- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 43827 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Bastani, Mohammad Hasan
- Employing array of antennas in amny signal processing application has received considerable attention in recent years due to major advances in design and implementation of large dimentional antennas. In many applications we deal with such large dimentional antennas which challenge the traditional signal processing algorithms. Since most of traditional signal processing algorithms assume that the number of samples is much more than the number of array elements while it is not possible to collect so many samples due to hardware and time constraints.
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices (SCM) in sample starved conditions. First employing these results we propose a new method to enumerate the incident waves impinging on an array. We use a number of moments of noise eigenvalues of the SCM in order to separate noise and signal subspaces more accurately. We also use an enhanced noise variance estimator to reduce the bias leakage between the subspaces.Numerical simulations demonstrate that the proposed method estimates the true number of signals for large arrays and a relatively small number of snapshots.
In the second part of this research, we investigate the limiting spectral distribution of the sample covariance matrix of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. For the commonly used exponential window, we derive an explicit expression for the limiting spectral distribution of noise-only data. In addition, we present a method to identify the support of eigenvalues in the general case of signal plus noise. Simulations are performed to support our theoretical claims.
We then employ the complex integration and residue theorem to design an estimator for the eigenvalues which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size situations. Simulation results show that the proposed estimator outperforms the traditional estimator, significantly
- Array Signal Processing ; Eigenvalue Estimation ; Spectral Distribution of Sample Covariance Matrix ; Random Matrix Theory ; Sources Identification ; Sources Enumeration