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

Analyse du système linéaire optimal pour les communications multiporteuses au-delà de la cadence de Nyquist

Les communications au delà de la cadence de Nyquist permettent une augmentation de l'efficacité spectrale en contre-partie d'une complexité plus élevée. Concernant les communications multiporteuses, les travaux menés jusque là se sont principalement focalisés sur l'étude des systèmes non-linéaires exploitant des techniques de codage et/ou d'égalisation, sans considération ou optimisation particulière de la partie linéaire du système. Dans cet article, nous analysons le compor-tement du système linéaire multiporteuse optimal lorsqu'il est utilisé seul ou avec des structures de réception non-linéaires (décodage itératif et égalisation à retour de décision). Nous nous intéressons également aux limites des hypothèses com-munément utilisées lors de l'implémentation de ces systèmes non-linéaires. L'utilisation du système linéaire optimal permet une expression analytique de la probabilité d'erreur qui peut être utilisée pour prédire les performances et aider la conception de systèmes codés. Ce travail met aussi en avant le bon compromis performances/complexité offert par l'égaliseur à retour de décision dans le contexte des communications au-delà de la cadence de Nyquist

Analysis of the optimal linear system for multicarrier FTN communications

National audienceFaster-than-Nyquist signalization allows for a better spectral efficiency at the expense of an increased complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization regarding the linear part of the system. In this paper, we analyse the behavior of the optimal linear multicarrier system when used with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the assumptions commonly made for the implementation of such non-linear systems. The use of this optimal linear system allows for a closed-form expression of the bit-error probability which can be used to predict the performances and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context.Les communications au delà de la cadence de Nyquist permettent une augmentation de l'efficacité spectrale en contre-partie d'une complexité plus élevée. Concernant les communications multiporteuses, les travaux menés jusque là se sont principalement focalisés sur l'étude des systèmes non-linéaires exploitant des techniques de codage et/ou d'égalisation, sans considération ou optimisation particulière de la partie linéaire du système. Dans cet article, nous analysons le compor-tement du système linéaire multiporteuse optimal lorsqu'il est utilisé seul ou avec des structures de réception non-linéaires (décodage itératif et égalisation à retour de décision). Nous nous intéressons également aux limites des hypothèses com-munément utilisées lors de l'implémentation de ces systèmes non-linéaires. L'utilisation du système linéaire optimal permet une expression analytique de la probabilité d'erreur qui peut être utilisée pour prédire les performances et aider la conception de systèmes codés. Ce travail met aussi en avant le bon compromis performances/complexité offert par l'égaliseur à retour de décision dans le contexte des communications au-delà de la cadence de Nyquist

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

Performance Evaluation of a Faster-than-Nyquist System Based on Turbo Equalization and LDPC Codes

In the frame of digital video broadcasting by satellite - second generation (DVB-S2), a faster-than-Nyquist (FTN) system based on turbo equalization and low-density parity-check (LDPC) codes is proposed. Truncated maximum a posteriori (MAP) and minimum mean square error (MMSE) equalizers provide a reduced complexity implementation of the FTN system. On the other hand, LDPC codes allow us to demonstrate attractive performance results over an additive white Gaussian noise (AWGN) channel while increasing spectral efficiency beyond the Nyquist rate up to 60 % and keeping a complexity comparable to a current DVB-S2 modem

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

Estudi d'un emissor-receptor faster-than-Nyquist de baixa complexitat per a les comunicacions per satèl·lit

Transmissor/receiver for ACARS systemCapacity increase in satelite communications systems is nowadays a main concern. In order to increase the spectral efficiency of such systems, a research topic consists in specifying non-orthogonal modulations called faster-than-Nyquist (FTN). By means of this technique, a capacity increase could be obtained at the cost of more complexity at the receiver side. The FTN system design consists in using pulse shaping and equalizing techniques such that a good compromise is obtained between spectal efficiency, level of interference and complexity. Within the frame of Direct-to-Home (DTH) satellite broadcast or mobile terminals, complexity becomes the main limiting factor in order to ensure low cost user terminal integration.El aumento de la capacidad de los sistemas de transmisión por satélite se encuentra en el centro de las preocupaciones actuales. Con el objetivo de augmentar la eficacidad espectral de tales sistemas, un tema de estudio consiste en especificar modulaciones no ortogonales llamadas faster-than-Nyquist (FTN). Con el uso de esta técnica, se podria augmentar la capacidad de los sistemas de transmisión a cambio de aumentar la complejidad de los receptores. El diseño de un sistema FTN consiste en determinar una estrategia de filtrado y de ecualización permitiendo un buen compromiso entre eficacidad espectral, nivel de interferencia y complejidad. En el contexto de difusión por satélite Direct-to-Home (DTH) o en el caso de terminales móviles, la limitación de complejidad es fundamental para garantizar la integración a bajo coste en los terminales de usuario.L'augment de la capacitat dels sistemes de transmissió per satèl·lit es troba al centre de les preocupacions actuals. Amb l'objectiu d'augmentar l'eficacitat espectral d'aquests sistemes, un eix de recerca consisteix en especificar modulacions no ortogonals anomenades faster-than-Nyquist (FTN). Utilitzant aquesta tècnica, es podria augmentar la capacitat dels sistemes de transmissió a canvi d'augmentar la complexitat dels receptors. El disseny d'un sistema FTN consisteix en determinar una estratègia de filtratge i d'equalització permetent un bon compromis entre eficacitat espectral, nivell d'interferència i complexitat. En el contexte de difusió per satèl ·lit Direct-to-Home (DTH) o en el cas de terminals mòbils, la limitació de complexitat és fonamental per garantir l'integració a baix cost als terminals d'usuari