Lattice reduction aided techniques have been successfully applied to a wide range of applications. Efficient and robust lattice basis reduction algorithms are valuable. In this thesis, we present an O(n^4 logB) hybrid Jacobi method for lattice basis reduction, where n is the dimension of the lattice and B is the maximum length of the input lattice basis vectors. Building upon a generic Jacobi method for lattice basis reduction, we integrate the size reduction into the algorithm to improve its performance. To ensure the convergence and the efficiency of the algorithm, we introduce a parameter to the Lagrange reduction. To improve the quality of the computed bases, we impose a condition on the size reduction, delay the structure restoration, and include a postprocessing in the hybrid method. Our experiments on random matrices show that the proposed algorithm produces better reduced bases than the well-known LLL algorithm and BKZ 2.0 algorithm, measured by both the orthogonality defect and the condition number of the basis matrix. Moreover, our hybrid method consistently runs faster than the LLL algorithm, although they have the same theoretical complexity. We have also investigated two potential applications of the hybrid method. The application simulations show that the hybrid method can improve the stability of the communication channels for Multi-Input Multi-Output systems, and can partially discover the plain text when attacking the GGH cryptosystem. / Thesis / Doctor of Philosophy (PhD) / Lattice reduction aided techniques have been successfully applied to a wide range of applications. Efficient and robust lattice basis reduction algorithms are valuable. In this thesis, we present an O(n^4 logB) hybrid Jacobi method for lattice basis reduction, where n is the dimension of the lattice and B is the maximum length of the input lattice basis vectors. Our experiments on random matrices show that the proposed algorithm produces better reduced bases than the well-known LLL algorithm and BKZ 2.0 algorithm, measured by both the orthogonality defect and the condition number of the basis matrix. We have also investigated two potential applications in MIMO systems and cryptosystems.

In todays society, a growing number of users are demanding more sophisticated services from wireless communication devices. In order to meet these rising demands, it has been proposed to increase the capacity of the wireless channel by using more than one antenna at the transmitter and receiver, thereby creating multiple-input multiple-output (MIMO) channels. Using MIMO communication techniques is a promising way to improve wireless communication technology because in a rich-scattering environment the capacity increases linearly with the number of antennas. However, increasing the number of transmit antennas also increases the complexity of detection at an exponential rate. So while MIMO channels have the potential to greatly increase the capacity of wireless communication systems, they also force a greater computational burden on the receiver. Even suboptimal MIMO detectors that have relatively low complexity, have been shown to achieve unprecedented high spectral efficiency. However, their performance is far inferior to the optimal MIMO detector, meaning they require more transmit power. The fact that the optimal MIMO detector is an impractical solution due to its prohibitive complexity, leaves a performance gap between detectors that require reasonable complexity and the optimal detector. The objective of this research is to bridge this gap and provide new solutions for managing the inherent performance-complexity trade-off in MIMO detection. The optimally-ordered decision-feedback (BODF) detector is a standard low-complexity detector. The contributions of this thesis can be regarded as ways to either improve its performance or reduce its complexity - or both. We propose a novel algorithm to implement the BODF detector based on noise-prediction. This algorithm is more computationally efficient than previously reported implementations of the BODF detector. Another benefit of this algorithm is that it can be used to easily upgrade an existing linear detector into a BODF detector. We propose the partial decision-feedback detector as a strategy to achieve nearly the same performance as the BODF detector, while requiring nearly the same complexity as the linear detector. We propose the family of Chase detectors that allow the receiver to trade performance for reduced complexity. By adapting some simple parameters, a Chase detector may achieve near-ML performance or have near-minimal complexity. We also propose two new detection strategies that belong to the family of Chase detectors called the B-Chase and S-Chase detectors. Both of these detectors can achieve near-optimal performance with less complexity than existing detectors. Finally, we propose the double-sorted lattice-reduction algorithm that achieves near-optimal performance with near-BODF complexity when combined with the decision-feedback detector.

Receiver design, especially equalizer design, in communications is a major concern in both academia and industry. It is a problem with both theoretical challenges and severe implementation hurdles. While much research has been focused on reducing complexity for optimal or near-optimal schemes, it is still common practice in industry to use simple techniques (such as linear equalization) that are generally significantly inferior. Although digital signal processing (DSP) technologies have been applied to wireless communications to enhance the throughput, the users' demands for more data and higher rate have revealed new challenges. For example, to collect the diversity and combat fading channels, in addition to the transmitter designs that enable the diversity, we also require the receiver to be able to collect the prepared diversity. Most wireless transmissions can be modeled as a linear block transmission system. Given a linear block transmission model assumption, maximum likelihood equalizers (MLEs) or near-ML decoders have been adopted at the receiver to collect diversity which is an important metric for performance, but these decoders exhibit high complexity. To reduce the decoding complexity, low-complexity equalizers, such as linear equalizers (LEs) and decision feedback equalizers (DFEs) are often adopted. These methods, however, may not utilize the diversity enabled by the transmitter and as a result have degraded performance compared to MLEs. In this dissertation, we will present efficient receiver designs that achieve low bit-error-rate (BER), high mutual information, and low decoding complexity. Our approach is to first investigate the error performance and mutual information of existing low-complexity equalizers to reveal the fundamental condition to achieve full diversity with LEs. We show that the fundamental condition for LEs to collect the same (outage) diversity as MLE is that the channels need to be constrained within a certain distance from orthogonality. The orthogonality deficiency (od) is adopted to quantify the distance of channels to orthogonality while other existing metrics are also introduced and compared. To meet the fundamental condition and achieve full diversity, a hybrid equalizer framework is proposed. The performance-complexity trade-off of hybrid equalizers is quantified by deriving the distribution of od. Another approach is to apply lattice reduction (LR) techniques to improve the ``quality' of channel matrices. We present two widely adopted LR methods in wireless communications, the Lenstra-Lenstra-Lovasz (LLL) algorithm [51] and Seysen's algorithm (SA), by providing detailed descriptions and pseudo codes. The properties of output matrices of the LLL algorithm and SA are also quantified. Furthermore, other LR algorithms are also briefly introduced. After introducing LR algorithms, we show how to adopt them into the wireless communication decoding process by presenting LR-aided hard-output detectors and LR-aided soft-output detectors for coded systems, respectively. We also analyze the performance of proposed efficient receivers from the perspective of diversity, mutual information, and complexity. We prove that LR techniques help to restore the diversity of low-complexity equalizers without increasing the complexity significantly. When it comes to practical systems and simulation tool, e.g., MATLAB, only finite bits are adopted to represent numbers. Therefore, we revisit the diversity analysis for finite-bit represented systems. We illustrate that the diversity of MLE for systems with finite-bit representation is determined by the number of non-vanishing eigenvalues. It is also shown that although theoretically LR-aided detectors collect the same diversity as MLE in the real/complex field, it may show different diversity orders when finite-bit representation exists. Finally, the VLSI implementation of the complex LLL algorithms is provided to verify the practicality of our proposed designs.

Cette thèse traite des systèmes MIMO à multiplexage spatial, associés à la modulation OFDM. L'étude s'attarde particulièrement sur les systèmes 4x4, inclus ou à l'étude dans les normes 3GPP LTE et 3GPP LTE-A. Ces dimensions particulières nécessitent une étude de conception poussée du récepteur. Il s'agit notamment de proposer des détecteurs qui affichent à la fois de bonnes performances, une faible latence et une complexité de calcul réalisable dans un système embarqué. Le défi consiste plus particulièrement à proposer un détecteur offrant des performances quasi-optimales, tout en ne nécessitant qu'une complexité de calcul polynomiale. Une attention particulière est prêtée aux problèmes d'implantation. Ainsi, avantage est donné aux algorithmes à complexité fixe et permettant la réalisation d'opérations en parallèle. En réponse aux problématiques rencontrées, l'architecture du détecteur requiert une attention particulière. Le choix stratégique adopté est de chercher à transférer au prétraitement - qui ne dépend pas des données - le plus possible de complexité de calcul. Au cours de ce travail et suite à l'introduction du contexte général et des principaux pré-requis, l'inventaire des grandes tendances dans la littérature en ce qui concerne les détecteurs à décision dure est fait. Ils constituent le coeur du sujet et un détecteur original est proposé, incluant notamment les aspects de réduction de réseau et de décodage sphérique. Son avantage par rapport aux techniques existantes est ainsi démontré, et les résultats prometteurs sont maintenus lors de son extension à la décision souple. Comme attendu, le choix de transférer au prétraitement la complexité de calcul s'avère gagnant. Notamment, la réduction de complexité de calcul qu'il permet est présentée dans cette thèse. Parmi les principaux résultats, ce travail a débouché sur la proposition d'un détecteur original, qui a démontré un compromis entre performance et complexité de calcul efficace. Notamment, il requiert une complexité de calcul presque constante - selon les tailles de constellation -, tout en offrant des performances proches du maximum de vraisemblance. Par conséquent, le détecteur à décision souple proposé se positionne par rapport à l'état de l'art comme une solution d'une grande efficacité dans les systèmes 4x4.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.

In wireless networks, reliable communication is a challenging issue due to many attenuation factors such as receiver noise, channel fading, interference and asynchronous delays. Lattice coding and decoding provide efficient solutions to many problems in wireless communications and multiuser information theory. The capability in achieving the fundamental limits, together with simple and efficient transmitter and receiver structures, make the lattice strategy a promising approach. This work deals with problems of lattice detection over fading channels and time asynchronism over the lattice-based compute-and-forward protocol. In multiple-input multiple-output (MIMO) systems, the use of lattice reduction significantly improves the performance of approximate detection techniques. In the first part of this thesis, by taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction methods are investigated. We show that updating the reduced lattice basis adaptively with a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance. Considering high data rate MIMO systems, we then investigate soft-output detection methods. Using the list sphere decoder (LSD) algorithm, an adaptive method is proposed to reduce the complexity of generating the list for evaluating the log-likelihood ratio (LLR) values. In the second part, by applying the lattice coding and decoding schemes over asynchronous networks, we study the impact of asynchronism on the compute-and-forward strategy. While the key idea in compute-and-forward is to decode a linear synchronous combination of transmitted codewords, the distributed relays receive random asynchronous versions of the combinations. Assuming different asynchronous models, we design the receiver structure prior to the decoder of compute-and-forward so that the achievable rates are maximized at any signal-to-noise-ratio (SNR). Finally, we consider symbol-asynchronous X networks with single antenna nodes over time-invariant channels. We exploit the asynchronism among the received signals in order to design the interference alignment scheme. It is shown that the asynchronism provides correlated channel variations which are proved to be sufficient to implement the vector interference alignment over the constant X network.

In wireless networks, reliable communication is a challenging issue due to many attenuation factors such as receiver noise, channel fading, interference and asynchronous delays. Lattice coding and decoding provide efficient solutions to many problems in wireless communications and multiuser information theory. The capability in achieving the fundamental limits, together with simple and efficient transmitter and receiver structures, make the lattice strategy a promising approach. This work deals with problems of lattice detection over fading channels and time asynchronism over the lattice-based compute-and-forward protocol. In multiple-input multiple-output (MIMO) systems, the use of lattice reduction significantly improves the performance of approximate detection techniques. In the first part of this thesis, by taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction methods are investigated. We show that updating the reduced lattice basis adaptively with a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance. Considering high data rate MIMO systems, we then investigate soft-output detection methods. Using the list sphere decoder (LSD) algorithm, an adaptive method is proposed to reduce the complexity of generating the list for evaluating the log-likelihood ratio (LLR) values. In the second part, by applying the lattice coding and decoding schemes over asynchronous networks, we study the impact of asynchronism on the compute-and-forward strategy. While the key idea in compute-and-forward is to decode a linear synchronous combination of transmitted codewords, the distributed relays receive random asynchronous versions of the combinations. Assuming different asynchronous models, we design the receiver structure prior to the decoder of compute-and-forward so that the achievable rates are maximized at any signal-to-noise-ratio (SNR). Finally, we consider symbol-asynchronous X networks with single antenna nodes over time-invariant channels. We exploit the asynchronism among the received signals in order to design the interference alignment scheme. It is shown that the asynchronism provides correlated channel variations which are proved to be sufficient to implement the vector interference alignment over the constant X network.

Systems with multiple transmitting and receiving antennas in large-scale (LS-MIMO - large-scale multipleinput multiple-output) enable high spectral and energy efficiency gains, which results in an increase in the data transmission rate in the same band, without increasing the transmitted power per user. In addition, with the increase of the number of antennas in the base station (BS) it is possible to attend to a larger number of users per cell, in the same occupied band. Furthermore, it has been found in the literature that the reported advantages of LS-MIMO systems can be obtained with a large number of antennas on at least one side of the communication, usually in BS due to physical restriction in user equipments. However, such advantages have their cost: the use of a large number of antennas also difficult tasks involving signal processing, such as estimation of channel coefficients, precoding and signal detection. It is at this juncture that this Doctoral Thesis is developed, in which the computational complexity of performing efficient detection methods in LSMIMO communication systems is explored through the analysis of algorithms and optimization techniques in the solution of specific problems and still open. More precisely, this Thesis discusses and proposes promising detection techniques in LS-MIMO systems, aiming to improve performance metrics - in terms of error rate - and computational complexity - in terms of the number of mathematical operations. Initially, the problem is introduced through a conventional MIMO system model, where channels with imperfect estimates and correlation between transmitter (Tx) and receiver (Rx) antennas are considered. Preprocessing techniques based on lattice reduction (LR) are applied in linear detectors, in addition to the sphere decoder (SD), which proposes a lookup table procedure in order to provide a reduction in computational complexity. It is shown that the LR method in the pre-detection results in a significant performance gain in both the condition of uncorrelated and correlated channels, and in the latter scenario the improvement is even more remarkable due to the diversity gain provided. On the other hand, the complexity involved in the application of LR in high correlation scenarios becomes preponderant in linear detectors. In the LR-SD using the lookup table procedure, the optimum gain was reached in all scenarios, as expected, and resulted in a lower complexity than maximum likelihood (ML) detector, even with maximum correlation between antennas, which represents the most complex scenario for the LR technique. Next, the message passing (MP) detector is investigated, which makes use of Markov random fields (MRF) and factor graph (FG) graphical models. Moreover, it is shown in the literature that the message damping (MD) method applied to the MRF detector brings relevant performance gain without increasing computational complexity. On the other hand, the DF value is specified for only a restricted range of scenarios. Numerical results are extensively generated, in order to obtain a range of analysis of the MRF with MD, which resulted in the proposition of an optimal value for the DF, based on numerical curve fitting. Finally, in the face of the MGS detector, two approaches are proposed to reduce the negative impact caused by the random solution when high modulation orders are employed. The first is based on an average between multiple samples, called aMGS (averaged MGS). The second approach deploys a direct restriction on the range of the random solution, limiting in d the neighborhood of symbols that can be sorted, being called d-sMGS. Numerical simulation results show that both approaches result in gain of convergence in relation to MGS, especially: in regions of high system loading, d-sMGS detection demonstrated significant gain in both performance and complexity compared to aMGS and MGS; although in low-medium loading, the aMGS strategy showed less complexity, with performance marginally similar to the others. Furthermore, it is concluded that increasing the dimensions of the system favors a smaller restriction in the neighborhood. / Sistemas com múltiplas antenas transmissoras e múltiplas antenas receptoras em larga escala (LS-MIMO - large-scale multiple-input multiple-output) possibilitam altos ganhos em eficiência espectral e energética, o que resulta em aumento da taxa de transmissão de dados numa mesma banda ocupada, sem acréscimo da potência transmitida por usuário. Além disso, com o aumento do número de antenas na estação rádio-base (BS- base station) possibilita-se o atendimento de maior número de usuários por célula, em uma mesma banda ocupada. Ademais, comprovou-se na literatura que as vantagens relatadas dos sistemas LS-MIMO podem ser obtidas com um grande número de antenas em, pelo menos, um dos lados da comunicação, geralmente na BS devido à restrição física nos dispositivos móveis. Contudo, tais vantagens têm seu custo: a utilização de um grande número de antenas também dificulta tarefas que envolvem processamento de sinais, como estimação dos coeficientes de canal, precodificação e detecção de sinais. É nessa conjuntura em que se desenvolve esta Tese de Doutorado, na qual se explora o compromisso desempenho versus complexidade computacional de métodos eficientes de detecção em sistemas de comunicações LS-MIMO através da análise de algoritmos e técnicas de otimização na solução de problemas específicos e ainda em aberto. Mais precisamente, a presente Tese discute e propõe técnicas promissoras de detecção em sistemas LS-MIMO, visando a melhoria de métricas de desempenho - em termos de taxa de erro - e complexidade computacional - em termos de quantidade de operações matemáticas. Inicialmente, o problema é introduzido através de um modelo de sistema MIMO convencional, em que são considerados canais com estimativas imperfeitas e com correlação entre as antenas transmissoras (Tx) e entre as receptoras (Rx). Aplicam-se técnicas de pré-processamanto baseadas na redução treliça (LR - lattice reduction) em detectores lineares, além do detector esférico (SD - sphere decoder), o qual é proposto um procedimento de tabela de pesquisa a fim de prover redução na complexidade computacional. Mostra-se que o método LR na pré-detecção resulta em ganho de desempenho significante tanto na condição de canais descorrelacionados quanto fortemente correlacionados, sendo que, neste último cenário a melhoria é ainda mais notável, devido ao ganho de diversidade proporcionado. Por outro lado, a complexidade envolvida na aplicação da LR em alta correlação torna-se preponderante em detectores lineares. No LR-SD utilizando o procedimento de tabela de pesquisa, o ganho ótimo foi alcançado em todos os cenários, como esperado, e resultou em complexidade inferior ao detector de máxima verossimilhança (ML - maximum likelihood), mesmo com máxima correlação entre antenas, a qual representa o cenário de maior complexidade a técnica LR. Em seguida, o detector por troca de mensagens (MP - message passing) é investigado, o qual faz uso de modelos grafos do tipo MRF (Markov random fields) e FG (factor graph). Além disso, mostra-se na literatura que o método de amortecimento de mensagens (MD - message damping) aplicado ao detector MRF traz relevante ganho de desempenho sem aumento na complexidade computacional. Por outro lado, o valor do DF (damping factor) é especificado para somente uma variedade restrita de cenários. Resultados numéricos são extensivamente gerados, de forma a dispor de uma gama de análises de comportamento do MRF com MD, resultando na proposição de um valor ótimo para o DF, baseando-se em ajuste de curva numérico. Finalmente, em face ao detector MGS (mixed Gibbs sampling), são propostas duas abordagens visando a redução do impacto negativo causado pela solução aleatória quando altas ordens de modulação são empregadas. A primeira é baseada em uma média entre múltiplas amostras, chamada aMGS (averaged MGS). A segunda abordagem realiza uma restrição direta no alcance da solução aleatória, limitando em até d a vizinhança de símbolos que podem ser sorteados, sendo chamada de d-sMGS (d-simplificado MGS). Resultados de simulação numérica demonstram que ambas abordagens resultam em ganho de convergência em relação ao MGS, destacando-se: em regiões de alto carregamento, a detecção d-sMGS demonstrou ganho expressivo tanto em desempenho quanto em complexidade se comparada à aMGS e MGS; já em baixo-médio carregamentos, a estratégia aMGS demonstrou menor complexidade, com desempenho marginalmente semelhante às demais. Além disso, conclui-se que o aumento do número de dimensões do sistema favorece uma menor restrição na vizinhança.