A deep learning assisted sum-product detection algorithm (DL-SPDA) for faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed detection algorithm works on a modified factor graph which concatenates a neural network function node to the variable nodes of the conventional FTN factor graph to approach the maximum a posterior probabilities (MAP) error performance. In specific, the neural network performs as a function node in the modified factor graph to deal with the residual intersymbol interference (ISI) that is not considered by the conventional detector with a limited complexity. We modify the updating rule in the conventional sum-product algorithm so that the neural network assisted detector can be complemented to a Turbo equalization receiver. Furthermore, we propose a compatible training technique to improve the detection performance of the proposed DL-SPDA with Turbo equalization. In particular, the neural network is optimized in terms of the mutual information between the transmitted sequence and the extrinsic information. We also investigate the maximum-likelihood bit error rate (BER) performance of a finite length coded FTN system. Simulation results show that the error performance of the proposed algorithm approaches the MAP performance, which is consistent with the analytical BER.
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 multiple-input multiple-output (MIMO) channels. We show that precoding in time and waterfilling in space is capacity achieving for frequency-flat MIMO FTN. For frequency-selective fading, joint waterfilling in time, space and frequency is required.
In this letter, we propose a new symbol detection method for faster-than-Nyquist signaling (FTNS) systems. Based on frame theory, we formulate a symbol detection problem as a under-determined linear equation on a finite set. The problem is reformulated as a sum-of-absolute-values (SOAV) optimization that can be efficiently solved by the fast iterative shrinkage thresholding algorithm (FISTA). The proximity operator for the convex optimization is derived analytically. Simulation results are given to show that the proposed method can successfully detect symbols in faster-than-Nyquist signaling s…
In this letter, we analyze the performance of covert communications under faster-than-Nyquist (FTN) signaling in the Rayleigh block fading channel. Both Bayesian criterion- and Kullback-Leibler (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.
In this paper, we investigate the detection problem of binary faster-than-Nyquist (FTN) signaling and propose a novel sequence estimation technique that exploits its special structure. In particular, the proposed sequence estimation technique is based on sphere decoding (SD) and exploits the following two characteristics about the FTN detection problem: 1) the cor- relation between the noise samples after the receiver matched filter, and 2) the structure of the intersymbol interference (ISI) matrix. Simulation results show that the proposed SD-based sequence estimation (SDSE) achieves the opti…
Oversampling combined with low quantization resolutions has been shown to be a viable option when aiming for energy efficiency in multigigabit/s communications systems. This work considers the case of 1-bit quantization combined with oversampling and shows how the performance of such a system can be improved by using matched pulse shaping filters and faster than Nyquist signaling. The channel is considered with additive Gaussian noise and the performance of the system is evaluated in terms of achievable information rate under symbol-by-symbol detection.
Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal physical layer transmission technique to improve the spectral efficiency of future communication systems but at the expense of intersymbol-interference (ISI). In this paper, we investigate the detection problem of FTN signaling and formulate the sequence estimation problem of any $M$-ary phase shift keying (PSK) FTN signaling as an optimization problem that turns out to be non-convex and nondeterministic polynomial time (NP)-hard to solve. We propose a novel algorithm, based on concepts from semidefinite relaxation (SDR) and Gau…
Capacity computations are presented for Faster-Than-Nyquist (FTN) signaling in the presence of interference from neighboring frequency bands. It is shown that Shannon's sinc pulses maximize the spectral efficiency for a multi-access channel, where spectral efficiency is defined as the sum rate in bits per second per Hertz. Comparisons using root raised cosine pulses show that the spectral efficiency decreases monotonically with the roll-off factor. At high signal-to-noise ratio, these pulses have an additive gap to capacity that increases monotonically with the roll-off factor.
In this paper, we consider communication over the bandwidth limited analog white Gaussian noise channel using non-orthogonal pulses. In particular, we consider non-orthogonal transmission by signaling samples at a rate higher than the Nyquist rate. Using the faster-than-Nyquist (FTN) framework, Mazo showed that one may transmit symbols carried by sinc pulses at a higher rate than that dictated by Nyquist without loosing bit error rate. However, as we will show in this paper, such pulses are not necessarily well localized in time. In fact, assuming that signals in the FTN framework are well loc…
In this paper, we propose a serially concatenated turbo-encoded faster-than-Nyquist signaling (FTNS) transceiver that takes into account FTNS-specific colored noise effects. The proposed low-complexity receiver carries out soft-decision frequency-domain equalization with the aid of the minimum-mean square error criterion while whitening the colored noise. Simulation results demonstrate that the proposed multi-stage-concatenated FTNS system achieves a better error-ratio performance than previous systems that do not consider colored noise effects in the high-symbol-packing FTNS regime. Furthermo…
This letter proposes the Faster-than-Nyquist signaling (FTNS) using overlap frequency domain equalization (FDE), which compensates the inter-symbol interference (ISI) due to band limiting filters of the FTNS at the transmitter and the receiver as well as the frequency selective fading channel. Since overlap FDE does not require any guard interval (GI) at the transmitter such as cyclic prefix (CP), higher spectral efficiency can be achieved compared to FTNS scheme using the conventional FDE. In the proposed method, the equalizer weight is derived based on minimum mean square error (MMSE) criter…
A rateless transmission architecture is developed for communication over Gaussian intersymbol interference channels, based on the concept of super-Nyquist (SNQ) signaling. In such systems, the signaling rate is chosen significantly higher than the Nyquist rate of the system. We show that such signaling, when used in conjunction with good "off-the-shelf" base codes, simple linear redundancy, and minimum mean-square error decision feedback equalization, results in capacity-approaching, low-complexity rateless codes for the time-varying intersymbol-interference channel. Constructions for both sin…
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…
Faster-than-Nyquist (FTN) signal achieves higher spectral efficiency and capacity compared to Nyquist signal due to its smaller pulse interval or narrower subcarrier spacing. Shannon limit typically defines the upper-limit capacity of Nyquist signal. To the best of our knowledge, the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal is first demonstrated in this paper. The mathematical expression shows that FTN NOFDM signal has the potential to achieve a higher capacity limit compared to Nyquist signal. In this paper, we demonst…
Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal pulse modulation technique that can improve the spectral efficiency (SE) of next generation communication systems at the expense of higher detection complexity to remove the introduced inter-symbol interference (ISI). In this paper, we investigate the detection problem of ultra high-order quadrature-amplitude modulation (QAM) FTN signaling where we exploit a mathematical programming technique based on the alternating directions multiplier method (ADMM). The proposed ADMM sequence estimation (ADMMSE) FTN signaling detector demons…
Ultra-reliable low-latency communication (URLLC) requires short packets of data transmission. It is known that when the packet length becomes short, the achievable rate is subject to a penalty when compared to the channel capacity. In this paper, we propose to use faster-than-Nyquist (FTN) signaling to compensate for the achievable rate loss of short packet communications. We investigate the performance of a combination of a low complexity detector of FTN signaling used with nonbinary low-density parity-check (NB-LDPC) codes that is suitable for low-latency and short block length requirements …
In this paper, we investigate the sequence estimation problem of faster-than-Nyquist (FTN) signaling as a promising approach for increasing spectral efficiency (SE) in future communication systems. In doing so, we exploit the concept of Gaussian separability and propose two probabilistic data association (PDA) algorithms with polynomial time complexity to detect binary phase-shift keying (BPSK) FTN signaling. Simulation results show that the proposed PDA algorithm outperforms the recently proposed SSSSE and SSSgb$K$SE algorithms for all SE values with a modest increase in complexity. The PDA a…
In this paper, we investigate the sequence estimation problem of binary and quadrature phase shift keying faster-than-Nyquist (FTN) signaling and propose two novel low-complexity sequence estimation techniques based on concepts of successive interference cancellation. To the best of our knowledge, this is the first approach in the literature to detect FTN signaling on a symbol-by-symbol basis. In particular, based on the structure of the self-interference inherited in FTN signaling, we first find the operating region boundary---defined by the root-raised cosine (rRC) pulse shape, its roll-off …
This work addresses the issue of interference generated by co-channel users in downlink multi-antenna multicarrier systems with frequency-packed faster-than-Nyquist (FTN) signaling. The resulting interference stems from an aggressive strategy for enhancing the throughput via frequency reuse across different users and the squeezing of signals in the time-frequency plane beyond the Nyquist limit. The error-free spectral efficiency is proved to be increasing with the frequency packing and FTN acceleration factors. The lower bound for the FTN sampling period that guarantees information losslesness…
A deep learning assisted sum-product detection algorithm (DL-SPA) for faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed detection algorithm concatenates a neural network to the variable nodes of the conventional factor graph of the FTN system to help the detector converge to the a posterior probabilities based on the received sequence. More specifically, the neural network performs as a function node in the modified factor graph to deal with the residual intersymbol interference (ISI) that is not modeled by the conventional detector with a limited number of ISI taps. …
Continuous phase modulation (CPM) with 1-bit quantization at the receiver is promising in terms of energy and spectral efficiency. In this study, CPM waveforms with symbol durations significantly shorter than the inverse of the signal bandwidth are proposed, termed faster-than-Nyquist CPM. This configuration provides a better steering of zero-crossings as compared to conventional CPM. Numerical results confirm a superior performance in terms of BER in comparison with state-of-the-art methods, while having the same spectral efficiency and a lower oversampling factor. Moreover, the new waveform …
Faster-than-Nyquist (FTN) signaling aided non-orthogonal multiple access (NOMA) is conceived and its achievable rate is quantified in the presence of random link delays of the different users. We reveal that exploiting the link delays may potentially lead to a signal-to-interference-plus-noise ratio (SINR) gain, while transmitting the data symbols at FTN rates has the potential of increasing the degree-of-freedom (DoF). We then unveil the fundamental trade-off between the SINR and DoF. In particular, at a sufficiently high symbol rate, the SINR gain vanishes while the DoF gain achieves its max…
One possibility to break down the capacity limit in optical transmission systems are higher spectral efficiencies, enabled by Faster-than-Nyquist signaling. Here we present the utilization of non-orthogonal time division multiplexing of sinc pulse sequences for this purpose. The mathematical expression, with a representation of the Nyquist sinc sequence by a cosine Fourier series and simulation results show that non-orthogonal time-division multiplexing increases the transmittable symbol rate by up to 25%.
Faster-than-Nyquist (FTN) signaling is a candidate non-orthonormal transmission technique to improve the spectral efficiency (SE) of future communication systems. However, such improvements of the SE are at the cost of additional computational complexity to remove the intentionally introduced intersymbol interference. In this paper, we investigate the use of deep learning (DL) to reduce the detection complexity of FTN signaling. To eliminate the need of having a noise whitening filter at the receiver, we first present an equivalent FTN signaling model based on using a set of orthonormal basis …
Faster-than-Nyquist (FTN) signaling can improve the spectral efficiency (SE); however, at the expense of high computational complexity to remove the introduced intersymbol interference (ISI). Motivated by the recent success of ML in physical layer (PHY) problems, in this paper we investigate the use of ML in reducing the detection complexity of FTN signaling. In particular, we view the FTN signaling detection problem as a classification task, where the received signal is considered as an unlabeled class sample that belongs to a set of all possible classes samples. If we use an off-shelf classi…
In this paper, we propose a faster-than-Nyquist (FTN) non-orthogonal frequency-division multiplexing (NOFDM) scheme for visible light communications (VLC) where the multiplexing/demultiplexing employs the inverse fractional cosine transform (IFrCT)/FrCT. Different to the common fractional Fourier transform-based NOFDM (FrFT-NOFDM) signal, FrCT-based NOFDM (FrCT-NOFDM) signal is real-valued which can be directly applied to the VLC systems without the expensive upconversion. Thus, FrCT-NOFDM is more suitable for the cost-sensitive VLC systems. Meanwhile, under the same transmission rate, FrCT-NO…
We propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer which considers both the intersymbol interference (ISI) and the effect of non-white noise inherent in Faster-than-Nyquist (FTN) signaling. In order to incorporate the statistics of noise signal into the factor graph over which the LMMSE algorithm is implemented, we suggest a method that models it as an autoregressive (AR) process. Furthermore, we develop a new mechanism for exchange of information between the proposed equalizer and the channel decoder through turbo iterations. Based on these improvements…
In 1975, the pioneering work of J. E. Mazo showed the potential faster-than-Nyquist (FTN) gain of single-carrier binary signal. If the inter-symbol interference is eliminated by an optimal detector, the FTN single-carrier binary signal can transmit 24.7% more bits than the Nyquist signal without any loss of bit error rate performance, which is known as the Mazo limit. In this paper, we apply sphere decoder (SD) with box optimization (BO) to reduce inter-carrier interference (ICI) in FTN non-orthogonal frequency division multiplexing (FTN-NOFDM) system. Compared with the conventional SD, SD wit…
In this work we compare the capacity and achievable rate of uncoded faster than Nyquist (FTN) signalling in the frequency domain, also referred to as spectrally efficient FDM (SEFDM). We propose a deep residual convolutional neural network detector for SEFDM signals in additive white Gaussian noise channels, that allows to approach the Mazo limit in systems with up to 60 subcarriers. Notably, the deep detectors achieve a loss less than 0.4-0.7 dB for uncoded QPSK SEFDM systems of 12 to 60 subcarriers at a 15% spectral compression.
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist theorem require the sampling rate to be at least twice the maximum frequency of the signal. This has triggered scientists to examine the possibilities of creating a new path for recovering signals using much less samples and therefore speeding up the process and satisfying the need for faster realization. As a result the compressive sensing approach has emerg…
We address the problem of interference management and power control in terms of maximization of a general utility function. For the utility functions under consideration, we propose a power control algorithm based on a fixed-point iteration; further, we prove local convergence of the algorithm in the neighborhood of the optimal power vector. Our algorithm has several benefits over the previously studied works in the literature: first, the algorithm can be applied to problems other than network utility maximization (NUM), e.g., power control in a relay network; second, for a network with $N$ wi…
