Time-domain Equalizer Research Articles

Low complexity equalization in coherent optical communication based on Fermat number transform.

In order to reduce the power consumption of digital signal processing (DSP) in a coherent optical communication system, a low complexity equalization scheme in DSP flow of a 400 Gb/s DP-16QAM system has been proposed. This scheme is based on Fermat number transform (FNT), which sequentially performs static equalization (SE) and dynamic equalization (DE) in the transform domain. For different distances, the proposed scheme finds the optimal solution under the condition that transform length and data bit width are mutually restricted under different transmission distances while achieving low complexity and optimal performance. The experimental results show that the adopted transform-domain equalization (TrDE) scheme has much lower computational complexity than the traditional frequency-domain equalization (FDE) and time-domain equalization (TDE) nearly without any performance loss. In the 80, 160, and 240 km scenarios, the number of multiplier is reduced by more than 72%, and the advantage becomes more obvious as the transmission capacity increases.

Demonstration of IM/DD 3-Tbit/s PS-PAM8 transmission with wavelength and mode multiplexing based on neural network equalizer

We experimentally demonstrate 8-channel wavelength division multiplexing (WDM) signal transmission in 4 modes over 20-m multimode fiber (MMF) in an intensity modulation and direct-detection (IM/DD) system. By combining the probabilistic shaping (PS) technique with high order pulse amplitude modulation (PAM) format, 40-GBaud PS-PAM8 signal transmission in the WDM + MDM IM/DD system achieves a total net bit rate of 3-Tbit/s. With the aid of a multiple input single output (MISO) neural network (NN) equalizer, we obtain a 1.6-dB receiver sensitivity gain compared with traditional digital signal processing (DSP), including multiple input multiple outputs (MIMO) time domain equalizer (TDE).

VAMP-Based Iterative Equalization for Index-Modulated Multicarrier FTN Signaling

The spectrally efficient multicarrier faster-than-Nyquist (MFTN) signaling provides an efficient and robust solution for enhancing transmission rate and resisting channel impairments. In this paper, an evolutionary non-orthogonal physical waveform is proposed for simultaneously achieving high spectral and energy efficiency via combining MFTN signaling with index modulation (IM). Exploiting the implicit transmission of IM, the inactivated subcarriers alleviate the inherent two-dimensional interferences imposed by time-frequency packing in MFTN. Then, we develop a pair of iterative equalization algorithms based on vector approximate message passing (VAMP). For the first time-domain equalization (TDE), an extended constellation set is constructed for uniformly characterizing the activated and inactivated subcarriers. To further reducing the computational complexity, we establish a subcarrier-based segment-wise frequency-domain received signal model and accordingly develop low-complexity VAMP-based frequency-domain equalization (FDE) combined with interference elimination. Corroborated by simulations, the novel MFTN-IM waveform achieves superior bit error rate (BER) performance over benchmark waveforms in the high signal noise ratio (SNR) regions. Interestingly, while the proposed VAMP-TDE outperforms the proposed VAMP-FDE in BER performance, the latter is more competitive in balancing demodulation performance and computational complexity.

Sub-Mbps key-rate continuous-variable quantum key distribution with local local oscillator over 100-km fiber.

We experimentally demonstrated a sub-Mbps key rate Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) over a 100-km transmission distance. To efficiently control the excess noise, the quantum signal and the pilot tone are co-transmitted in the fiber channel based on wideband frequency and polarization multiplexing methods. Furthermore, a high-accuracy data-assisted time domain equalization algorithm is carefully designed to compensate the phase noise and polarization variation in low signal-to-noise ratio. The asymptotic secure key rate (SKR) of the demonstrated CV-QKD is experimentally calculated to be 7.55 Mbps, 1.87 Mbps, and 0.51 Mbps over a transmission distance of 50 km, 75 km, and 100 km, respectively. The experimentally demonstrated that the CV-QKD system significantly improves the transmission distance and SKR compared to the state-of-art GMCS CV-QKD experimental results, and shows the potential for long-distance and high-speed secure quantum key distribution.

Per-Wavelet Equalization for Discrete Wavelet Transform Based Multi-Carrier Modulation Systems

The Discrete Wavelet Transform (DWT) has gained attention in the area of Multi-Carrier Modulation (MCM) because it can overcome some well known limitations of Discrete Fourier Transform (DFT) based MCM systems. Its improved spectral containment removes the need for a cyclic prefix, be it that appropriate equalization then has to be added as the cyclic convolution property no longer holds. Most DWT based MCM systems in the literature use Time-domain EQualizers (TEQs) to mitigate the channel distortion. In this paper, a Per-Wavelet EQualizer (PWEQ) is proposed which directly maximizes the Signal-to-Interference-plus-Noise Ratio (SINR) per symbol and is applicable to any wavelet family. The proposed PWEQ provides a performance upper bound for the TEQs for DWT based MCM systems. The computational complexity of the PWEQ is reduced by modifying the Filter Bank (FB) structure of the DWT. Simulations are performed to compare the PWEQ performance against the TEQs for DWT based MCM systems and the similar Per-Tone EQualizer (PTEQ) for DFT based MCM systems. The simulations are performed using measured Asymmetric Digital Subscriber Line (ADSL) and G.fast channels with Fejér-Korovkin (FK) wavelets. The proposed PWEQ increases the SINR on the received symbols compared to the TEQs at the cost of an increased computational complexity.

1120-channel OAM-MDM-WDM transmission over a 100-km single-span ring-core fiber using low-complexity 4×4 MIMO equalization.

A successful transmission of 14 multiplexed orbital angular momentum (OAM) channels each carrying 80 wavelengths over a 100-km single-span ring-core fiber (RCF) is experimentally demonstrated. Each transmission channel is modulated by a 20-GBaud quadrature phase-shift keying (QPSK) signal, achieving a record spectral-efficiency-distance product of 1870 (bit/s/Hz)·km for the single-core RCF based mode division multiplexing (MDM) transmissions. In addition, only low-complexity 2×2 or 4×4 multiple-input multiple-output (MIMO) equalization with time-domain equalization tap number no more than 25 is required to deal with the crosstalk among the highly degenerate intra-MG modes at the receiving end of the demonstrated OAM-MDM-WDM system, showing great potential in large-capacity and relatively long-distance MDM transmission with low digital signal processing (DSP) complexity.

Low-Complexity Chromatic Dispersion Equalization FIR Digital Filter for Coherent Receiver

This paper proposes a novel and efficient low-complexity chromatic dispersion equalizer (CDE) based on finite impulse response (FIR) filter architecture for polarization-multiplexed coherent optical communication systems. The FIR filter coefficients are optimized by weights to reduce the energy leakage caused by the truncation effect, and then quantization is used uniformly to reduce the number of real number additions and real number multiplications by utilizing the diversity of the quantized coefficients. Using Optisystem 15 to build a coherent optical communication system for simulation and experimental demonstration, the results show that after the filter coefficients are optimized by weights. Compared with the time-domain chromatic dispersion equalizer (TD-CDE), the proposed design has a lower bit error rate (BER) and better equalization effect. When the transmission distance is 4000 km and the system quantization stages M = 16, the multiplication operation and addition operations reduce computing resources by 99% and 43%, and the BER only increases by 5%. Compared with frequency-domain chromatic dispersion equalizer (FD-CDE), widely used in long-distance communication, the multiplication operation reduces computing resources by 30%. The proposed method provides a new idea for high-performance CDE in long-distance coherent optical communication systems.

Low Complexity Single Carrier Frequency Domain Detectors for Internet of Underwater Things (IoUT)s

This paper proposes low complexity detection for internet of underwater things communication. The signal is transmitted from the source to the destination using several sensors. To simplify the computational operations at the transmitter and the sensory nodes, a single carrier frequency domain equalizer is proposed and amplify-and-forward protocols are employed. Fast Fourier transform and use of cyclic prefix are also proposed to simplify these algorithms when compared to time-domain equalization. As precise channel data is difficult to capture in underwater communications, the adaptive implementation of FDE is proposed as a solution that can be employed when the channel experiences a fast doppler shift. The two adaptive detectors are based on the least mean-square and recursive least square principles. Numerical simulations show that the performance of the bit error rate performance of the proposed detectors is close to that of the ideal minimum mean square error.

Neural network-based time-domain equalization without training signal in OFDM systems without CP

Neural network-based time-domain equalization without training signal in OFDM systems without CP

A new FWHT‐CMF‐DFE based approach for channel equalization in CP‐free OFDM systems

Orthogonal frequency division multiplexing (OFDM) has been widely used in wireless communication systems due to its robustness against the frequency selectivity of fading channels. It provides optimal performance and it also meets the requirements of the next generation communication systems. Although OFDM has these advantages, its spectrum efficiency is usually degraded significantly due to the use of cyclic prefix (CP). In this paper, motivated to deal with this issue, the combined structure of Fast Walsh-Hadamard Transform (FWHT) and Time Domain Equalizer (TDE) is proposed to use in CP-free OFDM systems. The results validated by Monte Carlo simulations decipher the improved performances in terms of spectral efficiencies, bit error rate, peak to average power ratio and out of band emission for using this structure over frequency selective multipath fading channels in CP-free OFDM systems. The acquired simulation results have illustrated that the proposed method provides 20% spectral efficiency without compromising the BER performance.

Mitigation of Phase Noise and Nonlinearities for High Capacity Radio-over-Fiber Links

Radio-over-fiber (RoF) links successfully provide high data rates and bandwidth capacity with a low complexity system architecture, as compared to its counterpart digital-RoF. In addition, the compound of quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexed (OFDM) modulation schemes further enhance the process of these achievements. However, high data rates and bandwidth-capacity-supported RoF links face nonlinearities (NLs), linear distortions (LDs), and phase noise challenges that degrade the reliability of communication networks (CNs). Therefore, in this paper, to suppress NLs, LDs, and phase noise, next generation cloud radio access networks (CRANs) are investigated using RoF links and wavelength division multiplexing (WDM) methodology based on 16, 32, and 64 QAM-OFDM modulation schemes. The receiver of the proposed framework is designed, applying an improved digital signal processing (DSP) system that includes overlap frequency domain equalization (OFDE), a synchronization process, and time domain equalization (TDE). Theoretical and simulation models are organized for estimating the proposed RoF link with the aid of different values of transmission ranges, input power, output power, bit rate, bits per symbol, channel spacing, and the number of users. The fitness of the model matches that of existing approaches.

Signal Impropriety in Discrete Multi-Tone Systems and Widely Linear Per-Tone Equalization

In the context of digital subscriber line (DSL) systems, where the long-reach (LR) extension of G.fast has recently been proposed, interest in techniques dealing with long channel impulse responses (CIRs) without increasing the cyclic prefix (CP) length of the discrete multi-tone (DMT) modulation has recently resurfaced. The technique under consideration in this article is referred to as channel shortening, and applies FIR filters to the received signal to shorten the apparent CIR. Time-domain equalization (TEQ) as well optimal per-tone equalization (PTEQ) FIR filters will be considered. When channel shortening techniques are analyzed, it is often overlooked that the received signals after DMT demodulation are generally improper when the CP is too short. Hence, the state-of-the-art signal-to-interference-plus-noise ratio (SINR) and bit loading expressions employed to assess system performance, which implicitly assume the received signals to be proper, misrepresent the true achievable performance. New expressions for the SINR and bit loading are therefore presented that explicitly take signal impropriety into account. Based on these expressions, it is then observed that - if the received signals are improper - the PTEQ FIR filters are no longer optimal, and that the achievable bit loading depends on a particular phase shift experienced by the transmitted signals. This article therefore introduces a novel widely linear PTEQ - which is again optimal when the received signals are improper - and additionally proposes to optimally rotate signals in the complex plane prior to transmission. Finally, this article assesses the performance increase obtainable by explicitly accounting for signal impropriety.

Differential Edge-Modulated Signaling With Encoded Clock and Dynamic Data Rate Scaling

This letter describes a differential edge modulation signaling scheme for a wireline link where the edge position is differentially modulated on a pair of wires such that data bits are recovered when these signals sample each other. Therefore, this clock-encoded modulation scheme eliminates the need for receiver side clock generation and timing recovery and enables matched source-synchronous jitter tracking with >500-MHz bandwidth. An agile multiplying injection-locked oscillator drives the link and dynamically scales the data rate from 3 to 10 Gb/s with less than 10-ns response time. Using a decision-based time-domain equalizer, the link can compensate the 20-dB loss at 10-Gb/s consuming only 19.4 mW, and scales to 10 mW at 3 Gb/s without supply scaling.

Enhanced Performance of a VLC and ULEAPS Fiber Seamless Integrated System Employing Novel Weighted Pre-FDE)

We reported and experimentally demonstrated a 1 Gbit/s guided visible light transparent based on weighted pre frequency domain equalization (Pre-FDE) and post time domain equalizer over a 100 m ULEAPS fiber. The experimental results verified the effectiveness and improvement of the proposed method comparing with the traditional post-equalizers. To the best of our knowledge, this is the highest data rate ever achieved in a VLC transparent employing a commercially available blue LED.

Time-Domain vs. Frequency-Domain Equalization for FTN Signaling

Faster-than-Nyquist (FTN) signaling has been recognized as a promising technique for next-generation high data rate communications. By intentionally reducing the symbol interval, FTN signaling is capable of transmitting more symbols than classic Nyquist signaling within the same time period and bandwidth. However, the intentional non-orthogonality of the bandlimited signaling pulses imposes severe inter-symbol interference (ISI), which requires powerful equalization at the receiver. Hence, we embark on the comparison of time- and frequency-domain equalization for FTN signaling both by theoretical analysis and numerical simulations. It is shown that frequency-domain equalization fails to reliably detect the FTN signal with a low FTN packing factor, while the time-domain equalization still performs well.

Blind Adaptive Low-Complexity Time-Domain Equalizer for 100-Gb/s Direct-Detection Optical OFDM Systems Over Long-Reach SSMF

In this article, we report a low-complexity blind adaptive time-domain equalizer (TEQ) to reduce the cyclic prefix (CP) length for 100-Gb/s direct-detection optical orthogonal frequency-division multiplexing (OFDM) system combined with wavelength-division multiplexing system over 400-km standard single-mode fiber length. We show that a significant complexity reduction can be achieved by designing a modified cost function of multicarrier equalization based on orthogonality restoration (MERO) algorithm on one hand, and on deploying the symmetrical TEQ property on the other hand. Our article shows that the reduction of the system adaptation complexity can be realized up to 50% when designing and optimizing the stated system parameters. Our low-complexity MERO simulation model exhibits better performance, for a shorter CP length equal to $0.39$ % of the OFDM symbol duration, than the existing conventional algorithms in term of bit error rate versus optical signal-to-noise ratio with a much lower complexity.

Time Domain Equalization and Digital Back-Propagation Method-Based Receiver for Fiber Optic Communication Systems

Fiber optic communication systems (FOCSs) have attained a lot of attention by revolutionizing the telecommunication industry and offering new possibilities with the technical advancements in state-of-the-art high speed digital electronics. Advanced modulation formats make use of the phase, amplitude, and polarization of the optical signals at the same time to provide high spectral efficiency as compared with 1 bit/s/Hz for the intensity modulation direct detection system (IMDD), but are highly prone to transmission impairments. Thus, the effects that add up to the optical fiber impairments such as optical fiber chromatic dispersion (OFCD), polarization model dispersion (PMD), and phase offset and noise (POaN) need to be addressed at the receiver side. The development of components and algorithms to minimize these effects in next generation FOCSs with 100 Gbps data rate and beyond with long-haul transmission is still a challenging issue. In this paper, digital signal processing- (DSP-) assisted dispersion and nonlinear compensation techniques are presented to compensate for physical layer impairments including OFCD, PMD, and POaN. The simulations are performed considering Dual Polarization- (DP-) QPSK modulation format to achieve two-fold data rate to achieve spectral efficiency of 3.28 bits/s/Hz by making use of the polarization diversity and system performance is investigated in terms of bit error rate (BER), constellation diagrams, and quality factor (Q-factor) for different values of optical signal-to-noise ratio (OSNR), launch power (PL), and fiber length.

MIMO Time Domain Equalizer Design for Long Reach xDSL MIMO Channel Shortening

In discrete multi-tone (DMT) transmission based digital subscriber line (DSL) systems, a cyclic prefix (CP) is added to each symbol before transmission, where the length of the CP is larger than the estimated channel impulse response (CIR) length. This ensures the elimination of inter-symbol interference (ISI) and inter-carrier interference (ICI) between the carriers of the same symbol, and allows for single tap frequency domain equalizers and crosstalk cancellation at the receiver. Recently, long reach xDSL (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. With the extended loop lengths, the required CP length increases, in order to match the larger CIR length. The longer CP adds a large overhead and results in overall throughput loss. A more efficient way to deal with extended loop lengths is to use a channel shortening filter - commonly referred as a time domain equalizer (TEQ), to reduce the length of the CIR to the length of CP. This paper focuses on minimum mean square error (MMSE) based multiple input multiple output (MIMO) TEQ design for LR-xDSL MIMO channel shortening. Constraints are applied to the minimization problem to eliminate the trivial solution. This paper proposes two new constraints for the MMSE based MIMO TEQ design for upstream scenarios, which result in a lower complexity and provide better (or similar) performance compared to existing MMSE based MIMO TEQ design methods. Furthermore, a diagonal MIMO TEQ with lower memory requirement and lower computational complexity is presented based on the proposed constraints, which can be applied in upstream as well as downstream scenarios.

BGD-based Adam algorithm for time-domain equalizer in PAM-based optical interconnects

To the best of our knowledge, for the first time, we propose an adaptive moment estimation (Adam) algorithm based on batch gradient descent (BGD) to design a time-domain equalizer (TDE) for pulse-amplitude modulation (PAM)-based optical interconnects. The Adam algorithm has been applied widely in the fields of artificial intelligence. For TDE, the BGD-based Adam algorithm can obtain globally optimal tap coefficients without being trapped in locally optimal tap coefficients. Therefore, fast and stable convergence can be achieved by the BGD-based Adam algorithm with low mean square error. Meanwhile, the BGD-based Adam algorithm is implemented by parallel processing, which is more efficient than conventional serial algorithms, such as least mean square and recursive least square algorithms. The experimental results demonstrate that the BGD-based Adam feed-forward equalizer works well in 120-Gbit/s PAM8 optical interconnects. In conclusion, the BGD-based Adam algorithm shows great potential for converging the tap coefficients of TDE in future optical interconnects.

Beyond 100 Gb/s SEFDM Signal IM/DD Transmission Utilizing TDE With 20% Bandwidth Compression

We experimentally demonstrate a beyond 100 Gb/s intensity modulation/direct detection (IM/DD) 16-QAM optical spectrally efficient frequency division multiplexing (SEFDM) transmission over 2-km standard single mode fiber (SSMF) with 20% signal bandwidth compression. Time-domain equalization (TDE), which outperforms frequency-domain equalization (FDE) in our system, is adopted for SEFDM system due to the inter-carrier interference (ICI) induced by the spectrum compression. A hybrid cascaded binary-phase-shift-keying iterative detection (CBID) together with fixed sphere decoder (FSD) is successfully utilized to eliminate ICI in such a high-speed interconnection system. Experiment results show that SEFDM outperforms conventional discrete multi-tone (DMT), occupying less frequency spectrum resource and achieving superior resistance to bandwidth limitation and dispersion-induced power fading in fiber links. We also show that CBID is a more effective scheme with 10% bandwidth compression, considering the receiver complexity, while CBID-FSD is proposed for further bandwidth compression.