On Linear Frequency Domain Turbo-Equalization of Non Linear Volterra Channels

International audienceThis article deals with iterative Frequency Domain Equalization (FDE) for Single Carrier (SC) transmissions over Volterra non linear satellite channels. SC-FDE has gained much importance in recent research for its efficient implementation at the receiver and its interesting low Peak to Average Power Ratio (PAPR) at the transmitter. However, nearly saturated power amplifiers on board satellites generate linear and non linear Inter Symbol Interference (ISI) at the receiver. It is thus interesting to investigate the implementation of SC-FDE for non linear channels. To do so, a frequency domain equivalent satellite channel is derived based on the time domain Volterra series representation of the non linear channel. Then a Minimum Mean Square Error (MMSE)-based iterative frequency domain equalizer is designed. It is shown that the proposed equalizer consists of a Soft Interference Canceller (SIC) which subtracts both the linear and non-linear soft frequency symbols. The equalizer performance is then compared to the equivalent time domain implementation. Results show that a channel-memory independent efficient implementation is achieved at the price of a negligible spectral efficiency loss due to cyclic prefix insertion

Non-linearized amplifier and advanced mitigation techniques: DVB-S2X spectral efficiency improvement

The latest standardization DVB-S2X increases the achievable spectral efficiency of the satellite communications by around 15% in AWGN channel. In order to benefit from those improvements, the strong non-linear distortions introduced by the payload have to be overcome, mostly taking high back-off on the amplifier operation point. Nowadays, on- board amplifiers are linearized before being deployed, allowing low-complexity transmitters and receivers at the detriment of the payload's cost and reduced energy efficiency. In this paper, various techniques are investigated for the purpose of spectral efficiency improvement while releasing the amplifier linearization constraint. Iterative pre-distortion at the transmitter, turbo- equalization at the receiver and appropriate waveforms for transmission through non-linearized payload appear as strong candidates considering the results of this study

Formes d'ondes avancées et traitements itératifs pour les canaux non linéaires satellites

L'augmentation de l'efficacité spectrale des transmissions mono-porteuses sur un lien de diffusion par satellite est devenu un défi d'envergure afin de pallier la demande croissante en débits de transmission. Si des techniques émergentes de transmissions encouragent l'utilisation de modulations à ordre élevé telles que les modulations de phase et d'amplitude (APSK), certaines dégradations sont encourues lors du traitement à bord du satellite. En effet, en raison de l'utilisation d'amplificateurs de puissance ainsi que de filtres à mémoires, les modulations d'ordre élevé subissent des distorsions non-linéaires dues à la fluctuation de leur enveloppe, ce qui nécessite des traitements au sein de l'émetteur ou bien au sein du récepteur. Dans cette thèse, nous nous intéressons au traitement de l'interférence non-linéaire au sein du récepteur, avec une attention particulière aux égaliseurs itératifs qui améliorent les performances du système au prix d'une complexité élevée. A partir du modèle temporel des interférences non-linéaires induites par l'amplificateur de puissance, des algorithmes de réception optimaux et sous optimaux sont dérivés, et leurs performances comparées. Des égaliseurs à complexité réduite sont aussi étudiés dans le but d'atteindre un compromis performances-complexité satisfaisant. Ensuite, un modèle des non-linéarités est dérivé dans le domaine fréquentiel, et les égaliseurs correspondants sont présentés. Dans un second temps, nous analysons et dérivons des récepteurs itératifs pour l'interférence entre symboles non linéaire. L'objectif est d'optimiser les polynômes de distributions d'un code externe basé sur les codes de contrôle de parité à faible densité (LDPC) afin de coller au mieux à la sortie de l'égaliseur. Le récepteur ainsi optimisé atteint de meilleures performances comparé à un récepteur non optimisé pour le canal non-linéaire. Finalement, nous nous intéressons à une classe spécifique de techniques de transmissions mono-porteuse basée sur le multiplexage par division de fréquence (SC-OFDM) pour les liens satellites. L'avantage de ces formes d'ondes réside dans l'efficacité de leur égaliseur dans le domaine fréquentiel. Des formules analytiques de la densité spectrale de puissance et du rapport signal sur bruit et interférence sont dérivées et utilisées afin de prédire les performances du système. ABSTRACT : Increasing both the data rate and power efficiency of single carrier transmissions over broadcast satellite links has become a challenging issue to comply with the urging demand of higher transmission rates. If emerging transmission techniques encourage the use of high order modulations such as Amplitude and Phase Shift Keying (APSK) and Quadrature Amplitude Modulation (QAM), some channel impairments arise due to onboard satellite processing. Indeed, due to satellite transponder Power Amplifiers (PA) as well as transmission filters, high order modulations incur non linear distortions due to their high envelope fluctuations which require specific processing either at the transmitter or at the receiver. In this thesis, we investigate on non linear interference mitigation at the receiver with a special focus on iterative equalizers which dramatically enhance the performance at the cost of additional complexity. Based on the time domain model of the non linear interference induced by the PA, optimal and sub-optimal receiving algorithms are proposed and their performance compared. Low complexity implementations are also investigated for the sake of a better complexity-performance trade-off. Then, a non linear frequency domain model is derived and the corresponding frequency equalizers are investigated. In the second part, we analyse and design an iterative receiver for the non linear Inter Symbol Interference (ISI) channel. The objective is to optimize an outer Low Density Parity Check (LDPC) code distribution polynomials so as to best fit the inner equalizer Extrinsic information. The optimized receiver is shown to achieve better performance compared to a code only optimized for linear ISI channel. Finally, we investigate on a specific class of single carrier transmissions relying on Single Carrier Orthogonal Frequency Division Multiplexing (SCO-FDM) for satellite downlink. The advantage of such waveforms lies in their practical receiver implementation in the frequency domain. General analytical formulas of the power spectral density and signal to noise and interference ratio are derived and used to predict the bit error rate for frequency selective multiplexers

FTN Signaling In the Saturation Regime: Spectral Efficiency Improvement

Faster-than-Nyquist (FTN) signaling is investigated in future satellite communication standardization for an improved spectral efficiency considering the increasingly constrained resource. Previous studies showed that FTN lower modulation orders compressed in time-domain could reach the spectral efficiency of uncompressed higher modulation orders. The FTN gain in terms of transmission rate is obtained at the price of a turbo-equalization at the receiver, increasing the complexity. The increased capacity in DVB-S2X’s transmissions is due to innovations increasing the fluctuation of the complex envelop of the transmitted signal. Since the satellite’s payload introduces higher non-linear distortions with increased fluctuations, the growing receiver’s complexity is unavoidable. However, in this non linear regime, the complexity of the FTN receiver is not this detrimental compared with those of a classical Nyquist receiver. For a similar spectral efficiency, its lower Peak to Average Power Ratio (PAPR), making the non-linearities treatment easier, makes this innovation suitable for future satellite communications, especially when the payload is operated in the saturation regime. In this paper, we show that compression offers a gain between 10 and 20 in terms of spectral efficiency when compared to Nyquist signaling, both equalized thanks to the MAP symbol detection based on the Volterra series model of non-linearities

Multichannel Nonlinear Equalization in Coherent WDM Systems based on Bi-directional Recurrent Neural Networks

Kerr nonlinearity in the form of self- and cross-phase modulation imposes a fundamental limitation to the capacity of wavelength division multiplexed (WDM) optical communication systems. Digital back-propagation (DBP), that requires solving the inverse-propagating nonlinear Schr\"odinger equation (NLSE), is a widely adopted technique for the mitigation of impairments induced by Kerr nonlinearity. However, multi-channel DBP is too complex to be implemented commercially in WDM systems. Recurrent neural networks (RNNs) have been recently exploited for nonlinear signal processing in the context of optical communications. In this work, we propose multi-channel equalization through a bidirectional vanilla recurrent neural network (bi-VRNN) in order to improve the performance of the single-channel bi-VRNN algorithm in the transmission of WDM M-QAM signals. We compare the proposed digital algorithm to full-field DBP and to the single channel bi-RNN in order to reveal its merits with respect to both performance and complexity. We finally provide experimental verification through a QPSK metro link, showcasing over 2.5 dB optical signal-to-noise ratio (OSNR) gain and up to 43% complexity reduction with respect to the single-channel RNN and the DBP.Comment: 9 page

Advanced DSP Techniques for High-Capacity and Energy-Efficient Optical Fiber Communications

The rapid proliferation of the Internet has been driving communication networks closer and closer to their limits, while available bandwidth is disappearing due to an ever-increasing network load. Over the past decade, optical fiber communication technology has increased per fiber data rate from 10 Tb/s to exceeding 10 Pb/s. The major explosion came after the maturity of coherent detection and advanced digital signal processing (DSP). DSP has played a critical role in accommodating channel impairments mitigation, enabling advanced modulation formats for spectral efficiency transmission and realizing flexible bandwidth. This book aims to explore novel, advanced DSP techniques to enable multi-Tb/s/channel optical transmission to address pressing bandwidth and power-efficiency demands. It provides state-of-the-art advances and future perspectives of DSP as well

Neural Network Equalizers and Successive Interference Cancellation for Bandlimited Channels with a Nonlinearity

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to approach the information rates of joint detection and decoding (JDD) with considerably less complexity than JDD and other existing equalizers. Simulations for short-haul optical fiber links with square-law detection illustrate the gains of NNs as compared to the complexity-limited FBA and Gibbs sampling.Comment: Submitted to IEEE Trans. Commun. on January 11, 2024

Digital signal processing for fiber nonlinearities [Invited]

This paper reviews digital signal processing techniques that compensate, mitigate, and exploit fiber nonlinearities in coherent optical fiber transmission systems