Matching Items (2)
Description
Waveform design that allows for a wide variety of frequency-modulation (FM) has proven benefits. However, dictionary based optimization is limited and gradient search methods are often intractable. A new method is proposed using differential evolution to design waveforms with instantaneous frequencies (IFs) with cubic FM functions whose coefficients are constrained to the surface of the three dimensional unit sphere. Cubic IF functions subsume well-known IF functions such as linear, quadratic monomial, and cubic monomial IF functions. In addition, all nonlinear IF functions sufficiently approximated by a third order Taylor series over the unit time sequence can be represented in this space. Analog methods for generating polynomial IF waveforms are well established allowing for practical implementation in real world systems. By sufficiently constraining the search space to these waveforms of interest, alternative optimization methods such as differential evolution can be used to optimize tracking performance in a variety of radar environments. While simplified tracking models and finite waveform dictionaries have information theoretic results, continuous waveform design in high SNR, narrowband, cluttered environments is explored.
ContributorsPaul, Bryan (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Bliss, Daniel W (Thesis advisor) / Tepedelenlioğlu, Cihan (Committee member) / Arizona State University (Publisher)
Created2014
Description
Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.
ContributorsJones, Scott, Ph.D (Author) / Cochran, Douglas (Thesis advisor) / Berisha, Visar (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ (Committee member) / Arizona State University (Publisher)
Created2019