In this thesis channel capacity of a special type of multiple-input multiple-output (MIMO) Rayleigh fading channels is studied, where the transmitters are subject to a finite phase-shift keying (PSK) input alphabet. The constraint on the input alphabet makes an analytical solution for the capacity beyond reach. However we are able to simplify the final expression, which requires a single expectation and thus can be evaluated easily through simulation. To facilitate simulations, analytical expressions are derived for the eigenvalues and eigenvectors of a covariance matrix involved in the simplified capacity expression. The simplified expression is used to provide some good approximations to the capacity at low signal-to-noise ratios (SNRs). Involved in derivation of the capacity is the capacity-achieving input distribution. It is proved that a uniform prior distribution is capacity achieving. We also show that it is the only capacity-achieving distribution for our channel model. On top of that we generalize the uniqueness case for an input distribution to a broader range of channels.

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Integrations over the unitary group are required in many applications including the joint eigenvalue distributions of the Wishart matrices. In this thesis, a universal integration framework is proposed to use the character expansions for any unitary integral with general rectangular complex matrices in the integrand. The proposed method is applied to solve some of the well--known but not solved in general form unitary integrals in their general forms, such as the generalized Harish--Chandra--Itzykson--Zuber integral. These integrals have applications in quantum chromodynamics and color--flavor transformations in physics. The unitary integral results are used to obtain new expressions for the joint eigenvalue distributions of the semi--correlated and full--correlated central Wishart matrices, as well as the i.i.d. and uncorrelated noncentral Wishart matrices, in a unified approach. Compared to the previous expressions in the literature, these new expressions are much easier to compute and also to apply for further analysis. In addition, the joint eigenvalue distribution of the full--correlated case is a new result in random matrix theory. The new distribution results are employed to obtain the individual eigenvalue densities of Wishart matrices, as well as the capacity of multiple--input multiple--output (MIMO) wireless channels. The joint eigenvalue distribution of the i.i.d. case is used to obtain the largest eigenvalue density and the bit error rate (BER) of the optimal beamforming in finite--series expressions. When complete channel state information is not available at the transmitter, a codebook of beamformers is used by the transmitter and the receiver. In this thesis, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum--distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. By employing a geometrical approach, an approximate BER for limited feedback beamforming is derived in finite--series expressions.

As the demand of high data rate is increasing, a lot of research is being conducted in the field of wireless communication. A well-known channel coding technique called Space-Time Coding has been implemented in the wireless Communication systems using multiple antennas to ensure the high speed communication as well as reliability by exploiting limited spectrum and maintaining the power. In this thesis, Space-Time Coding is discussed along with other related topics with special focus on Alamouti Space-Time Block Code. The Alamouti Codes show good performance in terms of bit error rate over Rayleigh fading channel. The performance of Altamonte’s code and MIMO capacity is evaluated by using MATLAB simulation.

Στην παρούσα διδακτορική διατριβή παρουσιάζεται µια εκτενής µελέτη συστηµάτων απόκλισης τυπωµένων κεραιών για ασύρµατες συσκευές. Η εξέλιξη των ασύρµατων επικοινωνιών και ειδικότερα η κατανόηση των φαινοµένων που λαµβάνουν χώρα στο ασύρµατο κανάλι µετάδοσης έδωσε ώθηση στην ανάπτυξη τεχνικών αντιµετώπισης φαινοµένων όπως η πολυοδευτική εξασθένηση και η διασυµβολική παρεµβολή. Τέτοιες τεχνικές είναι οι τεχνικές απόκλισης και ειδικότερα οι τεχνικές απόκλισης κεραιών (χώρου, πόλωσης και διαγράµµατος ακτινοβολίας) οι οποίες συνδυάζουν τα λαµβανόµενα από διαφορετικές κεραίες σήµατα µε σκοπό την δηµιουργία ενός σήµατος υψηλότερης στάθµης. Η µεθοδολογία αξιολόγησης της ικανότητας απόκλισης ενός συστήµατος κεραιών περιλαµβάνει τα κριτήρια του συντελεστή συσχέτισης των λαµβανοµένων σηµάτων και του λόγου των µέσων ενεργών κερδών των κεραιών που αποτελούν το σύστηµα. Καθοριστικό ρόλο στην τεχνική απόκλισης διαδραµατίζει ο τρόπος που συνδυάζονται τα λαµβανόµενα σήµατα στον δέκτη, µε την τεχνική του µεγίστου λόγου να αποτελεί την βέλτιστη λύση από πλευράς απόδοσης, αλλά ταυτοχρόνως την πιο δύσκολα υλοποιήσιµη. Η ποσοτικοποίηση της ικανότητας απόκλισης ενός συστήµατος πραγµατοποιείται µε το κέρδος απόκλισης το οποίο λαµβάνει διαφορετικές µορφές και ουσιαστικά παρέχει την πληροφορία του ποσοστού βελτίωσης του συνδυασµένου σήµατος σε σχέση µε µία κεραία αναφοράς. Στα πλαίσια της διατριβής αναπτύχθηκαν συστήµατα απόκλισης τυπωµένων κεραιών δύο, τριών, τεσσάρων έως και έξι στοιχείων. Χρησιµοποιήθηκαν κεραίες γεωµετρίας fractal λόγω της σπουδαίας ικανότητας σµίκρυνσης που παρέχει η εν λόγω τεχνική καθώς και το µονόπολο γεωµετρίας ανεστραµµένου F. Ακολουθήθηκε η µεθοδολογία αξιολόγησης της ικανότητας απόκλισης για όλα τα προτεινόµενα συστήµατα και έγινε σύγκριση µεταξύ των συστηµάτων. Μελετήθηκε αφ’ ενός η επίδραση της θέσης της κεραίας σε µία ασύρµατη συσκευή και αφ’ ετέρου η επιλογή της καταλληλότερης προς χρήση κεραίας στην µείωση του φαινοµένου της αµοιβαίας σύζευξης, φαινόµενο το οποίο αποτελεί τον κυριότερο παράγοντα µείωσης της συνολικής ικανότητας απόκλισης σε ένα σύστηµα πολλαπλών κεραιών. Ακόµη, µελετήθηκαν συστήµατα απόκλισης κεραιών τα οποία λειτουργούν σε διαφορετικές µπάντες συχνοτήτων. Τέλος, έγινε µια συγκριτική µελέτη για τον ρόλο που διαδραµατίζει το περιβάλλον και ο τρόπος που κατανέµεται η προσπίπτουσα ισχύς στην συµπεριφορά της απόκλισης των µελετηθέντων συστηµάτων. / This thesis presents a comprehensive study on printed antenna diversity systems for wireless devices. The current upsurge in wireless communications systems and, in particular, the realization of the immanent propagation mechanisms that take place in the transmission medium led to the development of special techniques in order to mitigate the undesired phenomena such as multipath fading and intersymbol interference. Antenna diversity (space, polarization and pattern) is one of these techniques and is based on the assumption that the received signals of two or more antennas could be efficiently combined in order to produce a stronger signal. The evaluation of the diversity performance involves the correlation coefficient of the received signals and the mean effective gain ratio of the diversity antennas. A key role in diversity action plays the combining technique used with the maximum ratio technique producing the best results. Diversity performance is “quantified” by means of diversity gain, which gives the amount of improvement of the combined signal relative to a signal received from a reference antenna. In this thesis, printed antenna diversity systems comprising up to six elements were developed. Antennas of fractal geometry such as the Koch, Minkowski, Sierpinski and FRC monopoles, were utilized due to their inherent miniaturization ability as well as the printed inverted F antenna. All the proposed systems were evaluated according to the methodology mentioned earlier and a comparison of the diversity performance between the systems was carried out. The effect of the antenna placement as well as the proper antenna selection for each system on the reduction of mutual coupling was addressed, which is an issue of primal importance in multi element antenna systems. Multi band antenna diversity systems were also studied. Finally, the impact of the environment’s power distribution on the diversity performance of the antenna systems was considered.