Advancing OAM-Based FSO Systems: Tackling Pointing Errors for Next-Generation Space and Terrestrial Links

Architecture and channel assumptions

Multiple Laguerre–Gaussian modes carry intensity-modulated M-PAM data on one optical path. A finite receiver aperture and phase-based mode separation feed avalanche photodiodes. The noise model includes received-power-dependent shot noise and thermal noise.

The study isolates pointing error: turbulence is neglected for the assumed short clear-air links and is absent in the vacuum inter-satellite model. Zero-mean Gaussian transverse displacement shifts the beam relative to the aperture; overlap integrals determine a crosstalk matrix between transmitted and detected modes.

Manuscript · Sections II–III; Eqs. (1)–(23)

Detection and design method

Joint maximum-likelihood detection searches Mᴸ symbol combinations for L modes. When pointing errors are small and the coupling matrix is nearly diagonal, individual-mode detection followed by interference refinement reduces the two-stage search to approximately 2ML metric evaluations. This detector relies on the low-crosstalk regime.

For the long-link example, symmetric positive and negative mode groups can produce nearly indistinguishable received coefficients. An asymmetric transmitted set, such as {−5, −3, −1, 0, 2, 4}, separates the two grouped channels. Beam-size sweeps examine the trade-off between received power and tolerating angular error. Pilot-based channel estimation is discussed, with a corresponding overhead trade-off.

Manuscript · Section IV; Eqs. (24)–(34); Fig. 6

Simulation findings and engineering interpretation

The manuscript evaluates 100 m terrestrial and 1000 km inter-satellite links at 1550 nm. The short-link comparison keeps total transmitted power at 100 mW while changing mode count and modulation order. In its low-error regime, adding modes can be less damaging to BER than increasing modulation order.

Wider mode spacing helps the two-stage detector in the studied conditions, while its benefit is not automatic for joint ML detection because received power also changes. On a 1000 km link, 10 µrad angular error corresponds geometrically to about 10 m displacement. Asymmetric mode grouping and beam-size selection must therefore be evaluated separately from millimeter-error short-link detection.

Manuscript · Table I; Section V; Figs. 7–13

Scope and limitations

This is theoretical modeling and simulation, not an orbital demonstration or a measured high-capacity link. Conclusions depend on selected mode sets, aperture size, beam parameters, pointing statistics and channel estimation. The work does not prove unlimited OAM capacity, general immunity to turbulence or a cryptographic security guarantee. The decorative intensity maps in the concept image are not the manuscript’s numerical plots.

Manuscript · Sections II–VI