Pointing error evaluation in IRS-assisted VLC systems for indoor hospital environments: a comparative analytical study

1 Introduction

Visible light communication (VLC) has emerged as a promising wireless technology for indoor healthcare settings. It offers several inherent advantages, including immunity to electromagnetic interference, improved physical-layer security, and operation in an unlicensed optical spectrum (Hu and Uysal, 2026). In hospitals, where radio frequency emissions can interfere with sensitive medical equipment, VLC provides a safe and reliable alternative for wireless connectivity (Caputo et al., 2024).

Despite these advantages, VLC systems fundamentally rely on line-of-sight (LoS) transmission. In dynamic hospital environments, optical links are frequently obstructed by medical staff, equipment, movable beds, or curtains. Such blockages can severely degrade the communication link and compromise system reliability (Sun et al., 2025).

To overcome this limitation, intelligent reflecting surfaces (IRSs), also referred to as optical smart mirrors, have recently been proposed to enable non-line-of-sight (NLoS) communication (Sun et al., 2024b). An IRS consists of electronically controllable reflective elements that dynamically redirect incident optical beams toward the intended receiver. By appropriately adjusting the reflection angles, the reflected optical path can maintain connectivity even when the direct LoS path is blocked. Consequently, IRS-assisted VLC has attracted considerable attention for applications such as vehicular communications and indoor wireless networking (Rabiepoor et al., 2024).

Motivated by these advantages, several studies have investigated the design and performance of IRS-assisted VLC systems. The characterization of the channel in the frequency domain for IRS-assisted VLC was studied by Sun et al. (2022) and Chen et al. (2023a), while the optical IRS association model and beam steering design were addressed by Wang et al. (2023). Resource allocation strategies that exploit IRSs to minimize outage probability were examined by Guzman et al. (2020) and Genoves et al. (2025), and the performance of IRS-assisted systems under dynamic human blockages and random user equipment orientation was analyzed by Jamali et al. (2021). Although these studies have significantly advanced the understanding of IRS-assisted VLC systems, their primary focus has been on channel modeling, beam steering, resource allocation, and communication performance under ideal or simplified alignment conditions. In contrast, the statistical characterization of pointing errors in cascaded transmitter–IRS–receiver optical links has received considerably less attention.

Pointing errors are among the primary factors limiting the performance of VLC systems. They are defined as the displacement of the received beam footprint from the center of the photodetector (PD) active area (Chen et al., 2023b), resulting in reduced collected optical power and an increased outage probability (Singh et al., 2024). Pointing error modeling in conventional LoS VLC and free-space optical (FSO) links has been extensively studied using Rayleigh and Beckmann distributions to characterize radial beam displacement (Ghassemlooy et al., 2017). However, the analysis becomes considerably more challenging in IRS-assisted VLC systems, where beam alignment depends not only on the transmitter–receiver geometry but also on accurate IRS beam steering and user localization (Aalimahmoodi et al., 2018). Each stage of the cascaded transmitter–IRS–receiver link introduces an additional source of misalignment, and the combined impact of these impairments on system reliability has not yet been analytically quantified in the literature. In hospital environments, where reliable communication is critical for patient monitoring and emergency response, understanding the impact of these compounded errors is, therefore, essential (Rangappa and Kumar, 2024).

In this study, we develop a unified analytical framework to quantify pointing errors in conventional LoS and IRS-assisted VLC links operating in indoor hospital environments. The main contributions of this work are as follows:

• A comprehensive pointing error model is developed that accounts for all major physical impairment sources, including transmitter jitter, receiver orientation fluctuations, IRS controller inaccuracies, user localization uncertainty, and IRS element fabrication imperfections.
• Closed-form expressions are derived for the composite pointing-error variance for both LoS and IRS-assisted link configurations, with the resulting radial displacement modeled as a Rayleigh-distributed random variable.
• Analytical closed-form expressions are obtained for the average received optical power, electrical SNR, and outage probability under practical pointing error conditions for both link types.
• A comparative numerical analysis is presented that quantifies the reliability trade-off introduced by IRS deployment, revealing that IRS-assisted links exhibit a pointing-error variance approximately 3.5–4 times higher than conventional LoS links and suffer a notably steeper outage probability growth with increasing beam displacement.

To the best of the authors’ knowledge, this work is the first to develop a unified closed-form analytical framework that systematically quantifies the composite pointing-error statistics of IRS-assisted VLC systems by jointly incorporating all major practical impairment sources within a single statistical model. Unlike existing studies that primarily evaluate channel characteristics or communication performance under ideal alignment assumptions, the proposed framework explicitly derives the impact of realistic pointing errors on the received optical power, electrical SNR, and outage probability, thereby providing practical design insights for reliable VLC deployment in indoor hospital environments.

The remainder of this study is organized as follows. Section 2 describes the system model and channel characterization. Section 3 analyzes the statistical modeling of pointing errors. Section 4 derives expressions for the received power, SNR, and outage probability. Section 5 presents numerical results and discussions. Section 6 concludes the study.

2 System model

We consider a hospital environment modeled as a rectangular room with length l, width w, and height h. An optical access point equipped with a light-emitting diode (LED) transmitter is mounted on the ceiling and provides downlink communication to mobile or fixed receivers associated with patients or medical staff, as illustrated in Figure 1. The receiver is modeled as a PD with an active area A r and a field-of-view (FoV) Ψ c. Under LoS blockage, a wall- or ceiling-mounted IRS is activated to maintain an NLoS path (Hu and Uysal, 2026).

2.1 LoS link channel model

For the LoS link, the DC optical channel gain is given by the standard Lambertian model (Ghassemlooy et al., 2017) aswhere m = − ln ⁡ 2 / ln ( cos Φ 1 / 2 ) denotes the Lambertian emission order, with Φ 1 / 2 representing the LED semi-angle at half power; d is the distance between the transmitter and receiver; ϕ and ψ are the angles of irradiance and incidence, respectively; and 1 [ 0 , Ψ c ] ( ψ ) is the indicator function that ensures the receiver operates within its FoV.

H LOS = m + 1 A r 2 π d 2 cos m ϕ cos ψ 1 0 , Ψ c ψ , (1)

2.2 IRS-assisted NLoS link channel model

When the LoS path is blocked, communication is established via an IRS consisting of N reflective elements. Each element is assumed to be a small mirror with area A IRS and reflectivity coefficient ρ ∈ [ 0,1 ]. The IRS controller dynamically adjusts the orientation of each element to steer the reflected beam toward the receiver (Sun et al., 2024a; Abdelhady et al., 2020). The channel gain for the IRS-assisted link can be expressed as follows (Rabiepoor et al., 2024; Chen et al., 2023a):where d 1 , k and d 2 , k denote the IRS distances of the transmitter and the IRS distances of the receiver, respectively, and ϕ k , α k , β k , ψ k are the corresponding optical angles.

H IRS = ∑ k = 1 N m + 1 A r ρ k A IRS k 2 π d 1 , k 2 d 2 , k 2 cos m ϕ k cos α k cos β k cos ψ k , (2)

3 Pointing error analysis

As shown in Figure 2, pointing errors in IRS-aided optical links may originate from multiple mechanisms. In the first case (Figure 2a), misalignment arises when the transmitter fails to accurately illuminate the designated IRS unit. In the second scenario (Figure 2b), additional errors result from random receiver orientation fluctuations or imperfect steering of the reflected beam toward the photodetector (PD) by the IRS. These conditions highlight the multi-source nature of pointing uncertainty in IRS-enabled VLC systems and collectively contribute to the overall pointing-error variance. The following subsections describe the dominant sources of pointing error. The individual pointing-error sources, including transmitter jitter, receiver orientation fluctuations, IRS controller inaccuracies, user localization uncertainty, and IRS fabrication imperfections, are assumed to be statistically independent, consistent with the conventional assumption that these impairments arise from distinct physical mechanisms (Ghassemlooy et al., 2019). Furthermore, each angular error component is modeled as an independent zero-mean Gaussian random variable, a widely adopted assumption in optical wireless communication and FSO literature. Since the horizontal displacement components along the x- and y-axes are independent zero-mean Gaussian random variables with identical variances, the resulting radial displacement follows a Rayleigh distribution, which accurately characterizes isotropic beam misalignment under small random angular deviations (Henniger and Wilfert, 2010).

3.1 Composite pointing error in LoS link

Let r = [ x , y ] T represent the radial displacement vector. For LoS links, the pointing error is primarily determined by the combined effects of transmitter pointing jitter and receiver orientation errors. The horizontal displacement in the receiver plane due to the transmitter pointing error can be expressed as follows (Singh et al., 2024):where θ T = [ θ T , x , θ T , y ] T is the transmitter pointing error angle vector, and the approximation holds for small angles typical in practical systems. Similarly, receiver orientation errors cause effective displacementwhere h is the vertical separation between transmitter and receiver and θ R = [ θ R , x , θ R , y ] T represents the receiver tilt error angles. Assuming statistical independence between these error sources and zero-mean Gaussian distributions for the angular errors with variances σ T , x 2 = σ T , y 2 = σ T 2 and σ R , x 2 = σ R , y 2 = σ R 2, the total displacement variance in each axis becomes (Ghassemlooy et al., 2017)

r Tx = d ⋅ tan θ T ≈ d ⋅ θ T , (3)

r Rx = h ⋅ tan θ R ≈ h ⋅ θ R , (4)

σ LoS , x 2 = σ LoS , y 2 = d 2 σ T 2 + h 2 σ R 2 , (5)

The radial displacement r = x 2 + y 2, therefore, follows a Rayleigh distribution with scale parameter σ LoS = σ LoS , x 2 + σ LoS , y 2 = 2 ( d 2 σ T 2 + h 2 σ R 2 ):

f r , L o S r = r σ LoS 2 exp − r 2 2 σ LoS 2 , r ≥ 0 . (6)

3.2 Composite pointing error in IRS-assisted link

In IRS-assisted VLC links, additional pointing errors arise due to (i) IRS controller inaccuracies, (ii) user localization uncertainty, and (iii) fabrication imperfections of reflective elements. All error sources are modeled as independent zero-mean Gaussian random variables.

Let σ c 2, σ f 2, σ x y 2, and σ z 2 denote the per-axis variances of controller error, fabrication error, horizontal localization error, and vertical localization error, respectively. Due to the reflection law, angular deviations at the IRS result in doubled beam deviation, leading to displacement terms proportional to 2 d 2 , k. Aggregating all IRS-related contributions, the total displacement variance introduced by IRS mechanisms is

σ IRS,add 2 = 4 N 2 ∑ k = 1 N d 2 , k 2 σ c 2 + σ f 2 + 1 N 2 ∑ k = 1 N σ x y 2 + d 2 , k 2 ⁡ tan 2 β k σ z 2 . (7)

Combining these terms with the baseline LoS pointing errors, the overall per-axis displacement variance becomes

σ IRS 2 = d 2 σ T 2 + h 2 σ R 2 + σ IRS,add 2 . (8)

Accordingly, the radial displacement follows a Rayleigh distribution with probability density function

f r , I R S r = r σ IRS 2 exp − r 2 2 σ IRS 2 , r ≥ 0 . (9)

4 Outage probability analysis

When a pointing error with radial displacement r occurs, the received power is attenuated according to the beam profile and PD geometry (Chen et al., 2023b). For a circular PD of radius a and a Gaussian beam with waist w z, the beam intensity at the receiver plane is given bywhere P t is the transmitted optical power, ρ is a position vector in the receiver plane, and r is the displacement vector. The collected power is the integral of intensity over the PD area:

I ρ , r = 2 P t π w z 2 exp − 2 ‖ ρ − r ‖ 2 w z 2 , (10)

P col r = ∬ ‖ ρ ‖ ≤ a 2 P t π w z 2 exp − 2 ‖ ρ − r ‖ 2 w z 2 d ρ . (11)

To facilitate the analytical evaluation of the collected optical power, the two-dimensional surface integral in Equation 11 is transformed from Cartesian to polar coordinates by exploiting the circular symmetry of the photodetector (PD) aperture. Specifically, the integration variable is represented as ( ρ , θ ), while the coordinate system is selected such that the displacement vector r is aligned with the reference axis, allowing only its magnitude r = ‖ r ‖ to appear in the formulation. Consequently, the Euclidean distance is expressed as ‖ ρ − r ‖ 2 = ρ 2 + r 2 − 2 ρ r ⁡ cos ⁡ θ, and the differential area element becomes d A = ρ d ρ d θ. This coordinate transformation converts the original surface integral into a tractable polar-coordinate form, which serves as the basis for the subsequent analytical derivation. By transforming to polar coordinates, the collected power becomes (Bjrnson and Sanguinetti, 2020; Ajam et al., 2024):

P col r = 2 P t π w z 2 ∫ 0 a ∫ 0 2 π ⁡ exp − 2 ρ 2 + r 2 − 2 ρ r ⁡ cos ⁡ θ w z 2 ρ d θ d ρ . (12)

The angular integral yields the modified Bessel function of the first kind of order zero:

∫ 0 2 π ⁡ exp 4 ρ r ⁡ cos ⁡ θ w z 2 d θ = 2 π I 0 4 ρ r w z 2 . (13)

Thus,

P col r = 4 P t w z 2 exp − 2 r 2 w z 2 ∫ 0 a ρ exp − 2 ρ 2 w z 2 I 0 4 ρ r w z 2 d ρ . (14)

The remaining integral can be evaluated using the following identity (Aboagye et al., 2022):

∫ 0 a x e − α x 2 I 0 β x d x = 1 2 α 1 − e − α a 2 I 0 β a − β 2 4 α ∫ 0 a x e − α x 2 I 1 β x β x / 2 d x . (15)

After algebraic manipulation and considering that for practical systems a ≪ w z (tight focusing) or a ≫ w z (large-area detectors), we obtain the following closed-form approximationwhere A 0 = erf ( v ) 2 with v = π a / 2 w z and w z , eq 2 = w z 2 π erf ( v ) / 2 v e − v 2. The power loss factor due to pointing error is therefore

P col r ≈ P t ⋅ A 0 ⁡ exp − 2 r 2 w z , eq 2 , (16)

L p r = P col r P t = A 0 ⁡ exp − 2 r 2 w z , eq 2 . (17)

The average received power, accounting for the statistical distribution of pointing errors, is obtained by averaging the conditional received power over the PDF of r (Genoves et al., 2025):where H 0 represents the ideal channel gain without pointing errors (i.e., H LoS or H IRS with perfect alignment). For LoS links, substituting Equation 16 and Equation 17 into Equation 18 results in

P ̄ r = ∫ 0 ∞ P t H 0 L p r f r r d r , (18)

P ̄ r , LoS = P t H LoS ∫ 0 ∞ A 0 ⁡ exp − 2 r 2 w z , eq 2 r σ LoS 2 exp − r 2 2 σ LoS 2 d r . (19)

Combining exponents, we obtain

P ̄ r , LoS = P t H LoS A 0 σ LoS 2 ∫ 0 ∞ r ⁡ exp − r 2 1 2 σ LoS 2 + 2 w z , eq 2 . (20)

This integral is of the form ∫ 0 ∞ r e − α r 2 ⁡ d r = 1 / ( 2 α ) for α > 0. Let

α LoS = 1 2 σ LoS 2 + 2 w z , eq 2 . (21)

Then,

P ̄ r , LoS = P t H LoS A 0 σ LoS 2 ⋅ 1 2 α LoS = P t H LoS A 0 2 σ LoS 2 1 2 σ LoS 2 + 2 w z , eq 2 . (22)

On simplifying,

P ̄ r , LoS = P t H LoS A 0 1 + 4 σ LoS 2 w z , eq 2 . (23)

For IRS-assisted links, the identical integration procedure applies with σ IRS replacing σ LoS:

P ̄ r , IRS = P t H IRS A 0 1 + 4 σ IRS 2 w z , eq 2 . (24)

4.1 Signal-to-noise ratio analysis

The received electrical SNR after PD is given bywhere R is the PD responsivity and σ n 2 is the total noise variance comprising shot noise and thermal noise components. Substituting the average received power expressions (Ghassemlooy et al., 2017), we obtain

γ = R P ̄ r 2 σ n 2 , (25)

γ LoS = R 2 P t 2 H LoS 2 A 0 2 σ n 2 1 + 4 σ LoS 2 w z , eq 2 2 , (26)

γ IRS = R 2 P t 2 H IRS 2 A 0 2 σ n 2 1 + 4 σ IRS 2 w z , eq 2 2 . (27)

These closed-form expressions explicitly capture the SNR degradation due to pointing errors through the denominator terms involving σ LoS 2 and σ IRS 2 (Tripathi, 2025).

4.2 Outage probability

Outage probability is defined as the probability that the instantaneous SNR falls below a predefined threshold γ th required for reliable communication. Since the pointing error is the dominant random factor affecting received power, we can express the outage probability asThe threshold power loss factor is defined as L th = γ th σ n 2 / R 2 P t 2 H 2. From Equation 17, L p ( r ) = A 0 ⁡ exp − 2 r 2 / w z , eq 2. The condition L p ( r ) < L th is equivalent to

P out = Pr R P t H L p r 2 σ n 2 < γ th = Pr L p r < γ th σ n 2 R 2 P t 2 H 2 . (28)

A 0 ⁡ exp − 2 r 2 w z , eq 2 < L th ⇒ r > w z , eq 2 2 ln A 0 L th . (29)

Let r th = w z , eq 2 ⁡ ln A 0 / L th / 2. Then, the outage probability is simply the probability that the radial displacement exceeds this threshold

P out = ∫ r th ∞ f r r d r = exp − r th 2 2 σ 2 . (30)

For LoS links, substituting r th and σ LoS, we obtain

P out,LoS = exp − w z , eq 2 4 σ LoS 2 ln A 0 R 2 P t 2 H LoS 2 γ th σ n 2 . (31)

For IRS-assisted links,

P out,IRS = exp − w z , eq 2 4 σ IRS 2 ln A 0 R 2 P t 2 H IRS 2 γ th σ n 2 . (32)

The exponential dependence on 1 / σ 2 indicates that outage probability increases dramatically as pointing errors increase (Jia et al., 2024). To model different misalignment conditions, an error scaling factor α esf ≥ 1 scales all pointing error variances: σ 2 → α esf σ 2.

5 Numerical results

This section presents a quantitative comparison between conventional LoS and IRS-assisted NLoS VLC links. Unless otherwise stated, the system and channel parameters are listed in Table 1. The case α esf = 1 corresponds to the nominal parameter set, whereas α esf > 1 represents increasingly severe misalignment conditions, enabling a systematic sensitivity comparison between LoS and IRS-assisted links. The simulation parameters are adopted from representative optical wireless communication models and practical indoor VLC configurations. Parameters related to IRS control, fabrication imperfections, localization uncertainty, and beam propagation are selected within practical ranges to ensure a realistic performance evaluation of the proposed analytical framework.

TABLE 1. Simulation parameters.

Figure 3 shows the comparison of the contribution of different impairment sources to the total pointing-error variance in LoS and IRS-assisted VLC links. For the LoS case, receiver orientation fluctuations dominate the error budget, contributing nearly 64% of the total variance. In contrast, the IRS-assisted link exhibits a more distributed error profile, where localization uncertainty contributes approximately 40%, while IRS controller and fabrication errors also have a noticeable impact. Unlike LoS links, the IRS-assisted configuration is affected by multiple coupled impairments associated with the cascaded transmitter–IRS–receiver path, increasing sensitivity to localization and beam-steering inaccuracies.

Figure 4 shows the variation in the pointing-error variance, σ 2, with the error-scaling factor α esf for both LoS and IRS-assisted VLC links. In both cases, σ 2 increases linearly with α esf; however, the IRS-assisted link exhibits significantly larger variance due to additional controller, fabrication, and localization errors accumulated along the cascaded transmitter–IRS–receiver path. Across the considered range, the IRS-assisted variance remains approximately 3.5–4 times higher than that of the LoS link.

Figure 5 shows the received SNR versus radial displacement for LoS and IRS-assisted VLC links. In both cases, the SNR decreases as pointing error increases due to reduced collected optical power. The LoS link achieves approximately 19 d B at r = 0, while the IRS-assisted link starts near 9 d B because of the additional losses introduced by the cascaded transmitter–IRS–receiver path. At r ≈ 0.025 m, the SNR decreases to nearly − 8 d B for the LoS link and − 18 d B for the IRS-assisted link. The steeper degradation of the IRS-assisted case is mainly caused by the larger composite pointing-error variance associated with the IRS controller, fabrication, and localization errors.

Figure 6 shows the outage probability, P out, versus the radial displacement, r, for both LoS and IRS-assisted VLC links. In both cases, P out increases with increasing r due to the larger power loss caused by pointing errors. However, the IRS-assisted link exhibits a noticeably steeper growth trend. For small displacements ( r < 0.01 m ), both links maintain low outage probabilities around P out ≈ 0.02. As the displacement increases to r ≈ 0.02 m, the outage probability reaches approximately 0.14 for the LoS link and 0.20 for the IRS-assisted link. At r = 0.025 m, the probability of outage increases to nearly 0.38 and 0.55, respectively.

Figure 7 shows the comparison of the analytical electrical SNR derived in Section 4 with the corresponding Monte Carlo simulation results using 10⁵ (100,000) independent Monte Carlo realizations. Excellent agreement is observed over the entire range of radial displacements, confirming the accuracy of the proposed statistical model and the validity of the derived closed-form SNR expression. The slight deviations at larger displacements are mainly attributed to the finite number of Monte Carlo realizations and the increased sensitivity of the received optical power under severe pointing misalignment. The close correspondence between the analytical and simulated results verifies that the adopted Gaussian pointing-error model accurately captures the statistical behavior of practical IRS-assisted VLC links and provides a reliable basis for performance evaluation.

6 Conclusion

This study developed a unified analytical framework for characterizing pointing errors in conventional LoS and IRS-assisted VLC systems in indoor hospital environments. The proposed framework jointly incorporates the transmitter jitter, receiver orientation fluctuations, IRS controller inaccuracies, user localization uncertainty, and fabrication imperfections within a single statistical formulation. Closed-form expressions were derived for the composite pointing-error variance, average received optical power, electrical SNR, and outage probability, based on a Rayleigh-distributed radial displacement. The results reveal a clear reliability trade-off associated with IRS deployment. While IRS-assisted transmission restores connectivity when the direct LoS path is obstructed, the cascaded transmitter–IRS–receiver geometry substantially increases sensitivity to pointing errors. The composite variance is 3.5–4 times higher than for LoS links, yielding an additional SNR degradation of 3–5 dB and a markedly steeper increase in outage probability with beam displacement. Close agreement between the analytical expressions and Monte Carlo simulations confirms the accuracy of the proposed statistical model. These findings indicate that accurate user localization, high-precision IRS beam steering, and effective misalignment mitigation are the primary determinants of link reliability in IRS-assisted VLC deployments.

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Footnotes

Edited by: Hafiz Asif, Sultan Qaboos University, Oman

Reviewed by: Nasir Saeed, United Arab Emirates University, United Arab Emirates

Inam Ullah Khan, Multimedia University, Malaysia