Las técnicas de estimación de canal y de adaptación de la transmisión a las condiciones del entorno son temas de interés actual al estudiar la aplicación de técnicas de diversidad en transmisión en la tercera y cuarta generación de sistemas inalámbricos. En esta tesis se realiza un análisis del impacto del error de estimación de canal y la correlación en sistemas OFDM con diversidad en transmisión basados en codificación espacio-tiempo por bloques (STBC), se proponen técnicas de estimación de canal para estos sistemas y se propone una técnica de adaptación de la transmisión mediante la selección de código espacio-tiempo. En primer lugar, una técnica sencilla de mínimos cuadrados en el dominio de la frecuencia permite la estimación de canal en sistemas con dos antenas y constelaciones complejas, y con tres o cuatro antenas y constelaciones reales o complejas, utilizando STBCs ortogonales como bloques de entrenamiento. En segundo lugar, una representación 'sobre-completa' permite hacer una estimación diferencial de canal para un sistema con tres antenas transmisoras mediante la selección a partir de un banco de posibles estimadores, basándose en la redundancia provista por la matriz de transmisión no cuadrada del código ortogonal esporádico de tasa 3/4 para tres antenas transmisoras.En el contexto de sistemas con adaptación del transmisor, la técnica propuesta de diversidad por selección adaptativa de código espacio-tiempo se basa en el estado instantáneo del vector de canal y en un conjunto de niveles umbrales hallados fuera de línea en función del período de realimentación. Los resultados indican que esta técnica proporciona buenas prestaciones en canales correlados e incorrelados. Su aplicación a sistemas OFDM ha sido estudiada, superando a técnicas de selección de antena y a otras técnicas de transmisión adaptativa. / Channel estimation and adaptive transmission techniques are areas of increasing interest these days when considering transmit diversity systems for the 3G and 4G wireless communication systems. In this thesis an analysis of the channel estimation and channel correlation impact on transmit diversity OFDM systems based on space-time block coding (STBC) is presented, two channel estimation techniques are outlined and an adaptive space-time code selection technique is proposed. First, a simple frequency domain least square technique allows channel estimation for two transmitter systems with complex constellation, and three or four transmitter systems with real or complex constellation, using orthogonal STBCs as training blocks. Second, an 'overcomplete' representation allows a di.erential channel estimation for three transmitter systems through the instantaneous selection from a bank of estimators, based on the redundacy provided by the non-square transmission matrix of the sporadic 3/4-rate STBC for three transmitters.In the context of transmit adaptive systems, the proposed adaptive space-time code selection technique is based on both the instantaneous channel vector state and a set of predetermined threshold levels found o.-line as a function of the feedback period. Analytical and simulation results show that the proposed technique has a good performance in the presence of correlated and uncorrelated channels. Its application to OFDM systems has been considered, outperforming classical antenna selection techniques and other closed-loop adaptive transmission techniques.

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.

Η χωροχρονική μπλοκ κωδικοποίηση (STBC) αποτελεί μία αποδοτική και ευρέως διαδεδομένη τεχνική διαφορετικότητας μετάδοσης για την αντιμετώπιση του φαινομένου της εξασθένησης στις ασύρματες επικοινωνίες. Χαρακτηριστικό παράδειγμα είναι ο ορθογώνιος κώδικας του σχήματος Alamouti, ο οποίος με δύο κεραίες μετάδοσης επιτυγχάνει τη μέγιστη χωρική διαφορετικότητα στο μέγιστο δυνατό ρυθμό μετάδοσης, για οποιονδήποτε (πραγματικό ή μιγαδικό) αστερισμό συμβόλων. Ωστόσο, το σχήμα Alamouti έχει σχεδιαστεί για συχνοτικά επίπεδα κανάλια. Στην παρούσα εργασία μελετούμε την εφαρμογή STBC σε κανάλια συχνοτικά επιλεκτικής εξασθένησης. Εστιάζουμε κυρίως στο συνδυασμό του σχήματος Alamouti με τεχνικές εξάλειψης της διασυμβολικής παρεμβολής, εξετάζοντας τα σχήματα OFDM-STBC, FDE-STBC και TR-STBC, που έχουν προταθεί στη βιβλιογραφία. Επιπρόσθετα των συμβατικών δεκτών, για τα δύο τελευταία σχήματα περιγράφουμε και προσαρμοστικούς δέκτες, οι οποίοι παρακολουθούν τις μεταβολές του καναλιού, χωρίς να απαιτούν την ακριβή εκτίμησή του. Η έρευνα πάνω στα προηγούμενα σχήματα οδήγησε σε ορισμένα αξιόλογα αποτελέσματα. Κατ’ αρχήν, αποδεικνύουμε ότι τα σχήματα FDE-STBC και TR-STBC είναι ισοδύναμα, μολονότι καθένα εφαρμόζει διαφορετική κωδικοποίηση στα μεταδιδόμενα δεδομένα. Επίσης, σχεδιάζουμε έναν νέο δέκτη για το σχήμα TR-STBC, τον οποίο αναπτύσσουμε και σε προσαρμοστική μορφή. Βασικό πλεονέκτημα του προτεινόμενου δέκτη είναι ότι εκμεταλλεύεται τους κυκλικούς πίνακες συνέλιξης για τη μείωση της πολυπλοκότητας αποκωδικοποίησης. Τέλος, η απόδοση κάθε σχήματος και δέκτη αξιολογείται σε διάφορες συνθήκες εξασθένησης μέσω προσομοιώσεων σε υπολογιστικό περιβάλλον. / Space-time block coding (STBC) is an effective and widely used transmit diversity technique to combat multipath fading in wireless communication systems. A prominent example of STBC is the orthogonal code of Alamouti scheme, which achieves full spatial diversity at full transmission rate for two transmit antennas and any (real or complex) signal constellation. However, Alamouti scheme has been designed only for frequency-flat channels. In this thesis we study the application of STBC in frequency-selective channels. We mainly focus on combining Alamouti scheme with techniques for mitigating intersymbol interference, by studying several schemes (OFDM-STBC, FDE-STBC and TR-STBC) that have been proposed in literature. In addition to the conventional receivers, for FDE-STBC and TR-STBC we describe adaptive receivers too, which have the ability of tracking channel variations, without requiring explicit channel estimation. Research made upon the above schemes has come to some remarkable results. First, we prove that TR-STBC and FDE-STBC are equivalent, although each one encodes differently the transmitted data. Then, we design a new receiver for TR-STBC, which exploits the circulant convolution matrices, in order to reduce decoding complexity and we, also, develop an adaptive structure for the proposed receiver. At last, we evaluate the performance of all the described schemes and receivers in different fading conditions, by using computer simulations.

No description available.

The technique of cooperative communications is finding its way in the next generations of many wireless communication applications. Due to the distributed nature of cooperative networks, acquiring fading channels information for coherent detection is more challenging than in the traditional point-to-point communications. To bypass the requirement of channel information, differential modulation together with non-coherent detection can be deployed. This thesis is concerned with various issues related to differential modulation and non-coherent detection in cooperative networks. Specifically, the thesis examines the behavior and robustness of non-coherent detection in mobile environments (i.e., time-varying channels). The amount of channel variation is related to the normalized Doppler shift which is a function of user’s mobility. The Doppler shift is used to distinguish between slow time-varying (slow-fading) and rapid time-varying (fast-fading) channels. The performance of several important relay topologies, including single-branch and multi-branch dual-hop relaying with/without a direct link that employ amplify-and-forward relaying and two-symbol non-coherent detection, is analyzed. For this purpose, a time-series model is developed for characterizing the time-varying nature of the cascaded channel encountered in amplify-and-forward relaying. Also, for single-branch and multi-branch dual-hop relaying without a direct link, multiple-symbol differential detection is developed. First, for a single-branch dual-hop relaying without a direct link, the performance of two-symbol differential detection in time-varying Rayleigh fading channels is evaluated. It is seen that the performance degrades in rapid time-varying channels. Then, a multiple-symbol differential detection is developed and analyzed to improve the system performance in fast-fading channels. Next, a multi-branch dual-hop relaying with a direct link is considered. The performance of this relay topology using a linear combining method and two-symbol differential detection is examined in time-varying Rayleigh fading channels. New combining weights are proposed and shown to improve the system performance in fast-fading channels. The performance of the simpler selection combining at the destination is also investigated in general time-varying channels. It is illustrated that the selection combining method performs very close to that of the linear combining method. Finally, differential distributed space-time coding is studied for a multi-branch dual-hop relaying network without a direct link. The performance of this network using two-symbol differential detection in terms of diversity over time-varying channels is evaluated. It is seen that the achieved diversity is severely affected by the channel variation. Moreover, a multiple-symbol differential detection is designed to improve the performance of the differential distributed space-time coding in fast-fading channels.

Τα συστήματα πολλαπλών κεραιών στον πομπό και στο δέκτη (MIMO) αποτελούν βασικά μέτωπα ανάπτυξης των ασύρματων επικοινωνιών. Ωστόσο, η εφαρμογή της τεχνολογίας MIMO στα κινητά δίκτυα επικοινωνιών αντιμετωπίζει το πρακτικό πρόβλημα της ενσωμάτωσης πολλαπλών κεραιών σε μικρά κινητά τερματικά. Με σκοπό την αντιμετώπιση του εμποδίου αυτού, δημιουργήθηκε ένα άλλο σημαντικό μέτωπο έρευνας, αυτό των συνεργατικών επικοινωνιών. Στο πλαίσιο της παρούσας διδακτορικής διατριβής ασχοληθήκαμε με την ανάπτυξη και μελέτη αλγορίθμων επεξεργασίας σήματος για τα δύο παραπάνω συστήματα. Σχετικά με τα συστήματα MIMO η πρωτοποριακή έρευνα που πραγματοποιήθηκε στα Bell labs στα μέσα της δεκαετίας του ΄90, απέδειξε ότι η χρήση πολλαπλών κεραιών μπορεί να οδηγήσει σε σημαντική αύξηση της χωρητικότητας των ασύρματων συστημάτων βελτιώνοντας την αξιοπιστία της μετάδοσης. Προκειμένου να αξιοποιηθούν οι παραπάνω δυνατότητες απαιτείται η σχεδίαση σύνθετων δεκτών MIMO. Προς αυτήν την κατεύθυνση έχει στραφεί ένας μεγάλος αριθμός μεθόδων ισοστάθμισης του καναλιού και πιο συγκεκριμένα δεκτών ανατροφοδότησης αποφάσεων. Δεδομένου ότι σε ευρυζωνικά συστήματα επικοινωνιών το ασύρματο κανάλι είναι άγνωστο στο δέκτη και μεταβάλλεται χρονικά, στραφήκαμε προς τις προσαρμοστικές μεθόδους ισοστάθμισης. Στα πλαίσια της διαριβής αναζήτησαμε προσαρμοστικούς αλγόριθμους κατάλληλους για τη σχεδίαση προσαρμοστικών ισοσταθμιστών MIMO DFE με τα εξής χαρακτηριστικά: 1) να παρουσιάζουν απόδοση (ταχύτητα σύγκλισης) συγκρίσιμη με αυτή του RLS, 2) η υπολογιστική τους πολυπλοκότητα να είναι μικρότερη από αυτή του RLS και 3) να είναι αριθμητικά ευσταθείς. ΄Εχει αποδειχθεί ότι προσαρμοστικοί αλγόριθμοι που βασίζονται στη μέθοδο των συζυγών κλίσεων (conjugate gradient (CG)) πληρούν τις παραπάνω προϋποθέσεις. Αρχικά αναζητήσαμε τεχνικές που βασίζονται στη μέθοδο αυτή και χρησιμοποιούνται σε προβλήματα προσαρμοστικού φιλτραρίσματος και πιο ειδικά, στο πρόβλημα προσαρμοστικής ισοστάθμισης διαύλου στη περίπτωση SISO. Πιο συγκεκριμένα, υλοποιήσαμε έναν προσαρμοστικό αλγόριθμο στο πεδίο των συχνοτήτων που επεξεργάζεται τα δεδομένα κάθε φορά που λαμβάνεται ένα νέο εισερχόμενο πακέτο δεδομένων. Ο προτεινόμενος ισοσταθμιστής πετυχαίνει μια πολύ καλή απόδοση, ενώ οι υπολογιστικές του απαιτήσεις είναι πολύ χαμηλές. Στη συνέχεια αναπτύξαμε τρεις νέους αλγορίθμους προσαρμοστικής ισοστάθμισης συχνοτικά επιλεκτικών συστημάτων MIMO, που βασίζονται στη μέθοδο CG και στις προβολές Galerkin. Το πρόβλημα σχεδιασμού προσαρμοστικών MIMO DFE αντιμετωπίζεται ως ένα πρόβλημα επίλυσης γραμμικών εξισώσεων, με πολλαπλά δεξιά μέλη, που εξελίσσεται στο χρόνο. Επισημαίνουμε ότι τα σχήματα που προτείνουμε θα μπορούσαν να αποτελέσουν ένα γενικότερο πλαίσιο σχεδίασης προσαρμοστικών δεκτών για συχνοτικά επιλεκτικά συστήματα MIMO, με ιδιότητες σύγκλισης παρόμοιες με αυτές του RLS, έχοντας, ωστόσο, μικρότερες υπολογιστικές απαιτήσεις. Στα πλαίσια της παρούσας διδακτορικής διατριβής αναπτύξαμε τεχνικές εκτίμησης καναλιού για συνεργατικά δίκτυα με N αναμεταδότες που είτε ενισχύουν και αναμεταδίδουν ή αποκωδικοποιούν και αναμεταδίδουν το λαμβανόμενο σήμα. ΄Ολες οι τεχνικές εκτίμησης που προτείναμε υλοποιούνται εξ΄ ολοκλήρου στο πεδίο των συχνοτήτων. Αρχικά παρουσιάσαμε τεχνικές που βασίζονται στη μετάδοση πιλοτικών συμβόλων σε συγκεκριμένες συχνοτικές συνιστώσες. Στη συνέχεια αποδείξαμε ότι όλα τα κανάλια από την πηγή μέσω των αναμεταδοτών προς τον προορισμό μπορούν να εκτιμηθούν τυφλά εάν γνωρίζουμε τις φάσεις της απόκρισης συχνότητας του ασύρματου καναλιού μεταξύ πηγής και προορισμού.. Επιπρόσθετα, πραγματοποιήθηκε ϑεωρητική ανάλυση της απόδοσης των προτεινόμενων σχημάτων η οποία επαληθεύτηκε μέσω προσομοιώσεων σε υπολογιστή. Τέλος, αξιολογήσαμε πειραματικά διάφορα πρωτόκολλα συνεργατικής επικοινωνίας (AF, DF, SF) και τεχνικές κατανεμημένης χωροχρονικής επεξεργασίας DSTC για συνεργατικά δίκτυα σε μια πλατφόρμα υλοποίησης πραγματικού χρόνου που χρησιμοποιεί επεξεργαστές ψηφιακής επεξεργασίας σήματος. Διαπιστώσαμε ότι τα πειραματικά αποτελέσματα συμφωνούν πλήρως με τα θεωρητικά. / Systems employing multiple antennas at the transmitter and the receiver, known as MIMO (multiinput multioutput) systems, as well as space time coding techniques developed for such systems, are two of the main technologies employed for the evolution of wireless communications. However, the application of MIMO technology to mobile networks, often faces the practical implementation problem of having too many antennas on a small mobile terminal. In an attempt to overcome such a severe limitation, cooperative communication schemes have been proposed. This PhD dissertation, described our work on the design and analysis of signal processing algorithms for the two aforementioned systems, as is described in detail next. Concerning MIMO systems, the pioneering work performed at Bell Labs in the middle of the nineties, proved that the use of multiple antennas can lead to a significant increase in wireless systems capacity. To exploit this potential, sophisticated MIMO receivers should be designed. To this end, a large amount of channel equalizers and, more specifically, decision feedback equalizers has been proposed. Because these assumptions are difficult to meet in high rate single carrier systems, we have focused our attention on decision feedback equalizers. . Our main goal is to derive algorithms for updating the MIMO DFE filters with the following characteristics: 1) convergence properties similar to these of the RLS 2) more computationally efficient than RLS and 3) numerically stable. It is known that adaptive algorithms based on the CG (conjugate gradient) have the above characteristics We initially studied this method as an iterative method for solving linear equations and we pointed out the main differences with the steepest descent method, on which the LMS algorithm is based. An extended search of adaptive DFE algorithms, based on the CG method was carried out. More specifically, a new block adaptive CG algorithm was developed. In the resulting algorithm, one CG iteration per block update is executed. In order to reduce even more the complexity, the algorithm was implemented in the Frequency Domain. The proposed equalizer offers a good performance - complexity trade off. Three new adaptive equalization algorithms for wireless systems operating over frequency selective MIMO channels, based on the CG method and the Galerkin projection method, are proposed. The problem of MIMO decision feedback equalizer (DFE) design is formulated as a set of linear equations with multiple righthand sides (RHSs) evolving in time. These schemes provide a flexible framework in MIMO adaptive equalization design to implement schemes with convergence properties comparable to the RLS, but of lower computational cost. Furthermore, we worked on channel estimation for cooperative communication networks, where the nodes either simply amplify and forward the received signal, or they decode and transmit the signal (DF). We first propose efficient channel estimation techniques for relay networks with N relays. The new methods are implemented in the frequency domain (FD). Initially, training based techniques are presented, where the training pilots are multiplexed with the data in the frequency domain. It is then shown that all the channels in the network can be estimated blindly provided that we know the phases of the frequency response of the (Source → Destination) channel. Thus, by making use of a small number of pilots in only one link (the sourcetodestination link) we can estimate all the other channels (Source→Relay i→Destination) in the network. A theoretical performance study of the proposed algorithms is presented and closed form expressions for the mean squared channel estimation error are provided. The presented theoretical analysis is verified by extensive Monte Carlo simulations. The application of the derived schemes to the DF case, and the impact of erroneous detection to their performance are also studied. Finally, we investigated experimentally four cooperative relaying schemes: amplify and forward (AF), detect and forward (DF), cooperative maximum ratio combining (CMRC) and distributed spacetime coding (DSTC), and one novel selection relaying (SR) scheme on a realtime DSP based testbed. The experimental results are fairly close to the ones predicted by theory

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.

Network coding has emerged as an attractive alternative to routing because of the through put improvement it provides by reducing the number of channel uses. In a wireless scenario, in addition, further improvement can be obtained through Physical layer Network Coding (PNC), a technique in which nodes are allowed to transmit simultaneously, instead of transmitting in orthogonal slots. In this thesis, the design and analysis of network coding schemes are considered, for wireless two-way relaying, multi-user Multiple Access Relay Channel (MARC) and wireline networks. In a wireless two-way relay channel with PNC, the simultaneous transmissions of user nodes result in Multiple Access Interference (MAI) at there lay node. The harmful effect of MAI is the presence of signal set dependent deep channel fade conditions, called singular fade states, under which the minimum distance of the effective constellation at the relay become zero. Adaptively changing the network coding map used at the relay according to channel conditions greatly reduces the impact of this MAI. In this work, we obtain these adaptive PNC maps, which are finite in number ,by completing partially filled Latin Squares and using graph vertex coloring. Having obtained the network coding maps, the set of all possible channel realizations is quantized into a finite number of regions, with a specific network coding map chosen in a particular region and such a quantization is obtained analytically for 2λ-PSK signal set. The performance of the adaptive PNC scheme for two-way relaying is analyzed and tight high SNR upper bounds are obtained for the average end-to-end symbol error probability, in terms of the average error probability of a point-to-point fading channel. The adaptive PNC scheme is generalized for two-way relaying with multiple antennas at the nodes. As an alternative to the adaptive PNC scheme for two-way relaying, a Distributed Space Time Coding (DSTC) scheme is proposed, which effectively re-moves the effect of singular fade states at the transmitting nodes itself without any Channel State Information at the Transmitter (CSIT), and without any need to change the PNC map as a function of channel fade conditions. It is shown that the singular fade states can be viewed equivalently as vector subspaces of C2, which are referred to as the singular fade subspaces. DSTC design criterion to minimize the number of singular fade subspaces and maximize the coding gain is formulated and explicit low decoding complexity DSTC designs are provided. For the K-user MARC, in which K source nodes want to transmit messages to a destination node D with the help of are lay node R, a new PNC scheme is proposed. Use of a many-to-one PNC map with conventional minimum squared Euclidean distance decoding at D, results in a loss of diversity order due to error propagation from the relay node. To counter this, we propose a novel low complexity decoder which offers the maximum diversity order of two. Next, we consider wire line networks and explore the connections between linear network coding, linear index coding and discrete polymatroids, which are the multi-set analogue of matroids. We define a discrete polymatroidal network and show that a fractional vector linear solution over a field Fq exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over Fq.An algorithm to construct networks starting from certain class of discrete polymatroids is provided. Every representation over Fq for the discrete polymatroid, results in a fractional vector linear solution over Fq for the constructed network. It is shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

The importance of cooperative relaying communication in substituting for, or complementing, multiantenna systems is described, and a brief literature review is presented. Amplify-and-forward (AF) and decode-and-forward (DF) relaying are investigated and compared for a dual-hop relay channel. The optimal strategy, source and relay optimal power allocation, and maximum cooperative gain are determined for the relay channel. It is shown that while DF relaying is preferable to AF relaying for strong source-relay links, AF relaying leads to more gain for strong source-destination or relay-destination links. Superimposed and selection AF relaying are investigated for multirelay, dual-hop relaying. Selection AF relaying is shown to be globally strictly outage suboptimal. A necessary condition for the selection AF outage optimality, and an upper bound on the probability of this optimality are obtained. A near-optimal power allocation scheme is derived for superimposed AF relaying. The maximum instantaneous rates, outage probabilities, and average capacities of multirelay, dual-hop relaying schemes are obtained for superimposed, selection, and orthogonal DF relaying, each with parallel channel cooperation (PCC) or repetition-based cooperation (RC). It is observed that the PCC over RC gain can be as much as 4 dB for the outage probabilities and 8.5 dB for the average capacities. Increasing the number of relays deteriorates the capacity performance of orthogonal relaying, but improves the performances of the other schemes. The application of rateless codes to DF relaying networks is studied by investigating three single-relay protocols, one of which is new, and three novel, low complexity multirelay protocols for dual-hop networks. The maximum rate and minimum energy per bit and per symbol are derived for the single-relay protocols under a peak power and an average power constraint. The long-term average rate and energy per bit, and relay-to-source usage ratio (RSUR), a new performance measure, are evaluated for the single-relay and multirelay protocols. The new single-relay protocol is the most energy efficient single-relay scheme in most cases. All the multirelay protocols exhibit near-optimal rate performances, but are vastly different in the RSUR. Several future research directions for fixed-rate and rateless coded cooperative systems, and frameworks for comparing these systems, are suggested. / Communications

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