Research in wireless communications has been actively carried out in recent years. In order to enable a high data transmission rate, multiple-input multiple-output (MIMO) communications has been proposed and commonly adopted. Accurate channel identification and reliable data detection are major challenges in the implementation of a communications system operating over a wireless fading channel. These issues become even more challenging in MIMO systems since there are many more parameters involved in the estimation processes. This thesis, consisting of four major parts, focuses on applying convex optimization to solve design problems in both MIMO channel estimation and data detection. The first part proposes a novel orthogonal affine precoding technique for jointly optimal channel estimation and symbol detection in a general MIMO frequency-selective fading channel. Additionally, the optimal power allocation between the data and training signals is also analytically derived. The proposed technique is shown to perform much better than other affine precoding techniques in terms of detection error probability and computational complexity. The second part is concerned with the MIMO orthogonal frequency-division multiplexing (OFDM) systems. The superimposed training technique developed in the first part is applied and extended for MIMO-OFDM systems where all the involved transmitters and receivers are assumed to be uncorrelated. Analytical and numerical results confirm that the proposed design can efficiently identify the unknown wireless channel as well as effectively recover the data symbols, while conserving the transmission bandwidth. The third part considers training and precoding designs for OFDM under colored noise environment. The superiority of the proposed design over the previously-known design under colored noise is thoroughly demonstrated. The last part of the thesis develops the orthogonal affine precoder for spatially correlated MIMO-OFDM systems. The optimal superimposed training sequences are solved by tractable semi-definite programming. To have a better computational efficiency, two approximate design techniques are also presented. Furthermore, the non-redundancy precoder proposed in the third part is employed to combat channel correlation. As a result, the proposed designs are demonstrated to outperform other known designs in terms of channel estimation and data detection.

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Power system generators are interconnected in a distributed network to allow sharing of power. If one of the generators cannot meet the power demand, spare power is diverted from neighbouring generators. However, this approach also allows for propagation of electric disturbances. An oscillation arising from a disturbance at a given generator site will affect the normal operation of neighbouring generators and might cause them to fail. Hours of production time will be lost in the time it takes to restart the power plant. If the disturbance is detected early, appropriate control measures can be applied to ensure system stability. The aim of this study is to improve existing algorithms that estimate the oscillation parameters from acquired generator data to detect potentially dangerous power system disturbances. When disturbances occur in power systems (due to load changes or faults), damped oscillations (or &quotmodes") are created. Modes which are heavily damped die out quickly and pose no threat to system stability. Lightly damped modes, by contrast, die out slowly and are more problematic. Of more concern still are &quotnegatively damped" modes which grow exponentially with time and can ultimately cause the power system to fail. Widespread blackouts are then possible. To avert power system failures it is necessary to monitor the damping of the oscillating modes. This thesis proposes a number of damping estimation algorithms for this task. If the damping is found to be very small or even negative, then additional damping needs to be introduced via appropriate control strategies. This thesis presents a number of new algorithms for estimating the damping of modal oscillations in power systems. The first of these algorithms uses multiple orthogonal sliding windows along with least-squares techniques to estimate the modal damping. This algorithm produces results which are superior to those of earlier sliding window algorithms (that use only one pair of sliding windows to estimate the damping). The second algorithm uses a different modification of the standard sliding window damping estimation algorithm - the algorithm exploits the fact that the Signal to Noise Ratio (SNR) within the Fourier transform of practical power system signals is typically constant across a wide frequency range. Accordingly, damping estimates are obtained at a range of frequencies and then averaged. The third algorithm applied to power system analysis is based on optimal estimation theory. It is computationally efficient and gives optimal accuracy, at least for modes which are well separated in frequency.