Intelligent Reflecting Surfaces for Free Space Optical Communications

I. INTRODUCTION

• FSO systems provide high bandwidth but conventionally require a direct LOS, which optical IRSs can relax by redirecting beams between blocked transceivers.Simple mirrors can redirect optical beams with negligible scattering, while intelligent mirrors can control the reflected direction mechanically or electronically.Source: §I · p. 1, A. System Model · p. 1
• Prior optical reflecting-surface work addressed beam guidance, retro-reflection, or network planning, but did not study the IRS impact on the FSO channel model.Source: §I · p. 1

C. Problem Statement

• The paper characterizes end-to-end Tx-to-IRS-to-Rx geometric and misalignment losses as functions of IRS area, position, and orientation.It develops conditional and statistical models for performance analysis of IRS-based FSO systems.Source: §I · p. 1, C. Problem Statement · p. 2
• IRS reflection efficiency ζ accounts for practical absorption or scattering, with typical values in the range [0.95, 1].Absorption at the IRS is treated as part of the atmospheric loss.Source: C. Problem Statement · p. 2
• IRS position and orientation shape the reflected-power distribution, while IRS size determines which portion of the photodetector is covered and affects the mean GML.Source: C. Problem Statement · p. 2
• Building sway of the Tx, Rx, and IRS introduces randomness into geometric and misalignment loss through additional beam misalignment.The analysis considers a 2D model first and generalizes it to 3D.Source: C. Problem Statement · p. 2

A. Geometry of the Considered System

• The 2D geometry specifies the LS, IRS, and PD positions, their orientations, and their physical lengths, then uses a mirrored virtual LS to analyze reflection.The virtual beam angle is 2θrs − θb.Source: A. Geometry of the Considered System · p. 2

B. Spatial Distribution of the Reflected Power Density

• The reflected optical power is modeled as a Gaussian beam whose density varies with distance from the beam-footprint center on a perpendicular line.The beam width depends on propagation distance and atmospheric parameters including wavelength and refractive-index structure.Source: B. Spatial Distribution of the… · pp. 2–3
• The reflected beam is a truncated Gaussian originating from the virtual LS and confined to a region whose size depends on IRS size and orientation.This region determines the spatial extent of reflected power available to the PD.Source: B. Spatial Distribution of the… · p. 3
• Choosing the IRS orientation so the beam footprint center coincides with the PD center yields an optimal reflection angle θ*rs.The relevant propagation distance is the end-to-end distance de2e = dsr + drp.Source: B. Spatial Distribution of the… · p. 3

• The geometric-loss model integrates reflected power density over the photodetector to obtain the total captured power fraction.Source: C. Conditional GML Model · p. 3
• The closed-form geometric-loss expression uses the angle between the photodetector and beam line and the beam-line offset from the photodetector center.The non-orthogonality term is sin(ψ), and the offset is Lc = ∥cpd − pc∥.Source: C. Conditional GML Model · p. 3
• The closed-form result assumes the photodetector area and beam misalignment are both much smaller than the end-to-end transmission distance, conditions stated to hold in practice.The IRS size affects the geometric terms ρ1 and ρ2; for a sufficiently large IRS, they reduce to distances from p0 to p1 and p2.Source: C. Conditional GML Model · p. 3
• When the IRS is sufficiently large and the reflected beam strikes the photodetector center perpendicularly, the model reduces to a special-case captured-power expression.Source: C. Conditional GML Model · p. 3
• The maximum collected-power fraction for fixed end-to-end distance and photodetector area requires a sufficiently large IRS, zero misalignment, and a photodetector orthogonal to the beam line.Source: C. Conditional GML Model · p. 3

• The section examines the effect of building sway on the quality of the considered FSO channel.Source: §IV · p. 3

A. Building Sway Model

• Only fluctuations in one specific direction for each of the transmitter, IRS, and photodetector significantly affect the FSO channel, simplifying the statistical model derivation.Source: A. Building Sway Model · p. 4
• Transmitter displacement is decomposed into beam-direction and orthogonal components, while beam-direction displacement can be neglected relative to the transmitter-to-IRS distance.Source: A. Building Sway Model · p. 4
• IRS displacement is decomposed along the IRS line and its orthogonal direction; the along-line component has negligible impact when the beam passes through a sufficiently large IRS.Source: A. Building Sway Model · p. 4
• Receiver displacement is represented along and perpendicular to the reflected beam, with the along-beam component neglected because the IRS-to-receiver distance is much larger than the fluctuation.Source: A. Building Sway Model · p. 4
• The resulting misalignment depends on projected transmitter, IRS, and receiver fluctuations, with the IRS contribution governed by the angle between the beam and IRS directions.Source: A. Building Sway Model · p. 4
• The model assumes independent zero-mean Gaussian fluctuations for the building-sway components.Source: A. Building Sway Model · p. 4

B. PDF of Power Collected by the PD

• The GML is approximated as a function of beam-footprint misalignment because the exact power expressions are complicated and provide limited insight.Source: B. PDF of Power Collected by the PD · p. 4
• Using the approximation, the model derives a PDF for GML under Gaussian fluctuations.Source: B. PDF of Power Collected by the PD · p. 4
• The derived PDF reveals how the end-to-end distance de2e and fluctuation variance σ2 affect the distribution of geometric and misalignment loss.Source: B. PDF of Power Collected by the PD · p. 4

V. EXTENSION TO 3D SYSTEM MODEL

• The 3D model requires 15 position and orientation parameters, compared with 9 in 2D, motivating a complexity-reducing characterization based on 2D insights.The 3D formulation uses three position variables and two angular variables for each node.Source: §V · p. 4
• The 2D analysis represents the IRS-assisted link through a virtual laser source, whose reflected beam follows a truncated Gaussian profile and whose effective distance is the end-to-end path length.Truncation can be ignored when the IRS is sufficiently large and the photodetector lies completely inside region R.Source: §V · p. 5
• The conditional GML depends on misalignment u, end-to-end distance d_e2e, and angle ψ, with IRS orientation able to make the average misalignment vanish.Choosing θ_rs = θ*_rs according to the design condition gives E{u} = 0.Source: §V · p. 5
• The 3D approximation uses the reflected-beam angle to the photodetector plane and a circular detector's maximum captured-power fraction A_0, followed by a statistical model incorporating IRS effects.The exact GML expression is more involved than the approximation, so the statistical derivation builds on the approximate 3D model.Source: §V · p. 5
• Building sway is modeled with Gaussian fluctuations for the laser source, IRS, and photodetector, while only displacement components affecting GML are retained.IRS fluctuations are reduced to the component orthogonal to its plane, and photodetector fluctuations are represented in two directions perpendicular to the reflected beam.Source: §V · p. 5
• The GML is affected by the IRS only via variable ǫo_r; variations of ǫo_r lead to variations of the misalignment vector u along only one dimension, under the stated basis convention.Source: §V · p. 5

VI. SIMULATION RESULTS

• The simulations use stated default 2D and 3D geometric parameters and 10^6-sample Monte Carlo results for the reported PDF comparisons.The parameter settings include a_p = 10 cm and a_r = 50 cm for both dimensional cases.Source: §VI · p. 5
• Increasing misalignment magnitude |u| decreases channel gain, while beam truncation makes the approximation overestimate GML once the photodetector extends beyond region R.For IRS radius a_r > 50 cm, the approximation remains accurate even for |u| > 35 cm; no optical power is received when the detector has no overlap with R.Source: §VI · pp. 5–6, Figure 2 · p. 6
• The proposed statistical models show excellent agreement with simulation results for the 2D and 3D systems across three fluctuation scenarios with specified building-sway conditions.Scenario 1 uses (σs, σp, σr) = (5, 5, 5) cm; Scenario 2 uses (5, 5, 10) cm; and Scenario 3 uses (5, 10, 5) cm.Source: §VI · p. 6
• The IRS sway has a larger impact than photodetector or laser-source sway in the shown scenario because 2 cos(ψ_r) = 1.782 increases its associated variance.Scenario 2 is equivalent to swapping the larger sway between the photodetector and laser source because of problem symmetry.Source: §VI · p. 6

VII. CONCLUSIONS

• The proposed IRS-based FSO system relaxes the LOS requirement while characterizing how IRS size, position, and orientation affect end-to-end channel quality.The models target the geometric and misalignment losses of the Tx-to-IRS-to-Rx link.Source: §VII · p. 6
• Simulation results validate the developed channel models for typical IRS sizes a_r > 50 cm, where beam truncation is negligible.The models are intended for performance analysis of IRS-based FSO systems.Source: §VII · p. 6
• For beam-to-IRS-plane angles smaller than π/3, IRS building sway can have a larger impact on end-to-end channel quality than transmitter and receiver sway.The relative impact depends on the angle between the beam direction and the IRS plane.Source: §VII · p. 6

APPENDIX A

• The reflected-beam region is bounded by rays from the virtual laser source through the IRS corners, defining the nonzero power-density region R.The footprint center and geometric distances are then obtained from intersections with a line perpendicular to the beam.Source: Appendix A · p. 6

APPENDIX B

• The photodetector's collected power is computed by integrating the reflected power density along the detector line using the distance ρ from the beam-footprint center.The density is related to the orthogonal power profile through r = sin(ψ)ρ and d ≈ d_e2e when a_p, L_c ≪ d_e2e.Source: Appendix B · pp. 6–7
• The total captured fraction is obtained by integrating over the detector, with separate cases depending on whether the beam-footprint center lies on the detector.Evaluating the resulting integrals yields the main GML expression in (11).Source: Appendix B · p. 7

• The collected power is obtained by integrating the reflected irradiance over the photodetector line, using the offset u between beam-footprint and photodetector centers.Source: Appendix C · p. 7
• Equality (a) results from replacing Iorth.Source: Appendix C · p. 7
• A Taylor-series expansion of the exponential term is used to approximate h_g.Source: Appendix C · p. 7
• The first two terms are matched to those of a Gaussian pulse, yielding equation (15) and completing the proof.Source: Appendix C · p. 7