Performance of Kramers–Kronig Receivers in the Presence of Local Oscillator Relative Intensity Noise

We propose a deep learning-based phase retrieval method to accurately reconstruct the optical field of a singlesideband minimum-phase signal from the directly detected intensity waveform. Our method relies on a fully convolutional Neural Network (NN) model to realize non-iterative and robust phase retrieval. The NN is trained so that it performs fullfield reconstruction and jointly compensates for transmission impairments. Compared to the recently proposed Kramers-Kronig (KK) receiver, our method avoids the distortions introduced by the nonlinear operations involved in the KK phase-retrieval algorithm and hence does not require digital upsampling. We validate the proposed phase-retrieval method by means of extensive numerical simulations in relevant system settings, and we compare the performance of the proposed scheme with the conventional KK receiver operated with a 4-fold digital upsampling. The results show that the 7% hard-decision forward error correction (HD-FEC) threshold at BER 3.8e-3 can be achieved with up to 2.8 dB lower carrier-to-signal power ratio (CSPR) value and 1.8 dB better receiver sensitivity compared to the conventional 4-fold upsampled KK receiver. We also present a comparative analysis of the complexity of the proposed scheme with that of the KK receiver, showing that the proposed scheme can achieve the 7% HD-FEC threshold with 1.6 dB lower CSPR, 0.4 dB better receiver sensitivity, and 36% lower complexity.

Section: Transmission Performancesupporting

confidence: 83%

Section: Simulation Setupmentioning

confidence: 99%

Deep Learning-Based Phase Retrieval Scheme for Minimum-Phase Signal Recovery

Orsuti

Antonelli

Chiuso

et al. 2023

“…The resulting signal is sent to an ideal DAC (i.e., without quantization and without bandwidth limitation) where electrical to optical conversion is performed by an IQ modulator biased at the null point. The IQ modulator is driven by a laser source operating at 1550 nm with 1 MHz linewidth and a relative intensity noise of −139 dBc/Hz, which are typical values for low-cost distributed-feedback (DFB) laser diodes [28]. The WDM channels are multiplexed with a channel spacing of 40 GHz by a WDM-MUX that has the same channel spectral response of the optical filter employed at the receiver.…”

Section: System Descriptionmentioning

confidence: 99%

Edge-Carrier-Assisted Phase Retrieval at Low-CSPR and Low-Dispersion Diversity With Deep Learning

Orsuti,

Santagiustina,

Galtarossa

et al. 2024

We investigate the performance of deep learning in recovering the complex-valued field of a weak-carrier-assisted single side-band signal from two intensity measurements that are decorrelated by dispersion. The proposed scheme relies on a supervised learning-based convolutional neural network to map the intensity measurements to the full-field. Unlike conventional iterative phase retrieval schemes, the proposed scheme does not require any iterations, digital upsampling, or pilot symbols, and can operate both at low carrier-to-signal-power ratio (CSPR) and at low applied dispersion value. Through numerical simulations in relevant system settings, we compare the performance of the proposed scheme with two recently proposed carrier-assisted iterative phase retrieval schemes: one based on the solution of a nonlinear optimization problem, and the other based on a modified Gerchberg-Saxton algorithm. The results show that the proposed scheme complies with the 7% hard-decision forward error correction threshold after 24 GBaud 32-QAM transmission over 100 km of standard single-mode fiber at a CSPR of 0 dB, with 3.6 times lower applied dispersion value, 30% to 90% lower complexity, and with less than 2 dB sensitivity penalty compared to conventional iterative phase retrieval schemes. These results support the potential of deep learning to realize phase retrieval-based coherent receivers that are compatible with the low complexity requirements of short-reach optical networks.

“…the noise variance becomes non-stationary, and compresses the noise at high levels. Although the KK processing can theoretically reconstruct an output similar in quality to a balanced-photodiode coherent receiver, it requires that the carrier level be increased to between 6-10 dB above the signal level [20]. Thus, higher optical powers need to be transmitted to support this carrier level, unless a local oscillator provides a substitute carrier at the receiver [21].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Kramers-Kronig Single-Sideband Receivers

Lowery

Wang

Corcoran

2020

Theoretically, Kramer-Kronig (KK) receivers are able to fully cancel signal-signal beat interference (SSBI), which results from a field-modulated single-sideband (with carrier) transmitter being used with a direct-detection receiver. However, even for strong carriers, which should meet the minimum-phase (MP) condition, bits are frequently erroneous. In this paper, we simulate two methods of reducing error rates for weak carriers. The first is to limit the minimum value of the received signal, so that strong negative-going peaks are not produced by the logarithm function of the KK's 'correction path'. The second is to replace the square-root function in the main signal path with a logarithmic function. This is to allow analog processing using semiconductor diodes. Our numerical simulations show that grossly approximating the square-root function is actually beneficial to the system, as it reduces the power in the signal close to the clipping events. When both the first and second techniques are combined, low error rates can be obtained at 2-dB less carrier power than for conventional processing, and 0.25-dB better receiver sensitivity. When 100-km of standard fiber is included, the carrier can be reduced by 3 dB, and the system has a 0.18 dB better sensitivity, and potentially supports analog processing. This work suggests that there may be other improvements possible, in signal quality and computational load, by moving away from a theoretically perfect implementation of the KK algorithm.