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Wavefront Engineering for Physical Layer Security in Near-Field Wireless Communications
Sotiris Droulias, Angeliki Alexiou
TL;DR
Near-field wavefront curvature offers additional spatial control for physical layer security, while systematic comparison of beam types remains needed. The paper evaluates focused, curved, AAF, and cosine beams with ULAs and UPAs, and proposes vertical focusing and hollow-focused beams. Hollow-focused beams achieve the highest reported PLS performance among the investigated types in both LoS and VoU scenarios.
Problem
Although focused and curved beams have been studied for near-field PLS, many alternative beam configurations remain unexplored and need systematic comparison.
Source: A. Prior works · p. 2Method
The study evaluates focused, curved, AAF, and cosine beams with ULAs and UPAs using power-based metrics, and proposes vertical phase focusing and hollow-focused apertures.
Source: B. Our contributions · p. 2, §VII · p. 10Results
Hollow-focused beams achieve the highest PLS performance among the investigated beam types in both LoS and VoU scenarios.
Source: B. Our contributions · p. 2, §VII · p. 10Takeaways & Limitations
Tailored near-field wavefronts and aperture engineering provide degrees of freedom for improving PLS in the considered settings.
Source: §VII · p. 11
Abstract
from arXiv · showhide
With wireless transmission exposing information to potential interception by unintended receivers, physical layer security (PLS) offers a promising approach to securing wireless communications. Beamforming can mitigate this vulnerability by exploiting the spatial characteristics of wireless propagation to concentrate power toward the intended receiver while suppressing it at potential eavesdroppers. However, as wireless systems enter the radiating near field of large-aperture antenna arrays, the resulting wavefront curvature provides additional opportunities for spatial wavefront engineering to enhance PLS. In this work, we investigate the use of different beam types for PLS, including focused, curved, abruptly autofocusing, and cosine beams, generated using uniform linear and planar arrays (ULAs/UPAs). To quantify their performance, we introduce power-based metrics that characterize the power received by the legitimate user and a potential eavesdropper. For all beam types we introduce focusing along the vertical UPA direction, to independently control the phase distributions along the two UPA dimensions and enhance the power discrimination between the legitimate receiver and the eavesdropper. We also propose hollow-focused beams, in which an inactive strip is introduced in the transmitting aperture to create a protected low-power region between the transmitter and the legitimate receiver. The results demonstrate that vertical focusing dramatically enhances the PLS performance and that hollow-focused beams achieve superior PLS performance in both line-of-sight (LoS) and vicinity-of-user (VoU) scenarios.
I. INTRODUCTION
Wireless propagation exposes transmissions to interception, so physical layer security uses spatial power control to protect the intended receiver. This work compares near-field beam types and proposes UPA phase control and hollow-focused beams for improving that control.
A. Prior works
- Near-field wavefront curvature offers spatial control beyond conventional directional beamforming, while systematic comparison of alternative beam types remains needed.Prior work studied focused and curved beams, but many configurations remain unexplored.Source: §I · p. 1, A. Prior works · p. 2
B. Our contributions
- The study systematically evaluates focused, curved, AAF, and cosine beams generated with ULAs and UPAs using power-based metrics in LoS and VoU scenarios.The metrics characterize power at the legitimate receiver relative to a potential eavesdropper.Source: B. Our contributions · p. 2
- UPA phase control independently shapes both aperture dimensions, preserving each beam type horizontally while adding vertical cylindrical focusing to improve spatial power discrimination.Hollow-focused beams add an inactive aperture strip to create a low-power region between transmitter and receiver while retaining focused-beam power concentration.Source: B. Our contributions · p. 2
C. Organization
The paper models a single-antenna receiver served by a UPA and evaluates conventional beamforming against eavesdroppers on the link or near the user. Its organization proceeds from system modeling through beam design and performance evaluation.
C. Organization
- The paper proceeds from system and beam models to power-based metrics, ULA and UPA evaluations, hollow-focused beam analysis, and conclusions.The UPA analysis introduces cylindrical focusing in the vertical direction.Source: C. Organization · p. 2
II. SYSTEM MODEL AND CONVENTIONAL BEAMFORMING
- The model uses constant-amplitude UPA elements spaced at half a wavelength and numerically propagates their fields to observation points.For Ny = 1, the UPA reduces to a ULA; conventional beamforming steers using a ULA phase profile.Source: §II · p. 2
- LoS eavesdropping places Eve on the Tx–Rx link, whereas VoU evaluates average power ratio for Eve distributed within a disk centered at the receiver.The VoU disk has radius REve.Source: §II · p. 3
- With conventional beamforming, near-field LoS power ratios oscillate near unity, while VoU gains reverse once the Fraunhofer distance exceeds the receiver distance.In the example, the reversal occurs at Nx ≈70; at Nx = 1000, conventional beamforming gives no substantial improvement over smaller ULAs.Source: §II · p. 3
III. WAVEFRONT ENGINEERING
Focused beams concentrate transmitted power at a focal point by forming a converging spherical wavefront. In a ULA, the phase profile reduces to a cylindrical form.
A. Focused beams
- Focused beams converge toward a focal point and diverge beyond it, potentially circumventing an eavesdropper near that point.The design forms a converging spherical wavefront.Source: A. Focused beams · p. 3
- Focused-beam phase is chosen to make rays normal to concentric spheres converging at the focal point.This wavefront geometry provides the stated focusing mechanism.Source: A. Focused beams · p. 3
- The ULA phase uses the focal distance and steering angle, and suppressing its y-direction reduces the spherical phase to cylindrical phase.The supplied description identifies df as focal distance and θr as steering angle.Source: A. Focused beams · p. 3
B. Curved beams
Curved beams follow parabolic trajectories whose parameters can be set to pass through chosen points, including the receiver. The caustic describes the main-lobe path and can be arranged to bound a protected region along the link.
B. Curved beams
- The caustic is the envelope of geometric-optics rays and corresponds to the curved beam’s main-lobe trajectory in the wave description.Its intersection with the UPA edge is set to maximize array usage.Source: B. Curved beams · p. 4
- Trajectory parameters are solved from the caustic passing through a selected point and the receiver, together with its intersection at the array plane.The selected point can be placed on the Tx–Rx line of sight to define a protected region extending toward the receiver.Source: B. Curved beams · p. 4
- For a receiver directly in front of the UPA, the trajectory equations simplify using θLoS = 0° and xP = xRx = 0.In this case the protected line-of-sight interval is specified by rP–rRx.Source: B. Curved beams · p. 4
C. Abruptly auto-focusing beams
One-dimensional AAF beams combine oppositely directed curved beams to focus at a selected distance while keeping maximum intensity low along the propagation path. Their lenticular geometry and displaced main-lobe maximum guide beam design.
C. Abruptly auto-focusing beams
- 1D AAF beams combine opposite-directed curved beams to focus at a selected target distance while maintaining low maximum intensity along the propagation path.Their shape extends uniformly along the y-direction, creating larger low-power regions than conventional radially symmetric beams.Source: C. Abruptly auto-focusing beams · p. 4
- The two curved beams form a lenticular region whose long axis measures 2z0 and whose maximum short-axis width measures 2x0.Both caustics pass through the origin; applying the beam-design relation for xRx = 0 gives the beam parameters.Source: C. Abruptly auto-focusing beams · p. 4
- The main-lobe maximum is displaced from xc by δxm, so power concentrates along the z-axis slightly beyond 2z0.The long- and short-axis dimensions can be used as inputs to obtain β; for Airy beams, the displacement is given analytically.Source: C. Abruptly auto-focusing beams · p. 4
D. Cosine beams
A cosine beam is formed by two oppositely angled waves in one plane, implemented with opposite linear phase slopes around x = 0. Its convergence angle is controlled by βx, and its propagation creates a protected low-power region beyond zmax.
D. Cosine beams
- A cosine beam superposes two waves traveling at opposite oblique angles in the same plane, unlike the radially symmetric Bessel beams.Opposite linear phase slopes around x = 0 provide a straightforward implementation.Source: D. Cosine beams · p. 4
- For steering in the xz-plane at angle θr, the input-plane phase profile uses βx to control the convergence angle of the counter-propagating waves.βx is expressed in terms of zmax, where the waves cross, and the UPA width along x.Source: D. Cosine beams · p. 5
- Cosine beams create protected regions beyond zmax, and their near-invariance along y extends the low-power region across that direction.This can provide larger regions of extremely low power than conventional radially symmetric Bessel beams.Source: D. Cosine beams · p. 5
IV. PERFORMANCE METRICS
The secrecy rate complements the power ratio by accounting for noise, and it increases with higher receiver SNR and lower power ratio. The assessment places the link deep in the near field and finds conventional beamforming performs poorly against a line-of-sight eavesdropper.
IV. PERFORMANCE METRICS
- Secrecy rate can be expressed using the power ratio and receiver SNR, with Eve and receiver SNRs defined relative to noise power.SNR_Eve = P_Eve/P_N and SNR_Rx = P_Rx/P_N.Source: §IV · p. 5
- Higher receiver SNR and lower power ratio yield higher secrecy rate; at ρ = 0 it reaches Smax, while at very large receiver SNR it approaches −log2 ρ.The power ratio alone does not account for noise, whereas secrecy rate is the difference between legitimate-user and eavesdropper channel capacities.Source: §IV · p. 5
V. PLS PERFORMANCE ASSESSMENT
- The evaluation uses a 1 m ULA at 150 GHz with 1000 elements, operating deep in the near field where wavefront engineering is useful.The section assesses line-of-sight and vicinity-of-user eavesdropping scenarios.Source: §V · p. 5, A. LoS eavesdropping · p. 5
1) Conventional beamforming:
- Conventional beamforming gives extremely poor line-of-sight security because its high power ratio dominates secrecy rate, leaving it practically insensitive to noise level.The power ratio exceeds unity because the beam is stronger closer to the transmitter.Source: 1) Conventional beamforming · p. 5
2) Focused beam:
Focused, curved, AAF, and cosine beams offer different line-of-sight protection patterns. Their relative performance depends on Eve's location and, for some designs, the receiver location; cosine beams protect behind the receiver when tuned to it.
3) Curved beam:
- In the 2–5 m protected region, the curved beam suppresses eavesdropping more than the focused beam, but its high performance holds only across a limited range of receiver locations.The text attributes this range constraint to the large panels needed for sharp bends at long distances.Source: 3) Curved beam · p. 5, 5) Cosine beam · pp. 6–7
4) AAF beam:
- The AAF beam gives optimum performance when Eve lies on the transmitter-receiver line, but increasing receiver distance leaves a security gap behind the receiver.The text attributes that gap to stray radiation from the two constituent curved beams.Source: 4) AAF beam · p. 5, Figure 2 · p. 6, 5) Cosine beam · p. 7
2) Focused beam:
- The focused beam significantly suppresses Eve's power, bringing secrecy rate near its maximum for most Eve locations at low SNR.Its focal distance is set to the receiver location, and it offers a wide range of secure areas across receiver locations.Source: 2) Focused beam · p. 5, Figure 2 · p. 6, 5) Cosine beam · p. 6
5) Cosine beam:
- The cosine beam performs best against an eavesdropper behind the receiver, where its diverging waves create a low-power region.Tuning its range to the receiver extends the protected region behind the receiver as receiver location changes.Source: 5) Cosine beam · pp. 6–7, Figure 2 · p. 6
- The VoU assessment maps secrecy rate, averages ρ within a disk around the receiver, and plots the probability that S exceeds M Smax as disk radius varies.These panels characterize performance for Eve locations distributed around the receiver.Source: Figure 4 · p. 7
B. VoU eavesdropping
In vicinity-of-user eavesdropping, focused beams outperform the other evaluated beam types. Extending arrays into a second dimension enables independent phase control, while vertical focusing and parabolic phase approximations support UPA beam design.
B. VoU eavesdropping
- As Eve’s disk radius increases, average power ratio ⟨ρ⟩ decreases because spatial averaging includes progressively more low-power regions outside the beam.The same trend holds across beam types, despite differences in absolute performance.Source: B. VoU eavesdropping · p. 7
- Focused beams deliver the highest VoU performance, while conventional beamforming yields the lowest, and focused beams outperform all other beams across the evaluated threshold probabilities.The reported advantage is attributed to spatial power concentration at the focus and rapid power decay away from it.Source: B. VoU eavesdropping · p. 7
VI. FROM ULAS TO UPAS
- UPAs add a y-direction degree of freedom, but beams with y-invariant phase profiles remain approximately uniform along that axis and perform similarly to ULAs.Independent phase distributions along x and y allow 2D wavefront shaping; φx can use the beam profiles while φy is chosen independently.Source: §VI · pp. 7–8
- For LoS UPA evaluation, Fig. 5 plots power ratio against Ny, compares ULA- and square-UPA-limit cross-sections, and shows secrecy rate versus Eve’s LoS position at different SNRs.The figure uses Nx = 1000 for the Ny sweep and marks Smax for each SNR.Source: Figure 5 · p. 8
- A second-order expansion of the focused-beam phase around the UPA center yields a parabolic phase that approximates the spherical profile across a wide range of practical cases.The global phase term is omitted because it multiplies the entire field by the same complex factor.Source: §VI · p. 8
A. Vertical focusing
Cylindrical focusing along a UPA’s vertical dimension improves power discrimination between the receiver and eavesdropper. Hollow-focused beams add a central inactive strip, with different strip-width behavior in LoS and VoU scenarios.
A. Vertical focusing
- UPA phase control preserves each beam type’s horizontal profile while adding cylindrical focusing along the vertical dimension to concentrate power around the receiver.The xz-plane and yz-plane phase profiles can combine to produce spherical focusing.Source: A. Vertical focusing · pp. 8–9
- With cylindrical focusing, focused beams achieve the highest secrecy rates in LoS and best VoU performance; all beam types improve over ULA counterparts.The VoU comparison plots averaged power ratio and the probability that S exceeds M Smax as Ny varies.Source: A. Vertical focusing · p. 9, Figure 6 · p. 9
B. Hollow-focused beams
- A central inactive strip creates a low-power region along the Tx–Rx path while a relatively narrow strip is expected to preserve focusing; the approach applies to ULAs and UPAs.The UPA omits elements in a narrow strip centered on the x-axis.Source: B. Hollow-focused beams · p. 9
- In LoS, hollow-focused beams further boost PLS for ULAs and UPAs, with the power ratio optimized at roughly δw ≈ 40%Lx.Wider strips enlarge the protected region but deactivate more elements, reducing focusing efficiency and power at the receiver.Source: B. Hollow-focused beams · p. 9, Figure 7 · p. 10
- In VoU, PLS performance decreases monotonically as the inactive strip widens, unlike the LoS trade-off.The received power at the receiver decreases nonlinearly; for small strips, it is approximated by PRx ≈ 1 − 2(δw/Lx).Source: B. Hollow-focused beams · p. 9, Figure 8 · p. 10
VII. DISCUSSION AND CONCLUSION
Near-field wavefront engineering improves PLS by tailoring power around potential eavesdroppers, with hollow-focused beams achieving the highest performance among the investigated beam types in LoS and VoU scenarios. The results also show that vertical focusing improves power discrimination, while hollow-focused beams create a low-power region between the transmitter and receiver.
VII. DISCUSSION AND CONCLUSION
- Hollow-focused beams achieve the highest PLS performance among the investigated beam types in both LoS and VoU eavesdropping scenarios.They combine focused-beam power concentration with a protected low-power region between transmitter and receiver.Source: §VII · p. 10
- Vertical focusing can substantially improve PLS across all considered beam types by exploiting the UPA’s additional spatial degree of freedom.Independent phase control along the two aperture dimensions introduces cylindrical focusing along the vertical direction.Source: §VII · p. 10
- Focused beams generally provide the highest power discrimination, while curved and AAF beams suit LoS eavesdropping when zEve < zRx and cosine beams when zEve > zRx.Power-based metrics characterize performance in LoS and VoU scenarios.Source: §VII · p. 10
- Hollow-focused beams are formed by deactivating a narrow strip of the transmitting aperture, combining focused-beam power concentration with an intervening low-power region.The approach enhances protection against LoS eavesdropping while maintaining competitive performance in VoU scenarios.Source: §VII · p. 10
- Without a phase distribution along the vertical UPA direction, the UPA provides no substantial PLS benefit over ULA-based operation.Fig. 9 compares ULA and UPA power ratio and secrecy rate for the LoS scenario without vertical phase control.Source: Figure 9 · p. 11
APPENDIX
The appendix compares ULA and UPA performance when the UPA has no phase variation along its vertical direction. Under this condition, the UPA does not improve power ratio or secrecy rate substantially over ULA-based operation.
APPENDIX
- Without vertical phase control, transitioning from a ULA to a UPA does not improve the power ratio ρ in the LoS scenario.The UPA phases are y-invariant, producing a practically uniform vertical beam shape.Source: APPENDIX · p. 11
- Without exploiting the UPA’s vertical dimension, its secrecy rate offers no substantial PLS benefit over ULA-based operation.The comparison evaluates secrecy rate as Eve’s location varies along the Tx-Rx LoS at different SNR levels.Source: APPENDIX · p. 11
- In Fig. 9, the UPA uses Nx = Ny = 1000 with no vertical phase; under this condition, transition from ULA to UPA does not improve ρ or offer substantial PLS benefit.Source: APPENDIX · p. 11