The exponentially convergent trapezoidal rule

It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators

Boson-Fermion pairing in a Boson-Fermion environment

Propagation of a Boson-Fermion (B-F) pair in a B-F environment is considered. The possibility of formation of stable strongly correlated B-F pairs, embedded in the continuum, is pointed out. The new Fermi gas of correlated B-F pairs shows a strongly modified Fermi surface. The interaction between like particles is neglected in this exploratory study. Various physical situations where our new pairing mechanism could be of importance are invoked.Comment: 8 pages, 8 figers, to be published in Phys. Rev.

Simultaneous Transmission and Reception: Algorithm, Design and System Level Performance

Full Duplex or Simultaneous transmission and reception (STR) in the same frequency at the same time can potentially double the physical layer capacity. However, high power transmit signal will appear at receive chain as echoes with powers much higher than the desired received signal. Therefore, in order to achieve the potential gain, it is imperative to cancel these echoes. As these high power echoes can saturate low noise amplifier (LNA) and also digital domain echo cancellation requires unrealistically high resolution analog-to-digital converter (ADC), the echoes should be cancelled or suppressed sufficiently before LNA. In this paper we present a closed-loop echo cancellation technique which can be implemented purely in analogue domain. The advantages of our method are multiple-fold: it is robust to phase noise, does not require additional set of antennas, can be applied to wideband signals and the performance is irrelevant to radio frequency (RF) impairments in transmit chain. Next, we study a few protocols for STR systems in carrier sense multiple access (CSMA) network and investigate MAC level throughput with realistic assumptions in both single cell and multiple cells. We show that STR can reduce hidden node problem in CSMA network and produce gains of up to 279% in maximum throughput in such networks. Finally, we investigate the application of STR in cellular systems and study two new unique interferences introduced to the system due to STR, namely BS-BS interference and UE-UE interference. We show that these two new interferences will hugely degrade system performance if not treated appropriately. We propose novel methods to reduce both interferences and investigate the performances in system level.Comment: 20 pages. This manuscript will appear in the IEEE Transactions on Wireless Communication

Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations

We solve the impurity problem which arises within nonequilibrium dynamical mean-field theory for the Hubbard model by means of a self-consistent perturbation expansion around the atomic limit. While the lowest order, known as the non-crossing approximation (NCA), is reliable only when the interaction U is much larger than the bandwidth, low-order corrections to the NCA turn out to be sufficient to reproduce numerically exact Monte Carlo results in a wide parameter range that covers the insulating phase and the metal-insulator crossover regime at not too low temperatures. As an application of the perturbative strong-coupling impurity solver we investigate the response of the double occupancy in the Mott insulating phase of the Hubbard model to a dynamical change of the interaction or the hopping, a technique which has been used as a probe of the Mott insulating state in ultracold fermionic gases.Comment: 14 pages, 9 figure

Propagation channel characterisation and modelling for high-speed train communication systems

High-mobility scenarios, e.g., High-Speed Train (HST) scenarios, are expected to be typical scenarios for the Fifth Generation (5G) communication systems. With the rapid development of HSTs, an increasing volume of wireless communication data is required to be transferred to train passengers. HST users demand high network capacity and reliable communication services regardless of their locations or speeds, which are beyond the capability of current HST communication systems. The features of HST channels are significantly different from those of low-mobility cellular communication systems. For a proper design and evaluation of future HST wireless communication systems, we need accurate channel models that can mimic the underlying channel characteristics, especially the non-stationarity for different HST scenarios. Inspired by the lack of such accurate HST channel models in the literature, this PhD project is devoted to the modelling and simulation of non-stationary Multiple-Input Multiple-Output (MIMO) channels for HST communication systems. In this thesis, we first give a comprehensive review of the measurement campaigns conducted in different HST scenarios and address the recent advances in HST channel models. We also highlight the key challenges of HST channel measurements and models. Then, we study the characterisation of non-stationary channels and propose a theoretical framework for deriving the statistical properties of these channels. HST wireless communication systems encounter different channel conditions due to the difference of surrounding geographical environments or scenarios. HST channel models in the literature have either considered large-scale parameters only and/or neglected the non-stationarity of HST channels and/or only consider one of the HST scenarios. Therefore, we propose a novel generic non-stationary Geometry-Based Stochastic Model (GBSM) for wideband MIMO HST channels in different HST scenarios, i.e., open space, viaduct, and cutting. The corresponding simulation model is then developed with angular parameters calculated by the Modified Method of Equal Area (MMEA). The system functions and statistical properties of the proposed channel models are thoroughly studied. The proposed generic non-stationary HST channel models are verified by measurements in terms of stationary time for the open space scenario and the Autocorrelation Function (ACF), Level Crossing Rate (LCR), and stationary distance for the viaduct and cutting scenarios. Transmission techniques which are capable of utilising Three-Dimensional (3D) spatial dimensions are significant for the development of future communication systems. Consequently, 3D MIMO channel models are critical for the development and evaluation of these techniques. Therefore, we propose a novel 3D generic non-stationary GBSM for wideband MIMO HST channels in the most common HST scenarios. The corresponding simulation model is then developed with angular parameters calculated by the Method of Equal Volume (MEV). The proposed models considers several timevarying channel parameters, such as the angular parameters, the number of taps, the Ricean K-factor, and the actual distance between the Transmitter (Tx) and Receiver (Rx). Based on the proposed generic models, we investigate the impact of the elevation angle on some of the channel statistical properties. The proposed 3D generic models are verified using relevant measurement data. Most standard channel models in the literature, like Universal Mobile Telecommunications System (UMTS), COST 2100, and IMT-2000 failed to introduce any of the HST scenarios. Even for the standard channel models which introduced a HST scenario, like IMT-Advanced (IMT-A) and WINNER II channel models, they offer stationary intervals that are noticeably longer than those in measured HST channels. This has inspired us to propose a non-stationary IMT-A channel model with time-varying parameters including the number of clusters, powers, delays of the clusters, and angular parameters. Based on the proposed non-stationary IMT-A channel model, important statistical properties, i.e., the time-variant spatial Cross-correlation Function (CCF) and time-variant ACF, are derived and analysed. Simulation results demonstrate that the stationary interval of the developed non-stationary IMT-A channel model can match that of relevant HST measurement data. In summary, the proposed theoretical and simulation models are indispensable for the design, testing, and performance evaluation of 5G high-mobility wireless communication systems in general and HST ones in specific

Space-Time Trellis and Space-Time Block Coding Versus Adaptive Modulation and Coding Aided OFDM for Wideband Channels

Abstract—The achievable performance of channel coded spacetime trellis (STT) codes and space-time block (STB) codes transmitted over wideband channels is studied in the context of schemes having an effective throughput of 2 bits/symbol (BPS) and 3 BPS. At high implementational complexities, the best performance was typically provided by Alamouti’s unity-rate G2 code in both the 2-BPS and 3-BPS scenarios. However, if a low complexity implementation is sought, the 3-BPS 8PSK space-time trellis code outperfoms the G2 code. The G2 space-time block code is also combined with symbol-by-symbol adaptive orthogonal frequency division multiplex (AOFDM) modems and turbo convolutional channel codecs for enhancing the system’s performance. It was concluded that upon exploiting the diversity effect of the G2 space-time block code, the channel-induced fading effects are mitigated, and therefore, the benefits of adaptive modulation erode. In other words, once the time- and frequency-domain fades of the wideband channel have been counteracted by the diversity-aided G2 code, the benefits of adaptive modulation erode, and hence, it is sufficient to employ fixed-mode modems. Therefore, the low-complexity approach of mitigating the effects of fading can be viewed as employing a single-transmitter, single-receiver-based AOFDM modem. By contrast, it is sufficient to employ fixed-mode OFDM modems when the added complexity of a two-transmitter G2 scheme is affordable

Técnicas de pré-codificação para sistemas multicelulares coordenados

Doutoramento em TelecomunicaçõesCoordenação Multicélula é um tópico de investigação em rápido crescimento e uma solução promissora para controlar a interferência entre células em sistemas celulares, melhorando a equidade do sistema e aumentando a sua capacidade. Esta tecnologia já está em estudo no LTEAdvanced sob o conceito de coordenação multiponto (COMP). Existem várias abordagens sobre coordenação multicélula, dependendo da quantidade e do tipo de informação partilhada pelas estações base, através da rede de suporte (backhaul network), e do local onde essa informação é processada, i.e., numa unidade de processamento central ou de uma forma distribuída em cada estação base. Nesta tese, são propostas técnicas de pré-codificação e alocação de potência considerando várias estratégias: centralizada, todo o processamento é feito na unidade de processamento central; semidistribuída, neste caso apenas parte do processamento é executado na unidade de processamento central, nomeadamente a potência alocada a cada utilizador servido por cada estação base; e distribuída em que o processamento é feito localmente em cada estação base. Os esquemas propostos são projectados em duas fases: primeiro são propostas soluções de pré-codificação para mitigar ou eliminar a interferência entre células, de seguida o sistema é melhorado através do desenvolvimento de vários esquemas de alocação de potência. São propostas três esquemas de alocação de potência centralizada condicionada a cada estação base e com diferentes relações entre desempenho e complexidade. São também derivados esquemas de alocação distribuídos, assumindo que um sistema multicelular pode ser visto como a sobreposição de vários sistemas com uma única célula. Com base neste conceito foi definido uma taxa de erro média virtual para cada um desses sistemas de célula única que compõem o sistema multicelular, permitindo assim projectar esquemas de alocação de potência completamente distribuídos. Todos os esquemas propostos foram avaliados em cenários realistas, bastante próximos dos considerados no LTE. Os resultados mostram que os esquemas propostos são eficientes a remover a interferência entre células e que o desempenho das técnicas de alocação de potência propostas é claramente superior ao caso de não alocação de potência. O desempenho dos sistemas completamente distribuídos é inferior aos baseados num processamento centralizado, mas em contrapartida podem ser usados em sistemas em que a rede de suporte não permita a troca de grandes quantidades de informação.Multicell coordination is a promising solution for cellular wireless systems to mitigate inter-cell interference, improving system fairness and increasing capacity and thus is already under study in LTE-A under the coordinated multipoint (CoMP) concept. There are several coordinated transmission approaches depending on the amount of information shared by the transmitters through the backhaul network and where the processing takes place i.e. in a central processing unit or in a distributed way on each base station. In this thesis, we propose joint precoding and power allocation techniques considering different strategies: Full-centralized, where all the processing takes place at the central unit; Semi-distributed, in this case only some process related with power allocation is done at the central unit; and Fulldistributed, where all the processing is done locally at each base station. The methods are designed in two phases: first the inter-cell interference is removed by applying a set of centralized or distributed precoding vectors; then the system is further optimized by centralized or distributed power allocation schemes. Three centralized power allocation algorithms with per-BS power constraint and different complexity tradeoffs are proposed. Also distributed power allocation schemes are proposed by considering the multicell system as superposition of single cell systems, where we define the average virtual bit error rate (BER) of interference-free single cell system, allowing us to compute the power allocation coefficients in a distributed manner at each BS. All proposed schemes are evaluated in realistic scenarios considering LTE specifications. The numerical evaluations show that the proposed schemes are efficient in removing inter-cell interference and improve system performance comparing to equal power allocation. Furthermore, fulldistributed schemes can be used when the amounts of information to be exchanged over the backhaul is restricted, although system performance is slightly degraded from semi-distributed and full-centralized schemes, but the complexity is considerably lower. Besides that for high degrees of freedom distributed schemes show similar behaviour to centralized ones