QD-MLL-Based Single-Sideband Superchannel Generation Scheme With Kramers–Kronig Direct Detection Receivers

Photonics-assisted millimeter-wave (MMW) wireless communications are advancing rapidly driven by the escalating congestion in the lower-band spectrum and the growing demand for higher data rates. Concurrently, Kramers-Kronig (KK) receivers provide an economical solution ideally suited for cost-sensitive deployment and application. However, the conventional KK receiver is subject to performance degradation due to the nonlinearity and memory effects introduced by practical electronic devices. In this work, the performance degradation of the conventional KK receiver is investigated and quantitatively simulated, showing that the KK receiver exhibits greater sensitivity to nonlinearity and memory effects compared to the conventional coherent receiver. To enhance the performance of KK receivers deployed in MMW communication systems, we propose a modified KK receiver employing memory polynomial compensation, namely MP-KK receiver, capable of effectively compensating memory effects whilst simultaneously addressing nonlinearity. Crucially, the memory polynomial model is employed prior to the KK algorithm to prevent further signal degradation caused by the nonlinear operator in the KK algorithm in the scenario of photonics-assisted MMW wireless communication based on the KK receiver. For verification, we present a 95 GHz W-band MMW wireless transmission demonstration with 20 Gb/s QPSK and 40 Gb/s 16-QAM signals. The experimental results indicate that the MP-KK receiver can achieve more than 3.5 dB improvement in EVM and 71.25% reduction in BER compared to the conventional approaches.

The Kramers-Kronig (KK) receiver breaks through the limitation that a single photodetector (PD) can only process the intensity information, and has become a research hotspot in optical communication system. However, in the conventional KK algorithm, the required nonlinear operations (such as logarithm (log) and exponential and square-root (sqrt) functions) significantly broadens the signal spectrum, it is necessary to employ the digital upsampling at the beginning of the digital signal processing (DSP). The high sampling rate will bring multiple hardware resources and power consumption, which becomes a major obstacle to implement KK receiver. In this paper, we propose a novel improved algorithm for the KK receiver, which does not need the digital upsampling and lowers the required carrier-to-signal power ratio (CSPR) with a comparison of the typical upsampling-free KK receiver. In the proposed improved algorithm, we adopt the mathematical approximations of Taylor's expansion and Newton's tangent method to avoid the use of log and sqrt functions. Then we removed the exponential function by expressing complex signal in Cartesian form (i.e., real plus imaginary). Whereas the real part of it is induced by employing imaginary part-induced signal-signal beat interference (SSBI) removal and sqrt operation to recover. Meanwhile, we use the simplified hybrid KK-SSBI cancellation (SHKK-SSBIC) technology to reduce the required CSPR by the system. We validate our proposed algorithm by transmitting 160 Gb/s single-sideband (SSB) signal. The experimental results show that compared with the upsampling-free KK receiver, the proposed scheme can realize the reduction of the required CSPR by 1 dB and 0.8 dB respectively under the Nyquist sampling rate at (back-to-back) BTB and 80 km transmission. Moreover, our proposed method achieves a 2 dB system sensitivity improvement in the BTB scenario. We also discuss the hardware implementation of the improved KK algorithm and its computational complexity.

We present the design and optimization of the optical single side-band (SSB) Nyquist four-level pulse amplitude modulation (PAM-4) transmission using dual-drive Mach-Zehnder modulator (DDMZM)modulation and direct detection (DD), aiming at the C-band cost-effective, high-speed and long-distance transmission. At the transmitter, the laser line width should be small to avoid the phase noise to amplitude noise conversion and equalization-enhanced phase noise due to the large chromatic dispersion (CD). The optical SSB signal is generated after optimizing the optical modulation index (OMI) and hence the minimum phase condition which is required by the Kramers-Kronig (KK) receiver can also be satisfied. At the receiver, a simple AC-coupled photodiode (PD) is used and a virtual carrier is added for the KK operation to alleviate the signal-to-signal beating interference (SSBI).A Volterra filter (VF) is cascaded for remaining nonlinearities mitigation. When the fiber nonlinearity becomes significant, we elect to use an optical band-pass filter with offset filtering. It can suppress the simulated Brillouin scattering and the conjugated distortion by filtering out the imaging frequency components. With our design and optimization, we achieve single-channel, single polarization 102.4-Gb/s Nyquist PAM-4 over 800-km standard single-mode fiber (SSMF).

A Kramers-Kronig (KK) receiver is applied to a phase-sensitive optical time domain reflectometry based on direct detection. An imbalanced Mach-Zehnder interferometer with a 2×2 coupler is used in sensing system to encode the phase information into optical intensity. The directly obtained signal is treated as the in-phase component, and the KK receiver provides the quadrature component by Hilbert transform of the obtained signal, so that the optical phase can be retrieved by IQ demodulation. The working principle is well explained, and the obtained phase variance is theoretically analyzed. The experiment demonstrates the functionality of the sensor and validates the theoretical analysis.

Coherent detection provides the optimum performance for free space optical (FSO) communication systems. However, such detection systems are expensive and require digital phase noise compensation. In this paper, the transmission performance of long-haul FSO system for ground-to-satellite communication based on a Kramers–Kronig (KK) transceiver is evaluated. KK transceivers utilize inexpensive direct detection receivers and the signal phase is retrieved from the received current using the well-known KK relations. KK transceivers are not sensitive to the laser phase noise and, hence, inexpensive lasers with large linewidths can be used at the transmitter. The transmission performance of coherent and KK transceivers is compared in various scenarios such as satellite-to-ground, satellite-to-satellite, and ground-to-satellite for weak, moderate, and strong turbulence. The results show that the transmission performance of a system based on the KK transceiver is comparable to that based on a coherent transceiver, but at a significantly lower system cost and complexity. It is shown that in the absence of turbulence, the coherent receiver has a ~3 dB performance advantage over the KK receiver. However, in the presence of strong turbulence, this performance advantage becomes negligible.

This presentation reviews the operation principles and various implementations of the Kramers-Kronig (KK) receiver. We show that the KK scheme offers new ways of considering the process of data transmission and reception, with respect to the use of the spectral and polarization degrees of freedom. Some of the recently published experimental demonstrations are reviewed.

Joint equalization of CD and RSOP using a time–frequency domain Kalman filter structure in Kramers–Kronig system

High speed transmission systems (> 10 Gb/s) for cost-sensitive applications such as metropolitan network have attracted extensive interest due to the explosive data traffic growth in such applications. Optical orthogonal frequency division multiplexing (OFDM) based on direct modulation and direct detection for single-mode fiber (SMF) and multi-mode fiber (MMF) without optical amplification and chromatic dispersion (CD) compensation was proposed. Recent research has also shown that optical OFDM can be used with electronic dispersion compensation using direct detection in SMF. However, laser frequency chirp has been identified as a key limiting factor of capacity-versus-reach performance. In this paper, we present a novel concept of low cost optical OFDM with direct modulation of distributed feedback (DFB) lasers and coherent detection at 51.4 Gb/s and 64 QAM. A comprehensive theoretical model of the proposed system is developed. The proposed optical OFDM system concept and performance is based upon using electronic precompensation of laser frequency response, and electronic post compensation of DFB laser frequency chirp and CD. A numerical simulation of the transmission performance of the aforementioned system is conducted using different fiber lengths (40 km, 60 km, 120 km) and chirp parameters, which shows its attractiveness for access and metro applications.

A neural network (NN)-based electrical dispersion pre-compensation (pre-EDC) scheme in intensity-modulation and direct-detection (IM/DD) systems is proposed and experimentally demonstrated in this Letter. The scheme enables 56 Gbit/s four-level pulse amplitude modulation (PAM-4) generation at a transmitter over an 80 km single-mode fiber (SMF) transmission in the C-band. The NN is utilized to better fit nonlinear phase-amplitude transformation due to the chromatic dispersion (CD) in IM/DD systems, in place of the existing Gerchberg-Saxton (GS) iterative algorithm and linear GS-based finite impulse response (GS-FIR) non-iterative compensation schemes. The experimental results show that the measured bit error ratio (BER) can be reduced to below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10-3 with 0 dBm receiver optical power (ROP) by the NN-based non-iterative pre-EDC scheme, which also saves up to 81% of computational complexity compared to the GS-based scheme. The results indicate that our proposed scheme is promising for the CD pre-compensation at the transmitter.

Single-polarization, single-photodiode-based direct-detection (DD) transceivers offer advantages for metro networks due to their simple and low-cost optical hardware structure. Single-sideband Nyquist-pulse-shaped subcarrier modulation (SSB Nyquist-SCM) is a promising signal format to achieve high information spectral density (ISD) in such DD systems. In this paper, we present theoretical and experimental evaluations of a variety of direct-detection SSB Nyquist-SCM system designs, operating at 100 Gb/s per wavelength in wavelength division multiplexing (WDM) metro network scenarios. Through simulations, several receiver-based digital linearization techniques to overcome the effect of signal-signal beat interference were investigated, and their performance compared with alternative approaches, including optical beat-interference cancellation receivers (BICRx) and coherent receivers (both heterodyne and homodyne). Subsequently, experimental assessments of the digitally-linearized DD receivers were carried out. Spectrally efficient (net ISD exceeding 3 b/s/Hz) 4 × 112 Gb/s WDM DD single-sideband 16-QAM Nyquist-SCM transmission over distances of up to 240 km (multi-span links) and 160 km (single-span links without mid-span amplification) were shown to be possible using uncompensated standard single-mode fiber.

we experimentally investigate the performance of different interpolation functions in the practical Kramers-Kronig (KK) receiver through a single polarization (SP) 112-Gbit/s single-sideband (SSB) 16-QAM transmission link. The results show that the anti-aliasing finite impulse response (FIR) filter-based scheme outperforms other interpolation schemes and the complexity is reduced by at least 49.6%. We show that the anti-aliasing FIR filter-based scheme with a 9-tap Hilbert FIR (HT-FIR) filter and a resampling factor of 4 can transmit the signal up to 1440-km when the soft-decision forward error correction (SD-FEC) threshold of 2x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> is considered.

We experimentally demonstrate beyond 100G single sideband (SSB) 4-ary pulse amplitude modulation (PAM-4) signal generation with a silicon dual-drive Mach-Zehnder modulator (DD-MZM) operating at C-band. With Kramers-Kronig detection, a 128-Gb/s PAM-4 signal is transmitted over 80-km standard single mode fiber (SSMF) with a bit error rate (BER) below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . In comparison, a 168-Gb/s PAM-4 signal is transmitted over 80-km SSMF with a BER below the 20% HD-FEC threshold of 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . A two-tap digital post filter and maximum likelihood sequence detection are applied to compensate for the limited system bandwidth. To the best of our knowledge, this letter reports the highest single-lane bitrate of 80-km SSB transmission with a DD-MZM and direct detection. It provides an attractive low-cost solution for inter-datacenter interconnection and metro-haul transmission.

For short reach and metro applications, single sideband (SSB) is a promising scheme due to its high spectral efficiency and tolerance to chromatic dispersion. In this study, we propose a novel asymmetric twin-SSB scheme based on Nyquist pulse shaping. Without joint equalization, the two sidebands can be separately detected with a small guard band. We experimentally demonstrate 224-Gb/s 16-ary quadrature amplitude modulation (16-QAM) asymmetric twin-SSB transmission with direct detection. After 240-km standard single mode fiber (SSMF) transmission, the bit error rates (BERs) of the right-sideband (RSB) and the left-sideband (LSB) are 3.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and 2.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , respectively, which are below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The net bitrate is 203.7 Gb/s with consideration of both frame redundancy and HD-FEC overhead. To our best knowledge, we report the longest transmission distance for 200G single wavelength and single polarization direct detection systems. The advantages of the asymmetric twin-SSB scheme over the symmetric scheme are discussed through simulating the crosstalk resistance of both two schemes. We also demonstrate 300-Gb/s 32-QAM transmission over 80-km SSMF. The BERs of RSB and LSB are 1.50 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and 1.61 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , respectively, which are below the 15% soft-decision forward error correction (SD-FEC) threshold of 1.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . The net bitrate is 254.3 Gb/s with consideration of both frame redundancy and SD-FEC overhead. To our best knowledge, it is the maximum bitrate ever reported for C-band 80-km single wavelength and single polarization direct detection transmission. The proposed scheme provides a useful and low-cost solution for high speed datacenter interconnection and metro-scale transmission.

We demonstrate a 56 Gb/s four-level pulse-amplitude modulation (PAM-4) transmission using direct detection and a long-wavelength 18-GHz bandwidth vertical-cavity surface-emitting laser as directly modulated light source for short-reach inter- and intra-connects in datacenters and short-reach networks. Error-free transmission over 2 km at 7% hard-decision forward-error correction threshold is achieved by applying powerful equalization schemes at the receiver side. Three equalization schemes, i.e., a maximum likelihood estimation (MLSE), a feed-forward equalizer (FFE), and a combination of the FFE and the MLSE are thoroughly investigated, and the performance comparison between them is carried out.

In this paper, we demonstrate a newly designed multi-source domain transfer learning (MST) scheme to reduce the training cost of deep neural network (DNN) based equalizer in intensity-modulation and direct-detection (IMDD) systems. Different from a common transfer learning algorithm, in this scheme, data with different channel parameters is selected and proportionally used to construct a multi-source domain dataset. This allows training the source domain in a single task while ensuring the model's generalization ability and stability. In an 80Gb/s PAM-4 IMDD short reach system, our proposed MST equalizer was proven effective. The corresponding results demonstrate that, compared to a conventional DNN equalizer, the proposed MST equalizer can achieve a bit error rate that meets the hard decision-forward error correction threshold while saving 87% of the iteration epochs and 65% of the training data.