Some Contributions to Radar Detection Theory

This dissertation focuses on statistical signal processing theory and its applications to radar, complex-valued signal processing and model selection. The transmit signal critically affects a radar system\u27s performance. Its design is an important task and is an active research area. We provide an optimal design for detecting extended targets in colored noise based on the locally most powerful detector. We also establish a fundamental relationship between the Kullback-Leibler divergence, signal-to-noise ratio, and mutual information, all of which have been used as waveform design metrics the literature. The relationship explains the role of each metric. In space-time adaptive processing (STAP), the nonstationarity of the data samples causes a mismatch between the estimated covariance matrix and the true one, and consequently leads to the degradation of STAP performance. We propose an asymptotically optimal detector for testing the nonstationarity via the generalized likelihood ratio test and an alternative Rao test with lower computational cost. The Rao test is a very useful method in signal processing. A complex parameter Rao test is proposed and serves as a new method for complex-valued parameter testing. Different from the traditional way, it reformulates the calculations with respect to the complex-valued quantities directly and often leads to more intuitive, and more computationally efficient test statistics. Applying the complex parameter Rao test to the bandedness of the Cholesky factor of the inverse of a complex-valued covariance matrix is an example of its application. Model order selection is another fundamental but important task that arises in many areas. We propose a new Bayesian model order selection method by employing the exponentially embedded family (EEF) technique. In addition to the established important properties of EEF, the new Bayesian model selection method can use vague proper priors and improper non-informative priors without the criticisms of Lindley\u27s paradox and the Information paradox. The penalty term of the Bayesian EEF is shown to have a very intuitive meaning as the sum of the model parameter dimension and the estimated mutual information between the parameter and observed data. The EEF is also used to estimated the degree of noncircularity of a complex random vector and is shown to have good performance