Multivariate statistics play an important role in performance analysis of wireless communication systems in correlated fading channels. This thesis presents a framework which can be used to derive easily computable mathematical representations for some multivariate statistical distributions, which are derivatives of the Gaussian distribution, and which have a particular correlation structure. The new multivariate distribution representations are given as single integral solutions of familiar mathematical functions which can be evaluated using common mathematical software packages. The new approach can be used to obtain single integral representations for the multivariate probability density function, cumulative distribution function, and joint moments of some widely used statistical distributions in wireless communication theory, under an assumed correlation structure. The remarkable advantage of the new representation is that the computational burden remains at numerical evaluation of a single integral, for a distribution with an arbitrary number of dimensions. The new representations are used to evaluate the performance of diversity combining schemes and multiple input multiple output systems, operating in correlated fading channels. The new framework gives some insights into some long existing open problems in multivariate statistical distributions. / Communications

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Next generation of wireless communication mostly relies on multiple-input multipleoutput (MIMO) configuration and full-duplex relaying to improve data-rates, spectrale efficiency, spatial-multiplexing, quality-of-service and energy-efficiency etc. However, multiple radio frequency (RF) transceivers in MIMO system and multi-hops in relay networks, accumulate transceiver impairments, rendering an unacceptable system performance. Majority of the technical contributions either assume ideal hardware or inappropriately model hardware impairments which often induce misleading results especially for high data-rate communication systems. We propose statistical mathematical modeling of various hardware impairment (HWI) to characterize their deteriorating effects on the information signal. In addition, we model the aggregate HWI as improper Gaussian signaling (IGS), to fully characterize their asymmetric properties and the self-interfering signal attribute under I/Q imbalance. The proposed model encourages to adopt asymmetric transmission scheme, as opposed to traditional symmetric signaling. First, we present statistical baseband equivalent mathematical models for general MIMO system and two special scenarios of receive and transmit diversity systems under HWI. Then, we express their achievable rate under PGS and IGS transmit schemes. Moreover, we tune the IGS statistical characteristics to maximize the achievable rate. We also present optimal beam-forming/pre-coding and receive combiner vector for multiple-input single-output (MISO) and single-input multiple output (SIMO) systems, which lead to SDNR maximization. Moreover, we propose an adaptive scheme to switch between maximal IGS (MIGS) and PGS transmission based on the described conditions to reduce computational overhead. Subsequently, two case studies are presented. 1) Outage analysis has been carried out for SIMO, under transceiver distortion noise, for two diversity combining schemes 2) The benefits of employing IGS is investigated in full duplex relaying (FDR) suffering from two types of interference, the residual self-interference (RSI) and I/Q distortions. We further optimize the pseudo-variance to compensate the interference impact and improve end-to-end achievable rate. Finally, we validate the analytic expressions through simulation results, to quantify the performance degradation in the absence of ideal transceivers and the gain reaped from adopting IGS scheme compared with PGS scheme.

Employment of the multiple-antenna transmitters/receivers in communication systems is known as a promising solution to provide high-data-rate wireless links. In the multi-user environments, the problems of signaling and fairness for multi-antenna systems have emerged as challenging problems. This dissertation deals with these problems in several multi-antenna multi-user scenarios. In part one, a simple signaling method for the multi-antenna broadcast channels is proposed. This method reduces the MIMO broadcast system to a set of parallel channels. The proposed scheme has several desirable features in terms of: (i) accommodating users with different number of receive antennas, (ii) exploiting multi-user diversity, and (iii) requiring low feedback rate. The simulation results and analytical evaluations indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel. In part two, for multiple-antenna systems with two transmitters and two receivers, a new non-cooperative scenario of data communication is studied in which each receiver receives data from both transmitters. For such a scenario, a signaling scheme is proposed which decomposes the system into two broadcast or two multi-access sub-channels. Using the decomposition scheme, it is shown that this signaling scenario outperforms the other known non-cooperative schemes in terms of the achievable multiplexing gain. In particular for some special cases, the achieved multiplexing gain is the same as the multiplexing gain of the system, where the full cooperation is provided between the transmitters and/or between the receivers. Part three investigates the problem of fairness for a class of systems for which a subset of the capacity region, which includes the sum-capacity facets, forms a polymatroid structure. The main purpose is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. This problem is addressed in the cases where the complexity of achieving interior points is not feasible, and where the complexity of achieving interior points is feasible. In part four, $K$-user memoryless interference channels are considered; where each receiver sequentially decodes the data of a subset of transmitters before it decodes the data of the designated transmitter. A greedy algorithm is developed to find the users which are decoded at each receiver and the corresponding decoding order such that the minimum rate of the users is maximized. It is proven that the proposed algorithm is optimal. The results of the parts three and four are presented for general channels which include the multiple-antenna systems as special cases.

Employment of the multiple-antenna transmitters/receivers in communication systems is known as a promising solution to provide high-data-rate wireless links. In the multi-user environments, the problems of signaling and fairness for multi-antenna systems have emerged as challenging problems. This dissertation deals with these problems in several multi-antenna multi-user scenarios. In part one, a simple signaling method for the multi-antenna broadcast channels is proposed. This method reduces the MIMO broadcast system to a set of parallel channels. The proposed scheme has several desirable features in terms of: (i) accommodating users with different number of receive antennas, (ii) exploiting multi-user diversity, and (iii) requiring low feedback rate. The simulation results and analytical evaluations indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel. In part two, for multiple-antenna systems with two transmitters and two receivers, a new non-cooperative scenario of data communication is studied in which each receiver receives data from both transmitters. For such a scenario, a signaling scheme is proposed which decomposes the system into two broadcast or two multi-access sub-channels. Using the decomposition scheme, it is shown that this signaling scenario outperforms the other known non-cooperative schemes in terms of the achievable multiplexing gain. In particular for some special cases, the achieved multiplexing gain is the same as the multiplexing gain of the system, where the full cooperation is provided between the transmitters and/or between the receivers. Part three investigates the problem of fairness for a class of systems for which a subset of the capacity region, which includes the sum-capacity facets, forms a polymatroid structure. The main purpose is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. This problem is addressed in the cases where the complexity of achieving interior points is not feasible, and where the complexity of achieving interior points is feasible. In part four, $K$-user memoryless interference channels are considered; where each receiver sequentially decodes the data of a subset of transmitters before it decodes the data of the designated transmitter. A greedy algorithm is developed to find the users which are decoded at each receiver and the corresponding decoding order such that the minimum rate of the users is maximized. It is proven that the proposed algorithm is optimal. The results of the parts three and four are presented for general channels which include the multiple-antenna systems as special cases.

[pt] Os sistemas de múltiplas antenas empregam diferentes técnicas de processamento de sinais em ambos extremos do sistema de comunicações para se beneficiar das múltiplas dimensões espaciais e transmitir para diversos usuarios usando os mesmos recursos de tempo e frequência. Desta forma, uma alta eficiência espectral pode ser atingida sem precisar de largura de banda extra. No entanto, o desempenho depende de uma estimativa do canal altamente precisa do lado do transmissor, a qual é denominada channel state information at the transmitter (CSIT). Se o valor estimado do canal for perfeito, o sistema consegue suprimir a interferência multiusuário (MUI), que é a principal responsável pela degradação do desempenho do sistema. Porém, supor uma estimativa perfeita é bastante otimista pois sistemas reais introduzem incerteza devido ao processo de estimação, a erros de quantização e a retardos próprios dos sistemas. Nesse contexto, a técnica conhecida como divisão de taxas ou rate splitting (RS) surge como uma ferramenta promissora para lidar com as imperfeições na estimativa do canal. RS divide os dados em um fluxo comum e vários fluxos privados e então sobrepõe o fluxo comum no topo dos fluxos privados. Esta tese propõe várias técnicas de processamento que aumentam ainda mais os benefícios dos sistemas RS. Neste trabalho, consideramos o downlink (DL) de um sistema de comunicações sem fio onde o transmissor envia mensagens independentes para cada usuário. A métrica usada para avaliar o desempenho do sistema é a soma das taxas ergódica (ESR). Diferente dos trabalhos convencionais em RS, consideramos que os terminais dos usuários estão equipados com múltiplas antenas. Isso nos permite implementar na recepção combinadores de fluxos que aumentem a taxa do fluxo comum. Aumentar esta taxa é um dos grandes problemas dos sistemas RS, uma vez que a taxa comum é limitada pelo pior usuário o que pode degradar fortemente o desempenho do sistema. Assim, três combinadores de fluxos diferentes são propostos e as expressões analíticas para calcular a soma das taxas são apresentadas. Os combinadores são derivados empregando-se os critérios Min-Max, MRC e MMSE. O critério Min-Max seleciona para cada usuário a melhor antena para decodificar o símbolo comum. O MRC visa maximizar o SNR ao decodificar o símbolo comum. Finalmente, o critério MMSE minimiza o quadrado da diferença entre o símbolo comum e o sinal recebido. Até o momento, RS foi considerado com precodificadores lineares. Devido a isto, neste trabalho investigamos o desempenho do RS com precodificadores não lineares. Para este fim, usamos diferentes tipos de precodificador Tomlinson-Harashima (THP) baseados nos precodificadores lineares ZF e MMSE. Em seguida, propomos um algoritmo multi-branch (MB) adequado para o RS-THP proposto. Este algoritmo cria vários padrões de transmissão e seleciona o melhor padrão para efetuar a transmissão. Esta técnica de préprocessamento aumentam ainda mais a soma das taxas obtida, uma vez que o desempenho do THP depende da ordem dos símbolos, porém também aumenta a complexidade computacional. Expressões analíticas para calcular a soma das taxas das técnicas propostas são derivadas por meio de análises estatísticas dos principais parâmetros. Finalmente, propomos quatro técnicas adaptativas diferentes de alocação de potência, as quais se caracterizam por sua baixa complexidade computacional. Duas destas técnicas são projetadas para sistemas SDMA convencionais, enquanto as outras duas são projetadas para sistemas RS. Um dos principais objetivos dos algoritmos propostos é realizar uma alocação de potência robusta capaz de lidar com os efeitos prejudicias das imperfeições no CSIT. É importante mencionar que a alocação de potência em sistemas RS é uma das tarefas mais importantes e deve ser realizada com extremo cuidado. Se a potência não for alocada corretamente, o desempenho do sistema RS será bastante degradado e as arquiteturas convencionais, como SDMA e NOMA, poderão ter um desempenho melhor. No entanto, a alocação de potência em sistemas RS precisa da solução de problemas complexos de otimização, o que aumenta o tempo gasto no processamento do sinal. Os algoritmos adaptativos propostos reduzem a complexidade computacional e são uma solução atrativa para aplicações práticas em sistemas de grande porte. / [en] Multiple-antenna systems employ different signal processing techniques at both ends of the communication to exploit the spatial dimensions and serve multiple users simultaneously in the same time-frequency domain. In this way, high spectral efficiency can be reached without the need of extra bandwidth. However, such gain depends on a highly accurate channel state information at the transmitter (CSIT). Perfect CSIT allows the system to suppress the multi user interference (MUI), which is the main responsible of the performance degradation. Nonetheless, assuming perfect CSIT is rather optimistic since the estimation procedure, quantization errors and delays of real system lead to CSIT uncertainties. In this context, rate splitting (RS) has arisen as a promising technique to deal with CSIT imperfections. Basically, RS splits the data into a common stream and private streams and then superimposes the common stream on top of the private streams. This thesis proposes several processing techniques which further enhance the benefits of RS systems. We consider the downlink (DL) of a wireless communications system, where the transmitter sends independent messages to each receiver. The ergodic sum rate (ESR) is adopted as the main metric to evaluate the performance of the system. Different from conventional RS works, we consider that the users are equipped with multiple antennas. This allows us to implement stream combiners for the common stream at the receivers. The implementations of the stream combiners improves the common rate performance, which is a major problem of RS systems since the common rate is limited by the performance of the worst user and can be heavily degraded. In this work, three different stream combiners are proposed along with analytical expressions to compute their sum rate performance. Specifically, the combiners are derived employing the min-max, maximum ratio combining (MRC), and minimum mean square error (MMSE) criteria. The min-max criterion selects at each user the best receive antenna to decode the common symbol. The MRC criterion aims at maximizing the SNR when decoding the common symbol. Finally, the MMSE criterion minimizes the squared difference between the common symbol and the received signal. So far, RS has been predominantly considered with channel inversiontype linear precoders. Therefore, this motivates us to investigate the performance of RS with non-linear precoders. For this purpose, we employ different architectures of the Tomlinson-Harashima precoder (THP) which are based on the zero-forcing (ZF) and MMSE precoders. We then propose a multi-branch (MB) algorithm for the proposed RS-THP, which creates several transmit patterns and selects the best for transmission. This pre-processing techniques further enhance the sum rate obtained since the performance of THP is dependent on the symbol ordering but also increases the computational complexity. Analytical expressions to calculate the sum rate of the proposed techniques are derived through statistical evaluation of key parameters. Finally, we propose four different adaptive power allocation techniques, which are characterized by their low computational complexity. Two of them are designed for conventional SDMA systems whereas the other two are intended for RS systems. One major objective of the proposed algorithms is to perform robust power allocation capable of dealing with the detrimental effects of imperfect CSIT. It is important to mention that power allocation in RS systems is one of the critical tasks that should be carefully performed. If the power is not properly allocated the performance of RS systems is heavily degraded and conventional architectures such as SDMA and NOMA could perform better. However, RS rely on solving complex optimization problems to perform power allocation, increasing the time and effort dedicated to signal processing. The proposed adaptive power allocation algorithms reduce the computational complexity and are an attractive solution for practical applications with large-scale systems.

Multiple-Input Multiple-Output (MIMO) communication using multiple antennas has received significant attention in recent years, both in the academia and industry, as they offer additional spatial dimensions for high-rate and reliable communication, without expending valuable bandwidth. However, exploiting these promised benefits of MIMO systems critically depends on fast and accurate acquisition of Channel State Information (CSI) at the Receiver (CSIR) and the Transmitter (CSIT). In Time Division Duplex (TDD) MIMO systems, where the forward channel and the reverse channel are the same, it is possible to exploit this reciprocity to reduce the overhead involved in acquiring CSI, both in terms of training duration and power. Further, many popular and efficient transmission schemes such as beam forming, spatial multiplexing over dominant channel modes, etc. do not require full CSI at the transmitter. In such cases, it is possible to reduce the Reverse Channel Training (RCT) overhead by only learning the part of the channel that is required for data transmission at the transmitter. In this thesis, we propose and analyze several novel channel-dependent RCT schemes for MIMO systems and analyze their performance in terms of (a) the mean-square error in the channel estimate, (b) lower bounds on the capacity, and (c) the diversity-multiplexing gain tradeoff. We show that the proposed training schemes offer significant performance improvement relative to conventional channel-agnostic RCT schemes. The main take-home messages from this thesis are as follows: • Exploiting CSI while designing the RCT sequence improves the performance. • The training sequence should be designed so as to convey only the part of the CSI required for data transmission by the transmitter. • Power-controlled RCT, when feasible, significantly outperforms fixed power RCT.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.