Frequency-Based Radar Waveform Design for Target Classification Performance Optimisation Using Fisher Analysis

Abstract

This thesis presents non-adaptive radar waveform and receiver designs to improve radar target identification performance. The designs are based on the theory of Fisher discriminants analysis and Fisher separability functions. Introducing Fisher discriminants analysis in waveform design for target maximisation is the first contribution of this thesis. By using the concepts of Fisher analysis both for 2-class or multiclass scenarios, a separability rational function can be derived for practical extended targets classification. The separability functions are formulated to maximise the distance between the means of data classes while minimising their variance. Fisher separability is used as an objective function for the optimisation problem to find the optimal waveform that maximises it under constant energy constraints. The classifiers are derived and inspired by Fisher minimum distance classifiers. The second contribution of the thesis is deriving low-energy low-covariance (LELC) closed-form solutions for the optimisation problem under additive white Gaussian noise (AWGN) conditions. These solutions perform well especially when the signal-to-noise ratio is low. Further, a closed-form solution for the optimisation problem is derived for the 2-class scenario. The solution achieves classification performance comparable to solutions obtained using general optimisation solvers. The proposed waveform and receiver design methods are tested using synthetic and real target data and is shown to achieve better performance than the wideband chirp and other non-adaptive waveform design methods reported in the literature.