Spectral Segmented Linear Regression for Coarse Carrier Frequency Offset Estimation in Optical LEO Satellite Communications

Abstract

Carrier frequency offset estimation (CFOE) is a critical stage in modern coherent optical communication systems. Although conventional all-digital techniques perform reliably in typical fiber-optic communication links, CFOE often becomes a major bottleneck in low-symbol-rate scenarios with large carrier CFOs (approaching the signal bandwidth) and severe additive noise levels. These conditions are particularly prevalent in links between optical ground stations (OGSs) and low Earth orbit (LEO) satellites, where Doppler-induced frequency shifts of several gigahertz and atmospheric attenuation significantly degrade CFOE performance and can render traditional methods ineffective. In this paper, we propose a robust non-data-aided (NDA) scheme designed for wide-range CFOE. Such a coarse CFOE (C-CFOE) algorithm partially compensates for the CFO, enabling the operation of a subsequent fine CFOE algorithm. By applying low-complexity operations to the spectrum of the received signal, we recast the frequency estimation task as a segmented linear regression (SLR) problem. Numerical simulations in stress-test scenarios involving large CFOs, low SNR, and low symbol rates show that the proposed approach achieves good estimation accuracy and robust convergence. Experimental offline validation further confirms the practical feasibility of the method.

Figures (9)

• Figure 1: (a) Spectrum of a 2-GBd PM-QPSK signal, shaped by a root-raised-cosine (RRC) filter with roll-off factor $\alpha = 0.1$, at 1-dB SNR per bit and impaired by a 3.5-GHz CFO and its (b) corresponding normalized cumulative linear PSD -- with SNR, signal bandwidth ($R_s(1+\alpha)$), and CFO ($\Delta f$) indicated --, forming a characteristic three-segment piecewise-linear structure. Impact of different (c) per bit SNR levels, (d) symbol rates, and (e) CFOs in the cumulative PSD behavior. The accumulation process suppresses high-frequency fluctuations, yielding a more pronounced contrast across the noise-floor and signal-region regimes under SNR variation.
• Figure 2: Schematic of the C-CFOE method.
• Figure 3: Impact of FFT boundary-bin exclusion on frequency-estimation accuracy, emphasizing distortions introduced by pulse shaping and finite observation windows. Spectral-edge artifacts arise when the PSD is accumulated for a RRC-shaped 1-GBd PM-QPSK signal (span: 20 symbols, roll-off factor $\alpha = 0.1$), at 64 samples per symbol and impaired by a -5 GHz CFO. The blue and red squares mark the breakpoints $\psi_1$ and $\psi_2$, respectively, obtained from the full PSD and frequency vectors, whereas the circles indicate the estimates after excluding edge samples. For the considered FFT block, using the complete cumulative PSD and frequency vectors results in a CFO overestimation of approximately -140 MHz (green square). In contrast, removing boundary bins mitigates edge distortions and yields an accurate CFO estimate, as indicated by the green circle.
• Figure 4: SLR-based estimation applied to a 1-GBd QPSK signal affected by a 3-GHz CFO. Both axes are normalized to enhance numerical stability.
• Figure 5: Combinations of $f_{\mathrm{pk\text{-}pk}}$ (y-axis) and $f_j$ (x-axis) that produce four different tones (T$_1$–T$_4$), following the description in OIF800ZR2024.