Contributions to Parametric and Non-parametric Analysis of Mixed Spectra

The present thesis consists of four parts, all connected to sensor array signal processing in a wide sense. The rst part covers the optimal solution to a commonly occurring matrix optimization problem and the resulting implications for the best linear unbiased estimator (BLUE) and for spatial and temporal lter design. Non-parametric spectral estimation is covered in the second part. Here, we introduce the matchedlter bank class and evaluate the performance of the Capon and APES (Amplitude and Phase Estimation of a Sinusoid) spectral estimators. It is found that the Capon estimator gives a biased estimate, while the APES estimator will give an unbiased estimate at a similar computational load. In the third part, the problem of estimating the parameters of complex-valued sinusoidal signals from data corrupted by colored noise is examined. We present a simple formula for the asymptotic (large-sample) Cram er-Rao bound matrix associated with this problem, and show that it is attained by both the maximum likelihood estimator and the computationally much simpler nonlinear least-squares method. Finally, we consider the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas. Two asymptotically e cient estimators based on signal and noise subspace tting are proposed. Numerical examples are included in all the parts of the thesis to illustrate the performance that can be achieved with the proposed algorithms. iv Acknowledgment I would like to express my appreciation to my supervisor and co-author, Prof. Petre Stoica, for his excellent guidance, and for sharing his expert knowledge with me. I would also like to thank Prof. Torsten S oderstrom for accepting me as a PhD student and for his guidance and support. Furthermore, I would like to thank my co-authors Prof. Jian Li and Prof. Lee Swindlehurst for many stimulating discussions on the di erent topics presented in the thesis. I thank all the people at the Systems and Control Group and the Signals and Systems Group for creating a pleasant work environment. I would especially like to thank all those who have participated in our different social endeavors, most notably our numerous climbing adventures. Dr Peter Handel has my gratitude for serving as faculty opponent for my licentiate examination. I thank Dr Mats Cedervall for providing me with Figure 1.3, and Tekn lic Joakim Sorelius for Figure 1.4. This work has been nancially supported in part by the Swedish National Board for Technical Development (NUTEK) which is gratefully acknowledged. Last, but far from least, I would like to express my deepest appreciation to my anc e Ylva for her never-ending support and love.