In antenna array processing it is generally required to enhance the reception or detection of a signal from a particular direction while suppressing noise and interference signals from other directions. An optimisation problem often posed to achieve this result is to minimise the array processor mean output power (or variance) subject to a fixed response in the array look direction. The look direction requirement can be met by imposing a set of linear constraints on the processor weights to yield what is known as the Linearly Constrained Minimum Variance (LCMV) processor. It has been found, however, that LCMV processors are susceptible to errors in the assumed direction of arrival of the desired signal. To achieve robustness against directional mismatch, additional constraints known as derivative constraints can be introduced. These constraints force the first and second order spatial derivatives of the array power response in the look direction to zero. However, constraints corresponding to necessary and sufficient (NS) conditions for these spatial derivatives to be zero are in general quadratic, and the resulting weight vector solution space is non-convex. One approach to this complex problem has been to consider conditions which are only sufficient for the spatial derivatives to be zero. Whilst this results in linear constraints, it exhibits certain anomalous behaviour, for example, dependence on the choice of array phase centre.Recent work in the area of derivative constraints has resulted in a method for efficiently solving the non-convex output power minimisation problem with quadratic derivative constraints. The optimisation problem addressed assumes that the input signal statistics and hence the input signal autocorrelation matrix R are known. In practice, R must be estimated from the receiver data.The main contribution of this thesis is the derivation of a ++ / new adaptive algorithm which implements an adaptive array processor with look direction plus 1st and 2nd order NS derivative constraints. The new algorithm is derived from the well-known Recursive Least Squares (RLS) technique but allows linear and quadratic constraints to be incorporated within the recursive framework. The algorithm offers the high performance characteristics associated with RLS methods, namely, fast convergence and high steady-state accuracy. The work encompasses a study of the characteristics of the algorithm in terms of numerical robustness, convergence properties, tracking and computational complexity.The study of the numerical properties of the algorithm has led to the second important contribution of this thesis: the identification of a parameter which is central to the numerical stability of the algorithm in a practical fixed precision environment. We show that this parameter is bounded during stable operation and can therefore be used to detect the onset of numerical instability within the algorithm. In addition, we show how existing techniques can be used to significantly improve the numerical robustness of the algorithm.Another important contribution of the thesis stems from an investigation into the multimodal nature of the quadratic, equality constrained optimisation problem resulting from the use of second order NS derivative constraints. In particular, we show that for a linear antenna array operating under certain conditions, the complex multimodal optimisation problem can be greatly simplified. This has important implications in both optimum and adaptive array signal processing.

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OFDM is a promising technique for high-data-rate wireless communications because it can combat inter-symbol interference (ISI) caused by the dispersive fading of wireless channels. The proposed research focuses on techniques that improve the performance of OFDM-based wireless communications and its commercial and military applications. In particular, we address the following aspects of OFDM: inter-channel interference (ICI) suppression, interference suppression for clustered OFDM, clustered OFDM based anti-jamming modulation, channel estimation for MIMO-OFDM, MIMO transmission with limited feedback. For inter-channel interference suppression, a frequency domain partial response coding (PRC) scheme is proposed to mitigate ICI. We derive the near-optimal weights for PRC that is independent on the channel power spectrum. The error floor resulting from ICI can be reduced significantly using a two-tap or a three-tap PRC. Clustered OFDM is a new technique that has many advantages over traditional OFDM. In clustered OFDM systems, adaptive antenna arrays are used for interference suppression. To calculate weights for interference suppression, we propose a polynomial-based parameter estimator to combat the severe leakage of the DFT based estimator due to the small size of the cluster. An adaptive algorithm is developed to obtain optimal performance. For high data rate military communications, we propose a clustered OFDM base spread spectrum modulation to provide both anti-jamming and fading suppression capability. We analyze the performance of uncoded and coded system. Employing multiple transmit and receive antennas in OFDM systems (MIMO-OFDM) can increase the spectral efficiency and link reliability. We develop a minimum mean-square-error (MMSE) channel estimator that takes advantage of the spatial-frequency correlations in MIMO-OFDM systems to minimize the estimation error. We investigate the training sequence design and two optimal training sequence designs are given for arbitrary spatial correlations. For a MIMO system, the diversity and array gains can be obtained by exploiting channel information at the transmitter. For MIMO-OFDM systems, we propose a subspace tracking based approach that can exploit the frequency correlations of the OFDM system to reduce the feedback rate. The proposed approach does not need recalculate the precoding matrix and is robust to multiple data stream transmission.