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Doppler Effect in High-Mobility Free Space Optical Links with Multicarrier Intensity Modulation
Mahmudul Hasan Abid, Mohammad Ali Khalighi, Majid Safari
TL;DR
High mobility can impair multicarrier IM/DD FSO links even after optical-carrier phase removal, raising the question of how Doppler appears in the electrical domain. The paper models Doppler as analytic-signal single-sideband shifting and finds CPE plus ICI: pilot tracking handles small shifts, whereas larger shifts require ICI mitigation because BER floors emerge.
Problem
The paper addresses the previously uncharacterized manifestation of Doppler-induced CPE and ICI in high-mobility multicarrier IM/DD FSO links.
Method
The paper models Doppler-induced time scaling with a single-sideband frequency shift applied to the analytic signal of a DCO-OFDM waveform.
Results
At small Doppler shifts, pilot-aided CPE correction substantially recovers BER, while at µ = 0.2 residual ICI produces a BER floor.
Takeaways & Limitations
Multicarrier IM/DD links require CPE tracking and, at larger Doppler shifts, ICI-aware equalization.
Abstract
from arXiv · showhide
In this paper, we investigate the impact of Doppler-induced time scaling in intensity-modulation/direct-detection (IM/DD) multicarrier free-space optical links subject to high mobility. Modeling the Doppler effect as a single-sideband frequency shift applied to the analytic signal waveform, we show that it produces a baseband-equivalent phase rotation, resulting in a common-phase error (CPE), in addition to Dirichlet-kernel inter-carrier interference (ICI), even though the optical carrier phase is removed through photo-detection. The numerical results based on DC-biased optical orthogonal frequency-division multiplexing (DCO-OFDM), show that at small Doppler shifts, the CPE component dominates and can be effectively compensated through pilot-aided phase tracking, while the induced ICI remains rather negligible. At larger Doppler shifts, however, ICI becomes dominant and results in a bit-error-rate floor, highlighting the need for both CPE tracking and ICI mitigation. This is particularly relevant for optical links with small subcarrier spacing and large Doppler shifts, such as those in low-Earth-orbit satellite-to-ground and inter-satellite transmission scenarios.
I. Introduction
FSO systems commonly use simple IM/DD, while multicarrier signaling enables QAM-based transmission but preserves baseband phase effects. The paper identifies Doppler-induced CPE and ICI as previously uncharacterized impairments in high-mobility multicarrier IM/DD links.
- IM/DD remains conventional because it offers implementation simplicity compared with coherent modulation or detection.
- Although photo-detection removes optical-carrier phase, complex subcarrier symbols preserve baseband signal phase and expose frequency-domain channel effects.
- Multiple-subcarrier schemes such as O-OFDM and O-OTFS enable larger constellations such as QAM through Hermitian-symmetric subcarrier mapping.The resulting IDFT waveform is real-valued for intensity modulation.
- The paper formalizes baseband-equivalent phase and shows that Doppler-induced time scaling produces common phase rotation and Dirichlet-kernel ICI after direct detection and DFT demodulation.These effects motivate pilot-aided CPE tracking and, when needed, ICI-aware equalization.
- High-mobility FSO links use cases such as LEO-to-OGS and ISL, while multicarrier signaling supports turbulence mitigation and frontend-bandwidth constraints.
II. System Model
The system model isolates Doppler in a LOS IM/DD DCO-OFDM link by neglecting turbulence, clipping effects, channel loss, pointing errors, and channel delay spread. Hermitian symmetry and DC bias produce a real, non-negative waveform for optical transmission.
- The modeled link is a time-varying-delay LOS FSO channel between moving Tx and Rx platforms, with atmospheric turbulence neglected.
- DCO-OFDM uses an N-point IDFT and Hermitian-symmetric QAM symbols so the time-domain signal is real-valued.
- A bias b and zero-level clipping enforce waveform non-negativity before the signal drives the optical source.Clipping effects, including limited optical-source dynamic range, are neglected.
- The model neglects channel loss, pointing-error effects, and turbulence to focus on Doppler, while received noise is modeled as additive white Gaussian noise.
A. Doppler shift modeling
Doppler is modeled as time scaling from relative radial motion and approximated by a single worst-case reference frequency shift. The study then emulates that shift with an analytic-signal single-sideband operation and evaluates mobility-dependent effects.
- For constant radial velocity, propagation delay varies with Tx–Rx range, with negative velocity corresponding to an approaching pair.
- Time scaling by (1 + α) shifts each subcarrier at frequency f_i to (1 + α)f_i, producing a frequency offset of αf_i.
- The model approximates subcarrier-dependent Doppler with a fixed shift f_D = αf_m, using the band-edge frequency as a conservative worst-case reference.The band-center and band-edge nominal-frequency choices are specified for N-subcarrier DCO-OFDM.
- A single-sideband frequency shift is applied to the analytic signal of the zero-mean received waveform over one OFDM symbol.
- Doppler impairments are often negligible at low mobility but become noticeable as mobility and bandwidth increase.
B. Baseband Rx Model
The receiver model represents Doppler through a baseband-equivalent CFO whose zero-index coefficient causes common phase rotation and whose nonzero-index coefficients cause ICI. Pilot-based per-symbol estimation is used to correct the CPE before demapping.
- B. Baseband Rx Model: The DFT output combines Doppler-affected subcarriers through Dirichlet-kernel CFO coefficients and additive transformed noise.The coefficients are interpreted as a baseband-equivalent CFO in the IM/DD receiver model.
- B. Baseband Rx Model: The C0(ε) term produces common phase error, whereas Cℓ(ε) for ℓ ≠ 0 produces inter-carrier interference from other subcarriers.With ε = 0, the model reduces to the undistorted symbols plus noise, without CPE or ICI.
- B. Baseband Rx Model: Figure 4 compares BER versus SNR across QAM constellation orders for normalized Doppler values µ = 0 and µ = 0.05.The comparison uses no-Doppler and Doppler conditions across different constellation orders.
- B. Baseband Rx Model: Figure 5 evaluates 8-QAM BER versus SNR with CPE correction while varying the number of pilot subcarriers |P|.It compares no Doppler with µ = 0.05 under different pilot-count settings.
- B. Baseband Rx Model: CPE is estimated per symbol from pilot subcarriers and removed by rotating each received symbol before standard demapping.The proposed correction multiplies each received subcarrier by e^-j ˆϕ.
III. Numerical Results
Numerical simulations assess Doppler’s effect on BER in FSO links and evaluate the efficiency of the proposed CPE-tracking method.
- III. Numerical Results: Numerical simulations assess Doppler’s impact on bit-error-rate performance in free-space optical links.The simulations target DCO-OFDM-based links.
- III. Numerical Results: The simulations evaluate the efficiency of the proposed common-phase-error tracking method.The method is assessed alongside the Doppler-induced BER effects.
- III. Numerical Results: The numerical study jointly examines link performance and compensation effectiveness under Doppler impairment.Both objectives are explicitly included in the simulation assessment.
A. Simulation Parameters
The simulations use a large DCO-OFDM system with pilot-aided CPE correction and normalized Doppler values representing satellite-link scenarios plus a larger illustrative case.
- A. Simulation Parameters: The simulation uses N = 4096 subcarriers, Gray-mapped power-normalized QAM symbols, and no cyclic prefix.Channel delay spread is neglected to isolate Doppler and ICI.
- A. Simulation Parameters: Each OFDM symbol uses 32 pilot subcarriers for common-phase-error estimation and correction.The pilots support the proposed CPE-tracking procedure.
- A. Simulation Parameters: The study considers normalized Doppler values µ = 0.05, 0.1, and 0.2.The first two values represent LEO–OGS and LEO ISL scenarios, while µ = 0.2 illustrates a larger Doppler shift.
B. Illustration of Doppler Effect on Signal Constellation
Doppler rotates and spreads the received QAM constellation, with stronger rotation and ICI at larger normalized shifts; CPE correction removes rotation but leaves spreading.
- B. Illustration of Doppler Effect on Signal Constellation: With no Doppler, the 4-QAM constellation shows only receiver-noise effects.This provides the baseline for the Doppler-affected constellations.
- B. Illustration of Doppler Effect on Signal Constellation: At µ = 0.1, Doppler rotates the QAM clusters and increases their spreading through ICI.The constellation therefore departs from the transmitted cluster locations in both phase and dispersion.
- B. Illustration of Doppler Effect on Signal Constellation: At µ = 0.2, the constellation exhibits further phase rotation and stronger ICI with more pronounced cluster smearing.The larger normalized Doppler produces both effects more strongly than µ = 0.1.
- B. Illustration of Doppler Effect on Signal Constellation: CPE correction largely eliminates the phase rotation, while constellation spreading due to ICI remains almost unchanged.The correction separates the removable CPE component from the residual ICI component.
C. BER Performance
CPE correction substantially recovers BER performance at small normalized Doppler, whereas residual ICI causes a BER floor at higher Doppler and becomes more problematic for higher-order QAM.
- CPE correction substantially recovers performance at µ = 0.05 and 0.1, with remaining BER degradation attributed to residual ICI.
- At µ = 0.2, significant residual ICI produces a BER floor that requires ICI-aware equalization with a time-varying channel model to eliminate.
- Higher constellation orders make CPE and ICI more pronounced at µ = 0.05, and residual ICI leaves a BER floor after CPE correction.
- Increasing pilot count improves CPE estimation and BER for 8-QAM, but gains become marginal beyond a moderate number of pilots.
IV. Discussion and Conclusion
Multiple-subcarrier IM/DD links preserve baseband-equivalent subcarrier phase despite losing optical-carrier phase through direct detection. Doppler and related waveform impairments therefore induce CPE and ICI that require estimation and equalization.
- Direct detection removes optical-carrier phase but preserves baseband-equivalent phase in multiple-subcarrier IM/DD systems.
- Time shifts, time scaling, and frequency offsets appear after DFT demodulation as complex exponentials that induce constellation rotation and subcarrier mixing.
- Pilot-aided CPE tracking can estimate and equalize these baseband phase terms, especially in high-Doppler ISL and LEO-to-OGS links.
- Single-subcarrier IM/DD links are not sensitive to baseband-equivalent phase.
Appendix
The appendix quantifies representative Doppler shifts for LEO-to-ground and inter-satellite links using band-edge evaluation and relative satellite velocity. The resulting normalized Doppler is approximately 0.045 for the LEO-to-ground case and 0.1 for the considered ISL case.
- For the LEO-to-ground link, Doppler is evaluated at the nominal band-edge frequency fm,e = (N/2 −1)∆f as a worst-case value.
- For a 500 km LEO altitude and ∆f = 50 kHz, the calculated Doppler is fD = −2.23 × 10^3 Hz and normalized Doppler is µ = 0.045.
- The ISL Doppler approximation uses the relative velocity between satellites and the band-edge frequency through fD ≈ fm,evrel/c.
- For two counter-rotating satellites, the relative velocity is approximately 15.2 km/s, yielding normalized Doppler µ ≈ 0.1.