The main topic of this thesis is based on multiple-input multiple-output (MIMO) wireless communications, which is a novel technology that has attracted great interest in the last twenty years. Conventional MIMO systems using up to eight antennas play a vital role in the urban cellular network, where the deployment of multiple antennas have significantly enhanced the throughput without taking extra spectrum or power resources. The massive MIMO systems “scales” up the benefits that offered by the conventional MIMO systems. Using sixty four or more antennas at the BS not only improves the spectrum efficiency significantly, but also provides additional link robustness. It is considered as a key technology in the fifth generation of mobile communication technology standards network, and the design of new algorithms for these two systems is the basis of the research in this thesis. Firstly, at the receiver side of the conventional MIMO systems, a general framework of bit error rate (BER) approximation for the detection algorithms is proposed, which aims to support an adaptive modulation scheme. The main idea is to utilize a simplified BER approximation scheme, which is based on the union bound of the maximum-likelihood detector (MLD), whereby the bit error rate (BER) performance of the detector for the varying channel qualities can be efficiently predicted. The K-best detector is utilized in the thesis because its quasi- MLD performance and the parallel computational structure. The simulation results have clearly shown the adaptive K-best algorithm, by applying the simplified approximation method, has much reduced computational complexity while still maintaining a promising BER performance. Secondly, in terms of the uplink channel estimation for the massive MIMO systems with the time-division-duplex operation, the performance of the Grassmannian line packing (GLP) based uplink pilot codebook design is investigated. It aims to eliminate the pilot contamination effect in order to increase the downlink achievable rate. In the case of a limited channel coherence interval, the uplink codebook design can be treated as a line packing problem in a Grassmannian manifold. The closed-form analytical expressions of downlink achievable rate for both the single-cell and multi-cell systems are proposed, which are intended for performance analysis and optimization. The numerical results validate the proposed analytical expressions and the rate gains by using the GLP-based uplink codebook design. Finally, the study is extended to the energy efficiency (EE) of the massive MIMO system, as the reduction carbon emissions from the information and communication technology is a long-term target for the researchers. An effective framework of maximizing the EE for the massive MIMO systems is proposed in this thesis. The optimization starts from the maximization of the minimum user rate, which is aiming to increase the quality-of-service and provide a feasible constraint for the EE maximization problem. Secondly, the EE problem is a non-concave problem and can not be solved directly, so the combination of fractional programming and the successive concave approximation based algorithm are proposed to find a good suboptimal solution. It has been shown that the proposed optimization algorithm provides a significant EE improvement compared to a baseline case.

Neste trabalho apresentamos duas caracterizações para o K-funcional do tipo Peetre sobre os espaços compactos 2-homogêneos. Provamos a equivalência no sentido assintótico entre o módulo de suavidade de ordem fracionária e o K-funcional do tipo Peetre, e a equivalência deste último com o raio de aproximação de um operator multiplicativo definido para este propósito. Como consequência obtivemos a desigualdade de Marchaud, neste contexto. Estes resultados generalizam os equivalentes, e bem conhecidos, sobre o contexto esférico. As caracterizações foram aplicadas para mostrar que uma condição abstrata de Hölder, ou de diferenciabilidade de ordem finita, sobre núcleos que geram operadores integrais positivos, implica a obtenção de uma taxa de decrescimento polinomial para suas sequências de autovalores. / We prove two characterization for the Peetre type K-functional on M, a compact two-point homogeneous space. One in terms the rate of approximation of a family of multipliers operator defined to this purpose, and another in terms of the fractional moduli of smoothness. As a direct consequence of those we obtained the Marchaud inequality on this framework. These extend the well known results on the spherical setting. The characterizations are employed to show that an abstract Hölder condition or finite order of differentiability condition imposed on kernels generating certain operators implies a sharp decay rates for their eigenvalues sequences.