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Compared with high spectrum efficiency faster-than-Nyquist (FTN) backbone network, an enhanced carrier phase recovery based on dual pilot tones is more sensitive to capital cost in FTN metropolitan areas as well as inter-datacenter optical networks. The use of distributed feedback (DFB) lasers is a way to effectively reduce the cost. However, under high symbol rate FTN systems, equalization-enhanced phase noise (EEPN) induced by a DFB laser with large linewidth will significantly deteriorate the system performance. What is worse, in FTN systems, tight filtering introduces inter-symbol interference so severe that the carrier phase estimation (CPE) algorithm of the FTN systems is more sensitive to EEPN, thus it will lead to a more serious cycle slip problem. In this paper, an enhanced carrier phase recovery based on dual pilot tones is proposed to mitigate EEPN and suppress cycle slip, in which the chromatic dispersion (CD)-aware Tx and LO laser phase noise is estimated, respectively. Offline experiments results under 40 Gbaud polarization multiplexing (PM) 16-quadrature amplitude modulation (QAM) FTN wavelength division multiplexing (FTN-WDM) systems at 0.9 acceleration factor, 5 MHz laser linewidth, and 500 km transmission demonstrate that the proposed algorithm could bring about 0.65 dB improvement of the required SNR for the normalized generalized mutual information of 0.9 compared with the training sequence-based cycle slip suppression carrier phase estimation (TS-CSS) algorithm. [ABSTRACT FROM AUTHOR]

To mitigate inter-symbol interference (ISI) caused by Faster-than-Nyquist (FTN) technology in a multiple input multiple output (MIMO) optical wireless communication (OWC) system, we propose an ISI cancellation algorithm that combines multi-head self-attention (MHSA), a one-dimensional convolutional neural network (1D CNN), and bi-directional long short-term memory (Bi-LSTM). This hybrid network extracts data features using 1D CNN and captures sequential information with Bi-LSTM, while incorporating MHSA to comprehensively reduce ISI. We analyze the impact of antenna numbers, acceleration factors, wavelength, and turbulence intensity on the system's bit error rate (BER) performance. Additionally, we compare the waveform graphs and amplitude–frequency characteristics of FTN signals before and after processing, specifically comparing sampled values of four-pulse-amplitude modulation (4PAM) signals with those obtained after ISI cancellation. The simulation results demonstrate that within the Mazo limit for selecting acceleration factors, our proposal achieves a 7 dB improvement in BER compared to the conventional systems without deep learning (DL)-based ISI cancellation algorithms. Furthermore, compared to systems employing a point-by-point elimination adaptive pre-equalization algorithm, our proposal exhibits comparable BER performance to orthogonal transmission systems while reducing computational complexity by 31.15%. [ABSTRACT FROM AUTHOR]

Conventional multiple input multiple output (MIMO) detection algorithms face challenges related to computational complexity and limited performance when handling high-dimensional inputs and complex channel conditions. In order to enhance signal recovery accuracy in atmospheric turbulence channels for faster-than-Nyquist (FTN) optical wireless communication (OWC) systems, a deep learning (DL) based MIMO detector is proposed. By leveraging a deep neural network (DNN), it becomes possible to learn nonlinear mappings within MIMO systems, resulting in improved detection performance while reducing computational overheads. Simulation results validate that our proposed DNN detector achieves comparable performance to the maximum likelihood (ML) method, while reducing complexity by 40%.

The adoption of one-bit analog-to-digital converters (ADCs) in wireless communication has become increasingly popular, owing to their potential to reduce power consumption. However, there is a decreased spectral efficiency (SE) associated with their use, as they are unable to take advantage of high-modulation-order signaling. Faster-than-Nyquist (FTN) signaling along with oversampling are promising means of improving SE at the expense of additional inter-symbol interference (ISI). This study establishes a common platform for design and evaluation by providing a general system model and problem formulation, as well as proposing an alternative solution framework for the one-bit quantization system. By systematically evaluating optimizable factors that impact performance, such as signaling rate, transmit sequences, and error correction blocks, this study proposes a deep learning (DL)-based architecture, specifically channel autoencoders, for end-to-end communication over a one-bit quantization channel. Various transceiver designs are proposed for performance comparison as well as to enable one-bit quantized communication at previously unattainable information rates through conventional means. Numerical results showcase the superiority of jointly optimizing all blocks in an additive white Gaussian noise (AWGN) channel. The DL-based scheme operationalizes Bit Error Rate (BER) performance at information rates scaling up to 80% of Shamai’s limit. Beyond AWGN, the autoencoder-based transceiver design extends to make one-bit quantization viable over a challenging Rayleigh multipath fading channel. A detailed analysis compares a pilot-based scheme for one-bit quantization with a pilotless option, thereby revealing their SE and BER relationship. The pilot-based quantized scheme outperforms conventional fading channel transmission without quantization by up to 10 dB.

Compared with high spectrum efficiency faster-than-Nyquist (FTN) backbone network, an enhanced carrier phase recovery based on dual pilot tones is more sensitive to capital cost in FTN metropolitan areas as well as inter-datacenter optical networks. The use of distributed feedback (DFB) lasers is a way to effectively reduce the cost. However, under high symbol rate FTN systems, equalization-enhanced phase noise (EEPN) induced by a DFB laser with large linewidth will significantly deteriorate the system performance. What is worse, in FTN systems, tight filtering introduces inter-symbol interference so severe that the carrier phase estimation (CPE) algorithm of the FTN systems is more sensitive to EEPN, thus it will lead to a more serious cycle slip problem. In this paper, an enhanced carrier phase recovery based on dual pilot tones is proposed to mitigate EEPN and suppress cycle slip, in which the chromatic dispersion (CD)-aware Tx and LO laser phase noise is estimated, respectively. Offline experiments results under 40 Gbaud polarization multiplexing (PM) 16-quadrature amplitude modulation (QAM) FTN wavelength division multiplexing (FTN-WDM) systems at 0.9 acceleration factor, 5 MHz laser linewidth, and 500 km transmission demonstrate that the proposed algorithm could bring about 0.65 dB improvement of the required SNR for the normalized generalized mutual information of 0.9 compared with the training sequence-based cycle slip suppression carrier phase estimation (TS-CSS) algorithm.

To mitigate inter-symbol interference (ISI) caused by Faster-than-Nyquist (FTN) technology in a multiple input multiple output (MIMO) optical wireless communication (OWC) system, we propose an ISI cancellation algorithm that combines multi-head self-attention (MHSA), a one-dimensional convolutional neural network (1D CNN), and bi-directional long short-term memory (Bi-LSTM). This hybrid network extracts data features using 1D CNN and captures sequential information with Bi-LSTM, while incorporating MHSA to comprehensively reduce ISI. We analyze the impact of antenna numbers, acceleration factors, wavelength, and turbulence intensity on the system’s bit error rate (BER) performance. Additionally, we compare the waveform graphs and amplitude–frequency characteristics of FTN signals before and after processing, specifically comparing sampled values of four-pulse-amplitude modulation (4PAM) signals with those obtained after ISI cancellation. The simulation results demonstrate that within the Mazo limit for selecting acceleration factors, our proposal achieves a 7 dB improvement in BER compared to the conventional systems without deep learning (DL)-based ISI cancellation algorithms. Furthermore, compared to systems employing a point-by-point elimination adaptive pre-equalization algorithm, our proposal exhibits comparable BER performance to orthogonal transmission systems while reducing computational complexity by 31.15%.

Optical network monitoring and soft failure identification such as optical filter shifting and filter tightening are increasingly significant for the complex and dynamic optical networks of the future. Center frequency shift of optical filtering devices in optical networks has a serious impact on the performance of multi-span transmission, especially in high spectrum efficiency faster-than-Nyquist (FTN) transmission systems with various optical switching and add/drop nodes. Existing monitoring schemes generally have the problems of high cost, high complexity, and inability to realize multi-channel online monitoring, which makes it difficult for them to be applied in a wavelength division multiplexing (WDM) system with numerous nodes. In this paper, a monitoring scheme of frequency shift of optical filtering devices based on optical label (OL) is proposed and demonstrated. The signal spectrum of each channel is intentionally divided into many sub-bands with corresponding optical labels loading. The characteristics of spectrum power changing caused by frequency shift can be reflected on labels power changing of each sub-band, which are used to monitor and estimate the value of frequency shift via DSP algorithm. Simulation results show that the monitoring errors of frequency shift can be kept reasonably below 0.5 GHz after 10-span WDM transmission in FTN polarization multiplexing m-ary quadrature amplitude modulation (PM-mQAM) systems. In addition, 250 km fiber transmission experiments are also carried out, and similar results are obtained, which further verify the feasibility of our proposed scheme. The characteristics of low cost, high reliability, and efficiency make it a better candidate for practical application in future FTN-WDM networks. [ABSTRACT FROM AUTHOR]

This paper studies the application of neural networks to Viterbi detection of FTN signals in an intersymbol interference (ISI) channel. The main contribution of this paper is to propose a receiver structure for detecting FTN signals in unknown static ISI channel. In particular, we propose a novel low-complexity neural network structure for calculating the branch metrics, and we explore its suitability for FTN signalling with channel uncertainty. We compare the proposed network, which we call the Metric Net (MetNet), to a benchmark neural network-based technique for metric calculation, the ViterbiNet, which was originally designed for ISI channels. The simulation results confirm that the MetNet outperforms the ViterbiNet, with two orders of magnitude lower complexity, and is much more resilient to channel uncertainty than the traditional Viterbi detector, which uses Euclidean distance for metric calculations. We further show that the MetNet exhibits robustness to being trained at mismatched SNR values and FTN pulse acceleration factors, meaning that the number of trained models required can be significantly reduced. Additionally, the results show that the proposed MetNet remains a favorable alternative at much higher levels of channel uncertainties. The results also reflect that we can generalize the MetNet to work with different channel models defined by different decaying factors. Finally, we show that we succeed in achieving a bandwidth efficiency gain of 33% due to FTN by using the MetNet in the presence of channel uncertainty.

New applications for mobile networks are driving up data rates, requiring new solutions to meet the demand for throughput. In urban and densely populated areas, massive multiple-input multiple-output, high bands in millimeter waves, and ultra-dense networks based on small cells are being used to achieve high data rates. However, these solutions do not apply to the enhanced remote areas communications scenario, where large cells must be deployed using vacant VHF or UHF bands with an opportunistic spectrum allocation approach. In this case, a reasonable solution to increase the overall system data rate is to enhance the waveform spectral efficiency. This paper proposes a method to improve the spectral efficiency of the generalized frequency division multiplexing scheme by exploiting the faster-than-Nyquist principle in the time and frequency domains without introducing any penalties in terms of bit error rate. This achievement is obtained by under-sampling the time-frequency grid, which results in more data symbols being transmitted per waveform sample while introducing a controlled amount of interference into the transmitted waveform. On the receiver side, low complexity detectors, such as sphere decoder, successive symbol-by-symbol sequence estimation, successive symbol-by-symbol with go-back K sequence estimator, and frequency-domain equalization, can be used to reconstruct the transmitted data. This paper presents the details of adapting the mentioned detectors to the proposed waveform and analyzes their performance in terms of bit error rate under different channel models and implementation complexity. Among all the detectors considered in this paper, the sphere decoder stands out as it presents an interesting compromise between complexity and bit error rate, even in scenarios with high interference. Other detection techniques, originally proposed for multiple-input multiple-output systems, can be adapted to handle the interference introduced by the faster-than-Nyquist generalized frequency division multiplexing with reasonable complexity and acceptable bit error rate performance. Hence, one may conclude that the faster-than-Nyquist generalized frequency division multiplexing is a suitable candidate waveform for the enhanced remote areas communications scenario when high spectrum efficiency is required.

Optical network monitoring and soft failure identification such as optical filter shifting and filter tightening are increasingly significant for the complex and dynamic optical networks of the future. Center frequency shift of optical filtering devices in optical networks has a serious impact on the performance of multi-span transmission, especially in high spectrum efficiency faster-than-Nyquist (FTN) transmission systems with various optical switching and add/drop nodes. Existing monitoring schemes generally have the problems of high cost, high complexity, and inability to realize multi-channel online monitoring, which makes it difficult for them to be applied in a wavelength division multiplexing (WDM) system with numerous nodes. In this paper, a monitoring scheme of frequency shift of optical filtering devices based on optical label (OL) is proposed and demonstrated. The signal spectrum of each channel is intentionally divided into many sub-bands with corresponding optical labels loading. The characteristics of spectrum power changing caused by frequency shift can be reflected on labels power changing of each sub-band, which are used to monitor and estimate the value of frequency shift via DSP algorithm. Simulation results show that the monitoring errors of frequency shift can be kept reasonably below 0.5 GHz after 10-span WDM transmission in FTN polarization multiplexing m-ary quadrature amplitude modulation (PM-mQAM) systems. In addition, 250 km fiber transmission experiments are also carried out, and similar results are obtained, which further verify the feasibility of our proposed scheme. The characteristics of low cost, high reliability, and efficiency make it a better candidate for practical application in future FTN-WDM networks.

In order to improve the accuracy of signal recovery after transmitting over atmospheric turbulence channel, a deep-learning-based signal detection method is proposed for a faster-than-Nyquist (FTN) hybrid modulated optical wireless communication (OWC) system. It takes advantage of the long short-term memory (LSTM) network in the recurrent neural network (RNN) to alleviate the interdependence problem of adjacent symbols. Moreover, an LSTM attention decoder is constructed by employing the attention mechanism, which can alleviate the shortcomings in conventional LSTM. The simulation results show that the bit error rate (BER) performance of the proposed LSTM attention neural network is 1 dB better than that of the back propagation (BP) neural network and outperforms by 2.5 dB when compared with the maximum likelihood sequence estimation (MLSE) detection method. [ABSTRACT FROM AUTHOR]

In this paper, we present a new multi-user chaos-based communication system using Faster-than-Nyquist sampling to achieve higher data rates and lower energy consumption. The newly designed system, designated Multi-user Faster Than Nyquist Differential Chaos Shift Keying (MU-FTN-DCSK), uses the traditional structure of Differential Chaos Shift Keying (DCSK) communication systems in combination with a filtering system that goes below the Nyquist limit for data sampling. The system is designed to simultaneously enable transmissions from multiple users through multiple sampling rates resulting in semi-orthogonal transmissions. The design, performance analysis, and experimental results of the MU-FTN-DCSK system are presented to demonstrate the utility of the newly proposed system in enabling multi-user communications and enhancing the spectral efficiency of the basic DCSK design without the addition of new blocks. The MU-FTN-DCSK system presented in this paper demonstrates spectral gains for one user of up to 23% and a combined gain of 25% for four ( U = 4 ) users. In this paper, we present a proof of concept demonstrating a new degree of freedom in the design of Chaos-based communication systems and their improvement in providing wireless transmissions without complicated signal processing tools or advanced hardware designs. [ABSTRACT FROM AUTHOR]

Faster-than-Nyquist (FTN) coherent optical transmission technology is considered to be an outstanding solution to achieve higher spectral efficiency (SE), larger capacity, and greater achievable transmission by using advanced modulation formats in concert with highly efficient digital signal processing (DSP) to estimate and compensate various impairments. However, severe inter-symbol interference (ISI) caused by tight FTN pulse shaping will lead to intractable chromatic dispersion (CD) estimation problems, as existing conventional methods are completely ineffective or exhibit unaffordable computational complexity (CC). In this paper, we propose a low-complexity and highly robust scheme that could realize accurate and reliable CD estimation (CDE) based on a designed training sequence (TS) in the first stage and an optimized fractional Fourier transform (FrFT) in the second stage. The training sequence with the designed structure helps us to estimate CD roughly but reliably, and it further facilitates the FrFT in the second stage to achieve accurate CDE within a narrowed searching range; it thereby results in very low CC. Comprehensive simulation results of triple-carrier 64-GBaud FTN dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems demonstrate that, with only overall 3% computational complexity compared with conventional blind CDE methods, the proposed scheme exhibits a CDE accuracy better than 65 ps/nm even under an acceleration factor as low as 0.85. In addition, 60-GBaud FTN DP quadrature phase shift keying (DP-QPSK)/16QAM transmission experiments are carried out, and the results show that the CDE error is less than 70 ps/nm. The advantages of the proposed scheme make it a preferable candidate for CDE in practical FTN coherent optical systems. [ABSTRACT FROM AUTHOR]

The conventional multicarrier faster-than-Nyquist (MFTN) achieves the spectral efficiency (SE) gain by deep compression. However, deep compression leads to severe intersymbol interference (ISI) or intercarrier interference (ICI). We propose the MFTN based on efficient implementation and probabilistic amplitude shaping (PAS) to achieve the SE gain with low complexity. We use mild compression instead of conventional deep compression to achieve the compression gain. The MFTN transceiver with the mild compression can be efficiently implemented by fast Fourier transform (FFT)/inverse FFT (IFFT) and filtering operation. The linear pre-equalization (LPE) method eliminates the ISI for mild compression. The MFTN with efficient implementation employs PAS to achieve extra shaping gain. The theoretical results and simulation results show that our method can achieve better performance than the conventional FTN/MFTN with deep compression. The proposed method does not require a complex equalization algorithm and global turbo iteration so that the total complexity is reduced.

Faster-than-Nyquist (FTN) is a promising paradigm to improve bandwidth utilization at the expense of additional intersymbol interference (ISI). In this paper, we apply state-of-the-art deep learning (DL) technology into receiver design for FTN signaling and propose two DL-based new architectures. Firstly, we propose an FTN signal detection based on DL and connect it with the successive interference cancellation (SIC) to replace traditional detection algorithms. Simulation results show that this architecture can achieve near-optimal performance in both uncoded and coded scenarios. Additionally, we propose a DL-based joint signal detection and decoding for FTN signaling to replace the complete baseband part in traditional FTN receivers. The performance of this new architecture has also been illustrated by simulation results. Finally, both the proposed DL-based receiver architecture has the robustness to signal to noise ratio (SNR). In a nutshell, DL has been proved to be a powerful tool for the FTN receiver design.

In this study, we demonstrated generation and transmission of 114 Gbaud and 126 Gbaud faster-than-Nyquist (FTN) discrete Fourier transform-spread (DFT-spread) quadrature phase shift keying orthogonal frequency division multiplexing (QPSK-OFDM) with 88-Gsa/s sampling rate digital-to-analog converters (DACs) experimentally. It is the first time to realize 400G FTN DFT-spread QPSK-OFDM signal per optical carrier for metro and regional applications, which will be a solution for network operators to address the issue of increasing bandwidth derived from the rapid popularization of mobile Internet and the wide application of IoT (Internet of Things technology). Delay-and-add filter (DAF) is adopted to realize frequency shaping at the transmitter to keep higher portions of energy of signal at low frequencies, which makes the OFDM much more robust to strong filtering effect. After pre-equalization, bit error rate (BER) performance of 114 GBaud and 126 GBaud FTN DFT-spread QPSK-OFDM has been significantly improved, and maximum-likelihood sequence estimation (MLSE) shows a better effect than binary decoding in the aspect of against the inter symbol interference (ISI) introduced by spectrum compression. The effective bit rate of dual polarization 126 Gbaud FTN DFT-spread QPSK-OFDM which is generated with 88 GSa/s sampling rate is 410.08 Gb/s, to the exclusion of all overhead including TSs, cyclic prefix (CP), and 20% forward error correction (FEC) coding. We successfully transmit 8 × 400 Gbit/s FTN DFT-spread QPSK-OFDM signal generated from 88 Gsa/s sampling rate DAC over 420 km single mode fiber (SMF) with the BER under 2.4 × 10−2.

Faster-than-Nyquist (FTN) coherent optical transmission technology is considered to be an outstanding solution to achieve higher spectral efficiency (SE), larger capacity, and greater achievable transmission by using advanced modulation formats in concert with highly efficient digital signal processing (DSP) to estimate and compensate various impairments. However, severe inter-symbol interference (ISI) caused by tight FTN pulse shaping will lead to intractable chromatic dispersion (CD) estimation problems, as existing conventional methods are completely ineffective or exhibit unaffordable computational complexity (CC). In this paper, we propose a low-complexity and highly robust scheme that could realize accurate and reliable CD estimation (CDE) based on a designed training sequence (TS) in the first stage and an optimized fractional Fourier transform (FrFT) in the second stage. The training sequence with the designed structure helps us to estimate CD roughly but reliably, and it further facilitates the FrFT in the second stage to achieve accurate CDE within a narrowed searching range; it thereby results in very low CC. Comprehensive simulation results of triple-carrier 64-GBaud FTN dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems demonstrate that, with only overall 3% computational complexity compared with conventional blind CDE methods, the proposed scheme exhibits a CDE accuracy better than 65 ps/nm even under an acceleration factor as low as 0.85. In addition, 60-GBaud FTN DP quadrature phase shift keying (DP-QPSK)/16QAM transmission experiments are carried out, and the results show that the CDE error is less than 70 ps/nm. The advantages of the proposed scheme make it a preferable candidate for CDE in practical FTN coherent optical systems.

We propose in this paper the time-based receive transformation (TRT), which can be regarded as the time-based version of the decorrelation based receive transformation proposed in Wang (IEEE Wirel Commun Lett 3(3):305–308, 2014), to suppress the inter-block interference (IBI) in the faster-than-Nyquist (FTN) system. We show that TRT can completely eliminate the effect of IBI in the FTN system so that instead of compromising the performance, FTN with TRT can make the achievable rate reach the maximum rate of the FTN system while having acceptable delay and complexity. [ABSTRACT FROM AUTHOR]

We propose and experimentally demonstrate a Tomlinson–Harashima precoding (THP) scheme with the coefficients computed by simulations. It realizes spectrally efficient faster-than-Nyquist (FTN) signaling for quadrature amplitude modulation (QAM) format. In our scheme, the coefficients of the THP precoder are obtained by numerical simulations with an additive white Gaussian noise (AWGN) channel, in which the intersymbol interference (ISI) is induced by a digital FTN filter. Then, we experimentally apply these THP coefficients at the transmitter to mitigate the FTN-related ISI, while the ISI from the analog channel is suppressed by the receiver-side adaptive equalizer. By this means, the experimental estimation of the THP coefficients is not required, leading to a simplified system operation. We perform numerical simulations to study the impacts of FTN signaling and channel bandwidth limitation on the proposed THP scheme. A proof-of-concept experiment is conducted, in which a 28-GBaud FTN single-sideband (SSB) 16-QAM signal is transmitted over an 80-km single mode fiber (SMF). Compared to the conventional scheme with the experimentally estimated THP coefficients, a negligible sensitivity penalty is observed for the proposed scheme. We also achieve a record FTN rate of 21.73% and a high spectral efficiency of 4.30 b/s/Hz for the single-polarization 16-QAM format on a single wavelength. [ABSTRACT FROM AUTHOR]

As a nonorthogonal mode, faster-than-Nyquist (FTN) signaling transmission can effectively improve the spectrum efficiency of a system. However, FTN signaling inevitably causes inter-symbol interference (ISI). The ISI hinders traditional synchronization methods from operating accurately, and this makes the carrier synchronization of FTN systems more complex. To overcome this issue, we propose an iterative carrier frequency offset (CFO) estimation scheme for an FTN signaling system. The proposed CFO estimation scheme consists of two steps: i) a coarse estimation step based on discrete Fourier transform and ii) a fine estimation step based on a golden-section search algorithm. The simulation results show that the mean square error of the proposed scheme is lower than that of the conventional CFO estimation schemes and approaches the Cramer-Rao Bound, which is an optimal estimation performance bound. [ABSTRACT FROM AUTHOR]

In this article, we utilize the Faster‐Than‐Nyquist (FTN) mechanism combined with the deep neural network (DNN) nonlinear post‐equalization scheme to achieve spectrum compression of the multiband carrierless amplitude phase (CAP) signal in the case of a fixed channel spacing for visible light communication (VLC) system. We found that the number of input layer nodes plays a decisive role in the DNN equalization effect. And a 1.26 Gbps FTN CAP 49QAM VLC system over 1 m free space transmission is successfully demonstrated. We reduced the normalized bandwidth of the CAP 16QAM signal for each sub‐band from 1.05 to 0.9 after quadrature dual‐quaternary (QDQ) coding combined with DNN post‐equalizer, and the total bandwidth of three bands is compressed from 315 MHz to 270 MHz. The spectrum compression ratio is 14.29% while ensuring BER below 7% FEC threshold (3.8e−3), and the spectral efficiency (SE) is 4.67 b/s/Hz. To the best of our knowledge, this is the first time achieving such high compression ratio in Gb/s level DNN based multiband FTN CAP signals in VLC system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel differential faster-than-Nyquist (DFTN) signaling concept that allows us to dispense with any channel estimation at the receiver, while benefiting from a rate boost specific to faster-than-Nyquist (FTN) signaling. More specifically, at the transmitter, differentially modulated phaseshift keying (DPSK) symbols are transmitted with a symbol interval that is smaller than that defined by the Nyquist criterion. The receiver first equalizes the DPSK symbols, which suffer from the effects of FTN-specific inter-symbol interference (ISI), with the aid of frequency-domain equalization (FDE). Then, the equalized symbols are differentially demodulated in a noncoherent manner. This noncoherent detection is enabled, by relying on the fact that FTN-specific ISI is deterministic when the FTN's symbol packing ratio and the roll-off factor of a shaping filter are known in advance of transmissions. Moreover, we derive an analytical bound on the achievable bit error ratio for the proposed DFTN signaling, based on moment-generating functions. This is achieved by introducing an equivalent signal-to-interference-and-noise ratio for the DPSK symbols after FDE. Our simulation results demonstrate that our DFTN receiver is capable of noncoherently demodulating the DFTN symbols when the symbol packing ratio is not substantially low.

High peak-to-average power ratio (PAPR) is one of the common drawbacks of multicarrier signals at the transmitter. In this paper, we investigate the PAPR reduction of spectral efficient multicarrier faster-than-Nyquist (MFTN) signals, where the PAPR problem has still not been seriously considered yet in current literatures. Specifically, the low complexity deliberate clipping scheme is exploited in MFTN signaling system. In order to evaluate the practical system performance, we consider a memoryless high power amplifier PAPR-efficiency model, and the auxiliary channel model under low complexity symbol-by-symbol receiver is also derived. Moreover, the achievable spectral efficiency (ASE) which can be viewed as the low bound for any modulation and coding schemes is taken as a figure of merit throughout this paper. By jointly optimizing the time-frequency spacing and clipping ratio to maximization the ASE under the given shaping pulse and modulation format, we show that the ASE of clipping-based MFTN substantially outperforms conventional Nyquist signaling schemes.

Multicarrier faster-than-Nyquist (MFTN) is a spectral efficient transmission scheme for future communication systems. However, as one of the most important drawbacks of multicarrier transmission systems, the peak-to-average power ratio (PAPR) of MFTN signals is still not clear yet. In this paper, we investigate the PAPR of MFTN signals for nonlinear satellite communication systems. First of all, the PAPR distribution of MFTN signals under various practical situations is evaluated, and we show that the PAPR of MFTN signals is closely related to the number of subcarriers, the shaping pulse, and the time–frequency packing factors. Moreover, different from conventional Nyquist multicarrier signals, certain time–frequency packing in MFTN will however, improve the PAPR performance. Then, the PAPR of MFTN signals under the given spectral efficiency is considered. By jointly optimizing the time–frequency spacing to minimize the PAPR, we show that the MFTN combined with low-order modulation could be more energy efficient than the corresponding Nyquist high-order modulation signals. Finally, we investigate the PAPR reduction for MFTN signals. Specifically, a selective mapping-based alternative-signal scheme, which mainly intended for the conventional Nyquist multicarrier signals, is extended to the MFTN signaling system. It is shown that the PAPR reduction performance of the considered scheme is robust to the time–frequency packing, and even approaches the conventional orthogonal frequency-division multiplexing system. Our numerical results validate that besides the high spectral efficiency, the MFTN may be also an energy efficient transmission scheme for next-generation satellite communication systems.

Faster-than-Nyquist (FTN) signaling is regarded as a potential candidate for improving data rate and spectral efficiency of 5G new radio (NR). However, complex detectors have to be utilized to eliminate the inter symbol interference (ISI) introduced by time-domain packing and the inter carrier interference (ICI) introduced by frequency-domain packing. Thus, the exploration of low complexity transceiver schemes and detectors is of great importance. In this paper, we consider a discrete Fourier transform (DFT) block transmission for multi-carrier FTN signaling, i.e., DBT-MC-FTN. With the aid of DFTs/IDFTs and frequency domain windowing, time- and frequency domain packing can be implemented flexibly and efficiently. At the receiver, the inherent ISI and ICI can be canceled via a soft successive interference cancellation (SIC) detector. The effectiveness of the detector is verified by the simulation over the additive white Gaussian noise channel and the fading channel. Furthermore, based on the characteristics of the efficient architecture of DFT-MC-FTN, two pilot-aided channel estimation schemes, i.e., time-division-multiplexing DBT-MC-FTN symbol-level pilot, and frequency-division-multiplexing subcarrier-level pilot within the DBT-MC-FTN symbol, respectively, are also derived. Numerical results show that the proposed channel estimation schemes can achieve high channel estimation accuracy. [ABSTRACT FROM AUTHOR]

Faster-than-Nyquist (FTN) transmission is a promising technique to increase the spectral efficiency at a fixed constellation size. However, traditional timing synchronization algorithms mostly rely on the eye diagram opening after matched-filtering (e.g., Gardner and zero-crossing). Such approaches are, thus, unsuitable in the presence of the FTN-induced intersymbol interference. In this letter, we first show that FTN signals exhibit cyclostationarity at the $l$ th order ($l > 2$) according to their bandwidth and symbol period. Then, we derive non-data-aided timing offset estimators from the cyclic temporal cumulant function. Besides its relevance for strong FTN scenarios, the proposed solution is also robust to frequency and phase offsets. [ABSTRACT FROM AUTHOR]

Multicarrier faster-than-Nyquist (MFTN) signaling is a spectral efficient modulation scheme for future communication systems. In MFTN signaling, the intersymbol interference (ISI) and intercarrier interference (ICI) are introduced intentionally by the time interval packing between adjacent symbols and frequency spacing packing between adjacent subcarriers. It is known that for multicarrier transmission over ISI and ICI channel, conventional rectangular lattice is not the optimal lattice structure. In this paper, the optimal hexagonal lattice-based MFTN signaling scheme is proposed. By appropriate staggering for conventional rectangular lattice, it is shown that the minimum Euclidean distance (or 2-DMazo limit) performance can be improved than conventional rectangular lattice-based MFTN signaling scheme. Moreover, a simple symbol-by-symbol receiver coupled with successive soft interference cancellation has been employed to recover the MFTN signals. Numerical results demonstrate that the hexagonal MFTN owns better bit error rate performance than conventional rectangular MFTN signaling scheme.

In this paper, we deal with the intersymbol interference (ISI) cancellation problem induced by the faster-than-Nyquist (FTN) signaling. In the traditional FTN signaling, the detection delay at the receiver depends on the number of states of the ISI trellis. In this case, the corresponding Viterbi algorithm or the BCJR algorithm would be far too complex and introduce a huge delay when the ISI tap set is large. In this paper, we propose a novel interference cancellation scheme to combat the ISI for the FTN communication system which enables the parallel computations. Our proposed scheme adopts a pre-coding at the transmitter and a decomposition detection at the receiver. Particularly, with the help of the parallel computations, the running time of our proposed scheme is independent of the ISI trellis, which allows the application of a more severe FTN system with a smaller time acceleration factor. Besides, based on the pre-coding scheme and the decomposition detection, an adaptive transmission strategy is developed, which can improve the performance of the proposed scheme dramatically. Finally, we compare our scheme with the offset BCJR algorithm and the offset Viterbi algorithm benchmarks. The simulation results verify that our scheme can outperform previous decoders with a better bit error rate and a much less delay.

Multicarrier faster-than-Nyquist (MFTN) signaling is a spectral efficient transmission scheme for future communication systems. Similar as general multicarrier signals, the high peak-to-average power ratio (PAPR) is also one of the main drawbacks of MFTN signals. Unfortunately, the PAPR problem in MFTN signaling system has rarely been considered in the literatures. In this paper, we investigate the PAPR reduction for MFTN signals. First, we derive an inverse fast Fourier transform (IFFT)-based implementation of the MFTN transmitter. Based on which, a novel partial transmit sequence (PTS) scheme is proposed for the PAPR reduction of MFTN signals. The proposed PTS scheme relies on a two-stage optimization of the phase weighting factors for the parallel IFFT blocks as well as the phase weighting factors for the information symbols before the summation operation. It is shown that the proposed scheme substantially outperforms the direct employment of conventional Nyquist multicarrier transmission systems-based PTS scheme and also robust to the overlap-add operation introduced by pulse shaping.

In this paper, we propose a novel dual-mode time-domain single-carrier (SC) index modulation (DM-SCIM) scheme, where the combination of two constellation modes carries information bits further to modulated symbols, hence increasing the transmission rate. Accordingly, the proposed DM-SCIM scheme is capable of attaining a higher transmission rate than the conventional SC and SCIM schemes, without imposing any additional performance penalty. Furthermore, in order to maintain the detection complexity low enough to be tractable at the handset receiver, a successive detection algorithm, comprising minimum mean-square error (MMSE)-based frequency-domain equalization and log-likelihood ratio detection, is developed for both the conventional SCIM and the proposed DM-SCIM schemes. We also derive the error-rate bound of the proposed DM-SCIM scheme under the assumption of a channel-uncoded scenario. Moreover, in order to further increase bandwidth efficiency, the proposed DM-SCIM scheme is extended to the scenario supporting faster-than-Nyquist signaling, where the symbol interval in the time domain is set to be smaller than that defined by the Nyquist criterion. Our simulation results demonstrate the explicit performance advantage of the proposed schemes over the existing SC schemes. It is also revealed that our DM-SCIM scheme is capable of achieving a significantly lower peak-to-average power ratio than orthogonal frequency division multiplexing (OFDM) and OFDM with index modulation, while benefiting from a high reliability, which is achievable by multipath diversity.

As optical transceivers evolve toward 200G per lane, the comparatively low bandwidth and sampling speed of the commercially available high-speed digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) increasingly become the dominating obstacle toward success. On the other hand, DACs and ADCs are essential to make use of digital signal processing for impairment compensation and error correction; altogether driving systems’ engineers to a hard design dilemma. With the purpose of alleviating this compromise, we propose a transceiver structure—encompassing both hardware and software—enabling the generation, transmission, and detection of strongly over-filtered data signals whose baudrate exceeds the sampling rates of (potentially) both the DAC and ADC. We call this approach sub-baudrate sampling, a technique which does not increase the processing complexity at the transmitter side and does not even require the information about the channel state for pre-distortion or pre-coding purposes. We experimentally assess the performance of sub-baudrate sampled signals in two blocks of experiments: first the proof of concept in back-to-back configuration, including up to 112-Gbaud on–off keying at 0.785 samples per symbol in ∼25-GHz aggregate bandwidth. Then the C-band transmission demonstration, showing up to 100-Gbaud quaternary pulse-amplitude modulation (0.92 samples per symbol) and 125-Gbaud on–off keying (0.736 samples per symbol) over 1 and 80-km of single-mode fiber, respectively, with more than 3-dB receiver sensitivity margin at the 7% overhead hard-decision bit error rate limit. [ABSTRACT FROM AUTHOR]

In this paper, a pulse-overlapping super-Nyquist (Pol-SN) wavelength-division multiplexing (WDM) scheme is proposed to improve spectral efficiency of coherent optical transmission. In this scheme, two tributaries of polarization-division multiplexing quadrature phase-shift keying (PDM-QPSK) signals at the transmitter, carried by the same wavelength, are grouped together to allow for pulse overlapping in the time domain. Then, several wavelength channels are packed tightly in the frequency domain to form a super-Nyquist WDM system. At the receiver, three partial-response detection schemes are investigated and compared: 1) constant modulus algorithm (CMA) + duobinary shaping + maximum likelihood sequence estimation (MLSE); 2) duobinary shaping + multimodulus algorithm (MMA) + MLSE; and 3) channel shortening filter. Among these schemes, the easy-to-implement duobinary shaping +MMA + MLSE is selected by virtue of its best performance and lowest complexity. A 224-Gb/s Pol-SN PDM-QPSK system is investigated through numerical simulations. The simulation results show that the channel spacing of the 224 Gb/s Pol-SN PDM-QPSK system can be reduced to 20 GHz (11.2 bit/s/Hz SE) with 7% overhead hard-decision forward-error correction (HD-FEC, 3.8 × 10−3). At 26-GHz channel spacing, Pol-SN PDM-QPSK signals show 5.5-dB OSNR improvement, as compared with the signals of 224-Gb/s super-Nyquist PDM-16QAM. The simulation results also show that 224-Gb/s Pol-SN PDM-QPSK system, with 20-GHz spacing, can transmit up to 1000-km SSMF with 7% overhead HD-FEC. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the interference between multiple co-channel transmissions in the downlink of a multi-antenna wireless system. In this framework, symbol-level precoding (SLP) is a promising technique which is able to constructively exploit the multi-user interference and to transform it into useful power at the receiver side. While previous works on SLP were focused on exploiting the multi-user interference, in this paper, we extend this concept by jointly handling the interference both in the spatial dimension (multi-user interference) and in the temporal dimension (inter-symbol interference). Accordingly, we propose a novel precoding method, referred to as spatio-temporal SLP. In this new precoding paradigm, faster-than-Nyquist (FTN) signaling can be applied over multi-user MISO systems, and the inter-symbol interference can be tackled at the transmitter side, without additional complexity for the user terminals. While applying FTN signaling, the proposed optimization strategies perform a sum power minimization with quality-of-service constraints. Numerical results are presented in a comparative fashion to show the effectiveness of the proposed techniques, which outperform the state-of-the-art SLP schemes in terms of symbol error rate, effective rate, and energy efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we experimentally demonstrate a 1.28 Tb/s faster-than-Nyquist (FTN) wavelength division multiplexing (WDM) system with polarization division multiplexed (PDM) 16-ary quadrature amplitude modulation (16-QAM) signal and coherent detection. Note that intersymbol interference (ISI) and intercarrier interference (ICI) are two major problems in FTN-WDM systems. In our experiment, we use a digital brick-wall filter at the transmitter to reduce the signal bandwidth and fit the FTN-WDM channel spacing. In doing so, the ICI can be mostly suppressed when aggregating the WDM channels. The aggressive filtering induced ISI is compensated based on duobinary signal processing at the receiver. Through numerical simulation, we evaluate the robustness of the receiver-side duobinary signal processing against bandwidth truncation ratio of the digital brick-wall filter, the ICI from neighboring channels, and laser phase noise. The FTN WDM transmission is based on five-channel 32 Gbaud PDM 16-QAM signal with 29 GHz channel spacing. The gross data capacity is 1.28 Tb/s (5 × 256 Gb/s). After 80 km standard single-mode fiber transmission, the bit-error rates of the five WDM channels are all below than 7% hard-decision forward error correction threshold of 4.5 × 10−3. The net bit rate is 1.15 Tb/s and the net optical spectral efficiency achieves a record of 7.96 b/s/Hz for PDM 16-QAM format. To our best knowledge, our work is the first report of Terabit FTN-WDM system with high-order modulation of PDM 16-QAM signal. [ABSTRACT FROM AUTHOR]

The performance of faster-than-Nyquist intensity modulation and direct detection (IM/DD) systems can be severely degraded by the inter-symbol interference (ISI) due to the component bandwidth limitation and the faster-than-Nyquist filtering. In addition, nonlinearities caused mainly by optical modulation and square-law detection can further deteriorate signal quality. Here, we propose to incorporate transmitter-side Tomlinson-Harashima precoding to mitigate the ISI and a Volterra nonlinear equalizer (VNLE) to mitigate the nonlinear distortions for PAM4 faster-than-Nyquist systems. We experimentally demonstrate a single wavelength 145 Gb/s PAM4 IM/DD transmission with bandwidth limited commercial components and sub-Nyquist sampling at 70 GSa/s. The optimal VNLE filter length is also investigated to balance the implementation complexity and system performance. In addition, compared with the scheme using transmitter-side duobinary precoding, receiver-side VNLE and maximum likelihood sequence estimation, both performance improvement and implementation complexity reduction are achieved. [ABSTRACT FROM AUTHOR]

The problem of signal detection for faster-than-Nyquist (FTN) signaling system with imperfect channel state information (CSI) is studied. Also, the non-Gaussian noise in real applications is considered. A general model, Gaussian mixture noise (GMN) model, is applied to describe the unknown probability density function (PDF) of the non-Gaussian noise. After that, a framework over variational inference is constructed to simplify the problem through finding an auxiliary PDF with factorization form. Based on the factor graph over the signal, joint response and the parameters of GMN, an iterative solution is obtained. Simulations demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Faster-than-Nyquist (FTN) signaling is regarded as a potential candidate for improving data rate and spectral efficiency of 5G new radio (NR). However, complex detectors have to be utilized to eliminate the inter symbol interference (ISI) introduced by time-domain packing and the inter carrier interference (ICI) introduced by frequency-domain packing. Thus, the exploration of low complexity transceiver schemes and detectors is of great importance. In this paper, we consider a discrete Fourier transform (DFT) block transmission for multi-carrier FTN signaling, i.e., DBT-MC-FTN. With the aid of DFTs/IDFTs and frequency domain windowing, time- and frequency domain packing can be implemented flexibly and efficiently. At the receiver, the inherent ISI and ICI can be canceled via a soft successive interference cancellation (SIC) detector. The effectiveness of the detector is verified by the simulation over the additive white Gaussian noise channel and the fading channel. Furthermore, based on the characteristics of the efficient architecture of DFT-MC-FTN, two pilot-aided channel estimation schemes, i.e., time-division-multiplexing DBT-MC-FTN symbol-level pilot, and frequency-division-multiplexing subcarrier-level pilot within the DBT-MC-FTN symbol, respectively, are also derived. Numerical results show that the proposed channel estimation schemes can achieve high channel estimation accuracy.

In this letter, we investigate the lattice staggered multicarrier faster-than-Nyquist (MFTN) signaling. Specifically, we consider the time–frequency packing and optimal hexagonal lattice over additive white Gaussian noise channels. First, an efficient implementation of the lattice staggered MFTN based on the fast Fourier transform algorithm is proposed, and we show that the modulation and demodulation complexity could be substantially reduced. Furthermore, we consider, at the receiver, a low-complexity symbol-by-symbol detector. Our practical spectral efficiency and bit-error-rate performance investigation demonstrate that the MFTN with optimal hexagonal lattice outperforms the conventional rectangular lattice. [ABSTRACT FROM PUBLISHER]

In this letter, a novel maximizing signal-to-interference ratio (max-SIR) time–frequency packing scheme for multicarrier faster-than-Nyquist signaling is proposed. The proposed scheme is based on the low complexity symbol-by-symbol detector. Specifically, we optimize the time–frequency spacing under the given signaling efficiency to maximize the SIR, i.e., the ratio between the energy of useful signal and the intersymbol interference and intercarrier interference introduced by time–frequency packing. We show that the proposed max-SIR time–frequency packing outperforms other time–frequency packing schemes for both the symbol-by-symbol detection and coupled with successive interference cancellation. [ABSTRACT FROM PUBLISHER]

In this letter, we first apply simplified maximum likelihood detection (MLD) with QR decomposition and M-algorithm (QRM-MLD) to reduce inter-carrier interference (ICI) in a faster-than-Nyquist non-orthogonal frequency division multiplexing (FTN-NOFDM) system. A QRM-MLD algorithm has lower computational complexity than an MLD algorithm owing to the decrease of searched path number. In the experiment, 10-Gb/s FTN-NOFDM with the QRM-MLD algorithm was transmitted over 25-km standard single mode fiber. For 20% bandwidth saving, FTN-NOFDM with the QRM-MLD algorithm can achieve almost the same performance as FTN-NOFDM with the MLD algorithm when the path with minimal metric is not discarded before detecting the last subcarrier, meanwhile the bit error rate of FTN-NOFDM with the QRM-MLD algorithm or the MLD algorithm can achieve 7% forward error correction (FEC) limit, but that with an iterative detection (ID) algorithm only can achieve 20% FEC limit. For reducing ICI, the QRM-MLD algorithm has lower computational complexity but can obtain almost the same performance as the MLD algorithm, and the QRM-MLD algorithm also has much better performance than the ID algorithm. [ABSTRACT FROM PUBLISHER]

In the framework of digital video broadcasting by satellite-second generation (DVB-S2), we analyze a faster-than-Nyquist (FTN) system based on turbo equalization and low-density parity-check (LDPC) codes. Truncated maximum a posteriori and minimum mean square error equalizers provide a reduced-complexity implementation of the FTN system. On the other hand, LDPC codes allow us to demonstrate attractive performance results over an additive white Gaussian noise channel while increasing spectral efficiency beyond the Nyquist rate and keeping a complexity comparable to that of a current DVB-S2 modem. [ABSTRACT FROM AUTHOR]

A training symbol-based equalization algorithm is proposed for polarization de-multiplexing in quadrature duobinary (QDB) modulated polarization division multiplexed faster than-Nyquist (FTN) coherent optical systems. The proposed algorithm is based on the least mean square algorithm, and multiple location candidates of a symbol are considered in order to make use of the training symbols with QDB modulation. Results show that an excellent convergence performance is obtained using the proposed algorithm under different polarization alignment scenarios. The optical signal-to-noise ratio required to attain a bit error rate of 2\times 10^-2 is reduced by 1.7 and 1.8 dB using the proposed algorithm, compared with systems using the constant modulus algorithm with differential coding for four-ary quadrature amplitude modulation (4-QAM) and 16-QAM systems with symbol-by-symbol detection, respectively. Furthermore, comparisons with the Tomlinson–Harashima precoding-based FTN systems illustrate that QDB is preferable when 4-QAM is utilized. [ABSTRACT FROM PUBLISHER]

We investigate different techniques to improve the spectral efficiency of systems based on the DVB-S2 standard, when the transmitted signal bandwidth cannot be increased because it has already been optimized to the maximum value allowed by transponder filters. We will investigate and compare several techniques involving different sections of the transceiver scheme. The techniques that will be considered include the use of advanced detection algorithms, the adoption of time packing, and the optimization of the constellation and shaping pulses. The low-density parity-check codes recently proposed for the evolution of the DVB-S2 standard will be considered, as well as the adoption of iterative detection and decoding. Information-theoretical analysis will be followed by the study of practical modulation and coding schemes. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]