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

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

Analysis of a Multicarrier Communication System Based on Overcomplete Gabor Frames

A multicarrier signal can be seen as a Gabor family whose coefficients are the symbols to be transmitted and whose generators are the time-frequency shifted pulse shapes to be used. In this article, we consider the case where the signaling density is 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

Waveform Advancements and Synchronization Techniques for Generalized Frequency Division Multiplexing

To enable a new level of connectivity among machines as well as between people and machines, future wireless applications will demand higher requirements on data rates, response time, and reliability from the communication system. This will lead to a different system design, comprising a wide range of deployment scenarios. One important aspect is the evolution of physical layer (PHY), specifically the waveform modulation. The novel generalized frequency division multiplexing (GFDM) technique is a prominent proposal for a flexible block filtered multicarrier modulation. This thesis introduces an advanced GFDM concept that enables the emulation of other prominent waveform candidates in scenarios where they perform best. Hence, a unique modulation framework is presented that is capable of addressing a wide range of scenarios and to upgrade the PHY for 5G networks. In particular, for a subset of system parameters of the modulation framework, the problem of symbol time offset (STO) and carrier frequency offset (CFO) estimation is investigated and synchronization approaches, which can operate in burst and continuous transmissions, are designed. The first part of this work presents the modulation principles of prominent 5G candidate waveforms and then focuses on the GFDM basic and advanced attributes. The GFDM concept is extended towards the use of OQAM, introducing the novel frequency-shift OQAM-GFDM, and a new low complexity model based on signal processing carried out in the time domain. A new prototype filter proposal highlights the benefits obtained in terms of a reduced out-of-band (OOB) radiation and more attractive hardware implementation cost. With proper parameterization of the advanced GFDM, the achieved gains are applicable to other filtered OFDM waveforms. In the second part, a search approach for estimating STO and CFO in GFDM is evaluated. A self-interference metric is proposed to quantify the effective SNR penalty caused by the residual time and frequency misalignment or intrinsic inter-symbol interference (ISI) and inter-carrier interference (ICI) for arbitrary pulse shape design in GFDM. In particular, the ICI can be used as a non-data aided approach for frequency estimation. Then, GFDM training sequences, defined either as an isolated preamble or embedded as a midamble or pseudo-circular pre/post-amble, are designed. Simulations show better OOB emission and good estimation results, either comparable or superior, to state-of-the-art OFDM system in wireless channels

Multiple-Input Multiple-Output Detection Algorithms for Generalized Frequency Division Multiplexing

Since its invention, cellular communication has dramatically transformed personal lifes and the evolution of mobile networks is still ongoing. Evergrowing demand for higher data rates has driven development of 3G and 4G systems, but foreseen 5G requirements also address diverse characteristics such as low latency or massive connectivity. It is speculated that the 4G plain cyclic prefix (CP)-orthogonal frequency division multiplexing (OFDM) cannot sufficiently fulfill all requirements and hence alternative waveforms have been in-vestigated, where generalized frequency division multiplexing (GFDM) is one popular option. An important aspect for any modern wireless communication system is the application of multi-antenna, i.e. MIMO techiques, as MIMO can deliver gains in terms of capacity, reliability and connectivity. Due to its channel-independent orthogonality, CP-OFDM straightforwardly supports broadband MIMO techniques, as the resulting inter-antenna interference (IAI) can readily be resolved. In this regard, CP-OFDM is unique among multicarrier waveforms. Other waveforms suffer from additional inter-carrier interference (ICI), inter-symbol interference (ISI) or both. This possibly 3-dimensional interference renders an optimal MIMO detection much more complex. In this thesis, weinvestigate how GFDM can support an efficient multiple-input multiple-output (MIMO) operation given its 3-dimensional interference structure. To this end, we first connect the mathematical theory of time-frequency analysis (TFA) with multicarrier waveforms in general, leading to theoretical insights into GFDM. Second, we show that the detection problem can be seen as a detection problem on a large, banded linear model under Gaussian noise. Basing on this observation, we propose methods for applying both space-time code (STC) and spatial multiplexing techniques to GFDM. Subsequently, we propose methods to decode the transmitted signals and numerically and theoretically analyze their performance in terms of complexiy and achieved frame error rate (FER). After showing that GFDM modulation and linear demodulation is a direct application of Gabor expansion and transform, we apply results from TFA to explain singularities of the modulation matrix and derive low-complexity expressions for receiver filters. We derive two linear detection algorithms for STC encoded GFDM signals and we show that their performance is equal to OFDM. In the case of spatial multiplexing, we derive both non-iterative and iterative detection algorithms which base on successive interference cancellation (SIC) and minimum mean squared error (MMSE)-parallel interference cancellation (PIC) detection, respectively. By analyzing the error propagation of the SIC algorithm, we explain its significantly inferior performance compared to OFDM. Using feedback information from the channel decoder, we can eventually show that near-optimal GFDM detection can outperform an optimal OFDM detector by up to 3dB for high SNR regions. We conclude that GFDM, given the obtained results, is not a general-purpose replacement for CP-OFDM, due to higher complexity and varying performance. Instead, we can propose GFDM for scenarios with strong frequency-selectivity and stringent spectral and FER requirements

Spectrally efficient multicarrier communication systems: signal detection, mathematical modelling and optimisation

This thesis considers theoretical, analytical and engineering design issues relating to non-orthogonal Spectrally Efficient Frequency Division Multiplexing (SEFDM) communication systems that exhibit significant spectral merits when compared to Orthogonal FDM (OFDM) schemes. Alas, the practical implementation of such systems raises significant challenges, with the receivers being the bottleneck. This research explores detection of SEFDM signals. The mathematical foundations of such signals lead to proposals of different orthonormalisation techniques as required at the receivers of non-orthogonal FDM systems. To address SEFDM detection, two approaches are considered: either attempt to solve the problem optimally by taking advantage of special cases properties or to apply sub-optimal techniques that offer reduced complexities at the expense of error rates degradation. Initially, the application of sub-optimal linear detection techniques, such as Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE), is examined analytically and by detailed modelling. To improve error performance a heuristic algorithm, based on a local search around an MMSE estimate, is designed by combining MMSE with Maximum Likelihood (ML) detection. Yet, this new method appears to be efficient for BPSK signals only. Hence, various variants of the sphere decoder (SD) are investigated. A Tikhonov regularised SD variant achieves an optimal solution for the detection of medium size signals in low noise regimes. Detailed modelling shows the SD detector to be well suited to the SEFDM detection, however, with complexity increasing with system interference and noise. A new design of a detector that offers a good compromise between computational complexity and error rate performance is proposed and tested through modelling and simulation. Standard reformulation techniques are used to relax the original optimal detection problem to a convex Semi-Definite Program (SDP) that can be solved in polynomial time. Although SDP performs better than other linear relaxations, such as ZF and MMSE, its deviation from optimality also increases with the deterioration of the system inherent interference. To improve its performance a heuristic algorithm based on a local search around the SDP estimate is further proposed. Finally, a modified SD is designed to implement faster than the local search SDP concept. The new method/algorithm, termed the pruned or constrained SD, achieves the detection of realistic SEFDM signals in noisy environments

Spectrum Optimisation in Wireless Communication Systems: Technology Evaluation, System Design and Practical Implementation

Two key technology enablers for next generation networks are examined in this thesis, namely Cognitive Radio (CR) and Spectrally Efficient Frequency Division Multiplexing (SEFDM). The first part proposes the use of traffic prediction in CR systems to improve the Quality of Service (QoS) for CR users. A framework is presented which allows CR users to capture a frequency slot in an idle licensed channel occupied by primary users. This is achieved by using CR to sense and select target spectrum bands combined with traffic prediction to determine the optimum channel-sensing order. The latter part of this thesis considers the design, practical implementation and performance evaluation of SEFDM. The key challenge that arises in SEFDM is the self-created interference which complicates the design of receiver architectures. Previous work has focused on the development of sophisticated detection algorithms, however, these suffer from an impractical computational complexity. Consequently, the aim of this work is two-fold; first, to reduce the complexity of existing algorithms to make them better-suited for application in the real world; second, to develop hardware prototypes to assess the feasibility of employing SEFDM in practical systems. The impact of oversampling and fixed-point effects on the performance of SEFDM is initially determined, followed by the design and implementation of linear detection techniques using Field Programmable Gate Arrays (FPGAs). The performance of these FPGA based linear receivers is evaluated in terms of throughput, resource utilisation and Bit Error Rate (BER). Finally, variants of the Sphere Decoding (SD) algorithm are investigated to ameliorate the error performance of SEFDM systems with targeted reduction in complexity. The Fixed SD (FSD) algorithm is implemented on a Digital Signal Processor (DSP) to measure its computational complexity. Modified sorting and decomposition strategies are then applied to this FSD algorithm offering trade-offs between execution speed and BER