Time-domain Equalizer Research Articles

Advanced DSP for Coherent Optical Fiber Communication

In this paper, we provide an overview of recent progress on advanced digital signal processing (DSP) techniques for high-capacity long-haul coherent optical fiber transmission systems. Not only the linear impairments existing in optical transmission links need to be compensated, but also, the nonlinear impairments require proper algorithms for mitigation because they become major limiting factors for long-haul large-capacity optical transmission systems. Besides the time domain equalization (TDE), the frequency domain equalization (FDE) DSP also provides a similar performance, with a much-reduced computational complexity. Advanced DSP also plays an important role for the realization of space division multiplexing (SDM). SDM techniques have been developed recently to enhance the system capacity by at least one order of magnitude. Some impressive results have been reported and have outperformed the nonlinear Shannon limit of the single-mode fiber (SMF). SDM introduces the space dimension to the optical fiber communication. The few-mode fiber (FMF) and multi-core fiber (MCF) have been manufactured for novel multiplexing techniques such as mode-division multiplexing (MDM) and multi-core multiplexing (MCM). Each mode or core can be considered as an independent degree of freedom, but unfortunately, signals will suffer serious coupling during the propagation. Multi-input–multi-output (MIMO) DSP can equalize the signal coupling and makes SDM transmission feasible. The machine learning (ML) technique has attracted worldwide attention and has been explored for advanced DSP. In this paper, we firstly introduce the principle and scheme of coherent detection to explain why the DSP techniques can compensate for transmission impairments. Then corresponding technologies related to the DSP, such as nonlinearity compensation, FDE, SDM and ML will be discussed. Relevant techniques will be analyzed, and representational results and experimental verifications will be demonstrated. In the end, a brief conclusion and perspective will be provided.

The Channel Shortening comparison between OFDM & MC-CDMA System over an ADSL Channel using a Water-filling

<p>In this paper our objective focuses on the development of digital transmission techniques in order to solve the problem of Inter-Symbol Interference (ISI) due to multiple paths and the improvement of Multi-Carrier Code Division Multiple Access (MC-CDMA) system performance. The both algorithm: MERRY algorithm (Multicarrier Equalization by Restoration of Redundancy) called TEQ (Time domain EQualizer) and the power allocation method to allocate appropriate power to each user (Water-filling technique (WF)) [1] is used. Finally, the numerical results show that combining Water Filling with TEQ technique allows to reduce the ISI for MC-CDMA systems.</p>

A Novel Receiver Design of Nonorthogonal FDM Systems in Underwater Acoustics Communication

While orthogonal frequency-division multiplexing (OFDM) has been studied for a decade, the study of nonorthogonal frequency-division multiplexing (NOFDM) in the underwater acoustics (UWA) communication has never been reported, to the best of our knowledge. Therefore, we investigate the NOFDM technique for the UWA communication considering the doubly dispersive channel. The main feature of the NOFDM is that it involves more closely packed subcarriers compared to the OFDM, which results in higher spectral efficiency. However, this transmission suffers from severe intercarrier interference. Since, we are considering the doubly dispersive channel, intersymbol interference is also encountered due to the multipath propagation. Therefore, the traditional receiver of the NOFDM system in the UWA channel tends to have high computational complexity. Considering this problem, we design a receiver for the NOFDM system, where the basis expansion model is used along with the compressed sensing channel estimation technique, i.e., orthogonal matching pursuit (OMP), which can effectively reduce the computational complexity. However, while implementing this technique in the real sea environment, the problem of long delay/Doppler spread is encountered due to guard intervals. Therefore, we propose the use of a time-domain equalizer to mitigate the effect of long delay/Doppler spread. Simulation and experimental results based on the bit error rate demonstrate the performance degradation due to severe interference in our proposed receiver. On the contrary, the mean-square-error performance shows that our proposed receiver with the OMP channel estimation outperforms the OFDM receiver. Similarly, higher spectral efficiency gain is attained due to the closely packed subcarriers.

Optimization Algorithms of Neural Networks for Traditional Time-Domain Equalizer in Optical Communications

Neural networks (NNs) have been successfully applied to channel equalization for optical communications. In optical fiber communications, the linear equalizer and the nonlinear equalizer with traditional structures might be more appropriate than NNs for performing real-time digital signal processing, owing to its much lower computational complexity. However, the optimization algorithms of NNs are useful in many optimization problems. In this paper, we propose and evaluate the tap estimation schemes for the equalizer with traditional structures in optical fiber communications using the optimization algorithms commonly used in the NNs. The experimental results show that adaptive moment estimation algorithm and batch gradient descent method perform well in the tap estimation of equalizer. In conclusion, the optimization algorithms of NNs are useful in the tap estimation of equalizer with traditional structures in optical communications.

A blind channel shortening for multiuser, multicarrier CDMA system over multipath fading channel

In this paper we derive the Multicarrier Equalization by Restoration of Redundancy (MERRY) algorithm: A blind, adaptive channel shortening algorithm for updating a Time-domain Equalizer (TEQ) in a system employing MultiCarrier Code Division Multiple Access (MC-CDMA) modulation. We show that the MERRY algorithm applied to the MC-CDMA system converges considerably more rapidly than in the Orthogonal Frequency Division Multiplexing (OFDM) system [1]. Simulations results are provided to demonstrate the performance of the algorithm.

Filter Bank Multi-Sub-Band Transmission for Optical Systems With Mode Multiplexing

Mode-multiplexed optical transmission is subject to mode coupling and potentially large differential mode delays. In most recent implementations, these effects are compensated for at the receiver by complex adaptive multiple-input multiple-output (MIMO) equalizers. Although frequency-domain MIMO equalization requires a moderate complexity compared to time-domain equalization, the long required fast Fourier transforms may face implementation issues. In this paper, we evaluate an alternative transceiver architecture based on sub-band partitioning, implemented by filter banks, which enables concurrent time-domain equalization. Single-carrier (SC) and multi-sub-band (MSB) mode division multiplexing transmission are simulated using frequency-domain equalization and time-domain equalization, respectively. Their performance is compared in terms of static transmission performance, channel tracking capability, phase noise tolerance, and computational complexity. The results indicate that compared with an equivalent SC solution, the MSB architecture provides a high degree of parallelism at the cost of a penalty of 0.7–1.3 dB for a laser linewidth of 25–100 kHz and a moderate increase in complexity.

Recent Advances in DSP Techniques for Mode Division Multiplexing Optical Networks with MIMO Equalization: A Review

This paper provides a technical review regarding the latest progress on multi-input multi-output (MIMO) digital signal processing (DSP) equalization techniques for high-capacity fiber-optic communication networks. Space division multiplexing (SDM) technology was initially developed to improve the demanding capacity of optic-interconnect links through mode-division multiplexing (MDM) using few-mode fibers (FMF), or core-multiplexing exploiting multicore fibers (MCF). Primarily, adaptive MIMO filtering techniques were proposed to de-multiplex the signals upon different modes or cores, and to dynamically compensate for the differential mode group delays (DMGD) plus mode-dependent loss (MDL) via DSP. Particularly, the frequency-domain equalization (FDE) techniques suggestively lessen the algorithmic complexity, compared with time-domain equalization (TDE), while holding comparable performance, amongst which the least mean squares (LMS) and recursive least squares (RLS) algorithms are most ubiquitous and, hence, extensively premeditated. In this paper, we not only enclose the state of the art of MIMO equalizers, predominantly focusing on the advantage of implementing the space–time block-coding (STBC)-assisted MIMO technique, but we also cover the performance evaluation for different MIMO-FDE schemes of DMGD and MDL for adaptive coherent receivers. Moreover, the hardware complexity optimization for MIMO-DSP is discussed, and a joint-compensation scheme is deliberated for chromatic dispersion (CD) and DMGD, along with a number of recent experimental demonstrations using MIMO-DSP.

A Hilbert Transform Equalizer Enabling 80 MHz RF Self-Interference Cancellation for Full-Duplex Receivers

A passive, time-domain equalizer is presented that achieves a broadband self-interference cancellation (SIC) over 80 MHz of RF bandwidth for simultaneous full-duplex radios. A baseband Hilbert transform technique reduces the number of equalizer taps needed for SIC, and with frequency translations, results in an equivalent RF-domain equalization. A proof-of-concept prototype in 0.13- $\mu \text{m}$ CMOS process attains a measured 23 dB of SIC over an 80 MHz signal bandwidth at 900 MHz, and consumes 13 mW of clocking power independent of SIC equalizer settings. Its impact on the receiver noise figure is 1.4 dB. The equalizer and the receiver together consume 64.4 mW from a 1.2 V supply in an active area of 0.72 mm2.

Hybrid Carrier Underwater Acoustic Communication Based on Joint Time-Frequency Domain Equalization

Weighted fractional Fourier transform-based hybrid carrier communication can be regarded as a combination of single-carrier communication and multicarrier communication, providing strong flexibility due to the changeable transform order. The hybrid carrier underwater acoustic communication based on the joint time-frequency domain equalization is proposed in this paper. With the time-domain equalization based on time reversal, multipath spreads of underwater acoustic channels can be greatly suppressed. Thus, the length of the required cycle prefix is shortened, improving the bandwidth efficiency. The residual inter-symbol interference can be removed using frequency-domain equalization based on the minimum mean square error or zero force. The experimental results show that the optimal transform orders to achieve the best communication performance are different in different environments. Compared with the traditional frequency-domain equalization method, the proposed method performs better with respect to bit error rate and bandwidth efficiency.

Joint Hartley-domain and time-domain equalizer for a 200-G (4×56-Gbit/s) optical PAM-4 system using 10G-class optics.

In this paper, we experimentally demonstrate a 200-G (4×56-Gbit/s) optical 4-level pulse-amplitude modulation (PAM-4) system using 10G-class optics over 10-km standard single-mode fiber and propose a joint Hartley-domain equalizer (HDE) and time-domain equalizer (TDE) algorithm for efficiently compensating the serious high-frequency distortions caused by the bandwidth-limited devices. To the best of our knowledge, the first HDE based on Hartley transform is designed for an optical PAM-4 system. Owing to the real-valued and self-inverse properties of the Hartley transform, the HDE has advantages in processing the real-valued PAM-4 signal. The experimental results show that the joint HDE and TDE algorithm has a better performance than only the HDE or only the TDE. Meanwhile, for obtaining a desired bit error rate, the computational complexity of the joint HDE and TDE algorithm is approximately 6% that of only the TDE with larger tap number. In conclusion, the joint HDE and TDE algorithm shows great potential for high-speed and cost-sensitive optical PAM-4 systems.

Convolution neural network-based time-domain equalizer for DFT-Spread OFDM VLC system

Abstract This paper presents a novel time-domain equalizer for visible light communication (VLC) system using machine learning (ML) method. In this work, we employ discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-S-OFDM) as modem scheme and convolution neural network (CNN) as kernel processing unit of equalizer. After estimating channel state information (CSI) from training sequence, the proposed equalizer recovers transmitted symbols according to the estimated CSI. Numerical simulations indicate that the equalizer can significantly enhance bit error rate (BER) performance. For example, when signal-to-noise ratio (SNR) is 20 dB and 16/32/64-quadrature amplitude modulation (QAM) is exploited, original BER is about 0.5 while the BER after recovery achieves 1 0 − 5 , which is much lower than forward error correction (FEC) limit 3 . 8 × 1 0 − 3 . This work promotes the application of ML in VLC domain. To the best of our knowledge, this is the first time a CNN-based equalizer has been explored.

MIMO Time-Domain Equalization for High-Speed Continuous Transmission Under Channel Variability

High-speed communication over mutually coupled channels can be severely affected by intersymbol interference (ISI) and crosstalk (XT). Multiple-input multiple-output (MIMO) equalization is known to mitigate both ISI and XT, but requires accurate channel information at the receiver (RX) and/or transmitter (TX), when the channel is stochastic. However, since adjusting the equalization filters to the specific channel realization involves a considerable implementational and computational complexity, it is desirable to keep the equalization filters fixed irrespective of the specific channel realization, especially when the channel variability is relatively small. Therefore, we propose a general MIMO transceiver scheme where the equalization filters depend on the channel statistics rather than the actual channel. More specifically, by considering the time-domain equalization with the fixed linear MIMO pre-equalization and adjustable MIMO decision feedback equalization, the complexity associated with passing channel information from the RX to the TX is avoided, and the computationally intensive and iterative calculations of the fixed pre-equalizer can be performed offline rather than on-chip. The proposed equalization scheme is shown to yield only a small performance degradation compared to fully adjustable equalization schemes, thereby enabling multi-Gbit/s chip-to-chip communication over low-cost electrical interconnects which are prone to manufacturing tolerances.

An Aerodynamic Calculation Model for anti-torque system of NOTOR

The existing experimental methods and numerical models were difficult to get accurate aerodynamic characteristics of the anti-torque system of a NOTOR under rotor wake. To solve this problem, a new three-dimensional aerodynamic model with momentum source based on finite volume method was proposed in this paper. By means of time domain equalization and spatial interpolation, the complicated dynamic meshes on blade were replaced by the non-blade fixed rotor domain with momentum source. And the model was calculated by steady, compressible and three-dimensional Reynolds averaged N-S equation. In this paper, a typical NOTAR was took for research, the aerodynamic characteristics including flow field and variation regularity of lateral force with momentum coefficient of anti-torque system during hover condition was obtained by applying the above computational model, and the accuracy of which was verified by corresponding experimental data. In addition, the model was also used to analyze the key factors that influence working condition of the tail boom, including length of tail boom, area of nozzle and fan pressurization. And the curves of variation regularity were given. The model and work in this paper could provide reference for further research and design on anti-torque system for NOTAR.Keywords: Calculation model; CFD; circulation control; momentum source; NOTAR. DOI: http://dx.doi.org/10.5755/j01.mech.24.2.19740

ML-Based Iterative Approach for Blind Frequency Domain Equalization and Combination Over Sparse Channels

This letter deals with blind spatial diversity equalization and combination of sparse channels. The equalization and combination problem of multiple signals is modeled as the maximum likelihood estimation of frequency domain symbol sequence from incomplete observations, and solved by means of the expectation-maximization (EM) algorithm. Closed-form expression of the equalization output is obtained, which shows that the complicated problem of signal equalization and combination in multipath channels is converted to the weighted summation of each discrete-frequency signals, eliminating the need of complicated maximum likelihood sequence estimation (MLSE) or de-convolution demanded by time domain equalization. Simulation results show that the proposed scheme enables evident performance improvement in terms of symbol error rate especially at low signal-to-noise ratio (SNR) values and short signal lengths compared with a typical scheme.

Efficient Use of Space-Time Clustering for Underwater Acoustic Communications

Underwater acoustical communication channels are characterized by the spreading of received signals in space (direction of arrival) and in time (delay). The spread is often limited to a small number of space-time clusters. In this paper, the space-time clustering is exploited in a proposed receiver designed for guard-free orthogonal frequency-division multiplexing with superimposed data and pilot signals. For separation of space clusters, the receiver utilizes a vertical linear array (VLA) of hydrophones, whereas for combining delay-spread signals within a space cluster, a time-domain equalizer is used. We compare a number of space-time processing techniques, including a proposed reduced-complexity spatial filter, and show that techniques exploiting the space-time clustering demonstrate an improved detection performance. The comparison is done using signals transmitted by a moving transducer, and recorded on a 14-element nonuniform VLA in sea trials at distances of 46 and 105 km.

Adaptive Equalizer Design for Unmanned Aircraft Vehicle Image Transmission over Relay Channels

A novel length adaptive method is proposed for time domain equalizer by taking the channel attenuation ratio between different multipath components into account in UAV‐UAV and UAV‐ground channels. Then, considering received image quality, the minimum bit error ratio (MBER) criterion is exploited to design adaptive equalizers for both amplify‐and‐forward (AF) and decode‐and‐forward (DF) relaying systems by the proposed length adaptive method. Results show that proposed MBER adaptive equalizers outperform the traditional ones in both AF relaying and DF relaying as channel attenuation ratio in UAV‐ground channel increases. Moreover, DF outperforms AF as channel attenuation ratio in UAV‐UAV channel increases. Furthermore, bit error ratio (BER) and peak signal‐to‐noise ratio (PSNR) performances in both AF and DF are evaluated to show the enhancement by the proposed MBER adaptive equalizers.

Single-Carrier Modulation Versus OFDM for Millimeter-Wave Wireless MIMO

This paper presents results on the achievable spectral efficiency and on the energy efficiency for a wireless multiple-input-multiple-output (MIMO) link operating at millimeter wave frequencies (mmWave) in a typical 5G scenario. Two different single-carrier modem schemes are considered, i.e., a traditional modulation scheme with linear equalization at the receiver, and a single-carrier modulation with cyclic prefix, frequency-domain equalization and FFT-based processing at the receiver; these two schemes are compared with a conventional MIMO-OFDM transceiver structure. Our analysis jointly takes into account the peculiar characteristics of MIMO channels at mmWave frequencies, the use of hybrid (analog-digital) pre-coding and post-coding beamformers, the finite cardinality of the modulation structure, and the non-linear behavior of the transmitter power amplifiers. Our results show that the best performance is achieved by single-carrier modulation with time-domain equalization, which exhibits the smallest loss due to the non-linear distortion, and whose performance can be further improved by using advanced equalization schemes. Results also confirm that performance gets severely degraded when the link length exceeds 90-100 meters and the transmit power falls below 0 dBW.

Robust multi-branch space–time beamforming for OFDM system with interference

Space–time receive beamforming is a promising technique to suppress co-channel multiuser interference for orthogonal frequency division multiplexing (OFDM) systems. However, the performance of existing receive beamforming methods is highly sensitive to the memory length of time–domain equalizer. In this paper, we propose a new robust solution of space–time receive beamforming to combat co-channel multiuser interference for OFDM systems. The proposed method performs subspace analysis for the received space–time snapshots from both the training block and few data blocks, and constrains the space–time beamforming vectors to lie in the corresponding signal subspace. A few beamforming vectors are then carefully designed to suppress interference as well as provide the potential multi-branch diversity gain. The numerical results are provided to corroborate the proposed studies. We show that the proposed method not only can outperform the exiting competitors but also has the advantage of being quite insensitive to the memory length of time–domain equalizer.

Analysis of chromatic dispersion compensation and carrier phase recovery in long-haul optical transmission system influenced by equalization enhanced phase noise

The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are considered: the time-domain equalization (TDE), the frequency-domain equalization (FDE), the least mean square (LMS) adaptive equalization are applied for EDC, and the dispersion compensating fiber (DCF) is employed for optical dispersion compensation (ODC). Meanwhile, three carrier phase recovery methods are also involved: a one-tap normalized least mean square (NLMS) algorithm, a block-wise average (BWA) algorithm, and a Viterbi-Viterbi (VV) algorithm. Numerical simulations have been carried out in a 28-Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) coherent transmission system, and the results indicate that the origin of EEPN depends on the choice of chromatic dispersion compensation methods, and the effects of EEPN also behave moderately different in accordance to different carrier phase recovery scenarios.

Comparing System Performance of Optical OFDM Systems Using LMSTE, NLMSTE and DFTE

The evaluation of Optical Orthogonal Frequency Division Multiplexing (OOFDM) using Least Mean Square Time-domain Equalizer (LMSTE), its normalized form (NLMSTE) and Decision Feedback Time-domain Equalizer (DFTE) to reduce Cyclic Prefix (CP) length over 1200 Km of Standard Single Mode Fiber (SSMF) is presented. All of these TEQs are used immediately after the fiber channel. They can cancel the residual Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) caused by both the Group Velocity Dispersion (GVD) and the CP length being shorter than the Channel Impulse Response (CIR). Using these TEQs allow the reduction in size of CP, and consequently leading to system performance improvement. Using DFTE can decrease the noise whereas using NLMSTE can solve the problem of choosing the gain of LMS algorithm to make it stable since LMS algorithm is sensitive to the scaling of its input.