Complexity Analysis of the Kramers–Kronig Receiver

Füllner, Christoph; Adib, Mosaddek Hossain; Wolf, S.; Kemal, J. N.; Freude, W.; Koos, C.; Randel, S.

doi:10.1109/jlt.2019.2923249

Cited by 31 publications

(40 citation statements)

References 39 publications

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“…By considering the tradeoff between equalization performance and computational complexity [9], the memory length of FFE and VE is set to (55) and (55,45,0), respectively. The sampling rate of the KK algorithm is set to 6 samples per symbol [12]. It can be seen in Fig.…”

Section: Simulation Setup and Resultsmentioning

confidence: 99%

“…9(a) presents the reduced complexity percentage using ℓ 0 -SR-VE described in Eq. (12) in terms of different  . In this test,  is fixed to 50, 2…”

Section: N Andmentioning

confidence: 99%

“…In contrast, the KK receiver eliminates the SSBI by accurately reconstructing the complex field of the transmitted SSB signal [10], thus the KK algorithm usually outperforms the IC algorithm as reported in [10], [11]. Nonetheless, the KK algorithm faces challenges of high complexity and high up-sampling factor [12], and a two-order VE is proved to have better bit error rate (BER) performance than the combination of KK algorithm and FFE after 80 km SSMF transmission as reported in [8]. Therefore, the VE algorithm has a promising prospect in the future cost-constrained highspeed optical transmission system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Robust Sparse RLS-Volterra Nonlinear Equalizer Using ℓ₀-Regularization for 4 × 150 Gbit/s IMDD-Based Optical Interconnect

Cheng

Song

et al. 2021

IEEE Access

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Volterra equalizer (VE) is a well-known and effective algorithm to deal with the linear and nonlinear distortions in optical interconnect, but the high computational complexity hinders its practical application. Generally, sparse VEs based on ℓ 1-or ℓ 0-regularization are good ways to reduce the complexity by discarding some inessential taps. However, a tap threshold needs to be chosen in these sparse VEs like the threshold-based pruned retraining VE (TR-VE) to decide the discarded taps. And this tap threshold should be adjusted fine to balance the reduced complexity and equalization performance, especially when the testing environments alter. Thus, the reduced complexity in these sparse VEs may fluctuate. To address this issue, a robust and stable complexity reduced sparse VE using ℓ 0-regularization (ℓ 0-SR-VE) is proposed in this paper. The recursive least square (RLS) algorithm is used to replace the least mean square algorithm for the faster convergence speed and better equalization performance. The complexity of this equalizer depends on its parameters but not the tap threshold. Once the equalizer parameters are determined, the complexity would not change with the system characteristics, contributing to higher practicability. In our experiment, a 150 Gbit/s PAM8 signal transmission system based on intensity modulation and direct detection (IMDD) is achieved, and a dual-drive Mach-Zehnder modulator for optical single-sideband signal generation is used to mitigate the power fading effect. The experimental results show that with the help of ℓ 0-SR-VE, the reduced complexity percentage is stable at 66.18% compared with the RLS-based VE, even after 75 km standard single-mode fiber (SSMF) transmission. By using this equalizer, 4×150 Gbit/s PAM8 signals have also been successfully transmitted over 30 km SSMF at C-band. The reduced complexity variation of ℓ 0-TR-VE is >20%, but the reduced complexity of the proposed ℓ 0-SR-VE is stable at 60% even after 30 km SSMF for all four lanes. INDEX TERMS PAM8, IMDD system, data center interconnect (DCI), sparse Volterra equalizer (VE).

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Section: Simulation Setup and Resultsmentioning

confidence: 99%

“…9(a) presents the reduced complexity percentage using ℓ 0 -SR-VE described in Eq. (12) in terms of different  . In this test,  is fixed to 50, 2…”

Section: N Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Robust Sparse RLS-Volterra Nonlinear Equalizer Using ℓ₀-Regularization for 4 × 150 Gbit/s IMDD-Based Optical Interconnect

Cheng

Song

et al. 2021

IEEE Access

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show abstract

“…However, the overall performance of the system is limited by the noise and the power of the pilot tone, and also signal-signal beat interference (SSBI) due to the use of direct detection. SSBI can be almost entirely compensated using Kramers-Kronig (KK) receiver DSP [19] [30]. The DSP chain for KK is shown in Figure 1, and includes a square-root function, a logarithm, and a Hilbert filter.…”

Section: A Kramers Kronig (Kk) Receiversmentioning

confidence: 99%

DSP Enabled Optical Detection Techniques for PON

Teixeira

Lavery

Ciaramella

et al. 2020

J. Lightwave Technol.

Self Cite

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Some of the different aspects of the DSP enabled receivers in access networks will be addressed in this work. A revision of the main topics which may impact DSP design will be discussed through application examples. Modulation formats, KK receivers and coherent receivers are analyzed at light of the DSP enabled receivers' impact. Also, relevant are FEC and burst mode which are debated at the light of PON requirements. Simplified analog coherent receivers are presented as a use case to serve as simplification path for non-DSP high performance receivers. On the other end, aiming at discussing current PON limits, an ultra dense wavelength division multiplexing (UDWDM) use case is also presented where several advanced topics, like pulse shaping, high density and simplified DSP operations are considered.

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“…A. J. Lowery et al [19] proposed clipping of the detected waveform before the log operation for the digital-to-analog converter (DAC) resolution limited scenarios. In [20] C. Füllner et al proposed DSP complexity reduction using FIR filter based Hilbert transform.…”

Section: Introductionmentioning

confidence: 99%

Impact of Sampling and Quantization on Kramers-Kronig Relation-Based Direct Detection

Fujita

Toba

Sampath

et al. 2020

IEICE Trans. Commun.

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Impact of sampling frequency and the number of quantization bit of analog-to-digital conversion (ADC) in a direct detection lightwave system using Kramers-Kronig (KK) relation, which has been attracting attention in recent years, are numerically investigated. We studied the effect of spectral broadening caused by nonlinear operations (logarithm, square root) of the KK algorithm when the frequency gap (shift frequency) between the modulated signal and the optical tone is varied. We found that reception performances depend on both the ADC bandwidth and the relative positions of the optical tone and the spectrum. Spectral broadening caused by the logarithm operation of the KK algorithm is found to be the dominant factor of signal distortion in an ADC bandwidth limited system. We studied the effect of the number of quantization bit on the error vector magnitude (EVM) of KK relation based reception in a carrier-to-signal power ratio (CSPR) adjustable transmission system. We found that performances of KK relation based receiver can be improved by increasing the number of quantization bits. For minimum-phase-condition satisfied KK receiver, the required number of quantization bit was found to be 5 bits or more for detection of QPSK, 16-QAM and 64-QAM-modulated signal after 20-km transmission.

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Complexity Analysis of the Kramers–Kronig Receiver

Cited by 31 publications

References 39 publications

A Robust Sparse RLS-Volterra Nonlinear Equalizer Using ℓ₀-Regularization for 4 × 150 Gbit/s IMDD-Based Optical Interconnect

A Robust Sparse RLS-Volterra Nonlinear Equalizer Using ℓ₀-Regularization for 4 × 150 Gbit/s IMDD-Based Optical Interconnect

DSP Enabled Optical Detection Techniques for PON

Impact of Sampling and Quantization on Kramers-Kronig Relation-Based Direct Detection

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