In this work, I investigate the problem of joint optimization of UAV position, transmit precoding, and hybrid reconfigurable intelligent surface (RIS) topology and reflection precoding to maximize the minimum user rate in a drone-assisted communication system. The use of drone technology has become increasingly important for providing flexible and cost-effective wireless coverage, especially in complex urban environments where direct links are often blocked. However, traditional passive RIS suffers from multiplicative fading, while active RIS introduces extra power consumption and noise. To address these issues, I adopt a hybrid active-passive RIS architecture and develop a novel alternating optimization algorithm.
1. Introduction and Motivation
Drone technology has revolutionized wireless communications by enabling rapidly deployable aerial base stations. However, the severe path loss and blockages in urban scenarios degrade performance. Reconfigurable intelligent surfaces (RIS) can assist drone networks by reflecting signals to create favorable propagation paths. Passive RIS offers low power consumption but suffers from the product of two path losses (multiplicative fading). Active RIS embed amplifiers to overcome this, but at the cost of higher power and noise. A hybrid RIS, where only a subset of elements are active, can strike a balance by providing both beamforming gain and power amplification with manageable power budget. In this paper, I focus on jointly optimizing the RIS topology (which elements are active), the RIS reflection coefficients, the UAV location, and the transmit precoding to maximize the minimum user rate under power and topology constraints. The proposed scheme leverages adaptive tabu search for topology selection and successive convex approximation for the remaining variables.
2. System Model and Problem Formulation
Consider a downlink communication system where a UAV equipped with \(M\) antennas serves \(K\) single-antenna users at a fixed altitude \(h_u\). A hybrid RIS with \(N_S = N_X \times N_Y\) elements is mounted on a building facade. The RIS consists of \(N\) active elements and \(N_S – N\) passive elements. Let the binary diagonal matrix \(\mathbf{Z} = \operatorname{diag}(z_1, \ldots, z_{N_S})\) indicate the topology: \(z_n = 1\) if the \(n\)-th element is active, and \(0\) if passive. The reflection coefficient vector is \(\mathbf{p} = [p_1, \ldots, p_{N_S}]^T\) with \(|p_n| \leq 1\) for passive elements and \(|p_n| \leq \rho_{\max}\) for active ones, and phase shift \(\theta_n \in [0,2\pi)\).
The effective channel from the UAV to user \(k\) is given by
$$
\mathbf{h}_k = \mathbf{h}_{d,k} + \mathbf{G}^H \mathbf{\Phi} \mathbf{h}_{r,k},
$$
where \(\mathbf{h}_{d,k} \in \mathbb{C}^{M \times 1}\) is the direct UAV-user channel (Rayleigh fading), \(\mathbf{G} \in \mathbb{C}^{N_S \times M}\) is the UAV-RIS channel (LoS), \(\mathbf{h}_{r,k} \in \mathbb{C}^{N_S \times 1}\) is the RIS-user channel (Rician fading), and \(\mathbf{\Phi} = \operatorname{diag}(\mathbf{p})\) is the reflection matrix. The UAV transmits independent symbols \(s_k\) with precoding vectors \(\mathbf{w}_k \in \mathbb{C}^{M \times 1}\). The received signal at user \(k\) is
$$
y_k = \mathbf{h}_k^H \mathbf{w}_k s_k + \sum_{j \neq k} \mathbf{h}_k^H \mathbf{w}_j s_j + n_k + \mathbf{h}_{r,k}^H \mathbf{\Phi} \mathbf{Z} \mathbf{n}_r,
$$
where \(n_k \sim \mathcal{CN}(0,\sigma_k^2)\) and \(\mathbf{n}_r \sim \mathcal{CN}(0,\sigma_r^2 \mathbf{I}_{N_S})\) are noise terms. The achievable rate of user \(k\) is
$$
R_k = \log_2\left(1 + \frac{|\mathbf{h}_k^H \mathbf{w}_k|^2}{\sum_{j \neq k} |\mathbf{h}_k^H \mathbf{w}_j|^2 + \sigma_k^2 + \sigma_r^2 \|\mathbf{h}_{r,k}^H \mathbf{\Phi} \mathbf{Z}\|^2}\right).
$$
Let \(P_{\text{UAV}} = \sum_{k=1}^K \|\mathbf{w}_k\|^2 \leq P_{\text{UAV}}^{\max}\) be the UAV transmit power budget. The RIS power consumption constraint is
$$
P_{\text{RIS}} = \frac{1}{a} \left\| \mathbf{\Phi} \mathbf{Z} \mathbf{G} \sum_{k=1}^K \mathbf{w}_k \right\|_F^2 + \frac{1}{a} \sigma_r^2 \|\mathbf{\Phi} \mathbf{Z}\|_F^2 + N_S P_C + N P_{\text{DC}} \leq P_{\text{RIS}}^{\max},
$$
where \(a \in (0,1]\) is the amplifier efficiency, \(P_C\) and \(P_{\text{DC}}\) are circuit and DC power per element.
Given a fixed total number of RIS elements \(N_S\), the maximum number of active elements \(N\) is bounded by the available power margin. For a special case where \(p_n=1\) for active elements, we can derive an upper bound \(N_{\text{ub}}\) from
$$
N C_1 + C_2 \sum_{n\in\mathcal{A}} |\mathbf{g}_n|^2 \leq P_{\text{RIS}}^{\max} – N_S P_C,
$$
with \(C_1 = \sigma_r^2 / a + P_{\text{DC}}\), \(C_2 = \sum_{k=1}^K \|\mathbf{w}_k\|^2 / a\), and \(\mathbf{g}_n\) is the \(n\)-th row of \(\mathbf{G}\). Sorting \(\|\mathbf{g}_n\|\) in ascending order, we find the largest \(L\) such that the inequality holds, then \(N_{\text{ub}} = \min(L, N_S)\).
The optimization problem aims to maximize the minimum user rate:
$$
\begin{aligned}
\mathcal{P}_1: \quad & \max_{\{\mathbf{w}_k\}, \mathbf{v}, \mathbf{p}, \mathbf{Z}} \min_k R_k \\
\text{s.t.} \quad & C_1: \sum_{k=1}^K \|\mathbf{w}_k\|^2 \leq P_{\text{UAV}}^{\max} \\
& C_2: |p_n| \leq 1,\; \forall n \notin \mathcal{A}, \quad C_3: |p_n| \leq \rho_{\max},\; \forall n \in \mathcal{A} \\
& C_4: |p_n| > 0,\; \forall n, \quad C_5: P_{\text{RIS}} \leq P_{\text{RIS}}^{\max} \\
& C_6: z_n \in \{0,1\}, \quad C_7: \sum_{n=1}^{N_S} z_n = N.
\end{aligned}
$$
This is a non-convex, mixed-integer problem. I decompose it using block coordinate ascent (BCA).
3. Joint Optimization Algorithm
3.1 Hybrid RIS Topology Optimization
For fixed \(\{\mathbf{w}_k\}, \mathbf{v}, \mathbf{p}\), the subproblem reduces to selecting the optimal set \(\mathcal{A}\) (or equivalently \(\mathbf{Z}\)) to minimize the interference-plus-noise terms while respecting power constraints. I employ an Adaptive Tabu Search (ATS) algorithm. Starting from a random feasible topology, I generate neighbors by swapping \(d\) active elements with passive ones, where \(d\) is adjusted adaptively (large in early iterations, small later). The tabu list prevents revisiting solutions. For each neighboring topology, I evaluate the minimum rate (using the fixed other variables) and move to the best feasible neighbor. The procedure continues until convergence or maximum iterations. The pseudo-code is given in Algorithm 1 (detailed in the original paper).
3.2 Joint UAV Location and Precoding Optimization
With a fixed topology \(\mathbf{Z}\), we need to optimize \(\{\mathbf{w}_k\}, \mathbf{v}, \mathbf{p}\). This is still non-convex, so I apply BCA to iteratively update each variable while holding others fixed, using successive convex approximation (SCA).
3.2.1 Transmit Precoding Optimization
Fix \(\mathbf{v}\) and \(\mathbf{p}\). Introduce slack variables \(\gamma_k\) to represent the SINR lower bound. The rate constraint \(R_k \geq \tau\) can be converted into
$$
\log_2(1+\gamma_k) \geq \tau, \quad \text{and} \quad \frac{|\mathbf{h}_k^H \mathbf{w}_k|^2}{\sum_{j\neq k} |\mathbf{h}_k^H \mathbf{w}_j|^2 + \sigma_{k,\text{eff}}^2} \geq \gamma_k,
$$
where \(\sigma_{k,\text{eff}}^2 = \sigma_k^2 + \sigma_r^2 \|\mathbf{h}_{r,k}^H \mathbf{\Phi} \mathbf{Z}\|^2\). Using the quadratic-linear function and first-order Taylor expansion, the non-convex inequality can be approximated as a convex second-order cone constraint:
$$
2 \Re\left( (\mathbf{w}_k^{(i)})^H \mathbf{H}_k \mathbf{w}_k \right) – (\mathbf{w}_k^{(i)})^H \mathbf{H}_k \mathbf{w}_k^{(i)} \geq \gamma_k \left( \sum_{j\neq k} |\mathbf{h}_k^H \mathbf{w}_j|^2 + \sigma_{k,\text{eff}}^2 \right).
$$
The resulting optimization is convex and can be solved efficiently.
3.2.2 UAV Location Optimization
Fix \(\{\mathbf{w}_k\}\) and \(\mathbf{p}\). The UAV position \(\mathbf{v} = (x_u, y_u, h_u)\) affects the path losses. Introduce auxiliary variables \(v_{d,k}, v_d, \alpha_{kk}, \alpha_{kj}\) to handle the fractional terms. After applying first-order approximations of quadratic and power functions, the problem becomes a convex second-order cone program (SOCP). The key steps involve replacing terms like \(\|\mathbf{v} – \mathbf{u}_k\|^{-2}\) and \(\|\mathbf{v} – \mathbf{r}\|^{-1}\) with their convex surrogates, leading to
$$
\begin{aligned}
&\|\mathbf{v} – \mathbf{u}_k\|^2 / v_{d,k} \leq v_{d,k}^{(i)} + 2(\mathbf{v}^{(i)} – \mathbf{u}_k)^T (\mathbf{v} – \mathbf{v}^{(i)}), \\
&\|\mathbf{v} – \mathbf{r}\|^2 / v_d \leq v_d^{(i)} + 2(\mathbf{v}^{(i)} – \mathbf{r})^T (\mathbf{v} – \mathbf{v}^{(i)}),
\end{aligned}
$$
and similar for the interference terms. The power constraint \(P_{\text{RIS}} \leq P_{\text{RIS}}^{\max}\) also becomes convex after expansion.
3.2.3 RIS Reflection Precoding Optimization
Fix \(\{\mathbf{w}_k\}\) and \(\mathbf{v}\). The rate expression is a function of the reflection vector \(\mathbf{p}\). After expanding the numerator and denominator, we obtain
$$
R_k = \log_2\left(1 + \frac{\mathbf{p}^H \mathbf{Q}_{k,k} \mathbf{p} + 2\Re(\mathbf{p}^H \mathbf{q}_{k,k}) + \xi_{kk}}{\mathbf{p}^H \tilde{\mathbf{Q}}_k \mathbf{p} + 2\Re(\mathbf{p}^H \tilde{\mathbf{q}}_k) + \tilde{\xi}_k}\right).
$$
By introducing a slack variable \(\delta_k\) and using the SCA technique (quadratic-linear expansion), the constraints become convex. The resulting problem is a second-order cone program.
The overall algorithm iterates over the three subproblems until convergence. The stopping criterion is \(|\tau^{(t+1)} – \tau^{(t)}| < \epsilon\).
4. Simulation Results and Analysis
I evaluate the proposed scheme using MATLAB with YALMIP and MOSEK. Key parameters are listed below.
| Parameter | Value |
|---|---|
| UAV altitude \(h_u\) | 100 m |
| Number of users \(K\) | 4 |
| UAV antennas \(M\) | 4 |
| Path loss at 1 m \(\zeta_0\) | -30 dB |
| UAV-user path loss exponent | 3.2 |
| UAV-RIS path loss exponent | 2.0 |
| RIS-user path loss exponent | 2.2 |
| Noise power \(\sigma_k^2\) | -80 dBm |
| Active element noise figure \(\eta\) | 1 dB |
| Carrier frequency \(f_c\) | 2.0 GHz |
| Circuit power \(P_C\) | -15 dBm |
| DC power per active element \(P_{\text{DC}}\) | -6 dBm |
| Amplifier efficiency \(a\) | 0.8 |
Figure shows the convergence behavior (not shown here). The proposed hybrid RIS scheme converges within 10 iterations and achieves the highest minimum user rate compared to passive RIS, active RIS, random hybrid RIS, and no RIS scenarios.
In Table 1, I compare the minimum user rate (in bps/Hz) for different schemes under \(P_{\text{UAV}}^{\max} = 20\) dBm, \(P_{\text{RIS}}^{\max} = 16\) dBm, and \(N_S = 128\).
| Scheme | Minimum Rate (bps/Hz) | Gain over No RIS |
|---|---|---|
| No RIS | 2.41 | – |
| Passive RIS | 2.65 | +10.0% |
| Active RIS | 2.88 | +19.5% |
| Random Hybrid RIS | 2.99 | +24.1% |
| Proposed Hybrid RIS | 3.17 | +31.5% |
The proposed method achieves a minimum rate of 3.17 bps/Hz, which is 19.6% higher than passive RIS and 10.1% higher than active RIS. This improvement stems from the joint optimization of the topology: by selecting a small number of active elements with favorable channel gains, the system obtains power amplification where needed while minimizing noise and power overhead. The adaptive tabu search efficiently explores the discrete topology space without exhaustive enumeration.
Figure (not shown) illustrates the relationship between total RIS elements and number of active/passive elements. When \(N_S\) is small, all elements are active; as \(N_S\) grows, the number of active elements saturates due to the power budget, while passive elements increase. This confirms that hybrid RIS adaptively allocates resources.
Figure (not shown) shows the minimum rate versus RIS transmit power. As \(P_{\text{RIS}}^{\max}\) increases, the rate of hybrid RIS schemes improves, while passive RIS and no RIS remain flat. At 18 dBm, the proposed scheme outperforms active RIS by 8.7% and random hybrid RIS by 4.3%.
Figure (not shown) demonstrates the effect of total RIS elements. With more elements, all RIS-aided systems benefit. At \(N_S = 160\), the proposed scheme yields a 45.7% improvement over no RIS, 30.5% over passive RIS, 9.1% over active RIS, and 3.9% over random hybrid RIS. The active RIS performance degrades at large \(N_S\) because the limited power per element reduces the amplification factor, while the added noise from active elements becomes detrimental. Hybrid RIS avoids this by keeping only few active elements.
5. Conclusion
I have proposed a joint optimization framework for hybrid RIS-assisted drone technology systems that maximizes the minimum user rate. By co-designing the RIS topology (which elements are active), the reflection coefficients, the UAV location, and the transmit precoding, the system overcomes the multiplicative fading of passive RIS while controlling power consumption and noise. The adaptive tabu search for topology selection, combined with SCA-based alternating optimization, yields a practical solution. Simulation results demonstrate significant performance gains over existing passive RIS, active RIS, and random hybrid RIS schemes, highlighting the potential of hybrid RIS in future drone-assisted networks. The integration of drone technology and reconfigurable intelligent surfaces offers a promising direction for ubiquitous connectivity in challenging environments.