Theory of radar imaging using time-frequency distribution

The concept of radar was developed for the estimation of the distance (range) and velocity of a target from a receiver. The distance measurement is obtained by measuring the time taken for the transmitted signal to propagate to the target and return to the receiver. The target's velocity is determined by measuring the Doppler induced frequency shift of the returned signal caused by the rate of change of the time- delay from the target. As researchers further developed conventional radar systems it become apparent that additional information was contained in the backscattered signal and that this information could in fact be used to describe the shape of the target itself. It is due to the fact that a target can be considered to be a collection of individual point scatterers, each of which has its own velocity and time- delay. DelayDoppler parameter estimation of each of these point scatterers thus corresponds to a mapping of the target's range and cross range, thus producing an image of the target. Much research has been done in this area since the early radar imaging work of the 1960s. At present there are two main categories into which radar imaging falls. The first of these is related to the case where the backscattered signal is considered to be deterministic. The second is related to the case where the backscattered signal is of a stochastic nature. In both cases the information which describes the target's scattering function is extracted by the use of the ambiguity function, a function which correlates the backscattered signal in time and frequency with the transmitted signal. In practical situations, it is often necessary to have the transmitter and the receiver of the radar system sited at different locations. The problem in these situations is 'that a reference signal must then be present in order to calculate the ambiguity function. This causes an additional problem in that detailed phase information about the transmitted signal is then required at the receiver. It is this latter problem which has led to the investigation of radar imaging using time- frequency distributions. As will be shown in this thesis, the phase information about the transmitted signal can be extracted from the backscattered signal using time- frequency distributions. The principle aim of this thesis was in the development, and subsequent discussion into the theory of radar imaging, using time- frequency distributions. Consideration is first given to the case where the target is diffuse, ie. where the backscattered signal has temporal stationarity and a spatially white power spectral density. The complementary situation is also investigated, ie. where the target is no longer diffuse, but some degree of correlation exists between the time- frequency points. Computer simulations are presented to demonstrate the concepts and theories developed in the thesis. For the proposed radar system to be practically realisable, both the time- frequency distributions and the associated algorithms developed must be able to be implemented in a timely manner. For this reason an optical architecture is proposed. This architecture is specifically designed to obtain the required time and frequency resolution when using laser radar imaging. The complex light amplitude distributions produced by this architecture have been computer simulated using an optical compiler.

The influence of habitat heterogeneity on patterns of connectivity among rabbit populations in southern Queensland

Patterns of connectivity among local populations influence the dynamics of regional systems, but most ecological models have concentrated on explaining the effect of connectivity on local population structure using dynamic processes covering short spatial and temporal scales. In this study, a model was developed in an extended spatial system to examine the hypothesis that long term connectivity levels among local populations are influenced by the spatial distribution of resources and other habitat factors. The habitat heterogeneity model was applied to local wild rabbit populations in the semi-arid Mitchell region of southern central Queensland (the Eastern system). Species' specific population parameters which were appropriate for the rabbit in this region were used. The model predicted a wide range of long term connectivity levels among sites, ranging from the extreme isolation of some sites to relatively high interaction probabilities for others. The validity of model assumptions was assessed by regressing model output against independent population genetic data, and explained over 80% of the variation in the highly structured genetic data set. Furthermore, the model was robust, explaining a significant proportion of the variation in the genetic data over a wide range of parameters. The performance of the habitat heterogeneity model was further assessed by simulating the widely reported recent range expansion of the wild rabbit into the Mitchell region from the adjacent, panmictic Western rabbit population system. The model explained well the independently determined genetic characteristics of the Eastern system at different hierarchic levels, from site specific differences (for example, fixation of a single allele in the population at one site), to differences between population systems (absence of an allele in the Eastern system which is present in all Western system sites). The model therefore explained the past and long term processes which have led to the formation and maintenance of the highly structured Eastern rabbit population system. Most animals exhibit sex biased dispersal which may influence long term connectivity levels among local populations, and thus the dynamics of regional systems. When appropriate sex specific dispersal characteristics were used, the habitat heterogeneity model predicted substantially different interaction patterns between female-only and combined male and female dispersal scenarios. In the latter case, model output was validated using data from a bi-parentally inherited genetic marker. Again, the model explained over 80% of the variation in the genetic data. The fact that such a large proportion of variability is explained in two genetic data sets provides very good evidence that habitat heterogeneity influences long term connectivity levels among local rabbit populations in the Mitchell region for both males and females. The habitat heterogeneity model thus provides a powerful approach for understanding the large scale processes that shape regional population systems in general. Therefore the model has the potential to be useful as a tool to aid in the management of those systems, whether it be for pest management or conservation purposes.