋅ ) T denote the trace, conjugate transpose, and transpose operations, respectively; ‖ x ‖ 2 represents the 2-norm of vector x; Q ⪰ 0 indicates that matrix Q is positive semidefinite; and C N ( 0 , σ 2 ) signifies circularly symmetric complex Gaussian distribution with mean 0 and variance σ 2.

2 System model

We investigate a ISAC scenario involving an UAV. In the considered system, the UAV operates as an aerial sensing platform while simultaneously maintaining a communication link with a ground base station (BS). In addition to transmitting sensing-related information, the UAV performs target monitoring by emitting a dedicated sensing beam toward a ground object. The ground BS is equipped with a uniform linear array consisting of N fixed antennas. A schematic representation of this system is provided in Figure 1.

To enhance the communication and sensing performances, the UAV is equipped with the FAS. In the considered FAS, M ports are aligned linearly, and during operation, k activated ports are selected from among the M total ports to send signals.

We assume that the UAV hovers at a given position p U = [ x U , y U ] and that the communicating BS is at p C = [ x C , y C ]. For convenience, we ignore the minor dynamics introduced by port switching in the FAS so that the power consumed by the UAV for hovering is P U. We assume that there are no external factors influencing the UAV and that it remains in the same position with the assistance of a stabilization system during the task. Thus, the power consumption P U of the UAV is static.

2.1 Communication model

The transmit signal is denoted by x ∈ C N × 1 ∼ C N ( 0 , Q ), where Q ∈ C N × N represents the transmit covariance matrix. The received signal is given by Equation 1:where z ∈ C N × 1 ∼ C N ( 0 , σ 2 I N ) is the complex additive white Gaussian noise in the BS and G is the transmit matrix.

y r = G H x + z , (1)

Since the UAV maintains a stationary position in air and allows direct flight to a location without obstructions between itself and the BS, we assume that the UAV-to-ground links are LoS channels. The mobility of the UAV allows it to maintain this LoS feature even in the presence of ground-level obstacles near the sensing target. On the UAV side, the transmitter is equipped with a fluid antenna system. A total of M ports are available. These ports are arranged evenly along a line perpendicular to the ground. The spacing between two adjacent ports is d _*U*. Among the M ports, only k are activated. The number k satisfies 1 ≤ k ≤ M. The indices of the activated ports form a vector a = [ a 1 , … , a m , … , a k ] T ∈ Z k × 1. Each entry am belongs to 1,2 , … , M. The indices are strictly increasing, i.e., a 1 < a 2 < ⋯ < a k. Ports are numbered such that a larger index indicates a greater distance from the ground. Accordingly, the three-dimensional coordinates of the a _*m*-th port are given as following:where [ x U , y U ] represents the UAV's horizontal location, and H denotes the vertical offset between the centre of receiving antenna array and the FAS. The term ym is defined as:

p a m = x U , y U , H + y m , (2)

y m = 2 a m − 1 − M + 1 2 d U . (3)

On the receiver side, a local coordinate system is similarly defined at the ground BS. The vertical coordinate of the n-th antenna element in the array is given by:Here, d C denotes the distance between adjacent receiver antennas.

y n a = 2 n − 1 − N + 1 2 d C . (4)

To construct the transmit matrix G, the steering vector needs to be characterized. For the communication link between the UAV and the BS, the path length difference between the signal transmitted from the m-th active port to the n-th receive antenna, relative to the FAS center, can be written asHere, L C = ‖ p C − p U ‖ is the horizontal distance between the UAV and the BS.

d C m , n = L C 2 + H + y m − y n a 2 − L C 2 + H 2 . (5)

Based on the path difference, the corresponding phase shift across transmit antennas can be obtained. Given the carrier wavelength λ, the transmit response vector associated with the n-th receive antenna is defined as

g C n ≜ e j 2 π λ d C 1 , n , … , e j 2 π λ d C k . n T ∈ C k × 1 . (6)

Furthermore, we can obtain the response matrix G using Equation 7:

G = g C 1 , … g C N ∈ C k × N . (7)

From Equation 7, the achievable communication rate obtained using Equation 8:where Q denotes the transmit covariance matrix of the FAS located on the UAV.

R = log ⁡ det I N + G H Q G σ 2 , (8)

2.2 Sensing model

In this work, we assume that the UAV continues to sense at a static target, so we adopt the beam-pattern gain as the primary metric to ensure sufficient sensing power and provide a foundation for subsequent tasks. The steering vector for sensing is given by Equation 9:Here, θ represents the angle for the sensing direction.

v θ = 1 , e j 2 π λ d U a m − a 1 sin ⁡ θ , … , e j 2 π λ d U a k − a 1 sin ⁡ θ T ∈ C k × 1 . (9)

From Equation 9, the sensing beam-pattern gain is given by Equation 10:

P S θ = v θ H Q v θ . (10)

To ensure adequate sensing performance, P S should meet the condition in Equation 11:where Γ is the predefined sensing beam-pattern gain that is fixed according to the sensitivity of the sensing hardware.

P S ≥ Γ , (11)

2.3 Problem formulation

We aim to maximize the transmission rate while maintaining satisfactory sensing performance. Hence, the maximization problem is formulated as shown in Equation 12:

max Q , a R , (12)

s . t . a m ∈ 1 , … , M , ∀ m ∈ 1 , … , k , (12a)

a 1 < a 2 < ⋯ < a k , (12b)

t r Q + P U ≤ P max , (12c)

P S θ ≥ Γ , (12d)

Q ⪰ 0 , (12e)

Here, Equations 12a, 12b are the numerical constraints for the port indices in the FAS. Equation 12c represents the total power budget, where the static P U limits the power available for communication and sensing; Equation 12d ensures that the sensing power is larger than the pre-defined threshold Γ. Finally, Equation 12e represents the property of the transmit covariance matrix Q.

3 Proposed algorithm

Owing to the discrete nature of the port selection vector a, Equation 12 is non-convex and difficult to solve directly. Hence, we propose the AO algorithm that divides the problem in Equation 12 into two subproblems and solves them alternatively until the solution converges to a given accuracy.

3.1 Optimization of the transmit covariance matrix Q

We first optimize the transmit covariance matrix Q. Given a fixed port selection vector a, Equation 12 reduces to Equation 13:

max Q R , (13)

s . t . t r Q + P U ≤ P max , (13a)

P S θ ≥ Γ , (13b)

Q ⪰ 0 . (14)

Since the hovering power of the UAV is static, by letting P C = P max − P U, Equation 13a is reduced to Equation 15:

t r Q ≤ P C . (15)

Thus, Equation 13 is reduced to a convex problem and can be efficiently solved using existing mathematical tools such as CVX (CVX Research, 2012; Grant and Boyd, 2000). The resulting transmit covariance matrix Q reflects the optimal power distribution across the selected ports, while the sensing constraint Equation 13b typically helps maintain a high-quality beamforming solution. And the semi-positive nature of *Q* reflected in Equation 14 can be automatically guaranteed by the mathematical solver.

3.2 Optimization for the port selection vector a

In this subproblem, we focus on optimizing the port selection vector a. With a determined Q, problem(12) is reduced to

max a R , (16)

s . t . a m ∈ 1 , … , M , (16a)

a 1 < a 2 < ⋯ < a k , (16b)

P S θ ≥ Γ . (16c)

However, the discrete nature of the elements in a_m, as presented in Equations 16a, 16b, makes the problem(16) difficult to handle directly. Although integer programming techniques—such as those implemented in tools like Gurobi—can be applied to obtain an optimal solution, the associated computational burden becomes prohibitive as the problem size increases. To reduce the complexity arising from combinatorial enumeration, we instead reformulate the problem by focusing on the optimization of individual elements a_m, while (Equation 16c) poses relatively little difficulty for the solution. Based on this idea, the subproblem can be further expressed as:

max a m log ⁡ det I N + G H Q G σ 2 , (17)

s . t . a m ∈ 1 , … , M , (17a)

a 1 < a 2 < ⋯ < a k , (17b)

P S θ ≥ Γ . (17c)

By trying the possible values of a m according to Equations 17a, 17b, we computed Equation 17 and updated a m when the new value of Equation 17c exceeded the current value and the new a m did not violate Equation 16, which ensured that the value of Equation 17 was non-decreasing during the optimization process. Thereafter, we iteratively optimized each item of a and found a suboptimal a for an optimized Q. Then, we repeated the process in an AO manner.

The process of the overall algorithm is as follows:

Algorithm 1 Alternating optimization for the beamforming matrix and port selection.

Algorithm 1 initializes a ( 0 ) with equidistant port spacing to maximize the initial spatial diversity. Solving the subproblem in Equation 13 with convex problem solvers yields promising convergence, while the subproblem in Equation 15 is solved using an exhaustive-search-like method. The value of the objective function in Equation 12 keeps increasing during optimization, and since Equation 12 is the boundary, the overall algorithm is promised to converge.

The semidefinite programming problem (Equation 13) can be solved with a worst-case time complexity O ( k 4.5 l o g ( 1 / ϵ ) ), where ϵ denotes the convergence accuracy; and the worst time complexity for port selection is O ( M k ). Hence, the worst-case time complexity for Algorithm 1 can be expressed as O ( M k k 4.5 l o g ( 1 / ϵ ) ). In simulation, the initialized a ( 0 ) is usually close to the suboptimal solution, and the algorithm converges in a few iterations (as shown in Section 4).

4 Simulation results

All the simulation parameters are summarized in Table 1. We focused on the convergence behaviors and final performances in terms of the communication rate and port selection. To compare the conventional and non-optimized schemes, we set a fixed-port baseline equivalent to a conventional fixed-position antenna system in which k antennas are deployed in a static and equidistant linear array. This serves as a representative benchmark for standard antenna technologies.

TABLE 1. Simulation parameters of the integrated signal and communication system.

Figure 2 presents the evolution of the communication rate across iterations, where a pronounced increase is observed at the initial stage. Although minor variations appear during the intermediate updates, the solution eventually converges to a stable point while satisfying the sensing constraint. This trend indicates that the proposed approach can effectively coordinate communication and sensing objectives through adaptive resource allocation. Furthermore, the convergence behavior of the port selection vector suggests that the algorithm is capable of approaching a high-quality solution within a discrete feasible set.

Figure 3 shows simulation results for communication rate performance. The proposed algorithm is compared with a fixed-port baseline. Maximum transmit power P _*max* varies across the tests. Both schemes achieve higher rates as P _*max* increases. The improvement is monotonic. Nevertheless, the proposed algorithm yields the largest gains when power is limited. In the high-power regime, the performance bottleneck shifts. The two curves converge. This indicates that the algorithm's main contribution is efficient power allocation. It maximizes communication rate under strict power constraints. Such a capability is both theoretically insightful and practically valuable for power-sensitive wireless applications.

Figure 4 illustrates how the communication rate varies with the number of active ports k. As k increases, the communication rate grows monotonically. This trend confirms that enlarging the antenna array aperture contributes positively to beamforming gain. In other words, activating more ports directly enhances the communication performance.

Notably, the performance gain from the proposed optimization algorithm is not uniform. It appears in an intermittent manner. For some values of k, the algorithm performs exactly as well as the fixed port scheme. This suggests that under those specific conditions, conventional port selection already yields a locally optimal solution. For most other values of k, however, the optimization algorithm achieves a clear rate improvement. It outperforms the conventional approach in the majority of cases. These observations strongly support the algorithm's effectiveness and robustness. It consistently meets or surpasses the baseline. It does so by intelligently selecting ports, thereby unlocking additional performance gains when the channel conditions permit.

5 Conclusion

In this study, we examined a UAV-assisted low-altitude ISAC system with a joint design between the UAV and the BS, whose primary objective was to maximize the communication performance for low-altitude links while maintaining reliable sensing capabilities. To render the original complex optimization tractable, the problem was decomposed into smaller subproblems and an AO framework was adopted to reduce the computational complexity. Convex optimization techniques were applied to obtain efficient solutions for the subproblems. The simulation results corroborated the effectiveness of the proposed algorithm. The proposed methodology is expected to be applicable to future ISAC deployments, particularly for low-altitude operations. Future works may incorporate sidelobe suppression to further minimize interference or apply more sophisticated ISAC metrics reported in recent works (Alexandropoulos and Gavras, 2025; Gavras and Alexandropoulos, 2024; Gavras and Alexandropoulos, 2025).

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Footnotes

Edited by: George Alexandropoulos, National and Kapodistrian University of Athens, Greece

Reviewed by: Kalpana, Indian Institute of Technology Guwahati, India

Ahmad Bazzi, New York University Abu Dhabi, United Arab Emirates