It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. It has been shown that coding across both spatial and temporal domains together, called Space-Time Coding (STC), achieves, a diversity order equal to the product of the number of transmit and receive antennas. Space-Time Block Codes (STBC) achieving the maximum diversity is called full-diversity STBCs. An STBC is called information-lossless, if the structure of it is such that the maximum mutual information of the resulting equivalent channel is equal to the capacity of the channel. This thesis deals with high-rate and information-lossless STBCs obtained from certain matrix algebras called Crossed-Product Algebras. First we give constructions of high-rate STBCs using both commutative and non-commutative matrix algebras obtained from appropriate representations of extensions of the field of rational numbers. In the case of commutative algebras, we restrict ourselves to fields and call the STBCs obtained from them as STBCs from field extensions. In the case of non-commutative algebras, we consider only the class of crossed-product algebras. For the case of field extensions, we first construct high-rate; full-diversity STBCs for arbitrary number of transmit antennas, over arbitrary apriori specified signal sets. Then we obtain a closed form expression for the coding gain of these STBCs and give a tight lower bound on the coding gain of some of these STBCs. This lower bound in certain cases indicates that some of the STBCs from field extensions are optimal m the sense of coding gain. We then show that the STBCs from field extensions are information-lossy. However, we also show that the finite-signal-set capacity of the STBCs from field extensions can be improved by increasing the symbol rate of the STBCs. The simulation results presented show that our high-rate STBCs perform better than the rate-1 STBCs in terms of the bit error rate performance. Then we proceed to present a construction of high-rate STBCs from crossed-product algebras. After giving a sufficient condition on the crossed-product algebras under which the resulting STBCs are information-lossless, we identify few classes of crossed-product algebras that satisfy this sufficient condition and also some classes of crossed-product algebras which are division algebras which lead to full-diversity STBCs. We present simulation results to show that the STBCs from crossed-product algebras perform better than the well-known codes m terms of the bit error rate. Finally, we introduce the notion of asymptotic-information-lossless (AILL) designs and give a necessary and sufficient condition under which a linear design is an AILL design. Analogous to the condition that a design has to be a full-rank design to achieve the point corresponding to the maximum diversity of the optimal diversity-multiplexing tradeoff, we show that a design has to be AILL to achieve the point corresponding to the maximum multiplexing gain of the optimal diversity-multiplexing tradeoff. Using the notion of AILL designs, we give a lower bound on the diversity-multiplexing tradeoff achieved by the STBCs from both field extensions and division algebras. The lower bound for STBCs obtained from division algebras indicates that they achieve the two extreme points, 1 e, zero multiplexing gain and zero diversity gain, of the optimal diversity-multiplexing tradeoff. Also, we show by simulation results that STBCs from division algebras achieves all the points on the optimal diversity-multiplexing tradeoff for n transmit and n receive antennas, where n = 2, 3, 4.

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Au cours de la dernière décennie, les communications optiques en espace libre (FSO) ont pris de l’ampleur dans les deux domaines académiques et industriels. L’importance de FSO s’appuie sur la possibilité de faire un système de transmission économique et écologique avec un débit élevé et sans licence à l’opposition des systèmes de transmission radiofréquences (RF). Dans la plupart des travaux antécédents sur les systèmes multi-émetteurs, seulement les canaux décorrélés ont été considérés. Un canal décorrélé nécessite un espace suffisant entre les émetteurs. Cette condition devient difficile et non-réalisable dans certaines applications. Pour cette raison, nos études se focalisent sur les performances des codes à répétition RC (Repitition Codes) et les codes OSTBC (Orthogonal Space-Time Block Codes) dans des canaux log-normaux corrélés en utilisant une modulation d’intensité et une détection directe (IM/DD). En addition, les effets des différentes conditions météorologiques sur le taux d’erreur moyen (ABER) sont étudiés. Les systèmes FSO à multi-entrées/ multi-sorties MIMO (Multiple-Input Multiple-Output) avec une modulation SSK (Space Shift Keying) ont été abordés. Les résultats obtenus montrent que la SSK est supérieure aux RC avec une modulation d’impulsion (Multiple Pulse Amplitude Modulation) pour toute efficacité spectrale égale ou supérieure à 4 bit/s/Hz. Nous avons aussi analysé les performances d’un système à sauts multiples (Multi-Hop) et des relais à transmission directe (forward relays). Nos simulations montrent que le système ainsi considéré est efficace pour atténuer les effets météorologiques et les pertes géométriques dans les systèmes de communication FSO. Nous avons montré qu’un tel système avec plusieurs entrées et une sortie (MISO, i.e. multiple-input single-output) à sauts multiples est supérieur à un système MISO avec un lien direct (direct link) avec une forte atténuation. Pour satisfaire la demande croissante des réseaux de communication à débits élevés, la communauté scientifique s'intéresse de plus en plus aux systèmes FSO avec des relais full-duplex (FD). Pour ces derniers systèmes, nous avons étudié la probabilité d'erreur moyenne (ABER) et nous avons analysé leurs performances. En considérant des différentes conditions de transmission, les performances de relais FD ont été comparées à celles d'un système avec un lien direct ou des relais half-duplex. Les résultats obtenus montrent que les relais FD ont le minimum ABER. En conséquence, les résultats obtenus dans cette thèse sont très prometteurs pour la prochaine génération de FSO. / Free-space optical (FSO) communication has been the subject of ongoing research activities and commercial attention in the past few years. Such attention is driven by the promise of high data rate, license-free operation, and cheap and ecological friendly means of communications alternative to congested radio frequency communications. In most previous work considering multiple transmitters, uncorrelated channel conditions have been considered. An uncorrelated channel requires sufficient spacing between transmitters. However, this can be difficult and may not be always feasible in some applications. Thereby, this thesis studies repetition codes (RCs) and orthogonal space-time block codes performance in correlated log-normal FSO channels using intensity modulation and direct detection (IM/DD). Furthermore, the effect of different weather conditions on the average bit error rate (ABER) performance of the FSO links is studied. Multiple-input multiple-output (MIMO) FSO communication systems using space shift keying (SSK) modulation have been also analyzed. Obtained results show that SSK is a potential technique for spectral efficiencies equal or greater than 4 bits/s/Hz as compared to RCs with multiple pulse amplitude modulations. The performance analysis of a multi-hop decode and forward relays for FSO communication system using IM/DD is also considered in this thesis. It is shown that multi-hop is an efficient technique to mitigate atmospheric turbulence and different weather attenuation effects and geometric losses in FSO communication systems. Our simulation results show that multiple-input single-output (MISO) multi-hop FSO systems are superior to direct link and MISO systems over links exhibiting high attenuation. Meeting the growing demand for higher data rates communication networks, a system with full-duplex (FD) relays is considered. For such a system, the outage probability and the ABER performance are analyzed under different turbulence conditions, misalignment error and path loss effects. FD relays are compared with the direct link and half-duplex relays. Obtained results show that FD relays have the lowest ABER and the outage probability as compared to the two other systems. Finally, the obtained results in this thesis are very promising towards the next generation of FSO systems.

Employing an error control code is one of the techniques to reduce the Peak-to-Average Power Ratio (PAPR) in an Orthogonal Frequency Division Multiplexing system; a well known class of such codes being the cosets of Reed-Muller codes. In this thesis, classes of such coset-codes of arbitrary linear codes are considered. It has been proved that the size of such a code can be doubled with marginal/no increase in the PAPR. Conditions for employing this method iteratively have been enunciated. In fact this method has enabled to get the optimal coset-codes. The PAPR of the coset-codes of the extended codes is obtained from the PAPR of the corresponding coset-codes of the parent code. Utility of a special type of lengthening is established in PAPR studies

Communication over a wireless channel is a challenging task because of the inherent fading effects. Any wireless communication system employs some form of diversity improving techniques in order to improve the reliability of the channel. This thesis deals with efficient code design for two different spatial diversity techniques, viz, diversity by employing multiple antennas at the transmitter and/or the receiver, and diversity through cooperative commu- nication between users. In other words, this thesis deals with efficient code design for (1) multiple-input multiple-output (MIMO) channels, and (2) wireless relay channels. Codes for the MIMO channel are termed space-time (ST) codes and those for the relay channels are called distributed ST codes. The first part of the thesis focuses on ST code construction for MIMO fading channel with perfect channel state information (CSI) at the receiver, and no CSI at the transmitter. As a measure of performance we use the rate-diversity tradeoff and the Diversity-Multiplexing Gain (D-MG) Tradeoff, which are two different tradeoffs characterizing the tradeoff between the rate and the reliability achievable by any ST code. We provide two types of code constructions that are optimal with respect to the rate-diversity tradeoff; one is based on the rank-distance codes which are traditionally applied as codes for storage devices, and the second construction is based on a matrix representation of a cayley algebra. The second contribution in ST code constructions is related to codes with a certain nonvanishing determinant (NVD) property. Motivation for these constructions is a recent result on the necessary and sufficient conditions for an ST code to achieve the D-MG tradeoff. Explicit code constructions satisfying these conditions are provided for certain number of transmit antennas. The second part of the thesis focuses on distributed ST code construction for wireless relay channel. The transmission protocol follows a two-hop model wherein the source broadcasts a vector in the first hop and in the second hop the relays transmit a vector that is a transformation of the received vector by a relay-specific unitary transformation. While the source and relays do not have CSI, at the destination we assume two different scenarios (a) destina- tion with complete CSI (b) destination with only the relay-destination CSI. For both these scenarios, we derive a Chernoff bound on the pair-wise error probability and propose code design criteria. For the first case, we provide explicit construction of distributed ST codes with lower decoding complexity compared to codes based on some earlier system models. For the latter case, we propose a novel differential encoding and differential decoding technique and also provide explicit code constructions. At the heart of all these constructions is the cyclic division algebra (CDA) and its matrix representations. We translate the problem of code construction in each of the above scenarios to the problem of constructing CDAs satisfying certain properties. Explicit examples are provided to illustrate each of these constructions.

In this thesis, we focus on interference cancelling (IC) detectors for advanced communication systems. The contents of this thesis is divided into the following four parts: 1. Multiuser interference (MUI) cancellation in uplink orthogonal frequency division multiple access (OFDMA). 2. Inter-carrier interference (ICI) and inter-symbol interference (ISI) cancellation in space-frequency block coded OFDM (SFBC-OFDM). 3. Single-symbol decodability (SSD) of distributed space-time block codes (DSTBC) in partially-coherent cooperative networks with amplify-and-forward protocol at the relays 4. Interference cancellation in cooperative SFBC-OFDM networks with amplify-and-forward (AF) and decode-and-forward (DF) protocols at the relays. In uplink OFDMA systems, MUI occurs due to different carrier frequency offsets of different users at the receiver. In the first part of the thesis, we present a weighted multistage linear parallel interference cancellation approach to mitigate the effect of this MUI in uplink OFDMA. We also present a minimum mean square error (MMSE) based approach to MUI cancellation in uplink OFDMA. We present a recursion to approach the MMSE solution and show structure-wise and performance-wise comparison with other detectors in the literature. Use of SFBC-OFDM signals is advantageous in high-mobility broadband wireless access, where the channel is highly time- as well as frequency-selective because of which the receiver experiences both ISI as well as ICI. In the second part of the thesis, we are concerned with the detection of SFBC-OFDM signals on time- and frequency-selective MIMO channels. Specifically, we propose and evaluate the performance of an interference cancelling receiver for SFBC-OFDM, which alleviates the effects of ISI and ICI in highly time- and frequency-selective channels The benefits of MIMO techniques can be made possible to user nodes having a single transmit antenna through cooperation among different nodes. In the third part of the thesis, we derive a new set of conditions for a distributed DSTBC to be SSD for a partially-coherent relay channel (PCRC), where the relays have only the phase information of the source-to-relay channels. We also establish several properties of SSD codes for PCRC. In the last part of the thesis, we consider cooperative SFBC-OFDM networks with AF and DF protocols at the relays. In cooperative SFBC-OFDM networks that employ DF protocol, i) ISI occurs at the destination due to violation of the `quasi-static' assumption because of the frequency selectivity of the relay-to-destination channels, and ii) ICI occurs due to imperfect carrier synchronization between the relay nodes and the destination, both of which result in error-floors in the bit error performance at the destination. We propose an interference cancellation algorithm for this system at the destination node, and show that the proposed algorithm effectively mitigates the ISI and ICI effects.

Στο πλαίσιο αυτής της διατριβής μελετάται η επίδοση συστημάτων διαφορισμού MIMO σε γενικευμένα κανάλια διαλείψεων. Αρχικά, εξετάζεται η επίδοση των OSTBC σε περιβάλλοντα διαλείψεων Hoyt. Αποδεικνύεται ότι, στην περίπτωση τέτοιων συστημάτων, ο σηματοθορυβικός λόγος (signal to noise ratio, SNR) εκφράζεται ως μία τετραγωνική μορφή κανονικών τυχαίων μεταβλητών και γίνεται χρήση της συνάρτησης πυκνότητας πιθανότητας και της αθροιστικής συνάρτησης κατανομής αυτής της μορφής για τον υπολογισμό των μετρικών επίδοσης. Επιπλέον, μελετάται η σύγκλιση των σειρών που χρησιμοποιούνται για τον υπολογισμό των δύο αυτών συναρτήσεων και κατασκευάζονται νέα άνω φράγματα για το σφάλμα αποκοπής των σειρών. Τα φράγματα αυτά είναι σαφώς πιο αυστηρά από τα ήδη γνωστά από τη βιβλιογραφία. Στη συνέχεια, εισάγεται ένα γενικευμένο μοντέλο διαλείψεων για την ανάλυση επίδοσης των OSTBC και των δεκτών MRC και υπολογίζονται όλες οι μετρικές επίδοσης των δύο συστημάτων για το συγκεκριμένο μοντέλο διαλείψεων. Το μοντέλο αυτό περιλαμβάνει ως ειδικές περιπτώσεις τα πλέον διαδεδομένα μοντέλα καναλιών διαλείψεων, ενώ επιπλέον, επιτρέπει την ανάλυση επίδοσης σε μικτά περιβάλλοντα διαλείψεων όπου τα πολλαπλά κανάλια μπορούν να ακολουθούν διαφορετικές κατανομές. Στη συνέχεια, μελετάται η επίδοση συστημάτων συνεργατικού διαφορισμού με χρήση αναμεταδοτών ανίχνευσης και προώθησης (Detect and Forward, DaF) σε περιβάλλοντα διαλείψεων Rayleigh. Εξετάζονται τρεις διαφορετικοί δέκτες και υπολογίζεται η πιθανότητα σφάλματος ανά bit γι' αυτούς. Τέλος προτείνεται ένας νέος δέκτης για συνεργατικά συστήματα DaF και αποδεικνύεται η ανωτερότητά του σε σύγκριση με τους υπόλοιπους μελετώμενους δέκτες. Όλα τα θεωρητικά αποτελέσματα που παρουσιάζονται στο πλαίσιο της διατριβής συγκρίνονται με αποτελέσματα προσομοιώσεων Monte Carlo που αποδεικνύουν την ορθότητα της ανάλυσης. / This thesis studies the performance of MIMO diversity systems in generalized fading channels. First, we examine the performance of OSTBC in Hoyt fading channels. It is proven that, for this fading model, and when an OSTBC is employed, the signal-to-noise ratio (SNR) of the OSTBC can be expressed as a quadratic form in normal random variables. Therefore, the performance analysis for OSTBC over Hoyt fading channels is performed using the PDF and the CDF of such quadratic forms. In the statistical literature, these functions are expressed in terms of infinite series. The convergence of the series is thoroughly studied and new expressions for the truncation error bound of these series are proposed. The proposed bounds are much tighter than the bounds that can be found in the literature. The expressions for the PDF and the CDF are then used for the performance analysis of OSTBC over Hoyt fading and several performance metrics are calculated. Then, a generalized fading model for the performance analysis of OSTBC and MRC is proposed and the theoretical performance analysis of both MRC and OSTBC is carried out. The main advantage of this model is the fact that it includes as special cases most of the widely used fading models. Furthermore, the performance of cooperative diversity systems employing Detect and Forward (DaF) relays is studied for Rayleigh fading channels. More specifically, three low complexity detection algorithms for these channels are examined and closed-form expressions of the bit error probability (BEP) for these receivers are derived. Finally, a new low complexity receiver for cooperative systems with DaF relays is proposed. Using Monte Carlo Simulations it is shown that this receiver outperforms the three receivers that have been studied. For the systems studied in the thesis, the performance analysis results that have been derived theoretically are compared with Monte Carlo simulations that prove the validity of the analysis.