Wireless systems with multiple antennas at both the transmitter and receiver (MIMO systems) have been the focus of research in the recent past due to their ability to provide higher data rates and better reliability than their single antenna counterparts. Designing a communication system for MIMO frequency selective channels provides many signal processing challenges. Popular methods like MIMOOFDM and space-time precoding linearly process blocks of data at both the transmitter and the receiver. Independence between the blocks is ensured by introducing sufficient redundancy between successive blocks. This approach has many pitfalls, including the limit on achievable data rate due to redundancy requirements and the need for additional coding/processing. In this thesis, we provide a filterbank precoding framework (FBP) for communication over MIMO frequency selective channels. By viewing the channel as a polynomial matrix, we derive the minimum redundancy required for achieving FIR equalization of the precoded channel. It is shown that, for most practical channels, a nominal redundancy is enough. The results are general, and hold for channels of any dimension and order. We derive the zero-forcing and MMSE equalizers for the precoded channel. The role of equalizer delay in system performance is analyzed. We extend the minimum redundancy result to the case of space-time filterbank precoding (STFP). Introducing the time dimension allows the channel to be represented by a block pseudocirculant matrix. By using the Smith form of block pseudocirculant matrices, we show that very high data rates can be achieved with STFP. When channel information is available at the transmitter, we derive an iterative algorithm for obtaining the MMSE optimal precoder-equalizer pair. We then provide a comparison of FBP with the block processing methods. It is shown that FBP provides better BER performance than the block processing methods at a lower computational cost. The reasons for the better performance of FBP are discussed.

Actualment estem entrant a una nova era de la informació amb gran demanda de sistemes de comunicació sense fils. Nous serveis com dades i video requereixen transmissions fiables d'alta velocitat, fins i tot en escenaris d'alta mobilitat. A més a més, la dificultat d'assignar el limitat espectre radioelèctric juntament amb la necessitat d'incrementar el temps de vida de les bateries dels terminals mòbils, requereix el diseny de transceptors que usin la potència i l'ampla de banda disponibles de manera eficient. Les comunicacions multiportadora basades en OFDM són capaces de satisfer la majoria d'aquests requeriments. Però, entre altres reptes, reduir la sensibilitat a la amplificació no-lineal és un factor clau durant el diseny. En aquesta tesi doctoral s'analitza la sensibilitat dels sistemes multiportadora basats en OFDM a l'amplificació no-lineal i es consideren formes eficients per superar aquest problema. La tesi s'enfoca principalment al problema de reduir les fluctuacions de l'envolupant del senyal transmès. En aquest sentit es presenta també un estudi de les mètriques de l'envolupant del senyal, PAPR i CM. A més a més, basant-nos en l'anàlisis presentat es proposen noves tècniques per sistemes OFDM i MC-SS. Per MC-SS, també es tracta el diseny d'una tècnica de postprocessament en forma de detector multiusuari per canals no-lineals. / Actualmente estamos entrando en una nueva era de la información donde se da una gran demanda de sistemas de comunicación inalámbricos. Nuevos servicios como datos y vídeo requieren transmisiones fiables de alta velocidad, incluso en escenarios de alta movilidad. Además, la dificultad de asignar el limitado espectro radioeléctrico junto con la necesidad de incrementar el tiempo de vida de las baterías de los terminales móviles, requiere el diseño de transceptores que usen eficientemente la potencia y el ancho de banda disponibles. Las comunicaciones multiportadora basadas en OFDM son capaces de satisfacer la mayoría de dichos requerimientos. Sin embargo, entre otros retos, reducir su sensibilidad a la amplificación no-lineal es un factor clave durante el diseño. En esta tesis se analiza la sensibilidad de los sistemas multiportadora basados en OFDM a la amplificación no-lineal y se consideran formas eficientes para superar dicho problema. La tesis se enfoca principalmente al problema de reducir las fluctuaciones de la envolvente. En este sentido también se presenta un estudio de las métricas de la señal, PAPR y CM. Además, basándonos en el análisis presentado se proponen nuevas técnicas para OFDM y MC-SS. Para MC-SS, también se trata el diseño de un detector multiusuario para canales no-lineales. / We are now facing a new information age with high demand of wireless communication systems. New services such as data and video require achieving reliable high-speed transmissions even in high mobility scenarios. Moreover, the difficulty to allocate so many wireless communication systems in the limited frequency band in addition to the demand for long battery life requires designing spectrum and power efficient transceivers. Multicarrier communications based on OFDM are known to fulfill most of the requirements of such systems. However, among other challenges, reducing the sensitivity to nonlinear amplification has become a design key. In this thesis the sensitivity of OFDM-based multicarrier systems to nonlinear amplification is analyzed and efficient ways to overcome this problem are considered. The focus is mainly on the problem of reducing the envelope fluctuations. Therefore, a study of the signal metrics, namely PAPR and CM, is also presented. From the presented analysis, several new techniques for OFDM and MC-SS are proposed. For MC-SS, the design of a post-processing technique in the form of a multiuser detector for nonlinearly distorted MC-SS symbols is also addressed.

Many communications signal formats are not power efficient because of their large peak-to-average power ratios (PARs). Moreover, in the presence of nonlinear devices such as power amplifiers (PAs) or mixers, the non-constant-modulus signals may generate both in-band distortion and out-of-band interference. Backing off the signal to the linear region of the device further reduces the system power efficiency. To improve the power efficiency of the communication system, one can pursue two approaches: i) linearize the PA; ii) reduce the high PAR of the input signal. In this dissertation, we first explore the optimal nonlinearity under the peak power constraint. We show that the optimal nonlinearity is a soft limiter with a specific gain calculated based on the peak power limit, noise variance, and the probability density function of the input amplitude. The result is also extended to the fading channel case. Next, we focus on digital baseband predistortion linearization for power amplifiers with memory effects. We build a high-speed wireless test-bed and carry out digital baseband predistortion linearization experiments. To implement adaptive PA linearization in wireless handsets, we propose an adaptive digital predistortion linearization architecture that utilizes existing components of the wireless transceiver to fulfill the adaptive predistorter training functionality. We then investigate the topic of PAR reduction for OFDM signals and forward link CDMA signals. To reduce the PAR of the OFDM signal, we propose a dynamic selected mapping (DSLM) algorithm with a two-buffer structure to reduce the computational requirement of the SLM method without sacrificing the PAR reduction capability. To reduce the PAR of the forward link CDMA signal, we propose a new PAR reduction algorithm by introducing a relative offset between the in-phase branch and the quadrature branch of the transmission system.

Considering the communication systems with cyclic prefix (CP), such as orthogonal frequency-division multiplexing (OFDM) modulation and single-carrier cyclic prefixed (SCCP) modulation, when the length of CP is longer than the channel length, the use of cyclic prefix (CP) does not only eliminate the inter-block interference, but also convert linear convolution of the transmitted signal with the channel into circular convolution. Unfortunately, the use of CP significantly decreases the bandwidth utilization. Therefore, to reduce the length of CP is a critical issue. The thesis investigates that how to design a channel-shortening equalizer (CSE) at receiver which forces the length of the effective channel response as short as the CP length. The thesis describes the signal model as a matrix form. The effect channel response after CSE is investigated and then the coefficient of channel shortening filter is obtained using singular value decomposition method under various criterions. We further propose a novel CSE maximizing the shortening signal-to-interference ratio. In addition, it is demonstrated that the proposed CSE has the same performance as the conventional scheme but a lower computation complexity.

Multi-carrier systems based on orthogonal frequency division multiplexing (OFDM) are efficient technologies for the implementation of broadband wireless communication systems. OFDM is widely used and has been adopted for current mobile broadband wireless communication systems such as IEEE 802.a/g wireless LANs, WiMAX, 3GPP LTE, and DVB-T/H digital video broadcasting systems. Despite their many advantages, however, OFDM-based systems suffer from potentially high peak-to-average power ratio (PAR). Since communication systems typically include nonlinear devices such as RF power amplifiers (PA) and digital-to-analog converters (DAC), high PAR results in increased symbol error rates and spectral radiation. To mitigate these nonlinear effects and to avoid nonlinear saturation effects of the PA, the operating point of a signal with high peak power must be backed off into the linear region of the PA. This so-called output backoff (OBO) results in a reduced power conversion efficiency which limits the battery life for mobile applications, reduces the coverage range, and increases both the cost of the PA and power consumption in the cellular base station. With the increasing demand for high energy efficiency, low power consumption, and greenhouse gas emission reduction, PAR reduction is a key technique in the design of practical OFDM systems. Motivated by the PAR reduction problem associated with multi-carrier systems, such as OFDM, this research explores the state of the art of PAR reduction techniques and develops new signal processing techniques that can achieve a minimum PAR for given system parameters and that are compatible with the appropriate standards. The following are the three principal contributions of this dissertation research. First, we present and derive the semi-analytical results for the output of asymptotic iterative clipping and filtering. This work provides expressions and analytical techniques for estimating the attenuation factor, error vector magnitude, and bit-error-rate (BER), using a noise enhancement factor that is obtained by simulation. With these semi-analytical results, we obtain a relationship between the BER and the target clipping level for asymptotic iterative clipping and filtering. These results serve as a performance benchmark for designing PAR reduction techniques using iterative clipping and filtering in OFDM systems. Second, we analyze the impact of the selected mapping (SLM) technique on BER performance of OFDM systems in an additive white Gaussian noise channel in the presence of nonlinearity. We first derive a closed-form expression for the envelope power distribution in an OFDM system with SLM. Then, using this derived envelope power distribution, we investigate the BER performance and the total degradation (TD) of OFDM systems with SLM under the existence of nonlinearity. As a result, we obtain the TD-minimizing peak backoff (PBO) and clipping ratio as functions of the number of candidate signals in SLM. Third, we propose an adaptive clipping control algorithm and pilotaided algorithm to address a fundamental issue associated with two lowcomplexity PAR reduction techniques, namely, tone reservation (TR) and active constellation extension (ACE). Specifically, we discovered that the existing low-complexity algorithms have a low clipping ratio problem in that they can not achieve the minimum PAR when the target clipping level is set below the initially unknown optimum value. Using our proposed algorithms, we overcome this problem and demonstrate that additional PAR reduction is obtained for any low value of the initial target clipping ratio. / text

Wireless communication systems require advanced techniques at the transmitter and at the receiver that improve the performance in hostile radio environments. The received signal is significantly distorted due to the dynamic nature of the wireless channel caused by multipath fading and Doppler spread. In order to mitigate the negative impact of the channel to the received signal quality, techniques as equalization and diversity are usually employed in the system design. During the transmission, the phenomenon of inter-symbol interference (ISI) occurs at the receiver due to the time dispersion of the involved channels. Hence, several delayed replicas of previous symbols interfere with the current symbol. Equalization is usually employed in order to combat the effect of the ISI. Several implementations for equalization filters have been proposed, including linear and non-linear processing, providing complexity-performance trade-offs. It is known that the length of the equalization filter determines the complexity of the technique. Since the wireless channels are characterized by long and sparse impulse responses, the conventional equalizers require high computational complexity due to the large size of their filters. In this dissertation, we have further investigated the long standing problem of equalization in light of the recently derived theory of compressed sampling (CS) for sparse and redundant representations. The developed heuristic algorithms for equalization, can exploit either the sparsity of the channel impulse response (CIR), or the sparsity of the equalizer filters, in order to derive efficient implementation designs. To this end, building on basis pursuit and matching pursuit techniques new equalization schemes have been proposed that exhibit considerable computational savings, increased performance properties and short training sequence requirements. Our main contribution for this part is the Stochastic Gradient Pursuit algorithm for sparse adaptive equalization. An alternative approach to combat ISI is based on the orthogonal frequency division multiplexing (OFDM) system. In this system, the entire channel is divided into many narrow subchannels, so as the transmitted signals to be orthogonal to each other, despite their spectral overlap. However, in the case of doubly selective channels, the Doppler effect destroys the orthogonality between subcarriers. Thus, similarly to ISI, the effect of intercarrier interference (ICI) is introduced at the receiver, where symbols which belong to other subcarriers interfere with the current one. Considering this problem, we have developed iterative algorithms which recursively cancels the ICI at the receiver, providing performance-complexity trade-offs. For low or medium Doppler spreads, the typical approach is to approximate the frequency-domain channel matrix with a banded one. On this premise, we derived reduced-rank preconditioned conjugate gradient (PCG) algorithms in order to estimate the equalization matrix with a reduced number of iterations. Also developed an improved PCG algorithm with the same complexity order, using the Galerkin projections theory. However, in rapidly changing environments, a severe ICI is introduced and the banded approximation results in significant performance degradation. In order to recover this performance loss, we developed regularized estimation framework for ICI equalization, with linear complexity with respect the the number of the subcarriers. Moreover, we proposed a new equalization technique which has the potential to completely cancel the ICI. This approach works in a successive manner through a number of stages, conveying from the fully-connected ordered successive interference cancellation architecture (OSIC) in order to fully suppress the residual interference at each stage of the equalizer. On the other hand, diversity can improve the performance of the communication system by sending the information symbols through multiple signal paths, each of which fades independently. One approach to obtain diversity is through cooperative transmission, considering a group of nearby terminals (relays) as forming one virtual antenna array and applying a spatial beamforming technique so as to optimize the communication via them. Such beamforming techniques differ from their classical counterparts where the array elements are located in a common processing unit, due to the distribution of the relays in the space. In this setting, we developed new distributed algorithms which enable the relay cooperation for the computation of the beamforming weights leveraging the computational abilities of the relays. Each relay can estimate only the corresponding entry of the principal eigenvector, combining data from its network neighbours. The proposed algorithms are applied to two distributed beamforming schemes for relay networks. In the first scheme, the beamforming vector is computed through minimization of a total transmit power subject to the receiver quality-of-service (QoS) constraint. In the second scheme, the beamforming weights are obtained through maximization of the receiver SNR subject to a total transmit power constraint. Moreover, the proposed algorithms operate blindly, implying that no training data are required to be transmitted to the relays, and adaptively, exhibiting a quite short convergence period. / Τα συστήματα ασύρματων επικοινωνιών απαιτούν εξειδικευμένες τεχνικές στον πομπό και στον δέκτη, οι οποίες να βελτιώνουν την απόδοση του συστήματος σε εχθρικά περιβάλλοντα ασύρματης μετάδοσης. Λόγω της δυναμικής φύσης του ασύρματου καναλιού, που περιγράφεται από τα φαινόμενα της απόσβεσης, της πολυδιόδευσης και του Doppler, το λαμβανόμενο σήμα είναι παραμορφωμένο σε σημαντικό βαθμό. Για να αναιρέσουμε αυτήν την αρνητική επίδραση του καναλιού στην ποιότητα του λαμβανόμενου σήματος, κατά τον σχεδιασμό του συστήματος συνήθως υιοθετούνται τεχνικές όπως η ισοστάθμιση και η ποικιλομορφία. Ένα φαινόμενο που προκύπτει στο δέκτη ενός ασύρματου συστήματος επικοινωνίας, λόγω της χρονικής διασποράς που παρουσιάζουν τα κανάλια, είναι η διασυμβολική παρεμβολή, όπου χρονικά καθυστερημένα αντίγραφα προηγούμενων συμβόλων παρεμβάλουν με το τρέχων σύμβολο. Ένας τρόπος για την αντιμετώπιση του φαινομένου αυτού, είναι μέσω της ισοστάθμισης στο δέκτη, όπου χρησιμοποιώντας γραμμικές και μη-γραμμικές τεχνικές επεξεργασίας, τα μεταδιδόμενα σύμβολα ανιχνεύονται από το ληφθέν σήμα. Ωστόσο, συνήθως τα ασύρματα κανάλια χαρακτηρίζονται από κρουστικές αποκρούσεις μεγάλου μήκους αλλά λίγων μη μηδενικών συντελεστών, και σε αυτήν την περίπτωση η υπολογιστική πολυπλοκότητα των συνήθων τεχνικών είναι πολύ υψηλή. Στα πλαίσια αυτής της διατριβής, αναπτύχθηκαν νέοι ευριστικοί αλγόριθμοι για το πρόβλημα της ισοστάθμισης, οι οποίοι εκμεταλλεύονται είτε την αραιότητα της κρουστικής απόκρισης είναι την αραιότητα του αντιστρόφου φίλτρου, προκειμένου να παραχθούν αποδοτικές υλοποιήσεις. Θεωρώντας τον μη γραμμικό ισοσταθμιστή ανατροφοδότησης-απόφασης, έχει δειχθεί ότι κάτω από συνήθεις υποθέσεις για τους συντελεστές της κρουστικής απόκρισης του καναλιού, το εμπρόσθιο φίλτρο και το φίλτρο ανατροφοδότησης μπορούν να αναπαρασταθούν από αραιά διανύσματα. Για τον σκοπό αυτό, τεχνικές Συμπιεσμένης Καταγραφής, οι οποίες έχουν χρησιμοποιηθεί κατα κόρον σε προβλήματα ταυτοποίησης συστήματος, μπορούν να βελτιώσουν σε μεγάλο βαθμό την απόδοση κλασσικών ισοσταθμιστών που δεν λαμβάνουν υπόψιν τους την αραιότητα των διανυσμάτων. Έχοντας ως βάση τις τεχνικές basis pursuit και matching pursuit, αναπτύχθηκαν νέα σχήματα ισοσταθμιστών τα οποία παρουσιάζουν αξιοσημείωτη μείωση στο υπολογιστικό κόστος. Επίσης, αντίθετα με τη συνήθη πρακτική ταυτοποίησης συστήματος, αναπτύχθηκε νέος ευριστικό αλγόριθμος για το πρόβλημα αραιής προσαρμοστικής ισοστάθμισης, με την ονομασία Stochastic Gradient Pursuit. Επιπλέον, ο αλγόριθμος αυτός επεκτάθηκε και για την περίπτωση όπου ο αριθμός των μη μηδενικών στοιχείων του ισοσταθμιστή είναι άγνωστος. Μία διαφορετική προσέγγιση για την αντιμετώπιση του φαινομένου της διασυμβολικής παρεμβολής είναι μέσω του συστήματος orthogonal frequency-division multiplexing (OFDM), όπου το συνολικό κανάλι χωρίζεται σε πολλά στενά υπο-κανάλια, με τέτοιον τρόπο ώστε τα μεταδιδόμενα σήματα να είναι ορθογώνια μεταξύ τους, παρότι παρουσιάζουν φασματική επικάλυψη. Ωστόσο, σε χρονικά και συχνοτικά επιλεκτικά κανάλια, το φαινόμενο Doppler καταστρέφει την ορθογωνιότητα των υπο-καναλιών. Σε αυτήν την περίπτωση, παρόμοια με το φαινόμενο της διασυμβολικής παρεμβολής, εμφανίζεται το φαινόμενο της διακαναλικής παρεμβολής, όπου τα σύμβολα που ανήκουν σε διαφορετικά υπο-κανάλια παρεμβάλουν στο τρέχον. Θεωρώντας αυτό το πρόβλημα, αναπτύχθηκαν νέα σχήματα ισοστάθμισης που ακυρώνουν διαδοχικά την παρεμβολή αυτή, παρέχοντας έναν συμβιβασμό μεταξύ της απόδοσης και της πολυπλοκότητας. Στις περιπτώσεις όπου το φαινόμενο Doppler δεν είναι τόσο ισχυρό, η συνήθης τακτική είναι η προσέγγιση του πίνακα του καναλιού με έναν πίνακα ζώνης. Με αυτό το σκεπτικό, αναπτύχθηκαν αλγόριθμοι μειωμένης τάξης που βασίζονται στην επαναληπτική μέθοδο preconditioned conjugate gradient (PCG), προκειμένου να εκτιμήσουμε τον πίνακα ισοστάθμισης με έναν μειωμένο αριθμό επαναλήψεων. Επίσης, αναπτύχθηκαν τεχνικές που βασίζονται σε προβολές Galerkin για την βελτίωση της απόδοσης των συστημάτων χωρίς να αυξάνουν σημαντικά την πολυπλοκότητα. Ωστόσο, για τις περιπτώσεις όπου το φαινόμενο Doppler έχει ισχυρή επίδραση στο δέκτη του τηλεπικοινωνιακού συστήματος, όπως στις περιπτώσεις πολύ δυναμικών καναλιών, τότε η προσέγγιση με τον πίνακα ζώνης μειώνει σημαντικά την απόδοση του συστήματος. Με στόχο να ανακτήσουμε την απώλεια αυτή, αναπτύχθηκαν τεχνικές κανονικοποιημένης εκτίμησης, με γραμμική πολυπλοκότητα σε σχέση με τον αριθμό των υπο-καναλιών. Επιπρόσθετα, αναπτύχθηκε ένα νέο σχήμα ισοστάθμισης που έχει την δυνατότητα να ακυρώσει πλήρως την διακαναλική παρεμβολή. Το συγκεκριμένο σχήμα λειτουργεί βασιζόμενο σε έναν αριθμό διαδοχικών σταδίων, ακολουθώντας την φιλοσοφία της αρχιτεκτονικής fully-connected ordered successive interference cancellation (OSIC), με στόχο να μειώσει την εναπομείναντα παρεμβολή σε κάθε στάδιο του ισοσταθμιστή Η απόδοση ενός τηλεπικοινωνιακού συστήματος μπορεί επίσης να βελτιωθεί με την χρήση τεχνικών ποικιλομορφίας, δηλαδή με την μετάδοση των συμβόλων μέσω πολλών ανεξάρτητων μονοπατιών. Μία τεχνική ποικιλομορφίας είναι η συνεργατική μετάδοση, όπου μία ομάδα κοντινών τερματικών (relays) σχηματίζουν μία εικονική συστοιχία κεραιών και τεχνικές διαμόρφωσης λοβού μετάδοσης χρησιμοποιούνται προκειμένου να βελτιστοποιηθεί η επικοινωνία μέσω των τερματικών. Οι συγκεκριμένες τεχνικές διαμόρφωσης λοβού μετάδοσης, διαφέρουν από τις κλασσικές όπου η συστοιχία κεραιών βρίσκεται τοποθετημένη σε έναν κόμβο, καθώς τα τερματικά κατανέμονται στον χώρο. Υπό αυτές τις συνθήκες, αναπτύχθηκαν κατανεμημένοι αλγόριθμοι οι οποίοι εκμεταλλεύονται την επικοινωνία και τις υπολογιστικές δυνατότητες των τερματικών για τον υπολογισμό των συνιστωσών του διανύσματος διαμόρφωσης λοβού μετάδοσης. Κάθε τερματικό εκτιμά μόνο την αντίστοιχη συνιστώσα από το κύριο ιδιοδιάνυσμα, συνδιάζοντας δεδομένα από τα γειτονικά τερματικά. Οι προτεινόμενοι αλγόριθμοι εφαρμόστηκαν σε δύο σχήματα κατανεμημένης μετάδοσης μέσω ενδιάμεσων κόμβων. Στο πρώτο σχήμα, τα βάρη του διανύσματος διαμόρφωσης λοβού μετάδοσης υπολογίστηκαν με βάση την ελαχιστοποίηση της συνολικής ισχύος μετάδοσης υπό τον περιορισμό συγκεκριμένου κατωφλίου για την ποιότητα του λαμβανόμενου σήματος. Στο δεύτερο σχήμα, υπολογίστηκαν μεγιστοποιώντας την ποιότητα του λαμβανόμενου σήματος υπό τον περιορισμό ενός κατωφλίου για την συνολική ισχύ μετάδοσης. Επιπλέον, οι αλγόριθμοι που αναπτύχθηκαν λειτουργούν τυφλά, δηλαδή χωρίς φάση εκπαίδευσης, και προσαρμοστικά με μικρό διάστημα σύγκλισης.

In this effort, we consider the performance of a dedicated short range communication (DSRC) system for inter-vehicle communications (IVC). The DSRC standard employs convolutional codes for forward error correction (FEC). The performance of the DSRC system is evaluated in three different channels with convolutional codes, regular low density parity check (LDPC) codes and quasi-cyclic (QC) LDPC codes. In addition, we compare the complexity of these codes. It is shown that LDPC and QC-LDPC codes provide a significant improvement in performance compared to convolutional codes. / Graduate

The central objective of this thesis is to suggest and develop one simple, unified method for communication over optical fiber networks, valid for all values of dispersion and nonlinearity parameters, and for a single-user channel or a multiple-user network. The method is based on the nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees of freedom in such models, in much the same way that the Fourier transform does for linear systems. In this thesis, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger (NLS) equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear spectrum of the signal. Just as the (ordinary) Fourier transform converts a linear convolutional channel into a number of parallel scalar channels, the nonlinear Fourier transform converts a nonlinear dispersive channel described by a \emph{Lax convolution} into a number of parallel scalar channels. Since, in the spectral coordinates the NLS equation is multiplicative, users of a network can operate in independent nonlinear frequency bands with no deterministic inter-channel interference. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This thesis lays the foundations of such a nonlinear frequency-division multiplexing system.

The central objective of this thesis is to suggest and develop one simple, unified method for communication over optical fiber networks, valid for all values of dispersion and nonlinearity parameters, and for a single-user channel or a multiple-user network. The method is based on the nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees of freedom in such models, in much the same way that the Fourier transform does for linear systems. In this thesis, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger (NLS) equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear spectrum of the signal. Just as the (ordinary) Fourier transform converts a linear convolutional channel into a number of parallel scalar channels, the nonlinear Fourier transform converts a nonlinear dispersive channel described by a \emph{Lax convolution} into a number of parallel scalar channels. Since, in the spectral coordinates the NLS equation is multiplicative, users of a network can operate in independent nonlinear frequency bands with no deterministic inter-channel interference. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This thesis lays the foundations of such a nonlinear frequency-division multiplexing system.

This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.