faster-than-Nyquist Signaling Research Articles

Multiplication-free and hardware-efficient baud-rate timing error detector for Nyquist and faster than Nyquist optical IM/DD systems.

Clock recovery (CR) algorithms that support higher baud rates and advanced modulation formats are crucial for short-distance optical interconnections, and it is desirable to push CR to operate at baud rate with minimal computing resources and power. In this Letter, we proposed a hardware-efficient and multiplication operation-free baud-rate timing error detector (TED) as a solution to meet these demands. Our approach involves employing both the absolute value of samples and the nonlinear sign operation to emphasize the clock tone, which is deteriorated by severe bandwidth limitation in Nyquist and faster than Nyquist (FTN) systems. Through experimental investigations based on a transceiver system with a 3 dB bandwidth of 30 GHz, the proposed baud-rate TED exhibits excellent performance. The proposed scheme successfully achieves clock synchronization of the received signals with the transmitted signals, including 50 GBaud PAM4/8, 80 GBaud PAM4, and up to 120 GBaud PAM4 FTN signals. To the best of our knowledge, the CR based on the proposed baud-rate TED is the most optimal solution for ultrahigh-speed short-reach IM/DD transmission, comprehensively considering the timing jitter, bit error rate (BER), and implementation complexity.

An LDPC-RS Concatenation and Decoding Scheme to Lower the Error Floor for FTN Signaling

Faster-than-Nyquist (FTN) signaling has attracted increasing interest in the past two decades. However, when the fifth-generation (5G) communication low-density parity check (LDPC) code is applied to FTN signaling with low Bahl–Cock–Jelinek–Raviv (BCJR) states of detection and few turbo equalization iterations, an error floor near 10−5 is found, which does not exist in the original LDPC used for orthogonal signaling. This can be eliminated through many detection and decoding iterations, but this is unacceptable considering the increase in latency and storage. To solve this problem, we propose an LDPC and Reed–Solomon (RS) concatenation code, shortening, and perturbation scheme to lower the error floor. We propose a parallel encoder architecture for RS component code and a concise algorithm to calculate its constant multiplier coefficients, leveraging a traditional serial encoder, which can also be used for other parallelisms, rates, and lengths. The simulation results show that the proposed concatenation and shortening scheme can lower the error floor to about 10−7. The proposed scheme has an error correction capability for coded FTN signaling and successfully lowers the error floor with the limitation of few turbo iterations and few BCJR states.

Effectiveness evaluation of coded FTN signaling in the presence of nonlinear distortion under multipath fading channels

Effectiveness evaluation of coded FTN signaling in the presence of nonlinear distortion under multipath fading channels

Pilot design and doubly-selective channel estimation for faster-than-Nyquist signaling

Being capable of enhancing the spectral efficiency (SE), faster-than-Nyquist (FTN) signaling is a promising approach for wireless communication systems. This paper investigates the doubly-selective (i.e., time- and frequency-selective) channel estimation and data detection of FTN signaling. We consider the intersymbol interference (ISI) resulting from both the FTN signaling and the frequency-selective channel and adopt an efficient frame structure with reduced overhead. We propose a novel channel estimation technique of FTN signaling based on the least sum of squared errors (LSSE) approach to estimate the complex channel coefficients at the pilot locations within the frame. In particular, we find the optimal pilot sequence that minimizes the mean square error (MSE) of the channel estimation. To address the time-selective nature of the channel, we use a low-complexity linear interpolation to track the complex channel coefficients at the data symbols locations within the frame. To detect the data symbols of FTN signaling, we adopt a turbo equalization technique based on a linear soft-input soft-output (SISO) minimum mean square error (MMSE) equalizer. Simulation results show that the MSE of the proposed FTN signaling channel estimation employing the designed optimal pilot sequence is lower than its counterpart designed for conventional Nyquist transmission. The bit error rate (BER) of the FTN signaling employing the proposed optimal pilot sequence shows improvement compared to the FTN signaling employing the conventional Nyquist pilot sequence. Additionally, for the same SE, the proposed FTN signaling channel estimation employing the designed optimal pilot sequence shows better performance when compared to competing techniques from the literature.

Faster-Than-Nyquist Signaling for MIMO Communications

Faster-than-Nyquist (FTN) signaling is a non-orthogonal transmission technique, which has the potential to provide significant spectral efficiency improvement. This paper studies the capacity of FTN signaling for both frequency flat and for frequency selective (FS) multiple-input multiple-output (MIMO) channels. As FTN is another reason of frequency selectivity, we find that precoding in time (or equivalently spectrum shaping in frequency) and waterfilling in spatial domain is capacity achieving for frequency flat MIMO channels with FTN. Meanwhile, waterfilling in both spatial domain and spectrum domain, followed by spectrum shaping, is capacity achieving for FS MIMO channels with FTN.

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

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

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.

Spatially-Coupled Faster-Than-Nyquist Signaling: A Joint Solution to Detection and Code Design

In this paper, we investigate two important issues of faster-than-Nyquist (FTN) signaling, namely, reduced-complexity detection and code design. Different from previous works, we consider these two issues jointly by designing a scheme that increases the minimum squared Euclidean distance of FTN signaling via repetition coding at a cost of an increased complexity. Furthermore, to reduce the rate loss of the repetition, we adopt the idea of spatially-coupling from coding theory to FTN signaling, and the resultant signaling scheme is therefore referred to as spatially-coupled faster-than-Nyquist (SC-FTN) signaling. The signal of SC-FTN signaling is generated in a continuous manner by interleaving and repeating the coded FTN signals and a graph-based iterative sliding-window detector is applied for signal detection. Both bounding and extrinsic information transfer chart analysis are provided to study the error-floor and convergence performances of SC-FTN signaling. These analyses unveil the intrinsic relationship between error floor, decoding threshold, and detection/decoding complexity, which provides guidelines for the designs of practical systems. Simulation results show that the promising error performance can be achieved with a simple FTN detection, where the bit error rate performance of coded SC-FTN signaling outperforms that of state-of-the-art coded FTN systems and the capacity of Nyquist signaling.

Precoded Faster-Than-Nyquist Signaling for Doubly Selective Underwater Acoustic Communication Channel

In this letter, we propose faster-than-Nyquist (FTN) signaling transmission that is robust for an underwater acoustic (UWA) doubly selective channel. Owning to the explicit benefits of a reduced symbol interval specific to FTN signaling, the detrimental effects of a time-selective channel are significantly relaxed. Furthermore, upon introducing single-carrier transmit precoding and equalization, the proposed FTN signaling achieves a high detection performance. Our simulation results demonstrate that the proposed FTN signaling outperforms the conventional Nyquist-based benchmark scheme in the doubly selective channel.

Optimization for faster‐than‐Nyquist signaling based combining under multi‐path channel

SummaryWe propose a faster‐than‐Nyquist (FTN) signaling based combining scheme to increase the achievable rate for the single‐input‐single‐output (SISO) system and the single‐carrier system under the multi‐path channel, where the combining scheme aims to combine the signals received at all symbol periods during the channel length for each transmitted symbol. An important feature of the FTN signaling based combining scheme is that the transmitter ceases the transmission for b symbol periods after transmitting each symbol. By proposing the optimization algorithm for finding the optimum b that maximizes the achievable (information) rate, we propose in this paper the optimal FTN signaling based combining scheme. We first establish the optimization problem and then present a theorem for proving the existence of the optimum b that maximizes the lower bound of the average achievable (information) rate. On the basis of this theorem, we present the steps of the proposed optimization algorithm. Numerical results are provided, and they confirm that the proposed optimization algorithm can find the optimum b.

Ergodic Capacity of MIMO Faster-Than-Nyquist Transmission Over Triply-Selective Rayleigh Fading Channels

Faster-than-Nyquist signaling (FTNS) has already been shown to increase the communication capacity on certain channels such as additive white Gaussian noise and block flat multiple-input multiple-output (MIMO) Rayleigh fading channels. The following issues, however, remain unresolved: 1) whether FTNS enables a capacity increase in generalized MIMO Rayleigh fading channels that are selective in time, frequency, and space; and 2) how channel selectivities affect the capacity and if present, the FTN capacity gain. To address the issues, this paper firstly investigates the ergodic capacity of MIMO-FTN transmission over triply-selective fading channels. We derive a low-complexity approximate capacity formula and also show how it degenerates in other channel models, such as doubly-selective single-input single-output fading channels, which can be considered as the special cases of triply-selective fading channels. The capacity evaluation results obtained under different channel conditions show that: 1) MIMO-FTN outperforms MIMO-Nyquist in terms of capacity; 2) the FTN gains are nearly consistent, while the FTN gains obtained in the frequency-selective fading channels are slightly higher than those obtained in the flat fading channels.

Performance Analysis for Covert Communications Under Faster-Than-Nyquist Signaling

In this letter, we analyze the performance of covert communications under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">faster-than-Nyquist</i> (FTN) signaling in the Rayleigh block fading channel. Both maximum likelihood criterion- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Kullback-Leibler</i> (KL) divergence-based covertness constraints are considered. Especially, for KL divergence-based one, we prove that both the maximum transmit power and covert rate under FTN signaling are higher than those under Nyquist signaling. Numerical results coincide with our analysis and validate the advantages of FTN signaling to realize covert data transmission.

The Optimal Precoded Faster-Than-Nyquist Signaling for Covert Communications

In this letter, we consider the covert communications under precoded faster-than-Nyquist (FTN) signaling. We first propose a general framework to analyze the detection performance of an illegal adversary for the precoded FTN signaling, and then derive a general principle for the optimal precoding scheme maximizing the covert throughput under the Kullback-Leibler (KL) divergence-based constraint. The covert throughput of the optimal precoding scheme is obtained based on the proposed framework, and it is theoretically proved to be higher than that of the non-precoded FTN as well as Nyquist ones. Numerical results also verify the superiority of the optimal precoded FTN signaling in terms of the covert throughput.

Joint Precoding and Pre-Equalization for Faster-Than-Nyquist Transmission Over Multipath Fading Channels

Faster-than-Nyquist signaling (FTNS) has emerged as a promising technique to increase communication capacity in bandwidth-limited channels. However, the presence of FTN-induced inter-symbol interference (FTN-ISI) in the received observations, is detrimental to channel estimation (CE) and data detection in terms of computational complexity and performance. This paper copes with these problems by incorporating linear pre-equalization (LPE) and composite precoding formed by linear spectral precoding and Tomlinson-Harashima precoding (THP), into the FTNS. Specifically, LPE completely pre-equalizes the FTN-ISI, while spectral precoding resolves the LPE-caused signal spectral broadening by introducing proper artificial ISI, which is pre-equalized by THP. Channel-induced ISI, as the only ISI component in the observations, is estimated and equalized using the classical frequency-domain low-complexity schemes. We show that there are four advantages of the LPE-aided CE over the CE designed for the FTN transmissions without FTN-ISI pre-equalization, namely lower pilot overhead, simpler yet optimal pilot sequence design, lower mean-squared error of CE, and more robust against the FTN-ISI. Simulation results show that our scheme improves the performance of CE and detection, compared to existing FTN frequency-domain CE and equalization schemes.

Eigendecomposition-Precoded Faster-Than-Nyquist Signaling With Optimal Power Allocation in Frequency-Selective Fading Channels

In this paper, we propose eigenvalue decomposition (EVD)-precoded faster-than-Nyquist (FTN) signaling with power allocation in a frequency-selective fading channel. More specifically, we derive the mutual information associated with the proposed FTN signaling. Then, the optimal power coefficients are calculated such that the derived mutual information is maximized. Our analytical performance results show that the proposed FTN signaling scheme achieves a higher information rate than the conventional FTN signaling scheme without relying on power allocation and the classic Nyquist signaling scheme, under the assumption that all the schemes employ a root-raised cosine shaping filter. Moreover, we derive the proposed scheme&#x2019;s achievable information rate in the presence of channel estimation errors. Furthermore, our numerical simulation results for the bit error ratio performance and the power spectral density demonstrate that the proposed FTN scheme outperforms the conventional Nyquist signaling scheme without incurring any bandwidth broadening.

Effectiveness evaluation of FTN signaling in the presence of nonlinear distortion under multipath fading channels

Effectiveness evaluation of FTN signaling in the presence of nonlinear distortion under multipath fading channels

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.

Reduced-Complexity FFT-Spread Multicarrier Faster-Than-Nyquist Signaling in Frequency-Selective Fading Channel

In this paper, we propose novel reduced-complexity fast Fourier transform (FFT)-spread multicarrier faster-than-Nyquist (MFTN) signaling with power allocation for a frequency-selective fading channel. The information rate of the proposed MFTN signaling is derived by relying on the circulant approximation of the FTN-specific intersymbol interference matrix and noise covariance matrix. This allows us to constitute efficient calculations of precoding and weighting matrices. The power allocation coefficients are optimized such that the approximated information rate is maximized. Our simulation results demonstrate that the proposed scheme with power allocation achieves the bit error ratio (BER) performance close to the conventional eigenvalue-decomposition (EVD)-precoded FTN signaling counterpart that is optimal in terms of an achievable information rate while significantly reducing the computational complexity as low as the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(N\log N)$ </tex-math></inline-formula> . While the proposed scheme exhibits a high peak-to-average-power ratio similar to the conventional EVD-precoded counterpart due to the effects of FFT-based precoding, it achieves better BER performance than the conventional open-loop single-carrier FTN signaling scheme and the Nyquist signaling scheme, employing the same root-raised cosine shaping filter. It is also confirmed that the proposed MFTN signaling scheme does not suffer from any significant bandwidth broadening.

Waveform Design for High-Order QAM Faster-Than-Nyquist Transmission in the Presence of Phase Noise

The state-of-the-art radio-frequency (RF) devices limit the deployment of extremely high-order quadrature amplitude modulation (QAM) formats (e.g., 16384-QAM) to meet the high-capacity demand on microwave backhaul links. This paper turns to faster-than-Nyquist (FTN) transmission using lower-order constellations and lower-cost RF devices as a solution to the demand. To realize low-complexity interference cancellation, we pre-equalize the FTN-induced inter-symbol interference at the transmitter by using Tomlinson-Harashima precoding (THP), while at the receiver suppressing the phase noise (PHN) generated by the RF local oscillators with pilot symbol assisted approaches. However, the THP may distort the pilots, which degrades the performance of PHN compensation. To resolve this problem, we propose two pilot designs that are distortion-free to precisely estimate the PHN samples. Moreover, we derive a closed-form expression of the symbol detection signal-to-noise ratio (SNR), in terms of the THP-FTN waveform parameters. With the SNR expression, a waveform optimization procedure is developed to maximize the SNR and enhance the achievable FTN capacity. The proposed scheme is validated in the simulated platform of 4096-QAM microwave link. The results demonstrate that the FTN signaling achieves the system capacity equivalent to that of the 16384-QAM Nyquist signaling with an SNR gain of 5.8 dB.

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.