Faster-than-Nyquist (FTN) signaling can improve the bandwidth utilization. In this paper, we will provide a comprehensive survey on the topic. The history and the applications of FTN signaling are first introduced. Then, the basic principles and the system framework of FTN signaling are presented. Next, more details on transmitter and receiver optimization are discussed. Finally, the current research challenges on FTN signaling are identified and conclusions are provided.

Faster-Than-Nyquist Signaling: An Overview

Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications, including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the $q$ -shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift $q$ , the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and $q$ -shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Cramer–Rao lower bound. Theoretical results are validated by extensive computer simulations.

Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients

The development of electronic equipment technology, followed by the advancement of electronic systems, has increased the sensitivity of signal identification. Control and monitoring is a matter that forces existing engineers to make decisions and protect systems. In this paper, the distributed least mean p-norm method (dLMP) has been evaluated and evaluated to estimate the distributed frequency of the signal in three incremental, consensus, and scattering strategies. In the proposed method, based on the definition of appropriate cost functions, a distributed method is used to estimate the frequency of common sinusoidal signals with a common frequency in a wireless sensor network. The results of simulation with MATLAB software showed that the proposed algorithm has better and more favorable performance compared to other methods such as single-sensor and distributed methods. In the proposed method simultaneously with the distributed frequency estimation, the domain and phase estimation with a suitable and fast convergence is possible locally. Due to this advantage compared to the distributed filter method, the proposed method is less complicated and the convergence rate is appropriate and better.

Frequency Estimation by the Method of Minimum Mean Squared Error and P-value Distributed in the Wireless Sensor Network

The fifty-year progress of faster-than-Nyquist (FTN) signaling is surveyed. FTN signaling exploits non-orthogonal dense symbol packing in the time domain for the sake of increasing the data rate attained. After reviewing the system models of both the conventional Nyquist-based and FTN signaling transceivers, we survey the evolution of FTN techniques, including their low-complexity detection and channel estimation. Furthermore, in addition to the classic FTN signaling philosophy, we introduce the recent frequency-domain filtering and precoding aided schemes. When relying on precoding, the information rate of FTN signaling becomes related to the eigenvalues of an FTN-specific intersymbol interference matrix, which provides a unified framework for the associated information-theoretic analysis and simplifies the associated power allocation specifically designed for increasing the information rate attained. We show that the FTN signaling scheme combined with bespoke power allocation employing a realistic raised-cosine shaping filter achieves the Shannon capacity associated with ideal rectangular shaping filters.

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The Evolution of Faster-Than-Nyquist Signaling

We consider channels affected by intersymbol interference with reduced-complexity, mutual information optimized, channel-shortening detection. For such settings, we optimize the transmit filter, taking into consideration the reduced receiver complexity constraint. As figure of merit, we consider the achievable information rate of the entire system and with functional analysis, we establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a corollary to our main result, we obtain some insight of the behavior of the standard waterfilling algorithm for intersymbol interference channels. With only some minor changes, the general form we derive can be applied to multiple-input multiple-output channels with intersymbol interference. To illuminate the practical use of our results, we provide applications of our theoretical results by deriving the optimal shaping pulse of a linear modulation transmitted over a bandlimited additive white Gaussian noise channel which has possible applications in the faster-than-Nyquist/time packing technique.

Optimal Transmit Filters for ISI Channels under Channel Shortening Detection

Frequency estimation of a single complex exponential waveform is an important problem in many fields. In this letter, a new frequency estimator for a complex exponential sine waveform observed under the additive white Gaussian noise (AWGN) is proposed. The proposed estimator is obtained by solving the nonlinear functions. The new estimator has an analytical expression based on interpolation method with three DFT samples. Numerical results demonstrate that the performance of the proposed estimator has lower SNR threshold to closely reach the Cramer-Rao bound (CRB) in the low SNR region and its performance also outperforms previous estimators in the high SNR region.

A New and Accurate Estimator With Analytical Expression for Frequency Estimation

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.

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

Proposed is a new estimator for the carrier frequency recovery in Nyquist and faster-than-Nyquist (FTN) signaling system. Considering the intentional inter-symbol interference caused by FTN, a discrete-time model for synchronization of FTN is built for the first time, which is different from the traditional model based on the Nyquist criterion. The discrete-time model is simplified assumed that the frequency offset is much smaller than the sampling rate and the shaping pulse is time-truncated adopted from the 3GPP standard. Furthermore, a novel frequency estimator with three discrete Fourier transform samples interpolation is proposed for FTN signaling over the additive white Gaussian noise channel. Comparing with the Cramer–Rao bound, numerical results show the performance of new frequency estimator in the transmission system with the Nyquist rate and beyond the Nyquist rate.

Feng Chen

Papers

A New and Accurate Estimator With Analytical Expression for Frequency Estimation

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

Carrier Frequency Recovery for Nyquist and Faster-than-Nyquist Signaling System