Introduces Intersymbol Interference Research Articles

Joint timing recovery and adaptive equalization based on training sequences for PM-16QAM faster-than-Nyquist WDM systems.

Since the timing error detectors sensitivity (TEDS) of the timing recovery algorithm is close to zero under the singularity condition of azimuth θ about ±π/4 and differential group delay (DGD) about n × 1/2T (n is an odd number, T is the symbol period), it makes the squared Gardner phase detector (SGPD) timing recovery algorithm fail to achieve timing synchronization. What's worse, in the faster-than-Nyquist wavelength division multiplexing (FTN-WDM) systems, the tight filtering introduces inter-symbol-interference (ISI) so severe that the convergence cost of the SGPD timing recovery algorithm is extremely large even under the non-singularity condition. This paper proposes a joint timing recovery and adaptive equalization scheme for FTN coherent systems based on training sequences that could calculate channel matrix and indicate polarization characteristics, thereby avoiding the influence of azimuth on adaptive equalization and polarization demultiplexing (AEPD) embedded in the timing recovery feedback loop. Since embedded AEPD could compensate for most of DGD, the TEDS could be restored and timing synchronization could be achieved under the above adverse conditions. Thanks to the innovative scheme, which equalizes ISI and DGD during the feedback process of the loop, the convergence cost of timing recovery could be reduced with similar computational complexity compared with the conventional one. The simulation results of 128 GBaud polarization multiplexing (PM) 16-quadrature amplitude modulation (QAM) FTN-WDM transmission systems demonstrate that the proposed scheme could stably achieve timing synchronization under the singularity condition. And compared with the conventional scheme, the convergence cost is reduced by at least 42% @ 0.9 acceleration factor. In addition, 40 GBaud PM-16QAM FTN experiment results show that the proposed scheme could not only achieve timing synchronization stably but also exhibit an optical signal-to-noise ratio tolerance gain of 0.8 dB compared with the conventional scheme under 800 km transmission.

Suppressed Noise Enhancement Equalization Combined With Nonlinear-MLSE Techniques for Bandwidth-Limitation IM/DD System

Bandwidth limitation introduced inter-symbol interference (ISI) is the major impediment for high baud rate intensity modulation and direct detection (IM/DD) system with commercial devices. Least mean square (LMS) criterion based feedforward equalizer (FFE) is the most common method to eliminate ISI in single-carrier system. However, there is a tradeoff between the residual ISI and enhanced noise when the system bandwidth is severely limited. Although a post filter (PF) followed by maximum likelihood sequence estimation (MLSE) can suppress the enhanced noise effectively, the residual ISI left by post-FFE will degrade the system performance as the subsequent MLSE only handles ISI introduced by PF. In this paper, an adaptive partial response equalization realized by a channel-shortening filter (CSF) is investigated, which is combined with MLSE. As the target of CSF is a partial response signal with desired low-pass feature, the noise will not be enhanced in this scheme. And the residual ISI with determined response can be fully solved by MLSE. The performance of CSF based MLSE (CSF-MLSE) is evaluated and compared to PF based MLSE (PF-MLSE) in 60/70/75Gbaud four-level pulse amplitude modulation (PAM-4) system with 10-dB bandwidth of 16.2GHz. The experimental results show that CSF-MLSE has a better capability of ISI elimination compared to PF-MLSE. The bit error rate (BER) can be reduced from 7.4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> to 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and from 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> to 1×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for 70Gbaud and 75Gbaud in optical back-to-back (OBTB) transmission. To further compensate the system nonlinear impairments, several nonlinear MLSE (NL-MLSE) techniques assisted by look-up table (LUT) or Volterra filter are proposed and investigated in this paper. The BER of 75Gbuad PAM-4 can be below 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> after using NL-MLSE schemes.

Hyperparameter-Free RFF Based Post-Distorter for OTFS VLC System

Visible light communication (VLC) has emerged as an eco-friendly and low-cost technology for the next-generation communication systems. However, for VLC systems, existing works report performance degradation due to light-emitting-diode (LED) non-linearity, multipath and relative mobility between the transmitter and the receiver. Additionally, multipath and user-mobility introduce inter-symbol-interference (ISI) and frequency-domain spreading which degrades the performance of VLC systems. For such scenarios, orthogonal time frequency space (OTFS) modulation is well-known to jointly addresses impairments due to multipath and user-mobility. To mitigate the distortions due to LED non-linearity, recently reproducing kernel Hilbert space (RKHS)-based random Fourier feature (RFF) techniques have emerged which alleviate the dependence on learning a dictionary and, outperforms classical polynomial based techniques. However, performance of these techniques is sensitive to the choice of kernel-width. Thus, for the OTFS systems impaired by LED non-linearity, this manuscript proposes a hyperparameter-free RFF-based post-distorter, under finite-memory budget without the need of explicitly tuning kernel-width for best performance. Analytical bounds for the bit-error-rate (BER) performance of the proposed post-distorter are presented, and validated via simulations over realistic VLC channels. From the results it is verified that the proposed receiver achieves better BER performance over uncompensated scenario and classical baseline polynomial based technique.

Coordinate Interleaved Faster-Than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling is an attractive transmission technique which accelerates data symbols beyond the Nyquist rate to improve the spectral efficiency; however, at the expense of higher computational complexity to remove the introduced intersymbol interference (ISI). In this work, we introduce a novel FTN signaling transmission technique, named coordinate interleaved FTN (CI-FTN) signaling that exploits the ISI at the transmitter to generate constructive interference for every pair of the counter-clockwise rotated binary phase shift keying (BPSK) data symbols. In particular, the proposed CI-FTN signaling interleaves the in-phase (I) and the quadrature (Q) components of the counter-clockwise rotated BPSK symbols to guarantee that every pair of consecutive symbols has the same sign, and hence, has constructive ISI. At the receiver, we propose a low-complexity detector that makes use of the constructive ISI introduced at the transmitter. Simulation results show the merits of the CI-FTN signaling and the proposed low-complexity detector compared to conventional Nyquist and FTN signaling.

A Transmission Scheme Based on Uniform Shortening LDPC Codes for Performance Improvement in Faster-Than-Nyquist Systems

Faster-than Nyquist (FTN) signaling is a research topic that has been drawing increased attention due to its capability of improving transmission speed without the need of extra bandwidth. However, the deployment of FTN signaling introduces inter-symbol interference (ISI) which severely degrade system performance. Interestingly, even without ISI equalizer, it has been recently shown that the joint application of LDPC codes with FTN signaling can exhibit rather good performance. To further improve the performance of LDPC codes over FTN systems, a transmission scheme that utilizes uniform shortening LDPC codes is proposed in this paper. It was found that their shortening counterpart can provide a coding gain at least 0.4 dB over a wide range of FTN factors compared with FTN systems that employ conventional LDPC codes. Moreover, using LDPC coded ISI-free system as the benchmark, the proposed transmission scheme can possibly provide 43&#x0025; improvement in data rate with rather small performance degradation.

Data-Driven and Model-Driven Joint Detection Algorithm for Faster-Than-Nyquist Signaling in Multipath Channels.

In recent years, Faster-than-Nyquist (FTN) transmission has been regarded as one of the key technologies for future 6G due to its advantages in high spectrum efficiency. However, as a price to improve the spectrum efficiency, the FTN system introduces inter-symbol interference (ISI) at the transmitting end, whicheads to a serious deterioration in the performance of traditional receiving algorithms under high compression rates and harsh channel environments. The data-driven detection algorithm has performance advantages for the detection of high compression rate FTN signaling, but the current related work is mainly focused on the application in the Additive White Gaussian Noise (AWGN) channel. In this article, for FTN signaling in multipath channels, a data and model-driven joint detection algorithm, i.e., DMD-JD algorithm is proposed. This algorithm first uses the traditional MMSE or ZFinear equalizer to complete the channel equalization, and then processes the serious ISI introduced by FTN through the deepearning network based on CNN or LSTM, thereby effectively avoiding the problem of insufficient generalization of the deepearning algorithm in different channel scenarios. The simulation results show that in multipath channels, the performance of the proposed DMD-JD algorithm is better than that of purely model-based or data-driven algorithms; in addition, the deepearning network trained based on a single channel model can be well adapted to FTN signal detection under other channel models, thereby improving the engineering practicability of the FTN signal detection algorithm based on deepearning.

Decision Feedback Kurtosis Minimum Crosstalk Mitigation in Super-Nyquist Multiband CAP Systems

In multiuser access visible light communication (VLC) systems, many multiplex techniques can be utilized to fully exploit the limited bandwidth. In frequency-division multiplexing systems, one possible solution is to dynamically allocate limited bandwidth resources for users to support multiple-service access. To enable high-speed transmissions, the super-Nyquist multiband concept has been proposed in recent years. Specifically, the center frequency spacing is narrowed, and the subcarriers are nonorthogonally overlapped to enable more services and users in multiband systems. Studies have shown that this strategy can support higher spectral efficiency (SE) while simultaneously, introducing intersymbol interference (ISI) and intercarrier interference (ICI). Therefore, a well-designed ICI mitigation scheme is required. In multiband carrierless amplitude phase ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -CAP) modulation systems, it is technically challenging to achieve the SE beyond one baud/s/Hz under the pre-forward error correction (pre-FEC) threshold without increasing the modulation order. Inspired by the distinctive pulse shaping filter (PSF) structure in a non-orthogonal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -CAP scheme, we propose the iterative decision feedback kurtosis minimum (DFKM) scheme and achieve the super-Nyquist SE of approximately 1.06 baud/s/Hz. In contrast to existing ICI mitigation schemes, the theoretical framework reveals that symbol-level crosstalk filters are indispensable to reap the benefit of super-Nyquist transmission, not limited to VLC.

A Novel Low Complexity Faster-Than-Nyquist Signaling Detector Based on the Primal-Dual Predictor-Corrector Interior Point Method

Faster-than-Nyquist signaling (FTNS) is a promising non-orthogonal physical layer transmission technique to improve the spectral efficiency of next-generation communication systems but at the expense of increased transciever complexity to remove the artificially introduced intersymbol-interference (ISI). In this paper, we investigate the detection problem of FTNS and propose a low-complexity sub-optimal detection algorithm, stemming in operations research, that is based on convex relaxation, primal-dual predictor-corrector interior point method, and quantization. The proposed convex quadratic relax-and-quantize sequence estimation (CQRAQSE) algorithm is suitable for low rates FTNS and demonstrates an excellent trade-off between the detection performance and computational effort.

Machine-Learning Based Equalizers for Mitigating the Interference in Asynchronous MIMO OWC Systems

The error performance of the optical wireless communication (OWC) link suffers from the effects of atmospheric turbulence and pointing errors. The multi-input-multi-output (MIMO) system can combat the damage by transmitting diverse replicas of symbols to the receivers, i.e. the spatial diversity. However, different delays between the transceivers can introduce inter-symbol interference (ISI) which degrades the system performance. The delays during transmission are mainly caused by placing locations and optical path differences. This article proposes algorithms to mitigate the ISI based on machine learning techniques, including both neural networks and the genetic algorithm. In the case of multi-input-single-output (MISO) system, we propose an algorithm based on a bidirectional long short-term memory (LSTM) recurrent neural network (RNN), which works as an equalizer. In the case of single-input-multiple-output (SIMO) system, additional delayers are utilized to align the signals in different apertures. The problem of deducing the values of the delayers is considered as seeking the minimum value in a high-dimensional space. With the help of the genetic algorithm, optimal values of the delayers are maintained, which is named as GAD (genetic algorithm-based delayers). In a more general MIMO case, the GAD and LSTM equalizers are further combined to deal with the ISI issue in the asynchronous MIMO OWC systems, (i.e. GAD-LSTM). Both experimental and simulation results show the remarkable performance improvement of the proposed method over conventional methods.

Bounds on the Constrained Capacity for the Diffusive Poisson Molecular Channel With Memory

This letter focuses on the analysis of a diffusion-based molecular communication (MC) system where the received signal is approximated as a Poisson random variable. Concentration shift keying (CSK) is used as the modulation technique for encoding information in the system. In particular, this work aims to study the performance of the MC system in terms of reliable information exchange for the channel with finite-state memory, which introduces intersymbol interference (ISI). The main objective is the derivation of analytical expressions for the upper and the lower bound of the constrained channel capacity for a range of values of the modulated symbols, i.e., for a number of different sets of amplitude levels of CSK modulation, and for various levels of ISI. In addition, the numerical evaluation of the derived expressions is presented. Results allow discussing the relationship between ISI level and achievable channel capacity. Moreover, numerical outcomes highlight how the estimation of the bounds is not affected by the presence of ISI in the case of binary CSK modulation, as the bounds remain quite tight.

A Novel Low Complexity Faster-than-Nyquist (FTN) Signaling Detector for Ultra High-Order QAM

Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal pulse modulation technique that can improve the spectral efficiency (SE) of next generation communication systems at the expense of higher detection complexity to remove the introduced inter-symbol interference (ISI). In this paper, we investigate the detection problem of ultra high-order quadrature-amplitude modulation (QAM) FTN signaling where we exploit a mathematical programming technique based on the alternating directions multiplier method (ADMM). The proposed ADMM sequence estimation (ADMMSE) FTN signaling detector demonstrates an excellent trade-off between performance and computational effort enabling, for the first time in the FTN signaling literature, successful detection and SE gains for QAM modulation orders as high as 64K (65,536). The complexity of the proposed ADMMSE detector is polynomial in the length of the transmit symbols sequence and its sensitivity to the modulation order increases only logarithmically. Simulation results show that for 16-QAM, the proposed ADMMSE FTN signaling detector achieves comparable SE gains to the generalized approach semidefinite relaxation-based sequence estimation (GASDRSE) FTN signaling detector, but at an experimentally evaluated much lower computational time. Simulation results additionally show SE gains for modulation orders starting from 4-QAM, or quadrature phase shift keying (QPSK), up to and including 64K-QAM when compared to conventional Nyquist signaling. The very low computational effort required makes the proposed ADMMSE detector a practically promising FTN signaling detector for both low order and ultra high-order QAM FTN signaling systems.

Probabilistic Shaping in Time-Frequency-Packed Terabit Superchannel Transmission

To combine the individual benefits of probabilistic-shaping (PS) and time-frequency-packing (TFP), we consider for the first time PS-TFP wavelength-division multiplexing (WDM) superchannels. However, TFP introduces inter-symbol interference (ISI) and/or inter-carrier interference (ICI). Moreover, the presence of reconfigurable optical add-drop multiplexers in the fiber links may further degrade the system performance. In this letter, we efficiently handle such challenges to present PS-TFP superchannels enabling Terabit-per-second data rates. For this, we perform a joint ISI and ICI channel estimation in tandem with turbo equalization to mitigate the interference. We investigate optimizing the parameters in the shaping and packing dimensions to achieve a desired target spectral efficiency. We show through our numerical results that such an optimized PS-TFP transmission leads up to 1.2 dB performance improvement over an unshaped Nyquist WDM system under similar conditions.

Design of Time-Frequency Packed WDM Superchannel Transmission Systems

We consider time and frequency-packing (TFP) wavelength division-multiplexing (WDM) superchannel systems for longhaul optical fiber communication. Employing very high baud rates in conjunction with higher-order modulation formats is challenging due to practical constraints. TFP superchannels therefore become an attractive choice to facilitate high data rates with improved spectral efficiency. However, TFP introduces inter-symbol interference (ISI) and/or inter-carrier interference (ICI) that necessitate efficient interference handling techniques. Moreover, phase noise (PN) due to wide laser linewidth (LLW) may cause significant signal distortion in WDM transmission, and the presence of ISI and ICI in TFP systems further complicates carrier phase recovery (CPR). In this article, we propose a spectrally efficient TFP superchannel design equipped with powerful interference cancellation and PN mitigation techniques, targeting Terabit-per-second (Tbps) data rates. First, we propose a joint ISI and ICI channel estimation algorithm coupled with polarization-recovery and a coarse PN cancellation method. Second, we investigate two iterative CPR algorithms to mitigate the distortion due to the residual PN. Third, a combination of successive and parallel interference cancellation methods for ICI mitigation is investigated in tandem with turbo ISI equalization. The effectiveness of the proposed algorithms is demonstrated through computer simulations of a coded TFP superchannel system in the presence of linear fiber impairments, targeting a throughput of 1.2 Tbps. Numerical results suggest that the proposed TFP design offers more than 2 dB performance gains and as high as 960 km transmission distance improvement over existing competitive super-Nyquist designs. Simulation results also indicate that the proposed design exhibits excellent tolerance to high LLWs and aggressive optical filtering stemming from cascaded reconfigurable optical add-drop multiplexers in the fiber link.

ANALYSIS OF DATA TRANSMISSION SCHEME FOR WIDE BAND CODE DIVISION MULTIPLE ACCESS WITH RAKE RECEIVER

Fifth generation systems are required to fulfill the objectives like compatibility, flexibility, high speed data rate and low cost. Universal Mobile Telecommunication System (UMTS) use WCDMA as the air interface for 4th generation mobile system. The performance of wireless communication system is often limited by the radio channel models. In urban areas, channel is modeled as Rayleigh fading channel. This channel causes multipath channels and other problems resulting degraded performance. Hence, channel estimation before receiver helps to receive the transmitted signal using rake receiver. Rake receiver is a conventional receiver for DS-CDMA system. In this, channel is estimated adaptively using LMS algorithm and performance of this algorithm is studied for various multipath channels and step sizes. Moreover, the channel introduces Inter Symbol Interference (ISI) and channel equalizers are used to compensate for the ISI. In this work, BER vs. SNR performance of Zero Forcing Equalizer (ZFE), Minimum Mean Square Error (MMSE) and MMSE- Decision Feedback Equalizer (MMSE-DFE) in WCDMA downlink system are compared with conventional rake receiver for various spread factors in Rayleigh multipath fading channel with Additive White Gaussian Noise.

Data Rate Enhancement in Optical Camera Communications Using an Artificial Neural Network Equaliser

In optical camera communication (OCC) systems leverage on the use of commercial off-the-shelf image sensors to perceive the spatial and temporal variation of light intensity to enable data transmission. However, the transmission data rate is mainly limited by the exposure time and the frame rate of the camera. In addition, the camera's sampling will introduce intersymbol interference (ISI), which will degrade the system performance. In this paper, an artificial neural network (ANN)-based equaliser with the adaptive algorithm is employed for the first time in the field of OCC to mitigate ISI and therefore increase the data rate. Unlike other communication systems, training of the ANN network in OCC is done only once in a lifetime for a range of different exposure time and the network can be stored with a look-up table. The proposed system is theoretically investigated and experimentally evaluated. The results record the highest bit rate for OCC using a single LED source and the Manchester line code (MLC) non-return to zero (NRZ) encoded signal. It also demonstrates 2 to 9 times improved bandwidth depending on the exposure times where the system's bit error rate is below the forward error correction limit.

Research on an Optimization Method for a Partially Responsive Continuous Phase Modulated (CPM) Signal Based on an Optimal Generic Function

This paper establishes an optimal generic function model in order to obtain a continuous phase modulated (CPM) signal with a smoother phase modulation function. This is achieved by finding the solution to the symbol signals at different lengths of the CPM function. In the solution process, the unknown amount that needs to be solved is reduced by using the even function symmetry characteristic of the signal to be solved. For each different form of the signal, the time domain form of the CPM function and the corresponding normalized energy spectral density are compared under the influence of the phase modulation signal length and the generic function parameter n. The data transmission rate is improved by introducing inter-symbol interference, and the modulation process is realized using six-way parallel transmission when the CPM function is 6T. The simulation results show that the CPM function obtained by establishing an optimal generic function model has high-quality time-frequency characteristics. The real-time phase trajectory and the high-order derivative are both continuous, and the modulated signal has constant envelope characteristics. The CPM function has a fast rolling-off in the frequency domain and small out-of-band radiation, which greatly improves the characteristics of the frequency band utilization.

Symbol Error Probability Analysis of DFrFT-Based OFDM Systems With CFO and STO in Frequency Selective Rayleigh Fading Channels

In this paper, we derive exact symbol error probability (SEP) expressions for orthogonal frequency-division multiplexing (OFDM) based on discrete fractional Fourier transform (DFrFT) when symbol timing offset (STO) and carrier frequency offset (CFO) are present together. Closed form expressions are derived for binary phase shift keying, quadrature phase shift keying, and 16-ary quadrature amplitude modulation in the case of transmission over a frequency selective Rayleigh fading channel. As it is well known, in OFDM the presence of CFO destroys the orthogonality between the sub-carriers, generating inter-carrier interference (ICI), while the presence of STO introduces intersymbol interference, between successive symbols, and phase rotations in frequency domain, within the same symbol. It is well recognized that an OFDM system based on DFrFT is more robust to ICI introduced by CFO than that based on discrete Fourier transform (DFT). Motivated by this, the combined effect of CFO and STO on the SEP of a DFrFT-based OFDM system is analyzed. Our results show that the DFrFT-based OFDM system outperforms that based on the DFT for different values of the DFrFT “angle parameter.” Monte Carlo simulations are used to demonstrate the correctness of the derived analytical expressions.

Method for carrier frequency‐offset estimation of faster‐than‐Nyquist signalling

A new non-data aided frequency-offset estimation scheme for faster-than-Nyquist (FTN) signalling system is proposed. Considering the intentionally introduced intersymbol interference, the envelope of carrier signals is time varying, which makes it difficult to estimate the carrier frequency-offset at the receiver. In order to improve the estimation performance, a new estimation scheme is proposed which is based on Newton's method for minimising the non-linear least-squares error. Moreover, the proposed estimation scheme can be also applied into M-ary pulse-amplitude modulation. Further, the performance of proposed frequency-offset estimation scheme for FTN is verified and tested.

Experimental Comparison of Transmission Performance for Nyquist WDM and Time–Frequency Packing

Several spectral efficient solutions for next-generation flexible optical networks are under investigation in order to cope with scalability issues while traffic demand is continuously increasing. Concerning transmission, Nyquist wavelength-division multiplexing (NWDM)—that confines the bandwidth within the Nyquist frequency of the signal—recently gained a momentum as one of the most suitable solutions for transmission over backbone networks and commercial solutions are available by now. Besides NWDM, other transmission techniques have been proposed to approach or overcome the Nyquist limit, thus further increasing the spectral efficiency (SE). Among them, time–frequency packing (TFP) is one candidate. This method builds a superchannel, whose subcarriers significantly overlap in frequency or time or both. This leads to an increased SE at the expenses of additional complexity within the transceiver to compensate for the introduced intersymbol interference. In this paper, we experimentally compare, for the first time, NWDM and TFP when employing the same identical test-bed. The experiment considered the two different terabit superchannels: a polarization multiplexed (PM)-16 quadrature amplitude modulation for the case of NWDM case, and a PM-quadrature phase-shift keying for TFP. The comparison and assessment of the results is carried out first in back-to-back configuration and, afterward, by propagating them over a recirculating loop consisting of a standard single-mode fiber, including spectrum selective switch to emulate node filtering.

EM‐based SNR estimator for faster‐than‐Nyquist signalling system

Considering the intentionally introduced inter-symbol interference and coloured noise, proposed is a new signal-to-noise ratio (SNR) estimator based on the expectation–maximisation algorithm for the faster-than-Nyquist signalling system. The proposed SNR estimator can maximise the likelihood function by iteratively using the soft information from the channel decoder. Moreover, the new SNR estimator can be applied into high-order modulation. The performance of the proposed SNR estimator is verified and tested.