Optimized transmission and selection designs in wireless systems
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Most modern wireless communication systems are hierarchical complex systems which consist of many levels of design elements and are subject to limited resources (e.g. power or bandwidth). Thanks to numerous newly-introduced devices in different forms such as sensors and relays and the integration of multiple antennas, spectral efficiency and reliability of wireless transmission could be significantly improved. Nevertheless, it also becomes much more challenging to control the devices and allocate the limited resources in an optimal fashion in order to approach capacity gains. This dissertation is concerned with mixed-binary or combinatorial optimization problems to improve various service goals for a variety of interesting yet difficult wireless communication applications. These problems are highly prized for academic significance but remained open due to their mathematical challenges. We shall explore the hidden d.c. (difference of convex (or concave) functions) structure of the objective functions as well as the binary constraints. Further, we will prove such general d.c. programs can be equivalently converted into canonical d.c. programs with d.c. objective functions that are subject to convex and/or affine constraints only. Although global optimal algorithms are generally possible for such d.c. programs, they are normally very computation-intensive. Instead, we propose tailored path-following local-optimal d.c. algorithms with significantly reduced computational complexity. Through extensive simulation results, the designed d.c. decompositions of the problems are proven effective. The proposed algorithms are efficient and computationally affordable while locating outstanding solutions in comparison with other existing algorithms. In those more sophisticated problem scenarios, the d.c. algorithm appears to be the only suitable option thanks to the superior flexibility. In the first part of the thesis, we will consider a sensor network for spectrum sensing in the context of cognitive radios. To improve sensing quality and prolong the battery life of sensors, the least correlated subset of sensors needs to be selected. A new Bregman matrix deviation-based framework is shown applicable to all the concerned correlation measure functions. The second research investigates a relay-assisted multi-user wireless network. Besides the relay beamforming variables, we add into consideration a set of binary link variables which represent on/off operations of individual relays in relation to transmitter-receiver links. To achieve the maximin SNR or SINR capacity, certain relays may be optimally deactivated. This leads to reduced power consumption and complexity/ overhead of management. The relay assignment and beamforming design is a joint mixed combinatorial nonlinear program which is non-convex and non-smooth. Nonetheless, we show the it can be fit into a canonical d.c. optimization framework. Simulation results demonstrate the benefits of relay selection and beamforming. The last research stems from the study of conventional coordinated transmission design with respect to transmit covariance and precoding matrix/vector variables. Inspired by the well-known Han-Kobayashi message splitting method in 2-user SISO interference channels, we further extend the idea of message splitting to the MIMO interference networks. An innovative non-smooth rate formula is discovered which builds the foundation of the work. The design in common and private covariance matrices or beamforming vectors, as well as the pairing variables, is formulated as a joint combinatorial nonlinear program which is non-convex and non-smooth. Due to the great difficulty, it is not imminently possible to jointly handle both variables. Therefore, we first propose an intuitive heuristic pairing algorithm to find excellent pairing choices. Then, the non-convex optimization problems in covariance matrices or beamforming vector variables are dealt with in the d.c. optimization framework. Finally, simulation results reveal the great potential of the novel message splitting scheme in approaching rate capacity.
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