Abstract This thesis is devoted to studying two wireless relay network models, namely wireless tandem multiple-input-multiple-output (MIMO) relay networks and wireless two-hop multicast relay networks. Regarding wireless tandem MIMO relay networks, we develop a systematic approach to analyze their fundamental diversity-multiplexing tradeoff (DMT) under the assumption that the relays implement a class of practical full-duplex techniques that enable them to opt for either full-duplex or half-duplex mode. Based on the analysis, we make contribution from the following aspects: First of all, we thoroughly compare the performance of full-duplex and half-duplex mode operations in the framework of wireless tandem relay networks. We find that both full-duplex and half-duplex modes have opportunity to outperform each other. Specifically, for many tandem relay networks, in the low multiplexing gain region, the best relay-mode configuration is to let all the relays operate in half-duplex mode since this relay-mode configuration achieves the best diversity gain in the low multiplexing gain region. However, in the high multiplexing gain region, the best diversity gain is usually achieved by switching some relays to full-duplex mode. Furthermore, we study how residual interference at relays working in full-duplex mode affects the DMT of a tandem network. We find that residual interference not only derogates the performance of full-duplex mode, but also affects the optimal power allocation of the network. Specifically, if residual interference is zero or has a sufficiently low power level, a linear power allocation scheme can achieve the optimal DMT of the network. Otherwise, the optimal DMT is achieved by a nonlinear power allocation scheme. Finally, the DMT analysis illustrates an effective principle to deal with general multi-hop wireless networks, which is to break them down into small scale subnetworks with certain key structures. Then, studying the general multi-hop wireless networks essentially becomes studying those small scale subnetworks and the relationship among them. Regarding wireless two-hop multicast relay networks, we focus on a case study where a single source multicasts to two destinations through the assistance of two relays. We propose and analyze the performance of a partial decode-and-forward protocol for the network, which includes the full decode-and-forward protocol as a special case and achieves a better performance in general. Specifically, we prove that the achievable rate of the partial decode-and-forward protocol can either reach arbitrarily close to the cut-set upper bound of the network or reach within 1 bit/s/Hz to that, asymptotically with respect to the transmit power. We also show that the partial decode-and-forward protocol can achieve the optimal DMT of the network. Then, we discuss the perspective of implementing the partial decode-and-forward strategy to more general multicast relay networks. / Tiivistelmä Tämä opinnäytetyö tutkii kahta langatonta välitysverkkomallia, nimittäin langatonta tandem multiple-input-multiple-output (MIMO) välitysverkkoa ja langatonta monilähetysvälitysverkkoa kahdelle hypylle. Kehitämme systemaattisen lähestymistavan diversiteetti-multipleksointi vaihtokaupan (DMT) analysointiin langattomiin tandem MIMO välitysverkkoihin, olettaen välittäjien käyttävän käytännöllisiä full-duplex lähetystekniikoita, jotka mahdollistavat valinnan joko full-duplex tai half-duplex lähetystilan välillä. Analyysin perusteella kontribuoimme seuraavilla tavoilla: Ensinnäkin, vertailemme perusteellisesti full-duplex sekä half-duplex lähetystiloja langattomissa tandem välitysverkoissa. Huomaamme, että molemmat full-duplex ja half-duplex lähetystilat voivat suoriutua toinen toistaan paremmin. Tarkemmin sanoen, monissa tandem välitysverkoissa silloin kun multipleksoinnin hyöty on alhainen, paras välitystapa on antaa kaikkien välittäjien käyttää half-duplex lähetystilaa, koska silloin saavutetaan paras diversiteettilisäys. Toisaalta, kun multipleksointilisäys on suuri, paras diversiteettilisäys saadaan yleensä asettamalla jotkin välittäjät full-duplex lähetystilaan. Lisäksi, tutkimme kuinka full-duplex lähetystilaa käyttävien välittäjien jäljelle jäävä interferenssi vaikuttaa tandemverkon DMT:aan. Huomaamme, että jäljelle jäävä interferenssi vähentää full-duplex mallin tehokkuutta ja lisäksi vaikuttaa optimaaliseen tehonjakamiseen verkossa. Tarkemmin sanoen, jos jäljelle jäävä interferenssin tehotaso on nolla tai tarpeeksi lähellä sitä, lineaarisella tehojaolla voi saavuttaa verkon optimaalisen DMT:n. Muutoin, optimaalinen DMT saavutetaan epälineaarisella tehojaolla. Lopuksi, DMT analyysi havainnollistaa tehokkaan periaatteen yleisluontoisten monihyppyverkkojen käsittelemiseen, eli verkon jakamisen pienempiin osiin erilaiin avainrakenteisiin. Tämän jälkeen yleisluntoisten langattoimen monihyppyverkkojen tutkiminen tapahtuu tutkimalla näitä pieniä osia ja niiden välisiä vuorovaikutussuhteita. Langattomaan kahden hypyn monilähetysvälitysverkkon osalta keskitymme tapaustutkimukseen, jossa yksi lähettäjä monilähettää kahdelle vastaanottajalle kahden välittäjän avulla. Ehdotamme tälle verkolle osittaista decode-and-forward protokollaa, joka sisältää täyden decode-and-forward protokollan erikoistapauksena ja saavuttaa yleisesti tätä protokollaa paremman tehokkuuden. Tarkemmin sanoen, todistamme että tällä protokollalla siirtonopeus lähetystehon suhteen joko lähenee asymptoottisesti verkon cut-set ylärajaa mielivaltaisen lähelle tai saavuttaa sen 1 bit/s/Hz sisään. Osoitamme myös, että osittainen decode-and-forward protokolla voi saavuttaa verkon optimaalisen DMT:n. Tämän jälkeen, käsittelemme osittaisen decode-and-forward strategian impelentointia yleisluontoisille monilähetysvälitysverkoille.

Avec la croissance rapide des appareils et des applications mobiles, les besoins en débit et en connectivité dans les réseaux sans fil augmentent rapidement. Il est prouvé que les communications coopératives peuvent augmenter significativement l’efficacité spectrale et la fiabilité des transmissions entre les nœuds extrémaux. Le concept de coopération dans un réseau sans fil compte parmi les sujets de recherche les plus actifs en télécommunications, le but étant d'identifier les stratégies de coopération qui maximiseraient les gains en efficacité spectrale et en puissance d'émission. Pour coopérer, les nœuds du réseau partagent leurs ressources (énergie, bande de fréquence, etc. ...) pour améliorer mutuellement leurs transmissions et leurs réceptions. Dans les réseaux sans fil avec relais, les relais sont des nœuds dédiés à améliorer la qualité de la communication entre les nœuds sources et destination.Dans la première partie de la thèse, nous nous concentrons sur un réseau sans fil avec relais spécifique où l'ensemble de sources (mobiles) veulent communiquer leurs messages à une destination commune (station de base) avec l'aide d'un ensemble de relais (contexte cellulaire, sens montant). Nous étudions, sur les plans théorique et pratique, un schéma coopératif dans lequel les relais, après une durée d'écoute fixée a priori, essayent de décoder les messages des sources et commencent à transmettre des signaux utiles pour ceux qui sont décodés correctement. Ces signaux utiles sont le résultat d'un codage canal-réseau conjoint.Une des limitations du système coopératif précédent est précisément que le temps d'écoute des relais est figé et ne peut pas être adapté à la qualité fluctuante (aléatoire) des liens instantanés sources-relais. Pour pallier cette difficulté, nous proposons et analysons, dans une seconde partie de la thèse, un schéma de coopération plus avancé où le temps d'écoute de chaque relais peut être dynamique. Dans ces conditions, un relais bénéficiant d'une meilleure qualité de réception des sources peut commencer à coopérer plus tôt que d'autres relais ayant une qualité de réception moindre.Enfin, dans la troisième et dernière partie de la thèse, nous considérons la présence d'une information de retour limitée (limited feedback) entre la destination et les sources et les relais, et tentons de caractériser l'efficacité spectrale d'un tel système. / With the rapid growth of wireless technologies, devices and mobile applications, the quest of high throughput and omnipresent connectivity in wireless networks increases rapidly as well. It is well known that cooperation increases significantly the spectral efficiency (coding gain) and the reliability (diversity gain) of the transmission between the nodes. The concept of cooperation in wireless relays network is still one of the most active research topics in wireless communication, scientists are still searching for the optimal cooperation strategies that make the possible gains at the maximum. Cooperation results when nodes in a network share their power and/or bandwidth resources to mutually enhance their transmissions and receptions. In wireless relay networks, the relays are special nodes that are used to improve the quality of communication between the source nodes and the destination nodes. In particular, the use of relays guarantees more efficient and reliable networks. In this work, we focus on a special wireless relay network where a set of sources (mobiles) want to communicate their messages to a common destination (base station) with the help of a set of relaysAt the beginning of this work, we focused on the cooperative scheme where the relay, after a fixed portion of time, tries to understand (decode) the source’s messages and forwards helpful signals for the correctly decoded ones. One of the limitations of the previous cooperative scheme is the fixe listening time of the relays, which cannot be adapted to the quality of the instantaneous sources-relays links. To solve this problem we propose a more advanced cooperative scheme where the listening time of each relay can be dynamic and not fixed in advanced. So the relay that has strong links with the sources can start cooperating earlier than the other relays with weak links. Currently, we are investigating other directions of possible improvements, for example, how can we use feedback signals to improve the efficiency of the network.

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.

This thesis addresses the design of low-complexity coding schemes for wireless relay networks and multiple access channels. The first part of the thesis is on wireless relay networks and the second part is on multiple access channels. Distributed space-time coding is a well known technique to achieve spatial diversity in wireless networks wherein, several geographically separated nodes assist a source node to distributively transmit a space-time block code (STBC) to the destination. Such STBCs are referred to as Distributed STBCs (DSTBCs). In the first part of the thesis, we focus on designing full diversity DSTBCs with some nice properties which make them amenable for implementation in practice. Towards that end, a class of full diversity DST-BCs referred to as Co-ordinate Interleaved DSTBCs (CIDSTBCs) are proposed for relay networks with two-antenna relays. To construct CIDSTBCs, a technique called co-ordinate vector interleaving is introduced wherein, the received signals at different antennas of the relay are processed in a combined fashion. Compared to the schemes where the received signals at different antennas of the relay are processed independently, we show that CIDSTBCs provide coding gain which comes in with negligible increase in the processing complexity at the relays. Subsequently, we design single-symbol ML decodable (SSD) DSTBCs for relay networks with single-antenna nodes. In particular, two classes of SSD DSTBCs referred to as (i) Semi-orthogonal SSD Precoded DSTBCs and (ii) Training-Symbol Embedded (TSE) SSD DSTBCs are proposed. A detailed analysis on the maximal rate of such DSTBCs is presented and explicit DSTBCs achieving the maximal rate are proposed. It is shown that the proposed codes have higher rates than the existing SSD DSTBCs. In the second part, we study two-user Gaussian Multiple Access Channels (GMAC). Capacity regions of two-user GMAC are well known. Though, capacity regions of such channels provide insights into the achievable rate pairs in an information theoretic sense, they fail to provide information on the achievable rate pairs when we consider finitary restrictions on the input alphabets and analyze some real world practical signal constellations like QAM and PSK signal sets. Hence, we study the capacity aspects of two-user GMAC with finite input alphabets. In particular, Constellation Constrained (CC) capacity regions of two-user SISO-GMAC are computed for several orthogonal and non-orthogonal multiple access schemes (abbreviated as O-MA and NO-MA schemes respectively). It is first shown that NO-MA schemes strictly offer larger capacity regions than the O-MA schemes for finite input alphabets. Subsequently, for NO-MA schemes, code pairs based on Trellis Coded Modulation (TCM) are proposed such that any rate pair on the CC capacity region can be approached. Finally, we consider a two-user Multiple-Input Multiple-Output (MIMO) fading MAC and design STBC pairs such that ML decoding complexity is reduced.