OHL-Assisted All-Optical Regenerative Relaying for Pointing-Impaired M-PAM Inter-Satellite Links

Meysam Ghanbari’s proposed regenerative relay

The first-author proposal addresses a concrete trade-off: transparent amplify-and-forward relays repeatedly amplify analog noise, while decode-and-forward relays recover symbols through optical-to-electrical-to-optical processing. The proposed forwarding path instead reshapes the signal into one of a fixed set of admissible optical power levels at each satellite.

A telescope and optical bandpass filter feed a variable-gain receive EDFA. A splitter sends the stabilized signal into M − 1 parallel optical hard-limiters; ordered thresholds produce a thermometer pattern that selects the regenerated M-PAM level. A transmit EDFA and output filter launch that level toward the next satellite. The analysis models this optical decision and regeneration function rather than demonstrating a complete fabricated payload.

Manuscript · Sections I–II; Fig. 1; Eqs. (1)–(5), (37)–(46)

Why low-delay forwarding is the design motivation

The proposed data path removes the O/E/O symbol-recovery, electrical decoding and buffering stages used by the compared DF architecture. Regeneration also stops the previous hop’s continuous analog noise waveform from being forwarded as in transparent AF. It does not remove propagation time or eliminate errors in the regenerated decisions.

The supplied preprint evaluates symbol-error probability, not a measured time budget. It gives no hardware latency, power-consumption campaign or end-to-end packet-delay experiment. “All-optical” describes the proposed forwarding path; the assumed channel estimation, frame-level gain updates, acquisition and spacecraft control still need an implementation. Their timing and overhead must be assessed in a prototype.

Manuscript · Sections I–II-C; Section IV; Sections VII–VIII

Pointing-aware gain stabilization and its failure region

Each hop is a vacuum Gaussian-beam link with finite receive aperture and Rayleigh-distributed pointing displacement. Atmospheric turbulence and weather are excluded. Residual angular jitter becomes spatial jitter in proportion to hop distance, and channel gains are assumed independent across hops and approximately constant over one frame.

With perfect block-wise channel estimation, a clipped inverse-channel receive gain aligns M-PAM means with fixed optical thresholds. Below the gain-limited boundary, the maximum EDFA gain cannot restore the target scale. The outage model collapses the output to the lowest level, producing a reliability floor that extra launch power alone cannot always remove. The upper gain boundary also matters when the minimum amplifier gain prevents target scaling.

Manuscript · Section III-A–B; Section IV-A–C; Eqs. (6)–(14), (27)–(36)

Noise model, closed forms and multi-hop error propagation

The decision statistic includes transmit-side ASE, receive ASE–ASE and signal–ASE beat noise, filtered background radiation and implementation-dependent decision noise. Independent components are combined in a conditional Gaussian approximation. Full-noise numerical integration provides a reference before a two-region closed form separates signal–ASE-dominant and constant-noise operation.

The compact closed form requires the target scaling to remain feasible throughout the non-outage region and appropriate noise-partition conditions; the paper directs the reader to the general numerical expression when the upper gain-boundary condition fails. It therefore should not be treated as an exact hardware model in every noise regime.

An M × M transition matrix describes the probability of regenerating each output symbol for each input symbol. Multiplying the hop matrices preserves structured decision-error propagation, including neighboring-level confusion and outage-induced collapse. Under equiprobable source symbols, end-to-end SER is one minus the normalized trace of the total matrix. Regeneration limits analog noise accumulation, while discrete symbol mistakes remain.

Manuscript · Sections III-C–E, V and VI; Eqs. (15)–(26), (47)–(107)

Validation settings and comparison with AF and DF

One-hop validation uses 600 km links at 1550 nm, a 6.75 cm transmitted beam waist and a 5 cm receive-aperture radius. The parameter table evaluates M = 4, 8 and 16, angular jitter from 1 to 4 µrad, transmit-amplifier gain 10, maximum receive gain 1000, optical bandwidth 50 GHz and decision bandwidth 25 GHz. Monte Carlo results, full-noise integration and the two-region approximation closely agree in the reported comparisons.

For the separate 4-PAM comparison with 500 km hops and a 5 cm launch waist, the proposed relay reaches the 10⁻⁴ SER region near 11 dBm for four hops, with an approximately 5 dB power penalty relative to the modeled DF baseline. AF remains more noise-limited in that comparison. This is a conditional reliability comparison, not evidence that the proposed architecture universally outperforms DF.

Manuscript · Section VII; Table I; Figs. 2–4

Design trade-offs and the next engineering step

Higher PAM order provides more bits per symbol but reduces decision margins. Beamwidth must balance aperture collection against pointing tolerance, and the gain target affects both threshold alignment and outage. The paper distinguishes adding hops of fixed distance from dividing a fixed total distance: the former adds decision stages, while the latter can improve each hop enough to outweigh those extra decisions.

The next meaningful validation is a calibrated optical implementation of the limiter bank, level selector and regeneration stage, including splitter loss, thresholds, amplifier gain dynamics, noise coefficients and imperfect channel estimation. Relay latency and energy need direct measurement. Route selection, packet scheduling, correlated motion and spacecraft qualification remain outside the supplied physical-layer study.

Manuscript · Sections II-C, IV and VII; Figs. 5–8; Section VIII