Time Localization and Capacity of Faster-Than-Nyquist Signaling

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 localized in time, one can construct a signaling scheme that violates the Shannon capacity bound. We also show directly that FTN signals are in general not well localized in time. Therefore, the results of Mazo do not imply that one can transmit more data per time unit without degrading performance in terms of error probability. We also consider FTN signaling in the case of pulses that are different from the sinc pulses. We show that one can use a precoding scheme of low complexity to remove the inter-symbol interference. This leads to the possibility of increasing the number of transmitted samples per time unit and compensate for spectral inefficiency due to signaling at the Nyquist rate of the non sinc pulses. We demonstrate the power of the precoding scheme by simulations

Improving Spectral Efficiency While Reducing PAPR Using Faster-Than-Nyquist Multicarrier Signaling

Multicarrier modulations are widely used in mobile radio applications due to their adaptability to the time-frequency characteristics of the channel, thus enabling low-complexity equalization. However, their intrinsically high peak-to-average power ratio (PAPR) is a major drawback with regard to implementation issues (e.g., power amplification efficiency, regulatory constraints...). In this paper, we confirm that the PAPR can be decreased as the signaling density (i.e., spectral efficiency at fixed constellation size) increases, even in the case where symbols cannot be perfectly reconstructed using a linear system. In such a two-dimensional generalization of faster-than-Nyquist (FTN) systems, PAPR distribution models from the literature are confirmed by simulation results. Furthermore, for a fixed number of subcarriers, we show that a sufficient condition to yield the optimal PAPR distribution at the output of a critically sampled transmitter is to specify pulse shapes as tight frames. Finally, simulation are performed in the more realistic case of an oversampled transmitted signal

Analysis of a FTN Multicarrier System: Interference Mitigation Based on Tight Gabor Frames

Cognitive radio applications require flexible waveforms to overcome several challenges such as opportunistic spectrum allocation and white spaces utilization. In this context, multicarrier modulations generalizing traditional cyclic-prefix orthogonal frequency-division multiplexing are particularly justified to fit time-frequency characteristics of the channel while improving spectral efficiency.In our theoretical framework, a multicarrier signal is described as a Gabor family the coefficients of which are the symbols to be transmitted and the generators are the time-frequency shifted pulse shapes to be used. In this article, we consider the case where non-rectangular pulse shapes are used with a signaling density increased such that inter-pulse interference is unavoidable. Such an interference is minimized when the Gabor family used is a tight frame. We show that, in this case, interference can be approximated as an additive Gaussian noise. This allows us to compute theoretical and simulated bit-error-probability for a non-coded system using a quadrature phase-shift keying constellation. Such a characterization is then used in order to predict the convergence of a coded system using low-density parity check codes. We also study the robustness of such a system to errors on the received bits in an interference cancellation context

On the study of faster-than-Nyquist multicarrier signaling based on frame theory

Multicarrier transmissions are classically based on undercomplete or exact Weyl-Heisenberg Riesz (biorthogonal or orthogonal) bases implemented thanks to oversampled filter-banks. This can be seen as a transmission below the Nyquist rate. However, when overcomplete Weyl-Heisenberg frames are used, we obtain a “faster-than-Nyquist” (FTN) system and it is theoretically impossible to recover exactly transmitted symbols using a linear receiver. Various studies have shown the interest of this high density signaling scheme as well as practical implementations based on trellis and/or iterative decoding. Nevertheless, there is still a lack of theoretical justifications with regard to pulse design in the FTN case. In this paper, we consider a linear transceiver operating over an additive white Gaussian noise channel. Using the frame theory and simulation results, we show that the mean squared error (MSE) is minimized when tight frames are used

FTN multicarrier transmission based on tight Gabor frames

A multicarrier signal can be synthesized thanks to a symbol sequence and a Gabor family (i.e., a regularly time-frequency shifted version of a generator pulse). In this article, we consider the case where the signaling density is increased such that inter-pulse interference is unavoidable.Over an additive white Gaussian noise channel, we show that the signal-to-interference-plus-noise ratio is maximized when the transmitter and the receiver use the same tight Gabor frame. What is more, we give practical efficient realization schemes and show how to build tight frames based on usual generators. Theoretical and simulated bit-error-probability are given for a non-coded system using quadrature amplitude modulations. Such a characterization is then used to predict the convergence of a coded system using low-density parity-check codes. We also study the robustness of such a system to errors on the received bits in an interference cancellation context

Low-complexity iterative receiver design for high spectral efficiency communication systems

University of Technology Sydney. Faculty of Engineering and Information Technology.With the rapid development of the modern society, people have an increasing demand of higher data rate. Due to the limited available bandwidth, how to improve the spectral efficiency becomes a key issue in the next generation wireless systems. Recent researches show that, compared to the conventional orthogonal communication systems, the non-orthogonal system can transmit more information with the same resources by introducing non-orthogonality. The non-orthogonal communication systems can be achieved by using faster-than-Nyquist (FTN) signaling to transmit more data symbols in the same time period. On the other hand, by designing appropriate codebook, the sparse code multiple access (SCMA) system can support more users while preserving the same resource elements. Utilisation of these new technologies leads to challenge in receiver design, which becomes severer in complex channel environments. This thesis studies the receiver design for high spectral efficiency communication systems. The main contributions are as follows: 1. A hybrid message passing algorithm is proposed for faster-than-Nyquist, which solves the problem of joint data detection and channel estimation when the channel coefficients are unknown. To fully exploit the known ISI imposed by FTN signaling, the interference induced by FTN signaling and channel fading are intentionally separated. 2. Gaussian message passing and variational inference based estimation algorithms are proposed for faster-than-Nyquist signaling detection in doubly selective channels. Iterative receivers using mean field and Bethe approximations based on variational inference framework are proposed. Moreover, a novel Gaussian message passing based FTN signaling detection algorithm is proposed. 3. An energy minimisation based SCMA decoding algorithm is proposed and convergence analysis of the proposed algorithm is derived. Following optimisation theory and variational free energy framework, the posterior distribution of data symbol is derived in closed form. Then, the convergence property of the proposed algorithm is analysed. 4. A stretched factor graph is designed for MIMO-SCMA system in order to reduce the receiver complexity. Then, a convergence guaranteed message passing algorithm is proposed by convexifying the Bethe free energy. Finally, cooperative communication methods based on belief consensus and alternative direction method of multipliers are proposed. 5. A low complexity detection algorithm is proposed for faster-than-Nyquist SCMA system, which enables joint channel estimation, decoding and user activity detection in grant-free systems. The combination of FTN signaling with SCMA to further enhance the spectral efficiency is first considered. Then, a merging belief propagation and expectation propagation algorithm is proposed to estimate channel state and perform SCMA decoding