The regular waterfilling(WF) policy maximizes the mutual information of parallel channels, when the inputs are Gaussian. However, Gaussian input is ideal, which does not exist in reality. Discrete constellations are usually used instead, such as $ M $-PAM and $ M $-QAM. As a result, the mercury/waterfilling (MWF) policy is introduced, which is a generalization of the regular WF. The MWF applies to inputs with arbitrary distributions, while the regular WF only applies to Gaussian inputs. The MWF-based optimal power allocation (OPA) is presented, for which an algorithm called the internal/external bisection method is introduced. The constellation-constrained capacity is discussed in the thesis, where explicit expressions are presented. The expression contains an integral, which does not have a closed-form solution. However, it can be evaluated via the Monte Carlo method. An approximation of the constellation-constrained capacity based on the sphere packing method is introduced, whose OPA is a convex optimization problem. The CVX was used initially, but it did not generate satisfactory results. Therefore, the bisection method is used instead. Capacities of the MWF and its sphere packing approximation are evaluated for various cases, and compared with each other. It turns out the sphere packing approximation has similar performances to the MWF, which validates the approximation. Unlike the MWF, the sphere packing approximation does not suffer from the loss of precision due to the structure of MMSE functions, which demonstrates its robustness.

Multiple input multiple output (MIMO) systems are now a proven area in current and future telecommunications research. MIMO wireless channels, in which both the transmitter and receiver have multiple antennas, have been shown to provide high bandwidth efficiency. In this thesis, we cover MIMO communications technology with a focus on cellular systems and the MIMO broadcast channel (MIMO-BC). Our development of techniques and analysis for the MIMO-BC starts with a study of single user MIMO systems. One such single user technique is that of antenna selection. In this thesis, we discuss various flavours of antenna selection, with the focus on powerful, yet straightforward, norm-based algorithms. These algorithms are analyzed and the results of this analysis produce a powerful and flexible power scaling factor. This power scaling factor can be used to model the gains of norm-based antenna selection via a single signal-to-noise ratio (SNR)-based parameter. This provides a powerful tool for engineers interested in quickly seeing the effects of antenna selection on their systems. A novel low complexity power allocation scheme follows on from the selection algorithms. Named “Poor Man’s Waterfilling” (PMWF), this scheme can provide significant gains in low SNR systems with very little extra complexity compared to selection alone. We then compare a variety of algorithms for the MIMO-BC, ranging from selection to beamforming, to the optimal, yet complex, iterative waterfilling (ITWF) solution. In this thesis we show that certain algorithms perform better in different scenarios, based on whether there is shadow fading or not. A power scaling factor analysis is also performed on these systems. In the cases where the user’s link gains are widely varying, such as when shadowing and distance effects are present, user fairness is impaired when optimal and near optimal throughput occurs. This leads to a key problem in the MIMO-BC, the balance between user fairness and throughput performance. In an attempt to find a suitable balance between these two factors, we modify the ITWF algorithm by both introducing extra constraints and also by using a novel utility function approach. Both these methods prove to increase user fairness with only minor loss in throughput over the optimal systems. The introduction of MIMO systems to the cellular domain has been hampered by the effects of interference between the cells. In this thesis we move MIMO to the cellular domain, addressing the interference using two different methods. We first use power control, where the transmit power of the base station is controlled to optimize the overall system throughput. This leads to promising results using low complexity methods. Our second method is a novel method of collaboration between base stations. This collaboration transforms neighbouring cell sectors into macro-cells and this results in substantial increases in performance.

Η συγκεκριμένη εργασία έχει ως αντικείμενο τη σύγκριση των ρυθμών μετάδοσης γραμμής VDSL που επιτυγχάνονται με δύο διαφορετικούς τρόπους κατανομής ισχύος: τις μάσκες ισχύος και τον αλγόριθμο iterative waterfilling. Οι μάσκες ισχύος είναι η μέθοδος που χρησιμοποείται σήμερα στις γραμμές DSL, ενώ ο αλγόριθμος iterative waterfilling έχει προταθεί ως εναλλακτική λύση που επιτυγχάνει καλύτερους ρυθμούς μετάδοσης. Για την πραγματοποίηση της σύγκρισης υλοποιήθηκαν προσομοιώσεις της κάθε μεθόδου σε περιβάλλον Matlab και έγινε σύγκριση των αποτελεσμάτων για διάφορες τιμές μήκους γραμμών VDSL και σε διαφορετικές συνθήκες θορύβου. Τα αποτελέσματα δείχνουν πως η μέθοδος iterative waterfilling αυξάνει το ρυθμό μετάδοσης των γραμμών VDSL και είναι πιο αποτελεσματική από τις μάσκες ισχύος σε περιβάλλον αυξημένου θορύβου. / The particular work has as object the comparison of the bit rates for a VDSL line that is achieved with two different ways of power distribution: the power masks and the algorithm iterative waterfilling.The power masks are the method that is used today in DSL lines, while the algorithm iterative waterfilling has been proposed as alternative solution that achieves better bit rates. For the purpose of this comparison were materialised simulations of each method in environment Matlab and it became comparison of results for different lengths of lines VDSL and in different conditions of noise. The results show that the method iterative waterfilling increases the bit rate of lines VDSL and is more effective than the power masks when the noise is big.

The optimum ordering strategies for the coded V-BLAST system with capacity achieving temporal codes on each stream are studied in this thesis. Mathematical representations of the optimum detection ordering strategies for the coded V-BLAST under instantaneous rate allocation (IRA), uniform power/rate allocation (URA), instantaneous power allocation(IPA) and instantaneous power/rate allocation (IPRA) are derived. For two transmit antennas, it is shown that the optimum detection strategies are based on the per-stream before-processing channel gains. Based on approximations of the per-stream capacity equation, closed-form expressions of the optimal ordering strategy under the IRA at low and high signal to noise ratio (SNR) are derived. Necessary optimality conditions under the IRA are given. Thresholds for the low, intermediate and high SNR regimes in the 2-Tx-antenna system under the IPRA are determined, and the SNR gain of the ordering is studied for each regime. Performances of simple suboptimal ordering strategies are analysed, some of which perform very close to the optimum one.

The optimum ordering strategies for the coded V-BLAST system with capacity achieving temporal codes on each stream are studied in this thesis. Mathematical representations of the optimum detection ordering strategies for the coded V-BLAST under instantaneous rate allocation (IRA), uniform power/rate allocation (URA), instantaneous power allocation(IPA) and instantaneous power/rate allocation (IPRA) are derived. For two transmit antennas, it is shown that the optimum detection strategies are based on the per-stream before-processing channel gains. Based on approximations of the per-stream capacity equation, closed-form expressions of the optimal ordering strategy under the IRA at low and high signal to noise ratio (SNR) are derived. Necessary optimality conditions under the IRA are given. Thresholds for the low, intermediate and high SNR regimes in the 2-Tx-antenna system under the IPRA are determined, and the SNR gain of the ordering is studied for each regime. Performances of simple suboptimal ordering strategies are analysed, some of which perform very close to the optimum one.

The optimum ordering strategies for the coded V-BLAST system with capacity achieving temporal codes on each stream are studied in this thesis. Mathematical representations of the optimum detection ordering strategies for the coded V-BLAST under instantaneous rate allocation (IRA), uniform power/rate allocation (URA), instantaneous power allocation(IPA) and instantaneous power/rate allocation (IPRA) are derived. For two transmit antennas, it is shown that the optimum detection strategies are based on the per-stream before-processing channel gains. Based on approximations of the per-stream capacity equation, closed-form expressions of the optimal ordering strategy under the IRA at low and high signal to noise ratio (SNR) are derived. Necessary optimality conditions under the IRA are given. Thresholds for the low, intermediate and high SNR regimes in the 2-Tx-antenna system under the IPRA are determined, and the SNR gain of the ordering is studied for each regime. Performances of simple suboptimal ordering strategies are analysed, some of which perform very close to the optimum one.

In this thesis, the process of optimizing Cooperative Spectrum Sensing in Cognitive Radio has been investigated in fast-fading environments where simulation results have shown that its performance is limited by the Probability of Reporting Errors. By proposing a transmit diversity scheme using Differential space-time block codes (D-STBC) where channel state information (CSI) is not required and regarding multiple pairs of Cognitive Radios (CR's) with single antennas as a virtual MIMO antenna arrays in multiple clusters, Differential space-time coding is applied for the purpose of decision reporting over Rayleigh channels. Both Hard and Soft combination schemes were investigated at the fusion center to reveal performance advantages for Hard combination schemes due to their minimal bandwidth requirements and simplistic implementation. The simulations results show that this optimization process achieves full transmit diversity, albeit with slight performance degradation in terms of power with improvements in performance when compared to conventional Cooperative Spectrum Sensing over non-ideal reporting channels. Further research carried out in this thesis shows performance deficits of Cooperative Spectrum Sensing due to interference on sensing channels of Cognitive Radio. Interference Alignment (IA) being a revolutionary wireless transmission strategy that reduces the impact of interference seems well suited as a strategy that can be used to optimize the performance of Cooperative Spectrum Sensing. The idea of IA is to coordinate multiple transmitters so that their mutual interference aligns at their receivers, facilitating simple interference cancellation techniques. Since its inception, research efforts have primarily been focused on verifying IA's ability to achieve the maximum degrees of freedom (an approximation of sum capacity), developing algorithms for determining alignment solutions and designing transmission strategies that relax the need for perfect alignment but yield better performance. With the increased deployment of wireless services, CR's ability to opportunistically sense and access the unused licensed frequency spectrum, without causing harmful interference to the licensed users becomes increasingly diminished, making the concept of introducing IA in CR a very attractive proposition. For a multiuser multiple-input-multiple-output (MIMO) overlay CR network, a space-time opportunistic IA (ST-OIA) technique has been proposed that allows spectrum sharing between a single primary user (PU) and multiple secondary users (SU) while ensuring zero interference to the PUs. With local CSI available at both the transmitters and receivers of SUs, the PU employs a space-time WF (STWF) algorithm to optimize its transmission and in the process, frees up unused eigenmodes that can be exploited by the SU. STWF achieves higher performance than other WF algorithms at low to moderate signal-to-noise ratio (SNR) regimes, which makes it ideal for implementation in CR networks. The SUs align their transmitted signals in such a way their interference impairs only the PU's unused eigenmodes. For the multiple SUs to further exploit the benefits of Cooperative Spectrum Sensing, it was shown in this thesis that IA would only work when a set of conditions were met. The first condition ensures that the SUs satisfy a zero interference constraint at the PU's receiver by designing their post-processing matrices such that they are orthogonal to the received signal from the PU link. The second condition ensures a zero interference constraint at both the PU and SUs receivers i.e. the constraint ensures that no interference from the SU transmitters is present at the output of the post-processing matrices of its unintended receivers. The third condition caters for the multiple SUs scenario to ensure interference from multiple SUs are aligned along unused eigenmodes. The SU system is assumed to employ a time division multiple access (TDMA) system such that the Principle of Reciprocity is employed towards optimizing the SUs transmission rates. Since aligning multiple SU transmissions at the PU is always limited by availability of spatial dimensions as well as typical user loads, the third condition proposes a user selection algorithm by the fusion centre (FC), where the SUs are grouped into clusters based on their numbers (i.e. two SUs per cluster) and their proximity to the FC, so that they can be aligned at each PU-Rx. This converts the cognitive IA problem into an unconstrained standard IA problem for a general cognitive system. Given the fact that the optimal power allocation algorithms used to optimize the SUs transmission rates turns out to be an optimal beamformer with multiple eigenbeams, this work initially proposes combining the diversity gain property of STBC, the zero-forcing function of IA and beamforming to optimize the SUs transmission rates. However, this solution requires availability of CSI, and to eliminate the need for this, this work then combines the D-STBC scheme with optimal IA precoders (consisting of beamforming and zero-forcing) to maximize the SUs data rates.

Στην παρούσα διπλωματική εργασία μελετάμε τα πλεονεκτήματα που επιφέρει η χρήση πολλαπλών κεραιών στον πομπό και στον δέκτη, κατά την μετάδοση, με στόχο την βελτίωση των παρεχομένων υπηρεσιών στο χρήστη. Στο Κεφάλαιο 1, γίνεται μια ιστορική αναδρομή των ασύρματων επικοινωνιών καθώς των σύγχρονων ασύρματων τεχνολογιών και κεραιών που χρησιμοποιούνται. Στη συνέχεια γίνεται μια αναφορά στις έννοιες του διαφορισμού, του κέρδους διάταξης και της χωρικής πολυπλεξίας οι οποίες συνδέονται άρρηκτα με τα συστήματα MIMO. Στο Κεφάλαιο 2, αναφερόμαστε σε όλα εκείνα τα χαρακτηριστικά που περιγράφουν το ασύρματο κανάλι και εξάγουμε την γραμμική σχέση εισόδου-εξόδου του ασύρματου καναλιού. Στην συνέχεια γίνεται μια ανάλυση των στοχαστικών μοντέλων περιγραφής του ασύρματου διαύλου διαλείψεων και πιο συγκεκριμένα των μοντέλων Rayleigh και Rice. Στο Κεφάλαιο 3 εξετάζουμε την αξιοπιστία διαφόρων τύπων κεραιοσυστημάτων, ως προς τον ρυθμό των ρυθμό των λανθασμένων συμβόλων στον δέκτη. Πιο συγκεκριμένα εξετάζεται η τεχνική Maximal Ratio Combining για τα συστήματα SIMO καθώς και του σχήματος Alamouti για τα συστήματα ΜISO. Συνεχίζοντας στα MIMO συστήματα αναλύουμε τις μεθόδους ισοστάθμισης για την ανάκτηση των δεδομένων, και πιο συγκεκριμένα τις τεχνικές Zero Forcing, Minimum Mean Square Error,V-Blast και καθώς και την βέλτιστη τεχνική Maximum Likelihood. Στο τελευταίο μέρος της εργασίας αναλύουμε τα πλεονεκτήματα των MIMO συστημάτων, ως προς την χωρητικότητα που προσφέρουν, σε στοχαστικά κανάλια διαλείψεων.Στη συνέχεια, γίνεται αναφορά στην μέθοδο SVD και στην αναπαράσταση του MIMO καναλιού από έναν αριθμό ανεξάρτητων SISO διαύλων. Κλείνοντας αναφέρουμε την μέθοδο βέλτιστης κατανομής ισχύος στις κεραίες του πομπού Water-filling, και στην περαιτέρω αύξηση της χωρητικότητας του διαύλου που προσφέρει. / In this diploma thesis we are investigating the benefits of using Multiple Input and Multiple Output antennas in information transmission, with final goal to improve Quality of Service. The first Chapter, includes a historical background of the wireless communications but also is a reference to the modern wireless and antenna technologies. Moreover, we introduce the definition of new concepts, such as diversity and array gain and also spatial multiplexing, which are closely connected with MIMO technology. In the second chapter, we introduce the characteristics which they are describe the wireless channel, while simultaneously we mention the linear input-output relationship of the wireless channel. Additionally, we analyze the stochastic wireless channel models, namely the Rayleigh and the Rician fading models. In the third chapter, we investigate the reliability of different types of antenna topologies, regarding the pace of the invalid symbols in the transmitter. More specifically, we examine the Maximal Ratio Combining and Alamouti technique, for SIMO and MISO systems respectively. The next step is to analyze the equalization methods, which are used in MIMO antennas, and more specifically are, Zero Forcing, Minimum Mean Square Error and V-Blast receivers, but also the optimal Maximum Likelihood equalizer. In the last part of this Thesis, we investigate the benefits of MIMO systems regarding the Capacity, in random channels. Also, a reference to the SVD method has been made,which we use to analyze the MIMO channel, in a number of parallel SISO channels. Lastly, we use the water-filling method to allocate, with the optimal way, the given power in the transmit antennas, a fact that leads to even greater Capacity gain.