A hybrid algorithmic model for enhancing security in intelligent reflecting surface-assisted wireless communication

Optimization techniques for IRS-assisted PLS

DRL approaches, such as those proposed in Liu et al. (2024), Ren et al. (2022), leverage long-term CSI to adaptively optimize IRS phase shifts. Although effective under ideal conditions, these methods are computationally intensive and require large training datasets, making them less viable for real-time applications. AO-based methods (Jiang, Huang & Zhang, 2024; Luo et al., 2021) simplify the design by alternating between IRS phase and beamforming updates, but they often suffer from slow convergence due to decoupled optimization steps. Techniques such as successive convex approximation (SCA) and convex relaxation (Gong et al., 2021; Nguyen et al., 2022) provide analytical tractability but can be computationally demanding, especially in large-scale IRS deployments. Active Reconfigurable Intelligent Surfaces with SCA (ARIS-SCA) combines active reflecting elements with successive convex approximation (Feng et al., 2021) further demonstrates how Reconfigurable Intelligent Surfaces (RIS) can significantly enhance PLS through optimized phase shifts; however, their framework lacks mechanisms to handle hardware limitations. Recent work by Sivasankar & Markkandan (2024) introduces intelligent beamforming strategies that enhance secrecy through optimized phase shifts, although their approach assumes continuous phase control and perfect CSI. Other active IRS configurations have been explored for secure integrated sensing and communication, demonstrating improved robustness, albeit often at the cost of increased power consumption.

Impact of CSI uncertainty and robustness

Accurate CSI is critical for optimal IRS-PLS performance. However, many studies assume perfect CSI, which is rarely feasible in practice. Some studies have addressed this by modeling statistical CSI uncertainty, however their robustness often degrades under high error conditions or rapid user mobility. Furthermore, these solutions typically do not consider real-time adaptation or mobility-aware learning strategies. For instance, Wang, Bai & Dong (2020) proposed secure transmission schemes without knowledge of the eavesdropper’s CSI, instead relying on worst-case assumptions. However, such methods may lead to overly conservative designs. Other approaches incorporate active IRS elements to dynamically adjust to channel variations, offering a promising direction for real-time adaptability. Wang et al. (2021) further explored IRS-aided secure broadcasting in mmWave symbiotic networks, highlighting the interplay between channel correlation and secrecy performance.

Channel estimation for IRS-assisted systems

Compressive sensing-based mmWave IRS channel estimation reduces pilot overhead. Two-stage Discrete Fourier Transform (DFT)-based pilot schemes and tensor decomposition techniques further reduce training complexity (Nandan & Rahiman, 2024). A recent work by Le et al. (2022) optimized spectral efficiency in IRS-aided Internet of Things (IoT) systems through adaptive resource allocation, although their channel estimation framework assumes static environments. Practical deployments must balance estimation accuracy with computational complexity, particularly under mobility-induced Doppler shifts.

IRS hardware constraints and phase quantization

Practical IRS implementations operate with low-resolution, discrete phase shifters, typically 1–2 bits. While early studies assumed continuous phase control, more recent analyses have evaluated performance under quantized conditions, showing that 2-bit quantization retains most of the secrecy performance. However, such studies often neglect the additional complexity introduced by real-time channel dynamics, imperfect CSI, or mobility. Some approaches integrate intelligent beamforming with quantized phase shifts, demonstrating improved energy efficiency, however they may not account for CSI uncertainties. Active IRS architectures offer enhanced beamforming capabilities but introduce new challenges in power management and hardware complexity.

Key contributions and novelty of this work

Despite substantial progress in IRS-assisted PLS, existing methods typically address isolated challenges such as convergence, robustness, or learning. In contrast, this study presents an integrated framework, SGP-DARE, which holistically addresses multiple practical issues. The key contributions are as follows:

• Joint optimization framework: The SGP algorithm enables low-complexity joint optimization of BS beamforming and IRS phase shifts under quantized constraints.

• Robust and adaptive design: The DARE module incorporates robust gradients and mobility-aware learning to maintain performance under CSI errors and dynamic user scenarios.

• Validated practicality: The proposed method supports 2-bit IRS quantization and demonstrates superior secrecy rate, energy efficiency, and SOP, with reduced runtime in realistic mmWave settings.

• Comprehensive evaluation: Unlike previous works, this study provides a detailed simulation analysis of robustness to channel correlation, mobility, quantization effects, and scalability.

Table 1 provides a comprehensive comparison of recent IRS-aided wireless communication approaches, highlighting their primary focus, technical contributions, and limitations.

Channel and signal model

Let $\mathbf{G}\in {\mathbb{C}}^{N\times M}$ denote the BS-to-IRS channel, ${\mathbf{h}}_{IU,k}\in {\mathbb{C}}^{N\times 1}$ the IRS-to-user- $k$ channel, and ${\mathbf{h}}_{BU,k}\in {\mathbb{C}}^{M\times 1}$ the direct BS-to-user- $k$ channel. The IRS phase shift matrix is defined as

(1) $$\text{Φ}=\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}(e^{j{\varphi }_1},\dots ,e^{j{\varphi }_N}),$$where each ${\varphi }_n$ is selected from a discrete set $\mathcal{Q}=\left\{0,\frac{2\pi }{Q},\dots ,\frac{2\pi (Q-1)}{Q}\right\}$, corresponding to Q-level quantization.

The received signal at the $k$-th legitimate user is given by

(2) $$y_k=\left({\mathbf{h}}_{BU,k}^H+{\mathbf{h}}_{IU,k}^H\text{Φ}\mathbf{G}\right)\sum _{i=1}^K{\mathbf{w}}_i{s}_i+n_k,$$where ${\mathbf{w}}_i\in {\mathbb{C}}^{M\times 1}$ is the beamforming vector for user $i$, $s_i$ is the unit-power transmitted symbol, and $n_k\sim \mathcal{C}\mathcal{N}(0,{\sigma }_k^2)$ represents additive noise. The effective channel for user $k$ becomes

(3) $${\mathbf{h}}_k^H={\mathbf{h}}_{BU,k}^H+{\mathbf{h}}_{IU,k}^H\text{Φ}\mathbf{G}.$$

The IRS reconfiguration period $T_c$ is set to $10$ ms to align with typical mmWave coherence intervals.

Secrecy rate formulation

The signal-to-interference-plus-noise ratio (SINR) for user $k$ is (see Jiao, Liu & Wang, 2022)

(4) $${\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_k=\frac{|{\mathbf{h}}_k^H{\mathbf{w}}_k{|}^2}{{\sum }_{i\ne k}|{\mathbf{h}}_k^H{\mathbf{w}}_i{|}^2+{\sigma }_k^2}.$$

The eavesdropper’s SINR when intercepting user $k$ is bounded by

(5) $${\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_e^{k,max}=\underset{e}{max}\frac{|{\mathbf{h}}_e^H{\mathbf{w}}_k{|}^2}{{\sum }_{i\ne k}|{\mathbf{h}}_e^H{\mathbf{w}}_i{|}^2+{\sigma }_e^2},$$where ${\mathbf{h}}_e$ denotes the equivalent eavesdropper channel. The achievable secrecy rate for user $k$ is then given by (See Eskandari et al. 2024)

(6) $$R_s^k={\left[{\log }_2(1+{\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_k)-{\log }_2(1+{\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_e^{k,max})\right]}^{+}.$$

Robust optimization under imperfect CSI

Adopting a bounded CSI error model, where the estimated channel $\hat{\mathbf{H}}$ deviates from the true channel $\mathbf{H}$ by $||\mathrm{\Delta }|{|}_F\le \epsilon$, the robust secrecy maximization problem is formulated as

(7a) $$\underset{\mathbf{W},\text{Φ}}{max}\underset{||\mathrm{\Delta }||\le \epsilon }{min}\sum _{k=1}^K{R}_s^k$$

(7b) $$\mathrm{s}.\mathrm{t}.\sum _{k=1}^K||{\mathbf{w}}_k|{|}^2\le P_{max},$$

(7c) $${\varphi }_n\in \mathcal{Q},\mathrm{\forall }n.$$

This problem is non-convex due to the coupling of variables and the presence of discrete phase constraints. Our proposed SGP-DARE framework addresses these limitations through two integrated components. The SGP module enables the joint optimization of $\mathbf{W}$ and $\text{Φ}$ by applying gradient steps that are directly projected onto the discrete phase set, ensuring feasibility throughout the optimization process. Complementing this, the DARE module modifies the gradient directions dynamically based on real-time CSI uncertainty and user mobility patterns. Together, SGP and DARE offer both computational efficiency and robustness against real-world impairments, as demonstrated in ‘Simulation Results’.

Synergistic gradient-projection

While phase quantization introduces discontinuities, the projection operator in Eq. (9) preserves gradient Lipschitz continuity over the feasible set. This follows from the $\eta$-smoothness of the composite objective $f\circ {\mathrm{\Pi }}_{\mathcal{Q}}$ for projected gradient methods with discrete constraints. Empirical Lipschitz constants L measured across trials with $N=128$ showed $L\le 2.1$ for 2-bit quantization, confirming bounded gradients. The SGP module performs joint optimization of the BS beamforming matrix $\mathbf{W}=[{\mathbf{w}}_1,\dots ,{\mathbf{w}}_K]$ and the IRS phase shift matrix $\text{Φ}$. The gradient of the secrecy rate objective $R_s$ is computed with respect to both $\mathbf{W}$ and $\text{Φ}$, followed by projection onto the feasible power and quantization domains. The updates follow

(8) $$\mathbf{W}\leftarrow {\mathrm{\Pi }}_P\left(\mathbf{W}+\eta {\mathrm{\nabla }}_{\mathbf{W}}{R}_s\right),{\varphi }_n\leftarrow \mathcal{Q}\left(e^{j\mathrm{\angle }({\mathrm{\nabla }}_{{\varphi }_n}{R}_s)}\right),$$where ${\mathrm{\Pi }}_P$ denotes projection onto the transmit power constraint ${\sum }_k||{\mathbf{w}}_k|{|}^2\le P_{max}$, $\eta$ is the step size, and $\mathcal{Q}(\cdot )$ represents quantization to the nearest phase in the discrete set $\mathcal{Q}$. The per-iteration complexity of SGP is $\mathcal{O}(KM+N^2)$, and empirical results show convergence typically within 15–20 iterations. The secrecy rate gradient with respect to the beamforming matrix $\mathbf{W}$ is derived as

(9) $${\mathrm{\nabla }}_{\mathbf{W}}{R}_s=\sum _{k=1}^K\frac{{\mathbf{h}}_k{\mathbf{h}}_k^H{\mathbf{w}}_k}{{\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_k+1}-\frac{{\mathbf{h}}_e{\mathbf{h}}_e^H{\mathbf{w}}_k}{{\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_e^{k,max}+1},$$where ${\mathbf{h}}_e$ is the worst-case eavesdropper channel. For IRS phases, the gradient with respect to ${\varphi }_n$ is

(10) $${\mathrm{\nabla }}_{{\varphi }_n}{R}_s=\mathfrak{I}\mathfrak{m}\left\{{\mathbf{w}}_k^H\mathbf{G}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}({\mathbf{h}}_{IU,k}){\text{Φ}}^{\mathit{H}}\right\}.$$

Quantization uses nearest-neighbor projection

(11) $$\mathcal{Q}(\varphi )=\arg \underset{\theta \in \{0,\frac{\pi }{2},\pi ,\frac{3\pi }{2}\}}{min}|\varphi -\theta |.$$

The $\mathcal{O}(KM+N^2)$ complexity arises from the gradient computations involved in updating both the beamforming vectors and the IRS phase shifts. Specifically, for beamforming, each user’s gradient computation requires $\mathcal{O}(M)$ operations due to vector multiplications, and with K users in the system, this leads to a total complexity of $\mathcal{O}(KM)$. On the other hand, the gradient computation for IRS phases involves N-dimensional matrix-vector products per element, and since there are N such elements, this results in a complexity of $\mathcal{O}(N^2)$. In contrast, traditional AO methods typically involve computationally expensive operations such as inverting $N\times N$ matrices with $\mathcal{O}(N^3)$ complexity, and solving beamforming optimization problems with a much higher $\mathcal{O}(K^3{M}^3)$ complexity.

Dynamic adaptive risk–expansion

DARE enhances robustness by adapting the SGP update rules in response to CSI uncertainty and user mobility. A detailed description of the DARE procedure is provided in Algorithm 2. During each coherence block, DARE performs the following steps

• 1.

  CSI estimation: The BS estimates the effective channel $\hat{\mathbf{H}}$ and evaluates the uncertainty level $\epsilon$.

• 2.

  Worst-case risk expansion: A sub-gradient is calculated with respect to the worst-case CSI perturbation ${\mathrm{\Delta }}^{\ast }$ using a first-order Taylor approximation.

• 3.

  Robust projection: Gradient updates are adjusted for uncertainty and mobility as (12) $$\mathbf{W}\leftarrow {\mathrm{\Pi }}_P\left(\mathbf{W}+\eta {\tilde{\mathrm{\nabla }}}_{\mathbf{W}}{R}_s\right),{\varphi }_n\leftarrow \mathcal{Q}\left(e^{j\mathrm{\angle }({\tilde{\mathrm{\nabla }}}_{{\varphi }_n}{R}_s)}\right),$$

• where $\tilde{\mathrm{\nabla }}$ indicates the robust gradient estimate.

• 4.

  Mobility-aware learning rate: The step size $\eta$ is dynamically scaled based on predicted user velocity $v$, using a linear model to improve convergence stability.

SGP convergence guarantee

The SGP algorithm iteratively updates the beamforming and IRS phase shift variables using projected gradient steps. The following theorem establishes convergence under standard assumptions.

Convergence of SGP: Let $f(\mathbf{W},\text{Φ})={\sum }_{k=1}^K{R}_s^k$ denote the secrecy rate objective. If $f$ has Lipschitz-continuous gradients with constant L and step size $\eta <1/L$, then SGP converges to a stationary point satisfying

(13) $$||\mathrm{\nabla }{R}_s({\mathbf{W}}^{\ast },{\text{Φ}}^{\mathbf{\ast }})||\le ϵ\mathrm{i}\mathrm{n}\mathcal{O}\left(\frac{1}{{ϵ}^2}\right)\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}.$$

Define projections onto the feasible sets

(14) $${\mathbf{W}}^{(t+1)}={\mathrm{\Pi }}_{\mathcal{P}}\left({\mathbf{W}}^{(t)}+\eta {\mathrm{\nabla }}_{\mathbf{W}}f\right),$$

(15) $${\text{Φ}}^{(t+1)}={\mathrm{\Pi }}_{\mathcal{Q}}\left({\text{Φ}}^{(t)}+\eta {\mathrm{\nabla }}_{\text{Φ}}f\right),$$where $\mathcal{P}=\{\mathbf{W}\mid ||\mathbf{W}|{|}_F^2\le P_{max}\}$ and $\mathcal{Q}=\{{\varphi }_n\mid |{\varphi }_n|=1,\mathrm{\forall }n\}$.

The projection onto $\mathcal{P}$ is given by:

(16) $${\mathrm{\Pi }}_{\mathcal{P}}(\mathbf{W})=\{\begin{array}{cc}\mathbf{W}\hfill & \mathrm{i}\mathrm{f}||\mathbf{W}|{|}_F^2\le P_{max},\hfill \\ \frac{\sqrt{P_{max}}}{||\mathbf{W}|{|}_F}\mathbf{W}\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\hfill \end{array}$$

For $\mathcal{Q}$, each phase shift is projected onto the unit circle as

(17) $${\mathrm{\Pi }}_{\mathcal{Q}}({\varphi }_n)=\frac{{\varphi }_n}{|{\varphi }_n|},n=1,\dots ,N.$$

Using the Lipschitz continuity of $\mathrm{\nabla }f$, the update rules Eqs. (14)–(17) guarantee a descent lemma

(18) $$f({\mathbf{W}}^{(t+1)},{\text{Φ}}^{(t+1)})\le f({\mathbf{W}}^{(t)},{\text{Φ}}^{(t)})-\frac{\eta }{2}||\mathrm{\nabla }f({\mathbf{W}}^{(t)},{\text{Φ}}^{(t)})|{|}^2.$$

Summing Eq. (18) over $t=1,\dots ,T$ yields the rate $\mathcal{O}(1/T)$ for the minimum gradient norm, implying the stated $\mathcal{O}(1/{\epsilon }^2)$ complexity.

Robustness of DARE under CSI uncertainty

To model CSI uncertainty, let

(19) $$\hat{\mathbf{H}}=\mathbf{H}+\mathrm{\Delta }$$where $||\mathrm{\Delta }|{|}_F\le \epsilon$. The robust gradient is adjusted as

(20) $$\tilde{\mathrm{\nabla }}f=\mathrm{\nabla }f(\hat{\mathbf{H}})+\lambda {\mathrm{\Delta }}^{\ast }$$where ${\mathrm{\Delta }}^{\ast }=\arg \underset{||\mathrm{\Delta }|{|}_F\le \epsilon }{max}⟨\mathrm{\nabla }f(\hat{\mathbf{H}}),\mathrm{\Delta }⟩$ is the worst-case perturbation, and $\lambda$ controls the robustness penalty.

Robust secrecy rate bound: For robustness parameter $\lambda =\sqrt{\frac{2\log (1/\delta )}{\epsilon }}$, DARE ensures that with probability at least $1\text{-}\delta$

(21) $$R_s(\hat{\mathbf{H}})\ge R_s(\mathbf{H})-\epsilon \sqrt{2\log (1/\delta )}.$$

Let $\xi =R_s(\hat{\mathbf{H}})-R_s(\mathbf{H})$. Using the Lipschitz continuity of $R_s$ and the Cauchy–Schwarz inequality,

(22) $$\xi \ge -||\mathrm{\nabla }{R}_s||\cdot ||\mathrm{\Delta }|{|}_F-\frac{L}{2}||\mathrm{\Delta }|{|}_F^2.$$

Substituting the worst-case perturbation ${\mathrm{\Delta }}^{\ast }=-\epsilon \mathrm{\nabla }{R}_s/||\mathrm{\nabla }{R}_s||$ into Eq. (22) yields:

(23) $$\xi \ge -\epsilon ||\mathrm{\nabla }{R}_s||-\frac{L{\epsilon }^2}{2}.$$

Applying Hoeffding’s inequality to the gradient noise term $⟨\mathrm{\nabla }f,\mathrm{\Delta }⟩$ gives

(24) $$\mathbb{P}\left(||\mathrm{\nabla }{R}_s||\ge \sqrt{2\log (1/\delta )}\right)\le \delta .$$

Combining Eqs. (23) and (24), and selecting $\lambda$ as in Eq. (20), we obtain the bound in Eq. (21).

This analysis confirms that SGP-DARE maintains reliable secrecy rate performance even under CSI estimation errors and supports theoretical guarantees on convergence and robustness.

Simulation setup

To evaluate the performance of the proposed SGP-DARE framework, simulations are conducted in a 28 GHz mmWave downlink scenario. The BS is equipped with $M=8$ antennas and operates at a maximum transmit power of 30 dBm. An intelligent reflecting surface (IRS) comprising $N=128$ passive elements, each with 2-bit (4-level) phase quantization, is deployed to enhance secure communication to $K=4$ legitimate users in the presence of $E=2$ passive eavesdroppers, as shown in Fig. 3.

Channels are modeled using a correlated Rayleigh fading environment with a spatial correlation coefficient $\rho$ ranging from 0 to 0.9. User mobility is taken into account by modeling terminal velocities of up to 30 km/h (Ji, Qin & Parini, 2022), with Doppler-induced fluctuations affecting both direct and IRS-assisted paths. The system operates under imperfect CSI, with a normalized CSI error bound of $\epsilon =0.1$. Channel estimation occurs every 10 ms (coherence interval), and performance metrics are computed as the average of 1,000 independent Monte Carlo trials to ensure statistical robustness. The gradient descent step size is fixed at $\eta =0.1$, and the optimization is terminated when convergence falls below a threshold of ${10}^{-3}$ or a maximum of 20 iterations is reached. All key simulation parameters are summarized in Table 2.

Performance evaluation

Figure 4 demonstrates the scalability of the proposed SGP-DARE framework with an increasing number of IRS reflecting elements. At $N=128$, the proposed method achieves a secrecy rate of 5.5 bps/Hz, which is 2.2 $\times$ higher than AO (2.5 bps/Hz) and 1.4 $\times$ higher than ARIS-SCA (3.9 bps/Hz). This superior scalability results from the linear complexity of SGP-DARE, which avoids the cubic growth of conventional AO methods while maintaining a runtime below 250 ms for real-time operation.

Figure 5 illustrates the impact of transmit power on the secrecy rate. At 30 dBm, SGP-DARE achieves 5.0 bps/Hz, outperforming AO (2.8 bps/Hz) by 1.8 $\times$ and ARIS-SCA (3.3 bps/Hz) by 1.5 $\times$. While competing methods saturate at high power due to fixed robustness margins, SGP-DARE’s dynamic risk adaptation sustains performance gains across the entire power range.

These performance gains are achieved through the joint optimization of active beamforming and IRS phase shifts, which balance secrecy improvements with power efficiency. Figure 6 shows the corresponding energy efficiency enhancements with respect to IRS size. At $N=128$, SGP-DARE achieves 7.2 bits/Joule, representing a 92% improvement over SCA methods, owing to its integrated active–passive beamforming design.

Sum rate vs. transmit power comparison

This section compares the sum rate performance of the proposed low-complexity fractional programming (FP) method and the SGP-DARE framework as a function of the base station transmit power P (in dBm). The sum rate, denoted by $R_{\mathrm{s}\mathrm{u}\mathrm{m}}$, is measured in bits/s/Hz and is calculated as

(25) $$R_{\mathrm{s}\mathrm{u}\mathrm{m}}=\sum _{k=1}^K{\log }_2\left(1+{\gamma }_k\right),$$where ${\gamma }_k$ represents the SINR for user $k$, defined by

(26) $${\gamma }_k=\frac{{\left|{\mathbf{h}}_k^H{\mathbf{w}}_k\right|}^2}{{{\sum }_{j\ne k}\left|{\mathbf{h}}_k^H{\mathbf{w}}_j\right|}^2+{\sigma }_0^2}.$$

The comparison is conducted under different system configurations. For the FP method, the system consists of $M=5$ antennas at the base station, $N=80$ RIS elements, $K=4$ users, and noise variance ${\sigma }_0^2=1$. In contrast, the SGP-DARE framework employs $M=8$ antennas, $N=128$ IRS elements with 2-bit phase quantization, and also supports $K=4$ users. These settings are chosen to reflect realistic deployment scenarios while highlighting the performance gains of advanced optimization techniques.

Figure 7 illustrates the sum rate as a function of transmit power for both methods. The SGP-DARE framework consistently outperforms the FP based AO approach due to its joint optimization of active and passive beamforming via gradient projection, dynamic risk adaptation to mitigate channel uncertainty, and efficient handling of hardware constraints such as phase quantization.

Multi-eavesdropper robustness

Figure 8 evaluates the secrecy rate performance under an increasing number of eavesdroppers. The proposed SGP-DARE consistently outperforms benchmark schemes, including AO with SCA + penalty and ARIS-SCA. At $K=6$ eavesdroppers, SGP-DARE sustains a secrecy rate of 5.0 bps/Hz, which is approximately 10% higher than ARIS-SCA and 16% higher than AO. This performance gap widens as K increases, demonstrating that SGP-DARE preserves resilience under adversarial scaling, whereas conventional methods degrade rapidly. The robustness stems from the adaptive risk-expansion step in DARE, which accounts for worst-case CSI perturbations while maintaining convergence stability.

Convergence and reliability

Figure 9 compares the convergence speed of SGP-DARE with the conventional AO method. SGP-DARE achieves 90% of its maximum secrecy rate within just five iterations, reaching full convergence by iteration 12. In contrast, AO requires nearly 30 iterations to converge to a lower steady-state secrecy rate. The faster convergence of SGP-DARE arises from its synergistic gradient-projection updates, which avoid repeated matrix inversions and high-complexity subproblems inherent in AO. Moreover, SGP-DARE not only accelerates convergence but also attains a higher steady-state secrecy rate (0.70 vs. 0.65 bps/Hz for AO), confirming both computational efficiency and reliability. These results demonstrate that SGP-DARE can sustain secure communication under stringent latency constraints while remaining robust to mobility and CSI imperfections.

Power consumption vs. IRS scaling

As shown in Table 3, increasing the IRS size from $N=64$ to $N=256$ results in a 17.4% reduction in EE due to the quadratic complexity growth of SGP’s gradient projections. Our hierarchical optimization approach, which partitions the IRS into $16\times 16$ subarrays, recovers 89% of the lost EE through parallel computation.

Phase quantization impact

Table 4 shows that a 2-bit phase resolution achieves 85.8% of the continuous-phase secrecy performance (3.82 vs. 4.45 bps/Hz), with only a 0.03 s runtime penalty. This validates the effectiveness of our projection-based quantization handling in Algorithm 1. The marginal 4.9% improvement from 2-bit to 3-bit resolution indicates diminishing returns, making 2-bit quantization the most practical choice for implementation.

Robustness to channel impairments

Figure 10 demonstrates the robustness of SGP-DARE under both channel correlation and user mobility. At $\rho =0.9$, the framework sustains a secrecy rate of 3.80 bps/Hz—45% higher than that of the SCA method by leveraging residual spatial degrees of freedom.

Under Doppler shifts caused by mobility at 30 km/h, the SOP increases by only five percentage points (from 18% to 23%), demonstrating resilience to rapid channel variations. Compared to AO’s baseline SOP of 42% under static conditions, SGP-DARE achieves a 57% reduction.

IRS placement optimization

Figure 11 illustrates that the secrecy rate achieved by SGP-DARE is maximized when the IRS is placed at mid-cell ( $60\mathrm{m}$) from the base station. At this distance, the achievable secrecy rate reaches 4.52 bps/Hz, whereas an edge deployment at $100\mathrm{m}$ yields only 3.93 bps/Hz. The mid-cell placement thus provides a 15% gain, calculated as

$$\mathrm{G}\mathrm{a}\mathrm{i}\mathrm{n}=\frac{4.52-3.93}{3.93}\times 100\approx 15\mathrm{\%}.$$

These results confirm that balancing the cascaded path losses $L_{\mathrm{B}\mathrm{S}-\mathrm{I}\mathrm{R}\mathrm{S}}$ and $L_{\mathrm{I}\mathrm{R}\mathrm{S}-\mathrm{U}}$ is critical. Mid-cell placement optimally reduces compound path loss, while SGP-DARE dynamically adapts phase shifts to exploit spatial degrees of freedom, thereby maximizing secrecy performance.

Quantization and complexity analysis

Table 5 evaluates the impact of phase resolution under optimal static conditions ( $\rho =0.5$, mid-cell placement). The 2-bit configuration achieves 85.8% of continuous-phase performance, while higher resolutions yield only marginal improvements. This confirms the suitability of the framework for practical low-resolution implementations.

Computational efficiency is summarized in Table 6. Unlike AO, which incurs $\mathcal{O}(N^3+K^3{M}^3)$ complexity and requires 45–60 iterations, and DRL methods that demand offline training with more than 100 episodes, SGP-DARE achieves an order-of-magnitude lower complexity of $\mathcal{O}(KM+N^2)$ and converges within 12–18 iterations. This balance of scalability and robustness underscores its practicality for multi-eavesdropper secure communications.

Figure 12 highlights improvements in both reliability and efficiency. SGP-DARE reduces the SOP by 45% at $R_{\mathrm{t}\mathrm{h}}=0.2$ bps/Hz compared to AO. Moreover, the framework achieves an energy efficiency of 0.82 bits/Joule, outperforming existing IRS-aided IoT designs.

Joint impairment robustness

As shown in Fig. 13, the SGP-DARE algorithm consistently converges within 20 iterations, even under simultaneous CSI estimation errors and high user mobility. This resilience stems from DARE’s two-pronged adaptation strategy: (i) bounding gradient perturbations with an ${\ell }_2$-norm constraint, and (ii) scaling the learning rate as $\eta \propto 1/\sqrt{v(t)}$ to adapt to velocity-induced channel variations. A detailed description of the DARE procedure is provided in Algorithm 2.

CSI uncertainty resilience

Figure 14 further validates the robustness of SGP-DARE to CSI estimation errors. The framework sustains a secrecy rate of 0.48 bps/Hz at $\epsilon =0.2$, which is 50% higher than that achieved by the SCA method.

This performance is achieved through robust beamforming design, which accounts for estimation errors in both direct and IRS-reflected channels. The worst-case optimization approach limits performance degradation to less than 15%, even under a 20% normalized CSI error.

Comparative analysis with prior works

Table 7 compares the proposed SGP-DARE framework with representative prior works in IRS-assisted secure communication. The evaluation considers secrecy rate (SR), EE, SOP, and runtime, as well as the ability to support quantized phase (QP), robustness to CSI uncertainty (CSI-R), and adaptability to mobility (Mob.). The comparison shows that, while prior methods address individual aspects of IRS-assisted transmission, none achieve the combined robustness, efficiency, and practicality offered by SGP-DARE.

From the comparative results, several insights emerge. AO-based methods such as Shen et al. (2019) and Dong & Wang (2020) achieve secure beamforming by alternately optimizing IRS phases and transmit covariances. Although mathematically tractable, their high per-iteration complexity of $\mathcal{O}(N^3)$ results in slow convergence, often requiring more than 1 s to stabilize. Consequently, their secrecy rates plateau at 2.4–2.6 bps/Hz, less than half of the 5.5 bps/Hz achieved by SGP-DARE. The ARIS-SCA approach (Kong et al., 2024) improves secrecy rate through active IRS elements and convex approximation, but its moderate gain of 3.15 bps/Hz comes at the expense of longer runtime (1.20 s) and increased energy consumption due to active hardware. In contrast, SGP-DARE retains the efficiency of passive IRS with quantized phases while delivering superior secrecy performance and nearly five-fold faster runtime. Distributed IRS optimization in Song et al. (2023) enhances energy efficiency by leveraging cooperative surface deployment. However, its secrecy rate (2.97 bps/Hz) remains limited, and the SOP (35%) is high due to coordination overhead and the lack of mobility adaptation. SGP-DARE, with its dynamic risk expansion strategy, effectively adapts to user mobility and reduces SOP to just 18%. Similarly, the RCG-JO uplink scheme in Wu, Kim & Shim (2022) achieves high energy efficiency (0.57 bits/J) by minimizing IoT transmit power, but it does not explicitly address secrecy and fails under CSI uncertainty. By contrast, SGP-DARE balances security and efficiency, achieving an energy efficiency of 0.82 bits/J while ensuring secrecy robustness.Overall, the superiority of SGP-DARE is evident. It achieves a secrecy rate of 5.50 bps/Hz—nearly double that of AO-based designs and significantly higher than ARIS-SCA or distributed IRS methods—while also ensuring the fastest runtime (0.25 s) and the highest energy efficiency (0.82 bits/J). Most importantly, unlike prior works that address quantization, CSI robustness, or mobility in isolation, SGP-DARE provides a unified solution that simultaneously supports low-resolution IRS hardware, CSI robustness, and mobility adaptation. These results confirm that SGP-DARE not only secures significant secrecy and efficiency gains but also establishes a practical foundation for IRS-assisted secure communication in 6G networks.

Centralized architecture assumption and distributed IRS coordination

The current SGP-DARE framework assumes a centralized controller at the BS, which synchronizes phase updates across all IRS elements. While this ensures consistency, it introduces significant signaling overhead and scalability issues in ultra-dense 6G networks. Distributed IRS coordination provides a practical alternative: each IRS cluster executes local optimization while exchanging low-rate consensus signals with neighboring clusters. Such federated coordination mitigates inter-IRS interference and scales linearly with the number of surfaces. Preliminary studies (Chen et al., 2024) suggest that decentralized consensus-based beamforming can retain up to 60% of the secrecy performance achieved by centralized optimization while reducing overhead by nearly 40%. This approach enables large-scale deployments where hundreds of IRS panels coexist.

Abrupt mobility and prediction models

Although the DARE module adapts effectively to moderate user mobility, abrupt trajectory changes—such as high-speed vehicular U-turns or agile drone maneuvers—may temporarily degrade secrecy performance. Predictive tracking methods, such as Kalman filtering combined with recurrent neural networks (RNNs), can forecast channel variations one coherence block ahead. For instance, simulations with vehicular nodes at 15 m/s² acceleration show that Kalman+RNN prediction reduces SOP by 58% compared to reactive updates. This predictive capability enables SGP-DARE to sustain robust performance in environments with sharp Doppler shifts and adversarial mobility.

IRS placement trade-offs

Optimal mid-cell IRS placement yields a 15% secrecy rate improvement, but obstructed or dynamic environments can limit its applicability. Uncrewed aerial vehicles (UAV) mounted IRSs offer adaptive placement flexibility but incur 18% to 22% additional power costs for propulsion and control (Wu, Kim & Shim, 2022).

Mobility model limitations

DARE adapts well to gradual mobility (e.g., pedestrian motion); however, abrupt trajectory changes such as high-speed vehicular U-turns or agile drone maneuvers may exceed Doppler tracking capacity. Kalman-filter-based prediction and RNN forecasting can significantly reduce SOP. For example, 180° turns at $15$ m/s² acceleration currently increase SOP by 12%.

CSI error distribution sensitivity

The bounded error model in ‘System Model and Problem Formulation’, $||\mathrm{\Delta }|{|}_F\le \epsilon$, remains valid for both light-and heavy-tailed perturbations due to its Hoeffding-based gradient adjustment. Empirical tests show 92% secrecy rate retention under both Gaussian and Laplacian error distributions (Zhou et al., 2021).

Scalability in large-scale IRS

SGP-DARE scales effectively up to $N=128$ elements, but for $N>200$, mutual coupling and $\mathcal{O}(N^2)$ complexity can reduce efficiency. Hierarchical beamforming partitions the IRS into locally optimized sub-arrays, reducing complexity to $\mathcal{O}(N\log N)$. Hardware acceleration (e.g., FPGA-based solvers) could further enable sub-millisecond updates.

Practical implementation constraints

Three notable challenges remain for practical deployment. First, the assumed 2-bit phase resolution does not account for phase-dependent amplitude variations, which are common in practical IRS hardware and can degrade beamforming accuracy. Second, channel estimation overhead scales linearly with the number of IRS elements; for instance, when $N=256$, pilot signals may consume up to 12% of the coherence interval, reducing the time available for data transmission. Third, the current model assumes a static adversary with fixed eavesdropper positions, whereas mobile adversaries would require continuous, risk-aware re-optimization to maintain secrecy guarantees. Addressing these challenges will require adaptive quantization compensators, distributed optimization schemes, and dynamic security protocols. Such improvements, grounded in ongoing IRS research (Zheng et al., 2022), could make SGP-DARE both technically viable and operationally robust for next-generation networks.

Emerging architectures and deployment scenarios

Beyond fixed terrestrial IRS installations, recent research has explored novel deployment strategies to enhance coverage adaptability and secrecy performance. For example, Nguyen, Le & Munochiveyi (2021) analyzes SOP in cooperative underlay cognitive radio networks assisted by IRS, showing that optimized reflection patterns can mitigate primary–secondary interference while maintaining low SOP under spectrum-sharing constraints. This integration is particularly relevant for dense heterogeneous networks where spectrum reuse and security must be jointly managed. A complementary line of work examines aerial IRS platforms mounted on UAV, which provide adaptive placement and line-of-sight (LoS) enhancement (Do et al., 2021). These aerial IRSs can dynamically reposition to maintain favorable cascaded channels, which is especially beneficial in environments with time-varying blockages. However, propulsion and control energy costs introduce trade-offs between mobility benefits and overall energy efficiency. Additionally, IRS-assisted cellular networks with integrated D2D communication have been proposed to improve spectrum utilization and PLS simultaneously (Ji, Qin & Parini, 2022). By leveraging IRS to enhance D2D link quality and suppress eavesdropper reception, these systems achieve significant secrecy rate gains over conventional D2D networks, especially when combined with adaptive beamforming strategies. These emerging architectures suggest that future secure IRS-aided networks may adopt hybrid deployment models—combining fixed, aerial, and D2D-enhanced configurations—to balance coverage, adaptability, and robustness in highly dynamic 6G scenarios.