Active IRS-Enhanced UAV Relaying for Secure Hybrid RF/FSO Communications: Joint Phase Shift, Beamforming, and Power Optimization

2.1 System and channel model

We consider a UAV-assisted secure communication network illustrated in Figure 1, where a ground source (S) transmits confidential information to a legitimate destination (Bob, B) via a UAV-mounted IRS relay (R), while an eavesdropper (Eve, E) attempts to intercept the transmission. The system employs a hybrid RF/FSO architecture operating in two distinct phases. In Phase 1, the S→R link operates over RF (Nakagami-m fading) to ensure reliable signal reception at the UAV relay under mobility conditions. In Phase 2, the R→B link operates over FSO (Gamma-Gamma atmospheric turbulence with pointing errors) to achieve high-capacity secure transmission to Bob. DF decoding takes place entirely at the UAV relay at the end of Phase 1: the UAV fully decodes the received signal before re-encoding and retransmitting in Phase 2. In the active IRS mode, each of the N reflecting elements phase-shifts and amplifies the impinging signal using an embedded low-noise amplifier, with element amplitude gain $\alpha_{\mathrm{n}}$, where in the passive IRS mode, each element only phase-shifts the signal, with unit amplitude gain $\alpha_{\mathrm{n}}$. Eve is assumed capable of intercepting transmissions in both phases, representing the worst-case eavesdropping scenario. In details, the UAV hovers at altitude $h_R$ and is equipped with an IRS comprising $N$ reconfigurable reflecting elements. The sourceto-relay link experiences Nakagami-$m$ with channel coefficient; $h_{S R}=\sqrt{\beta_{S R}} \cdot g_{S R}, g_{S R} \sim \operatorname{Nakagami}\left(m_{S R}, \Omega_{S R}\right)$ where $\beta_{\mathrm{SR}}=\rho_0\left(\mathrm{~d}_{\mathrm{SR}} / \mathrm{d}_0\right)^{-\alpha_{\mathrm{RF}}}$ represents large-scale path loss with reference distance $\mathrm{d}_0=1 \mathrm{~m}$, path loss exponent $\alpha_{\mathrm{RF}}=$ 2.5, and $\rho_0$ is the reference path gain. Then the instantaneous channel gain follows $\left|h_{S R}\right|^2 \sim \operatorname{Gamma}\left(m_{S R}, \frac{\Omega_{S R}}{m_{S R}}\right)$. The relay-to-destination FSO link is characterized by atmospheric turbulence modeled via Gamma-Gamma distribution and pointing errors. The channel coefficient is:

$h_{R B}^{\mathrm{FSO}}=h_a \cdot h_p \cdot h_l$        (1)

where, $\mathrm{h}_{\mathrm{a}} \sim \operatorname{Gamma}$-Gamma$(\alpha, \beta)$ is the atmospheric turbulence following a Gamma-Gamma distribution with shape parameters α and β (moderate turbulence, Rytov variance $\sigma^2{ }_R=0.5$), with PDF [14].

$f_{h_a}(x)=\frac{2(\alpha \beta)^{(\alpha+\beta) / 2}}{\Gamma(\alpha) \Gamma(\beta)} x^{(\alpha+\beta) / 2-1} K_{\alpha-\beta}(2 \sqrt{\alpha \beta x}), x>0$       (2)

The pointing error; $\mathrm{h}_{\mathrm{p}}=\mathrm{A}_0 \exp \left(-\frac{2 \mathrm{r}^2}{\mathrm{w}_{\mathrm{eq}}^2}\right)$, where r is radial displacement, $\mathrm{w}_{\mathrm{eq}}$ is equivalent beam radius, and $\mathrm{A}_0=$ $[\operatorname{erf}(\mathrm{v})]^2$ with $\mathrm{v}=\sqrt{\pi} \mathrm{a} /\left(\sqrt{2} \mathrm{w}_{\mathrm{eq}}\right)$. The pointing error coefficient follows $\left|\mathrm{h}_{\mathrm{p}}\right|^2 \sim \operatorname{Rayleigh}\left(\xi^2\right), \xi^2=\frac{\mathrm{w}_{\mathrm{eq}}^2}{4 \sigma_{\mathrm{s}}^2}$ where $\sigma_{\mathrm{s}}$ is the jitter standard deviation at the receiver. Besides, the path loss, $\mathrm{h}_1=\exp \left(-\sigma_{\mathrm{FSO}} \mathrm{d}_{\mathrm{RB}}\right)$ accounts for absorption/scattering over distance $d_{R B}$ (relay-to-Bob distance) with attenuation coefficient $\sigma_{\mathrm{FSO}}\left(\mathrm{dB} / \mathrm{km} ; \sigma_{\mathrm{FSO}}=0.43 \mathrm{~dB} / \mathrm{km}\right.$ for clear sky, 4.2 $\mathrm{dB} / \mathrm{km}$ for light fog, $20 \mathrm{~dB} / \mathrm{km}$ for moderate fog). Eavesdropper channels are modeled similarly as $\mathrm{h}_{\mathrm{SE}} \sim$ $\operatorname{Nakagami}\left(\mathrm{m}_{\mathrm{SE}}, \Omega_{\mathrm{SE}}\right), \mathrm{h}_{\mathrm{RE}}^{\text {FSO}} \sim \operatorname{Gamma-Gamma}\left(\alpha_{\mathrm{E}}, \beta_{\mathrm{E}}\right)$ with typically $\mathrm{m}_{\mathrm{SE}}<\mathrm{m}_{\mathrm{SR}}$ and $\alpha_{\mathrm{E}}<\alpha$, reflecting Eve's disadvantaged position.

The IRS phase shift matrix is defined as:

$\Theta=\operatorname{diag}\left(\theta_1, \theta_2, \ldots, \theta_N\right), \theta_n=\alpha_n e^{j \phi_n}$       (3)

where, $\alpha_{\mathrm{n}}$ as the element gain: passive IRS (unit gain, phaseshift only); $\alpha_n=1$; and active IRS: $\alpha_{\mathrm{n}}=\sqrt{\mathrm{G}_{\mathrm{n}}}$ (amplification gain, where $\mathrm{G}_{\mathrm{n}}$ is the element power gain; e.g., $\mathrm{G}_{\mathrm{n}}=4$ gives $\alpha_n=2$, equivalent to 6 dB$), \phi_{\mathrm{n}} \in[0,2 \pi]$.

Then, the cascaded channel from source to Bob through IRS is formulated as:

$h_{\text {eff}}^B=h_{R B}^T \Theta G h_{S R}$        (4)

where, $\mathrm{h}_{\mathrm{SR}} \in \mathrm{C}^{\mathrm{N} \times \mathbb{1}}$, is channel vector from S to IRS elements. $\mathrm{G}=\operatorname{diag}\left(\mathrm{g}_1, \ldots, \mathrm{~g}_{\mathrm{N}}\right)$ is the beamforming weight matrix at UAV, and $\mathrm{h}_{\mathrm{RB}} \in \mathrm{C}^{\mathrm{N} \times \mathbb{1}}$ is the channel vector from IRS elements to Bob.

Similarly, the effective eavesdropper channel is:

$h_{e f f}^E=h_{R E}^T \theta G h_{S E}$       (5)

To this end, the received signals at the UAV relay in the first phase (S→R) can be formulated as follows:

$y_R=\sqrt{P_S} h_{S R} x+n_R$       (6)

where, $x$ is the unit-power information symbol, $\mathrm{P}_{\mathrm{S}}$ is source transmit power ($P_S=P_T=1 \mathrm{~W}$ normalized), and $\mathrm{n}_{\mathrm{R}} \sim$ $\mathcal{C} \mathcal{N}\left(0, \sigma_{\mathrm{R}}^2\right)$ is the additive wight gaussian noise. Here $\sigma_{\mathrm{R}}^2, \sigma_{\mathrm{B}}^2$, and $\sigma_{\mathrm{E}}^2$ denote the noise powers at relay, Bob, and Eve respectively. In the second phase (R→B with artificial noise [15]), the relay employs DF with power splitting [16]. The transmitted signal is:

$s_R=\sqrt{\alpha P_R} G \hat{x}+\sqrt{(1-\alpha) P_R} w_{A N} z$        (7)

where, $\alpha \in(0,1)$ is the power allocation factor, $P_R$ is the relay transmit power, $\hat{x}$ is the decoded symbol, $w_{A N}$ is the artificial noise beamforming vector, $\left|w_{A N}\right|^2=1$, and $\mathrm{z} \sim \mathcal{C} \mathcal{N}(0,1)$ is the artificial noise.

To this end, Bob’s received signal can be obtained as:

$\begin{gathered}y_B=h_{e f f}^B s_R+n_B=\sqrt{\alpha P_R} h_{e f f}^B G \hat{x}+\sqrt{(1-\alpha) P_R} h_{e f f}^B w_{A N} z+n_B\end{gathered}$        (8)

Thus, the Bob SINR can be computed as:

$\gamma_B=\frac{\alpha P_R\left|h_{e f f}^B G\right|^2}{(1-\alpha) P_R\left|h_{e f f}^B w_{A N}\right|^2+\sigma_B^2}$       (9)

assuming $w_{A N}$ is designed to lie in the null-space of the estimated effective channel to $\operatorname{Bob}\left(h_{\text {eff }}^B \perp w_{A N}\right.$ under perfect CSI, so ideally $\left.h_{\text {eff }}^B \mathrm{w}_{\mathrm{AN}} \approx 0\right)$. The signal received at Eve can be calculated as follows:

$\begin{gathered}y_E=h_{e f f}^E s_R+n_E=\sqrt{\alpha P_R} h_{e f f}^E G \hat{x}+\sqrt{(1-\alpha) P_R} h_{e f f}^E w_{A N} z+n_E\end{gathered}$       (10)

Similarly, the Eve SINR can be calculated as:

$\gamma_E=\frac{\alpha P_R\left|h_{e f f}^E G\right|^2}{(1-\alpha) P_R\left|h_{e f f}^E w_{A N}\right|^2+\sigma_E^2}$      (11)

Finally, the instantaneous secrecy rate under DF is obtained by:

$R_S=\left[\min \left\{R_{S B}, R_{R B}\right\}-R_E\right]^{+}$        (12)

where, $\mathrm{R}_{\mathrm{SR}}=\log _2\left(1+\gamma_{\mathrm{SR}}\right)$, is $\mathrm{S} \rightarrow \mathrm{R}$ capacity with $\gamma_{\mathrm{SR}}=$ $\mathrm{P}_{\mathrm{S}}\left|\mathrm{h}_{\mathrm{SR}}\right|^2 / \sigma_{\mathrm{R}}^2$, the R→B capacity calculated by using $\mathrm{R}_{\mathrm{RB}}=$ $\log _2\left(1+\gamma_{\mathrm{B}}\right)$, and the eavesdropper rate over both phases (worst-case scenario where Eve intercepts both the S→E link in Phase 1 and the $\mathrm{R} \rightarrow \mathrm{E}$ link in Phase 2) is defined by the worst hop as: $R_E=\max \left\{R_E^1, R_E^2\right\}$, where $R_E^1=\log _2\left(1+\gamma_E^1\right)$ is Eve's rate in Phase 1 and $R_E^2=\log _2\left(1+\gamma_E^2\right)$ is Eve's rate in Phase 2; finally, $[x]^{+}=\max (0, x)$. Following DF relaying principles, the end-to-end achievable rate between S and Bob is limited by the weaker hop: $R_{S B}=\min \left\{R_{S R}, R_{R B}\right\}$. Therefore, the instantaneous secrecy rate $R_S$ in Eq. (12) explicitly incorporates the DF bottleneck and worst-case eavesdropping over both phases. On the other hand, the average secrecy capacity can be computed by using:

$C_s=E\left[R_s\right]$       (13)

And the secrecy outage probability for target rate obtained by [17]:

$P_{\text {out}}=\operatorname{Pr}\left(R_s<R_{t h}\right)$        (14)

1.png

Figure 1. UAV-IRS assisted secure hybrid radio frequency/free-space optical (RF/FSO) communication system model

2.2 Problem formulation

The goal is to maximize the average secrecy capacity of the two-hop UAV-IRS system while satisfying practical constraints. We formulate this as a joint optimization problem:

$\max _{\Theta, w, \alpha} C_s(\Theta, w, \alpha)=E\left[R_s\right]$        (15)

subject to:

$\alpha P_T+(1-\alpha) P_T \leq P_T$       (15a)

$\left|\varphi_n\right| \leq \varphi_m \alpha x, \forall n=1,2, \ldots, N$        (15b)

$0<\alpha<1$        (15c)

where, $w \in C^N$ is the beamforming weight vector at the UAV. The constraint Eq. (15a) ensures total power conservation at the relay (for passive IRS: $P_S+P_R=P_T$; for active IRS: $P_S+$ $P_R+N \cdot P_{a m p} \leq P_{b u d g e t}$, where $N \cdot P_{a m p}$ is the amplifier supply power consumption, thereby enforcing a fair power comparison with the passive baseline. The optimization variables are coupled through the secrecy rate expression:

$R_s=\left[\log _2\left(1+\gamma_B\right)-\log _2\left(1+\gamma_E\right)\right]^{+}$       (16)

where, $\gamma_B$ and $\gamma_E$ denote the SINR at the legitimate receiver Bob and Eavesdropper Eve, respectively.

2.3 Joint optimization via block coordinate descent

The formulated problem in Eqs. (15a)-(15c) is non-convex due to the coupled optimization variables in the cascaded channel model and the nonlinear SINR expressions. The coupling among different variables makes the direct solution of the original optimization problem challenging, as the variables cannot be optimized independently. We address this challenge using BCD combined with successive convex approximation (SCA), which has proven effective for similar IRS optimization problems [18, 19].

2.3.1 Block coordinate descent algorithm and convergence

BCD decomposes the joint optimization into three manageable subproblems, optimizing one variable while fixing the others. At each iteration $k$, we perform:

Step1:

$\Theta^{(k+1)}=\arg \max _{\Theta} C_s\left(\Theta, w^{(k)}, \alpha^{(k)}\right)$        (17)

Step2:

$w^{(k+1)}=\arg \max _w C_s\left(\Theta^{(k+1)}, w, \alpha^{(k)}\right)$        (18)

Step3:

$\alpha^{(k+1)}=\arg \max _\alpha C_s\left(\Theta^{(k+1)}, w^{(k+1)}, \alpha\right)$        (19)

This procedure repeats until convergence, defined by:

$\begin{aligned} \max \left(\mid \Theta^{(k+1)}-\right. & \Theta^{(k)}|,| w^{(k+1)}-w^{(k)}\left|,\left|\alpha^{(k+1)}-\alpha^{(k)}\right|\right)<\epsilon\end{aligned}$        (20)

where, $\epsilon=10^{-4}$ is the convergence tolerance. Under the standard BCD-SCA assumptions: (i) each per-block subproblem admits a well-defined solution up to a controlled tolerance, and (ii) the SCA surrogate is a tight lower bound of the objective at the current iterate with matching gradients, the objective sequence generated by the proposed algorithm is monotonically non-decreasing and bounded and therefore converges. Because the subproblems are solved iteratively rather than to global optimality, and because the joint problem is non-convex, this convergence is to a stationary point of the surrogate problem (in the KKT sense) rather than a global optimum, consistent with classical BCD-SCA analyses [20, 21]. Convergence to a stationary point of the original Lagrangian is therefore not claimed in the strict sense but is expected in practice; this is supported by the empirical monotonic convergence observed within a small number of iterations in our simulations.

2.3.2 Phase shift optimization via successive convex approximation

The IRS phase optimization subproblem is:

$\max _{\Theta} C_s(\Theta, w, \alpha)$ s.t. $\left|\theta_n\right| \in[0,2 \pi], \forall n$       (21)

This is non-convex due to the complex exponential coupling in the effective channel:

$h_{\mathrm{eff}}=h_{\mathrm{SI}}+h_{\mathrm{ID}} \odot(w \odot \Theta)$       (22)

where, $\odot$ denotes element-wise multiplication. We apply SCA by constructing a convex approximation of the secrecy capacity around the current solution $\Theta^{(k)}$. The effective channel gain can be expressed as:

$\left|h_{\mathrm{eff}}\right|^2=\left|h_{\mathrm{SI}}+h_{\mathrm{ID}} \odot(w \odot \Theta)\right|^2$       (23)

First-order Taylor expansion around $\Theta^{(k)}$ yields [22]:

$\left|h_{\mathrm{eff}}\right|^2 \approx\left|h_{\mathrm{eff}}^{(k)}\right|^2+2 \operatorname{Re}\left\{\left.\left(h_{\mathrm{eff}}^{(k)}\right)^* \nabla_\theta\left|h_{\mathrm{eff}}\right|^2\right|_{\theta^{(k)}}\right\}$       (24)

where the gradient is:

$\nabla_\theta\left|h_{\mathrm{eff}}\right|^2=\operatorname{conj}\left(h_{\mathrm{ID}} \odot w\right) \odot\left(h_{\mathrm{eff}}^{(k)}\right)^*$        (25)

The secrecy capacity is then approximated as:

$C_s \approx \log _2\left(1+\frac{\alpha P_T \mathrm{SNR} \cdot\left|h_{\mathrm{eff}}^{(k)}\right|^2}{1+\alpha P_T \mathrm{SNR} \cdot\left|h_{\mathrm{eff}}^{(k)}\right|^2}\right)-\log _2\left(1+\alpha P_T \mathrm{SNR} \cdot\left|h_{\mathrm{eve}}\right|^2\right)$       (26)

Projected gradient ascent update [23]:

$\Theta^{(k+1)}=\mathcal{P}\left(\Theta^{(k)}+\mu_{\Theta} \cdot \nabla_{\Theta} C_s\right)$       (27)

where, $\mu_{\Theta}=0.1$ is the step size and $\mathcal{P}(\cdot)$ projects the phases back to the unit circle:

$\mathcal{P}(z)=\frac{z}{|z|}$       (28)

To ensure monotonic improvement, we verify that $C_s\left(\Theta^{(k+1)}\right) \geq C_s\left(\Theta^{(k)}\right)$. If not, we reduce the step size by half and retry. This SCA procedure repeats for $I_{\text {SCA}}=5$ iterations per BCD iteration.

2.3.3 Beamforming vector optimization

The beamforming subproblem is:

$\max _w C_s(\Theta, w, \alpha)$ s.t. $|w|=1$       (29)

The effective channel at Bob is:

$h_{\text {eff, Bob}}=h_{\mathrm{SI}}+h_{\mathrm{ID}} \odot(\Theta \odot w)$        (30)

and the SINR becomes:

$h_{\text {eff, Bob}}=h_{\mathrm{SI}}+h_{\mathrm{ID}} \odot(\Theta \odot w)$       (31)

$\gamma_B=\alpha P_T \mathrm{SNR} \cdot\left|h_{\text {eff,Bob }}\right|^2=\alpha P_T \mathrm{SNR} \cdot\left|w^H\left(h_{\mathrm{ID}} \odot \Theta \odot h_{\mathrm{SI}}\right)\right|^2$        (32)

Gradient Computation:

$\nabla_w C_s=\frac{\partial C_s}{\partial \gamma_R} \cdot \nabla_w \gamma_B$        (33)

where,

$\nabla_w \gamma_B=2 \cdot \alpha P_T \mathrm{SNR} \cdot\left(h_{\mathrm{ID}} \odot \Theta\right) * \cdot\left(h_{\mathrm{SI}}\right)^T$       (34)

Gradient Ascent with Normalization:

$w^{(k+1)}=\frac{w^{(k)}+\mu_w \cdot \nabla_w C_s}{\left|w^{(k)}+\mu_w \cdot \nabla_w C_s\right|}$        (35)

where, $\mu_w=0.05$ is the beamforming step size. The normalization constraint $|w|=1$ is maintained at each update, which can be interpreted as normalizing the antenna gains. This optimization runs for $I_w=8$ iterations per BCD step.

2.3.4 Power allocation optimization via ternary search

The power allocation problem is:

$\max _{0 \leq \alpha \leq 1} C_s(\Theta, w, \alpha)$       (36)

Key observation: The secrecy capacity $C_s(\alpha)$ is a unimodal function in $\alpha$ it increases to a unique maximum and then decreases. This property arises from the competing effects of signal power and artificial noise power on the secrecy rate: for small $\alpha$, Bob's SINR is too low; for large $\alpha$, the AN power is insufficient to sufficiently degrade Eve's SINR. While strict analytical unimodality of $C_s(\alpha)$ is difficult to establish in closed form under active-IRS noise, DF relaying, and imperfect CSI, we have verified it numerically over an extensive range of conditions. Specifically, we swept $\alpha \in[0$, 1] in steps of 0.01 and computed $C_s(\alpha)$ at each of the operating points reported in the paper: $\mathrm{SNR} \in\{-10,0,10,20,30\} \mathrm{dB}$, CSI quality $\sigma^2{ }_{C S I} \in\{0,0.01,0.05,0.1\}$, IRS size $\mathrm{N} \in\{64$, 128, 256\}, and both passive and active IRS modes. In every tested scenario, $C_s(\alpha)$ exhibited a single global maximum with no observed local maxima. Under adverse conditions (e.g., $\sigma^2{ }_{C S I}=0.1$ combined with active IRS noise), the curve becomes flatter around the peak but remains unimodal. The unimodality assumption is therefore justified as an empirical property over the operating region of interest, and to exploit it, we employ ternary search, which converges to the global maximum in the unimodal regime in $O(\log (1 / \epsilon))$ function evaluations.

This method guarantees convergence to the global optimum with precision $10^{-6}$ in approximately $\log _3\left(10^6\right) \approx 13$ iterations per BCD step [24].

2.4 Handling practical impairments

In realistic deployments, perfect CSI, phase accuracy, and hardware performance cannot be guaranteed. We explicitly model these impairments.

2.4.1 Channel state information

The estimated channel is modeled as [25]:

$\hat{h}=h+\Delta h_{C S I}$       (37)

where, $\quad \Delta h_{\mathrm{CSI}} \sim \mathcal{C} \mathcal{N}\left(0, \sigma_{\mathrm{CSI}}^2|h|^2\right) \quad$ represents Gaussian estimation error such that $\hat{h}_{e f f}^B=h_{e f f}^B+\Delta h_{C S I}$. Because the AN vector $w_{A N}$ is designed in the null-space of the estimated channel $\hat{h}_{\text {eff}}^B$ rather than the true channel $h_{\text {eff}}^B$, a residual AN leakage appears at Bob under imperfect CSI: $\left|h_{\text {eff}}^B{ }^{\mathrm{H}} w_{A N}\right|^2=$ $\left|\Delta h_{C S I}{ }^{\mathrm{H}} w_{A N}\right|^2$, whose variance scales as $\sigma^2{ }_{\text {leak}}=\sigma^2{ }_{C S I}$. $\left|h_{\text {eff}}^B\right|^2 \cdot\left|w_{A N}\right|^2$. This leakage term is explicitly added to Bob's SINR denominator, so that Bob's effective SINR under imperfect CSI is reduced from its perfect-CSI value $\left(\gamma_B^{\text {perfect}}\right)$ to $\gamma_B^{\text {imp}}=\gamma_B^{\text {perfect}} /\left(1+\eta_{\text {leak}} \cdot \sigma^2{ }_C S I\right) \quad, \quad$ with $\eta_{\text {leak}}$ being the leakage sensitivity parameter. Consequently, a perfect null-space AN design is not assumed under imperfect CSI, and the residual leakage effect is quantified in all simulations reporting the imperfect-CSI results. In our simulations, we use three error levels:

Good CSI: $\sigma_{\mathrm{CSI}}^2=0.01$ (high-quality feedback)

Moderate CSI: $\sigma_{\mathrm{CSI}}^2=0.05$ (typical scenario)

Poor CSI: $\sigma_{\mathrm{CSI}}^2=0.1$ (low feedback capacity)

The optimization in Algorithm 1 uses $\hat{h}$ instead of perfect $h$, and we analyze performance degradation across all three scenarios.

2.4.2 Intelligent reflecting surfaces phase quantization

Practical IRS elements cannot achieve arbitrary phase values due to hardware limitations. We model quantized phases as [26, 27].

$\theta_{\text {quantized}}=\operatorname{round}\left(\frac{\theta_{\text {optimal}}}{\Delta \phi}\right) \times \Delta \phi$       (38)

where, $\Delta \phi=2 \pi / M$ and $M$ is the number of quantization levels. We test $M \in 4,8,16$ bits per element and report performance vs. quantization resolution.

2.4.3 Active intelligent reflecting surfaces amplifier noise

For active IRS (amplification gain $\alpha_n=\sqrt{ } G_{a m p}=\alpha_n=2$), each reflecting element includes a low-noise amplifier with gain $G_{\mathrm{amp}}=2$ and noise figure $N F=4 \mathrm{~dB}$. The output of element $n$ is [28, 29].

$y_n=G_{\mathrm{amp}}\left(h_{\mathrm{in}, n} x+n_{\mathrm{amp}, n}\right)$        (39)

where, $n_{\text {amp}, n} \sim \mathcal{C} \mathcal{N}\left(0, \sigma_{\text {amp}}^2\right)$ with $\sigma_{\text {amp}}^2$ determined by the noise figure as $\sigma^2{ }_{a m p}=(F-1) \cdot k_B \cdot T \cdot B \cdot G_{a m p}$, where $F=10^{(N F / 10)}$ is the noise figure in linear scale, $k_B$ is Boltzmann's constant, $\mathrm{T}=290 \mathrm{~K}$ is the operating temperature, and B is the signal bandwidth. This amplifier noise degrades Eve's SINR less than Bob's SINR (due to beamforming steering), but the effect is explicitly included in results. To properly account for the power cost of active IRS elements, we now define the total active-IRS power consumption as $P_{I R S}=$ $N \cdot P_{\text {amp}}$, where $P_{\text {amp}}$ is the per-element amplifier supply power ($P_{\text {amp}} \leq P_{\text {max}}=10 \mathrm{~mW}$ per element in our study). The overall system power budget is therefore extended as $P_{\text {total}}=$ $P_S+P_R+N \cdot P_{\text {amp}} \leq P_{\text {budget}}$, so active IRS is not evaluated with free amplification. Moreover, the accumulated amplifier noise scales linearly with the number of active elements: the total noise power at the IRS output is $\sigma^2{ }_{\text {amp}}^{\text {total}}=N \cdot\left|\alpha_n\right|^2$. $\sigma^2{ }_{a m p}$, which is included in all SINR expressions and results for both Bob and Eve.

2.5 Simulation methodology

All results are validated via Monte Carlo simulation with $M=10,000$ channel realizations per SNR point. The simulation parameters are:

FSO Channel: Gamma-Gamma distribution with $\alpha_{\text {turb}}=2.9,~ \beta_{\text {turb}}=2.1$ (moderate turbulence) and pointing error variance $\sigma_s=0.1$.  

RF Channels: Nakagami-m fading with shape parameters $m_{\mathrm{B}}=2.5$ (good link) and $m_{\mathrm{E}}=1.8$ (weaker link), reflecting the eavesdropper's disadvantageous position.

IRS Configuration: $N \in 64,128,256,512$ elements tested, with optimal value $N^*=128$ identified via complexity-performance trade-off analysis.

Active IRS Gain: $\alpha_n=2$ (6 dB amplification per element)

SNR Range: -10 to +30 dB.

Target Secrecy Rate: $R s_{t h}=2$ bits/s/Hz.

The complete set of simulation parameters used for reproducibility is summarized in Table 2.

Table 2. Complete simulation parameters for reproducibility

Each simulation was run independently with different random seeds to ensure statistical independence across trials.

This extensive investigation reveals that IRS with UAV relaying and hybrid RF/FSO architectures can offer great performance gains in secure wireless communications. The combined optimization of phases, beamforming, and power allocation leads to synergistic gains (total 185% improvement) larger than the sum of the individual component-wise gains. The qualitative statements below are backed by the following compact sensitivity summary, reported at:

• SNR = 20 dB, N* = 128 unless otherwise noted.
• Number of IRS elemen[ts N: at N = 64, secrecy capacity = 3.72 bits/s/Hz (77% of the N = 128 value); at N = 128, $C_s$ = 4.82 bits/s/Hz (100%, reference); at N = 256, $C_s$ = 4.95 bits/s/Hz (102.7%); at N = 512, $C_s$ = 4.99 bits/s/Hz (103.5%), confirming that the improvement diminishes after N = 128.
• CSI error $\sigma^2{ }_{C S I}$: perfect ($\sigma^2{ }_{C S I}$ = 0): 100% (reference); good CSI (0.01): 96.1%; moderate CSI (0.05): 88.3%; poor CSI (0.1): 82.0% (~4.0 bits/s/Hz), so degradation is smooth rather than abrupt.
• Phase-quantization bits B: continuous phases: 100% (reference); B = 4 bits: 99.1%; B = 3 bits: 95.9%; B = 2 bits: 88.4%; B = 1 bit: 72.7%.
• Active-IRS gain $G_{a m p}$: $G_{a m p}$ = 1 (passive): 54% (reference for passive); $G_{a m p}$ = 2 (6 dB): 100%; $G_{a m p}$ = 4 (12 dB): 106% but with 93% effective value after the amplifier noise (F = $10^{(N F / 10)}$ with NF = 4 dB) is included.
• The analysis of practical imperfections verifies the robustness of the system: The performance degrades gracefully with imperfect CSI (82% of the ideal value), with finite phase quantization (95.9% of the ideal value), and with realistic amplifier noise (93% of the ideal value).

The 60-meter optimal altitude and N = 128 element recommendation are two practical guidelines for the deployment. The 4.82 bits/s/Hz secrecy capacity at 20 dB SNR demonstrated by this design deems it as a viable candidate for 6G secure communication networks, thereby pushing the state-of-the-art in physical-layer security beyond the existing passive-IRS or beamforming-only approaches.