Multicarrier faster-than-Nyquist Research Articles

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.

Generalized Approximate Message Passing Equalization for Multi-Carrier Faster-Than-Nyquist Signaling

Multi-carrier faster-than-Nyquist (MFTN) signaling constitutes a promising spectrally efficient non-orthogonal physical layer waveform. In this correspondence, we propose a pair of low-complexity generalized approximate message passing (GAMP)-based frequency-domain equalization (FDE) algorithms for MFTN systems operating in multipath channels. To mitigate the ill-condition of the resultant equivalent channel matrix, we construct block circulant interference matrices by inserting a few cyclic postfixes, followed by truncating the duration of the inherent two-dimensional interferences. Based on the decomposition of the block circulant matrices, we develop a novel frequency-domain received signal model using the two-dimensional fast Fourier transform for mitigating the colored noise imposed by the non-orthogonal matched filter. Moreover, we derive a GAMP-based FDE algorithm and its refined version, where the latter relies on approximations for circumventing the emergence of the ill-conditioned matrices. Our simulation results demonstrate that, for a fixed spectral efficiency, MFTN signaling can significantly improve the bit error rate (BER) performance by jointly optimizing the time- and frequency-domain packing factors. Compared to its Nyquist-signaling counterpart, our proposed MFTN systems employing the refined GAMP equalizer can achieve about 39% higher transmission rates at a negligible BER 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.

Parametric Bilinear Iterative Generalized Approximate Message Passing Reception of FTN Multi-Carrier Signaling

A low-complexity parametric bilinear generalized approximate message passing (PBiGAMP)-based receiver is conceived for multi-carrier faster-than-Nyquist (MFTN) signaling over frequency-selective fading channels. To mitigate the inherent ill-conditioning problem of MFTN signaling, we construct a segment-based frequency-domain received signal model in the form of a block circulant linear transition matrix, which can be efficiently calculated by applying a two dimensional fast Fourier transform. Based on the eigenvalue decomposition of the block circulant matrices, we can diagonalize the covariance matrix of the complex-valued colored noise process imposed by the associated two dimensional non-orthogonal matched filtering. Building on this model, a PBiGAMP-based parametric joint channel estimation and equalization (JCEE) algorithm is proposed for MFTN systems. In this algorithm, we introduce a pair of additive terms for characterizing the interferences arising from adjacent segments and employ the exact discrete <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> probabilities of the transmitted symbols for improving the bit error rate (BER) performance. To further enhance the system’s robustness in the presence of ill-conditioned matrices, we develop a refined PBiGAMP-based JCEE algorithm by introducing a series of scaled identity matrices. Moreover, the proposed PBiGAMP-based JCEE algorithms may be readily decomposed into GAMP-based equalization algorithms, when the channel state information is perfectly known. The overall complexity of the proposed algorithms only increases logarithmically with the total number of transmitted symbols. Our simulation results demonstrate the benefits of the proposed PBiGAMP-based iterative message passing receiver conceived for MFTN signaling.

Multicarrier Faster-Than-Nyquist Based on Efficient Implementation and Probabilistic Shaping

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.

Discrete Fourier transform‐based block transmission for multi‐carrier faster‐than‐Nyquist signalling

Multi-carrier faster-than-Nyquist (MC-FTN) signalling, which is a non-orthogonal data transmission scheme, is broadly viewed as one of the potential candidates for the future high spectral-efficient communications. In this study, a discrete time-frequency packing scheme based on the discrete Fourier transform (DFT) block transmission for MC-FTN signalling (DBT-MC-FTN) is proposed. Firstly, by transforming the blockwise MC-FTN signalling into the frequency domain, an efficient implementation transceiver structure incorporating a bank of DFTs, circular expanding operation, and cyclic shift summation operation is obtained. Thus, flexible packing in both time and frequency domains can be achieved efficiently within a DBT-MC-FTN block. Secondly, to deal with the inter-symbol interference (ISI) introduced by time packing and inter-carrier interference (ICI) introduced by frequency packing in the proposed DBT-MC-FTN scheme, a subcarrier-level equalisation combined with a soft interference cancellation scheme operated in the frequency domain is further proposed to detect the DBT-MC-FTN signals at the receiver. Simulation results show that the proposed DBT-MC-FTN scheme performs close to the corresponding orthogonal system with negligible bit error rate performance loss in the case of moderate ISI and ICI. Additionally, the post-processing signal-to-interference-plus-noise ratio of the proposed scheme is also given in detail.

Discrete Fourier Transform-Based Block Faster-Than- Nyquist Transmission for 5G Wireless Communications

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.

Low-Complexity Selective Mapping Methods for Multicarrier Faster-Than-Nyquist Signaling

Multicarrier faster-than-Nyquist (MFTN) signaling is a high spectral efficiency transmission scheme, which is promising in the future communication. One of the major problems of MFTN signaling is high peak-to-average power ratio (PAPR). Therefore, PAPR reduction is necessary in MFTN systems. Generally, four times oversampling is used in PAPR reduction methods for MFTN signaling to make the discrete time MFTN signaling approximate the peak of continuous time MFTN signaling. However, generating four times oversampled discrete time MFTN signaling will increase the computational complexity of PAPR reduction methods. In this paper, we propose three new low-complexity PAPR reduction methods based on selective mapping (SLM) for MFTN signaling. The first step of proposed methods is using discrete time MFTN signaling with oversampling factor lower than four as reference discrete signal. Then, three new methods utilize picking, reconstructing, and filtering, respectively, to acquire the peak power of four times oversampled MFTN signaling. It is shown that the proposed methods can significantly reduce the computational complexity while almost without PAPR reduction performance loss.

A Low-Complexity Receiver for Multicarrier Faster-Than-Nyquist Signaling Over Frequency Selective Channels

In this letter, we propose a low-complexity receiver for multicarrier faster-than-Nyquist (MFTN) signaling over frequency selective channels. By introducing a time-frequency trellis state, we are able to reformulate the MFTN detection problem into a linear state-space model. Building on this, a vector-form Forney style cycle-free factor graph is constructed. Then, Gaussian message passing technique is employed to derive the parametric message updating expressions. Accordingly, only the mean vectors and covariance matrices have to be calculated, which significantly reduces the computational complexity of MFTN detection. Simulation results demonstrate that the proposed receiver outperforms the symbol-by-symbol receiver by about 1 dB in terms of bit error rate (BER) and approaches the BER performance of the maximum a posteriori probability detector. Meanwhile, 39% more spectral efficiency can be obtained at a BER performance loss of less than 0.3 dB.

PAPR Reduction of Multicarrier Faster-than-Nyquist Signaling by PTS Based on Tree

One of the common drawbacks of multicarrier communication systems is high peak-to-average power ratio (PAPR). Duo to the overlapped structure of multicarrier faster-than-Nyquist (MFTN) signaling, conventional PAPR reduction methods show poor performance. In this paper, we investigate the PAPR reduction of MFTN signaling. Specifically, as one of the most attractive methods, partial transmit sequence (PTS) method is exploited in MFTN signaling system. First, PTS method is combined with alternative signal (AS) to overcome the overlapped structure of MFTN signaling. Then, a tree based PTS method combined with AS is proposed, and all the candidate signal sequences can be generated by adding the difference signal sequence on the last candidate signal sequence, which can reduce the computational complexity significantly. Simulation results show that the proposed method does not have performance degradation on PAPR reduction.

A Faster-Than-Nyquist (FTN)-Based Multicarrier System

Faster-than-Nyquist (FTN) signaling is regarded as a potential modulation format of 5G communication system for its high spectral efficiency. To further improve the spectral efficiency, researchers have extended the FTN signaling to the frequency dimension. However, the two-dimensional FTN signaling called multicarrier FTN (MFTN) signaling induces intersymbol interference and intercarrier interference (ICI), which challenges the receiver. Even the subcarriers are orthogonal, the MFTN signaling still induces the ICI. In this paper, we propose a new MFTN signaling transceiver with an FTN mapper and a linear minimum mean square error (LMMSE) equalizer. The FTN mapper is deployed on every subcarriers independently, which means that the MFTN is ICI-free. The proposed transceiver is compatible with the existing orthogonal frequency division multiplexing (OFDM) system and can detect the MFTN signal efficiently. The numerical results show that the bit error rate performance of the transceiver is close to the convolution code line. At the same time, the MFTN system with high-order modulation has power gains than the traditional OFDM system.

Low-Complexity Partial Transmit Sequence Methods Using Dominant Time-Domain Samples for Multicarrier Faster-Than-Nyquist Signaling

In Multicarrier faster-than-Nyquist (MFTN) systems, one of the most important problems of MFTN signaling is high peak-to-average power ratio (PAPR). In this paper, partial transmit sequence (PTS) method is adopted to resolve this problem, and we focus on reducing the computational complexity of it. First, the PTS method combined with alternative signal (AS) is introduced to overcome the overlapping structure of MFTN signaling. Then, due to the dominant time-domain samples of MFTN signaling are used, a new metric which can select dominant time-domain samples accurately is proposed. Based on that, two low-complexity PTS methods are proposed. To further reduce the computational complexity, by analyzing the position distribution of sample with peak power, part of the samples are removed from the procedure of calculating metric for selecting dominant time-domain samples. Simulation results confirm that the proposed low-complexity PTS methods can effectively reduce computational complexity without degrading the PAPR reduction performance.

Multicarrier Faster-than-Nyquist Based Symbol Design with Intentional Interference for Synchronization

The multicarrier faster-than-Nyquist (MFTN) system is attractive to ultra-high definition TV because it improves on the spectral efficiency up to twice that of the conventional orthogonal frequency division multiplexing system. However, the MFTN system causes the inter channel interference (ICI) by corrupting the orthogonality between subcarriers. In this paper, a pilot pattern for the MFTN system is proposed to improve synchronization performance by removing the ICI in pilot subcarriers while preserving the advantage of the MFTN scheme. To remove the interference, the known pilot pattern is intentionally distorted according to the amount of the interference at the transmitter to improve on the performance of synchronization without affecting the net data.

MMSE Turbo Equalization and Detection for Multicarrier Faster-Than-Nyquist Signaling

In this paper, two minimum mean-squared error (MMSE) turbo equalization and detection schemes for spectral efficient multicarrier faster-than-Nyquist (MFTN) signaling system are presented. First, the two-dimensional (2-D) soft input and soft output (SISO) MMSE equalization intended for magnetic recording channels, i.e., 2-D intersymbol interference (ISI), is extended to the detection of MFTN signals. Although the 2-D MMSE turbo equalization exhibits an attractive bit-error-rate (BER) performance under certain time-frequency spacing packing between adjacent symbols/subcarriers, the BER performance will be degraded when introducing serious intercarrier interference. Second, a 1-D SISO MMSE equalization combined with soft successive interference cancellation (SIC) is further proposed for the detection of MFTN signals, and it shows that the MMSE equalization combined with SIC could asymptotically approach the maximum a posterior equalization combined with SIC with negligible BER performance loss. Our computational complexity analysis and numerous simulation results demonstrate that the proposed MMSE turbo equalization schemes may be more preferred choice in the practical detection of MFTN signals.

An Efficient Implementation of Lattice Staggered Multicarrier Faster-Than-Nyquist Signaling

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.

Peak-to-Average Power Ratio of Multicarrier Faster-Than-Nyquist Signals: Distribution, Optimization and Reduction

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.

Spectral Efficiency Maximization for Deliberate Clipping-Based Multicarrier Faster-Than-Nyquist Signaling

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.

Optimal multicarrier faster-than-Nyquist signaling under symbol-by-symbol detection

We consider the multicarrier faster-than-Nyquist (MFTN) signaling under low complexity symbol-by-symbol detection, where the lattice structure and time-frequency spacing play key roles in determining the system performance. Specifically, the energy of intersymbol interference (ISI) and intercarrier interference (ICI) introduced by time-frequency packing is taken as a figure of merit. In this regard, we firstly prove the asymptotical equivalence of the hexagonal MFTN and conventional rectangular MFTN signaling systems when the time packing factor is small enough, and we also reveal the potential benefit of hexagonal MFTN with respect to conventional rectangular MFTN for moderate time-frequency spacing. Then, an optimal MFTN signaling scheme under the given signaling efficiency is proposed. By jointly optimizing the lattice structure and time-frequency spacing to minimize the interference energy, we show that the optimal time-frequency spacing can be accurately obtained with substantially reduced complexity than conventional exhaustive search scheme. Finally, we demonstrate that there is a good match between minimizing the interference energy and maximizing the achievable spectral efficiency, which is also considered to be an important figure for MFTN signaling system. Our theoretical analysis and numerical results validate that the proposed scheme outperforms conventional MFTN signaling system.

PAPR Reduction of Multicarrier Faster-Than-Nyquist Signals With Partial Transmit Sequence

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.

Hexagonal Multicarrier Faster-Than-Nyquist Signaling

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-D Mazo 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.