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Li XF, Li JC, Ni X et al. Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection. Opto-Electron Sci 4, 240020 (2025). doi: 10.29026/oes.2025.240020
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Article Open Access
Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection
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Abstract
Complex-valued double-sideband direct detection (DD) can reconstruct the optical field and achieve a high electrical spectral efficiency (ESE) comparable to that of a coherent homodyne receiver, and DD does not require a costly local oscillator laser. However, a fundamental question remains if there is an optimal DD receiver structure with the simplest design to approach the performance of the coherent homodyne detection. This study derives the optimal DD receiver structure with an optimal transfer function to recover a quadrature amplitude modulation (QAM) signal with a near-zero guard band at the central frequency of the signal. We derive the theoretical ESE limit for various detection schemes by invoking Shannon’s formula. Our proposed scheme is closest to coherent homodyne detection in terms of the theoretical ESE limit. By leveraging a WaveShaper to construct the optimal transfer function, we conduct a proof-of-concept experiment to transmit a net 228.85-Gb/s 64-QAM signal over an 80-km single-mode fiber with a net ESE of 8.76 b/s/Hz. To the best of our knowledge, this study reports the highest net ESE per polarization per wavelength for DD transmission beyond 40-km single-mode fiber. For a comprehensive metric, denoted as 2ESE×Reach, we achieve the highest 2ESE×Reach per polarization per wavelength for DD transmission. -
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References
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Supplementary information for Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection 
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Li XF, Li JC, Ni X et al. Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection. Opto-Electron Sci 4, 240020 (2025). doi: 10.29026/oes.2025.240020
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Figure 1.
(a) Configuration of the phase-diversity coherent homodyne receiver. (b) Optimal DD receiver with three frequency-selective phase shifters. (c) Phase responses of h1(t), h2(t), and h3(t).
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Figure 2.
Proposed DD receiver with the optimal transfer function. (a) Optimal receiver structure. (b) Optimal amplitude and phase responses of h(t).
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Figure 3.
Schematic diagram of the iterative SSBI cancellation algorithm.
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Figure 4.
Alternative amplitude and phase responses of h(t).
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Figure 5.
Simulated BER versus θ for Solution 1 (a) without, and (b) with iterative SSBI cancellation. Simulated BER versus θ for Solution 2 (c) without, and (d) with iterative SSBI cancellation.
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Figure 6.
Solution 3: signal reconstruction and SSBI mitigation in one step with the CNN.
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Figure 7.
Solution 3: (a) Simulated BER versus θ at different CSPR and OSNR values. (b) Simulated BER versus OSNR for different schemes with a CSPR of 6 dB.
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Figure 8.
(a) Simulated BER versus CSPR for different schemes with a 30-dB OSNR. (b) Simulated BER versus OSNR for different schemes with a 3-dB CSPR.
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Figure 9.
(a) Theoretical ESE limits for different schemes. (b) Normalized theoretical ESE limit of our proposed scheme. (c) Normalized theoretical ESE limit of our proposed scheme versus OSNR for different net rates.
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Figure 10.
(a) Experimental setup and DSP flow charts. DAC: digital-to-analog converter; EA: electrical amplifier; IQM: in-phase and quadrature modulator; ECL: external cavity laser; PC: polarization controller; VOA: variable optical attenuator; EDFA: erbium-doped fiber amplifier; OBPF: optical bandpass filter; DSO: digital storage oscilloscope; MLSD: maximum-likelihood sequence decision. (b) Optical spectra of the 64-QAM signals measured at different stages. (c) BER versus CSPR in the transmission and OBTB cases. Insets (i-iv) show constellations at 12-dB CSPR. (d) BER versus ROP in the transmission and OBTB cases.
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Figure 11.
Visual representation of the state-of-the-art transmission results on DD systems. POLs: polarizations.
