Advanced optimization algorithms for sensor arrays and multi-antenna communications

Optimization problems arise frequently in sensor array and multi-channel signal processing applications. Often, optimization needs to be performed subject to a matrix constraint. In particular, unitary matrices play a crucial role in communications and sensor array signal processing. They are involved in almost all modern multi-antenna transceiver techniques, as well as sensor array applications in biomedicine, machine learning and vision, astronomy and radars. In this thesis, algorithms for optimization under unitary matrix constraint stemming from Riemannian geometry are developed. Steepest descent (SD) and conjugate gradient (CG) algorithms operating on the Lie group of unitary matrices are derived. They have the ability to find the optimal solution in a numerically efficient manner and satisfy the constraint accurately. Novel line search methods specially tailored for this type of optimization are also introduced. The proposed approaches exploit the geometrical properties of the constraint space in order to reduce the computational complexity. Array and multi-channel signal processing techniques are key technologies in wireless communication systems. High capacity and link reliability may be achieved by using multiple transmit and receive antennas. Combining multi-antenna techniques with multicarrier transmission leads to high the spectral efficiency and helps to cope with severe multipath propagation. The problem of channel equalization in MIMO-OFDM systems is also addressed in this thesis. A blind algorithm that optimizes of a combined criterion in order to be cancel both inter-symbol and co-channel interference is proposed. The algorithm local converge properties are established as well

Convolutive Reduced Rank Wiener Filtering

If two wide sense stationary time series are correlated then one can be used to predict the other. The reduced rank Wiener filter is the rank constrained linear operator which maps the current value of one time series to an estimate of the current value of the other time series in an optimal way. A closed form solution exists for the reduced rank Wiener filter. This paper studies the problem of determining the reduced rank FIR filter which optimally predicts one time series given the other. This optimal FIR filter is called the convolutive reduced rank Wiener filter, and it is proved that determining it is equivalent to solving a weighted low rank approximation problem. In certain cases a closed form solution exists, and in general, the iterative optimisation algorithm derived here can be used to converge to a locally optimal convolutive reduced rank Wiener filter