The theory of bootstrapped algorithms and their applications to cross polarization interference cancelation

Dual-polarized transmission has become an important method for frequency re-use, particularly in satellite and microwave radio communication. Nevertheless, cross-polarization interference, which is inherent to this method, may cause degradation in system performance. Different canceler [sic] structures have been proposed to mitigate the effect of cross-polarization. Among these are the diagonalizer, the least mean square (LMS) canceler [sic] and the bootstrapped cancelers [sic]. Bootstrapped canceler [sic] schemes have been proposed and implemented in different applications, such as satellites, tactical communications, and quadrature amplitude madulation [sic] (QAM) dual polarized microwave radio. Nevertheless, no attempt was made in the past to quantify the probability of error of dual polarized transmission systems when such cancelers [sic] are used, nor were important issues such as stability and the dynamic behavior of algorithms controlling such cancelers [sic] studied. In this thesis, the error probability performance of dual polarized QAM transmission, for nondispersive fading channels and different configurations of bootstrapped cross-pol cancelers [sic], is derived and compared to the performance for other cancelers [sic]. Stability analyses of different canceler [sic] configurations are investigated, and an application of orthogonal perturbation sequences in controlling the bootstrapped cancelers [sic] is considered. It is shown that the error probability performance of the bootstrapped canceler [sic] is always better than that of other cancellers, such as the LMS canceler [sic]. It is also shown that, when the bootstrapped canceler [sic] is designed to meet certain conditions, it is asymptotically stable in converging to the calculated optimal points. Controlling the cancelers [sic] with adaptive algorithms using orthogonal dithering sequences is shown to be satisfactory; the canceler [sic] converges in the mean to the optimal condition. The results indicate that bootstrapped algorithms are faster than other algorithms. Considering the fact such cancelers [sic] do not require decision feedback for their operation, we can conclude that bootstrapped algorithms are not only advantageous for cross polarization cancelation [sic], but perhaps suitable for other adaptive signal processing applications, as well

MIMO Systems

In recent years, it was realized that the MIMO communication systems seems to be inevitable in accelerated evolution of high data rates applications due to their potential to dramatically increase the spectral efficiency and simultaneously sending individual information to the corresponding users in wireless systems. This book, intends to provide highlights of the current research topics in the field of MIMO system, to offer a snapshot of the recent advances and major issues faced today by the researchers in the MIMO related areas. The book is written by specialists working in universities and research centers all over the world to cover the fundamental principles and main advanced topics on high data rates wireless communications systems over MIMO channels. Moreover, the book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Polarization-dependent nonlinear effects in coherent detection systems

In the last decades the demand for data capacity has increased exponentially. Optical Coherent Detection, firstly proposed at the end of the 1980s to improve receiver sensitivity, has proved as one of the most powerful techniques to increase the optical communication spectral efficiency and so the total per channel capacity. Indeed, thanks to the recent advances in digital signal processing (DSP) and high speed electronics, the DSP-based coherent detection in optical networks expedited the use of polarization division multiplexing (PDM) as a cost-effective way of doubling system capacity. Furthermore, coherent detection presents many others advantages with respect to direct detection such as the use of multilevel optical modulation formats like N-PSK and N-QAM and compensating linear propagation effects in the electrical domain as chromatic dispersion, polarization mode dispersion (PMD) and optical filtering. On the other hand, transmission reach of WDM systems is a major concern for the deployment of such a solution and is usually mainly limited by cross-nonlinear effects. In WDM transmission systems, the cross-nonlinearities make neighboring channels interact depending on their power and state of polarization (SOP). The last is of particular concern in PDM systems since they are more sensitive to a new kind of distortion that has been generally referred to as cross-polarization modulation (XPolM) as a way to distinguish it from the well known cross-phase modulation (XPM). At the beginning of our research activity in 2009, despite the growing interest and the number of publications on XPolM, many of its features were still unknown. For example, in Sept. 2009 Winter et al. provided a model that successfully measured the degree of polarization degradation in presence of XPolM, but it was still not clear when the bit error rate (BER) is dominated by XPolM and how XPolM relates to the other relevant nonlinear effects, such as XPM and self-phase modulation (SPM). With the investigations presented in this thesis we want to fill the gap, by providing a systematic simulation study of system performance where each nonlinear effect acts individually. Furthermore, thanks to the possibility in Optilux software to take into account separately the nonlinear terms of the propagation equation, we add some new piece of knowledge about XPolM. We quantify the XPolM-induced penalty as a function of transmission parameters such as the channel power, spacing and state of polarization (SOP). We also clarify the role of the Viterbi and Viterbi-based carrier phase estimator in mitigation of XPM and XPolM. We focused our investigation mainly on PDM-quadrature phase shift keying (QPSK) modulation format. The thesis is organized as follows. In the first chapter the principal impairments for long haul transmissions are briefly recalled. They are divided into linear and nonlinear effects, according to whether they are independent of the signal power or not. The first group is composed of fiber attenuation, chromatic dispersion and polarization mode dispersion. The second group is composed of nonlinear polarization-independent effects: such as SPM and XPM. Other linear effects such as polarization dependent loss and nonlinear effects as intra channel cross phase modulation, four wave mixing, nonlinear phase noise and non elastic scattering effects (stimulated Raman and Brillouin scattering) are not included in our discussion, while the XPolM is discussed at length in Ch. 3. The second chapter discusses the joint use of PDM and the coherent detection, as a solution to increase the transmission capacity. We also discuss a new technique, namely mode division multiplexing (MDM), to further increase the transmission capacity thanks to the joint use with PDM and coherent detection. In Ch.3, after the definition of the XPolM term in the propagation equation, we show the polarization rotation and the PDM-QPSK constellation distortion induced by XPolM as a function of the rotation axis orientation. We perform such analysis both mathematically and by simulation. In Ch. 4 we show when the bit error rate (BER) of a PDM-QPSK channel is dominated by XPolM, through a massive use of simulation in a wide range of system setups. We analyze different pulse shapes, transmission links and transmission fibers in both hybrid (PDM-QPSK -- OOK) and homogeneous systems (PDM-QPSK). Furthermore we clarify the role of channel power, spacing, state of polarization (SOP) and Viterbi and Viterbi-based carrier phase estimator on the XPM- and XPolM-induced penalty. In the last part of the chapter we quantify the nonlinear penalty in a PDM-BPSK transmission system, showing the average performance and its fluctuation induced by the transmission sequences and SOPs. In Ch. 5 we compare different optical methods to improve the resilience of coherent 112-Gb/s PDM-QPSK WDM transmissions against cross-channel nonlinearities. Such methods consist of increasing the line group velocity dispersion (GVD), or the line PMD, or inserting in-line XPM suppressors, which are passive devices that introduce different delays on adjacent channels at specific points of the line. In Ch. 6 we summarize the experimental results obtained during the research activity at Alcatel-Lucent Bell-Labs France on MDM. In such an activity we employ a mode converter based on a liquid-crystal on silicon (LCOS) spatial modulator and a prototype few mode fiber (FMF). Last but not least, in the Appendix we discuss three different rules to correctly simulate the cross-nonlinearities, showing also some artifacts that can arise with a non-correct setting of some numerical parameters, such as the nonlinear step of Split-Step Fourier method, the sequence length and the sequence type

Transmission optique longue distance avec le format MB-OFDM cohérent à 100 Gbps

Today the 100 Gbps coherent dual polarization quadrature phase shift keying (Co-DP-QPSK) is standardized as the industrial solution for long-haul WDM transmission. Another alternative format to DP-QPSK that permits also to reach a data rate of 100 Gbps and beyond is the coherent orthogonal frequency division multiplexing (OFDM) format. However a doubt exists over the ability of OFDM to be as efficient as QPSK for long-haul WDM transmission due to its supposed higher sensitivity to nonlinear effects . In this thesis, we have investigated the potential of Co-DP-OFDM for 100 Gbps WDM transport. The digital signal processing algorithms are detailed as well as the various experimental set-ups required to carry out and validate the 100 Gbps transceiver. We also present the transmission results obtained with several configurations. In one of these configurations, the 100 Gbps Co-DP-OFDM channel is multiplexed with forty 100 Gbps DP-QPSK channels and all these channels are transmitted over 1000 km of DCF-free G.652 fiber, while in another configuration, the Co-DP-OFDM and Co-DP-QPSK channels are combined with seventy eight 10 Gbps NRZ-OOK channels and transmitted over 1000 km of dispersion managed G.652 fiber line. We have demonstrated that OFDM and QPSK have nearly the same performance after a transmission over 1000 km, and also we have demonstrated that the transmission of these two formats over legacy fiber infrastructure is possible under the condition of decreasing by 5 dB the 10 Gbps NRZ-OOK channel power with respect to the 100 Gbps channels. The results presented in this thesis are very valuable when considering the next generation of 400 Gbps or 1 Tbps for WDM systems.Aujourd'hui, le format « Quadrature Phase Shift Keying » avec multiplexage de polarisation (DP-QPSK) opérant à 100 Gbps est devenue un standard pour la transmission WDM longue distance. Une alternative au format DP-QPSK permettant d’atteindre des débits de 100 Gbps et plus (400 G & 1Tbps) est l’ « Orthogonal Frequency Division Multiplexing » (OFDM). Mais, des interrogations subsistent quant à sa robustesse aux effets non linéaires. Dans cette thèse nous avons étudié le potentiel de la technologie OFDM pour la transmission WDM longue distance à 100 Gbps. Le traitement du signal est détaillé ainsi que la mise en œuvre du transmetteur et récepteur OFDM cohérent. Nous présentons aussi les résultats expérimentaux de la transmission obtenus dans plusieurs configurations. Dans l’une de ces configurations, le canal modulé avec le format DP-OFDM coherent (Co-DP-OFDM) est multiplexé avec 40 canaux modulés en DP-QPSK à 100 Gbps. Les canaux ont ensuite été transmis sur 1000 km de fibre G.652 sans gestion de dispersion chromatique. Dans une autre configuration, les canaux Co-DP-OFDM et Co-DP-QPSK sont combinés avec 78 canaux 10 Gbps NRZ-OOK et transmis sur 1000 km de fibre G.652 avec gestion de dispersion. Nous avons montré que le Co-DP-OFDM et Co-DP-QPSK ont des performances similaires après une transmission de 1000 km sur une ligne sans gestion de dispersion, et nous avons aussi montré que la transmission de ces formats sur une infrastructure de fibre deployée est possible à condition de réduire de 5 dB la puissance des canaux 10 Gbps NRZ-OOK par rapport aux canaux à100 Gbps. Ces résultats sont précieux pour la prochaine génération de systèmes WDM à 400 Gbps ou 1 Tbps

1-D broadside-radiating leaky-wave antenna based on a numerically synthesized impedance surface

A newly-developed deterministic numerical technique for the automated design of metasurface antennas is applied here for the first time to the design of a 1-D printed Leaky-Wave Antenna (LWA) for broadside radiation. The surface impedance synthesis process does not require any a priori knowledge on the impedance pattern, and starts from a mask constraint on the desired far-field and practical bounds on the unit cell impedance values. The designed reactance surface for broadside radiation exhibits a non conventional patterning; this highlights the merit of using an automated design process for a design well known to be challenging for analytical methods. The antenna is physically implemented with an array of metal strips with varying gap widths and simulation results show very good agreement with the predicted performance