In this paper, we study the problem of noise with regard to the perfect reconstruction of non-bandlimited signals, the class of signals having a finite number of degrees of freedom per unit time. The finite rate of innovation (FRI) method provides a means of recovering a non-bandlimited signal through using of appropriate kernels. In the presence of noise, however, the reconstruction function of this scheme may become ill-conditioned. Further, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In this paper, to obtain improved noise robustness, we propose the matrix pencil (MP) method for sample signal reconstruction, which is based on principal component analysis (PCA). Through the selection of an adaptive eigenvalue, a non-bandlimited signal can be perfectly reconstructed via a stable solution of the Yule-Walker equation. The proposed method can obtain a high signal-to-noise-ratio (SNR) for the reconstruction results. Herein, the method is applied to certain non-bandlimited signals, such as a stream of Diracs and nonuniform splines. The simulation results demonstrate that the MP and PCA are more effective than the FRI method in suppressing noise. The FRI method can be used in many applications, including those related to bioimaging, radar, and ultrasound imaging.

The conventional covariance matrix technique based subspace methods, such as the 2-D Capon algorithm and computationally efficient ESPRIT-type algorithms, are invalid with a single snapshot in a bistatic MIMO radar. A novel matrix pencil method is proposed for the direction of departures (DODs) and direction of arrivals estimation (DOAs) estimation. The proposed method constructs an enhanced matrix from the direct sampled data, and then utilizes the matrix pencil approach to estimate DOAs and DODs, which are paired automatically. The proposed method is able to provide favorable and unambiguous angle estimation performance with a single snapshot. Simulation results are presented to verify the effectiveness of the proposed method.

We describe an extension of the wideband direction-of-arrival (DOA) estimation method using a frequency-domain frequency-invariant beamformer (FDFIB). The technique uses the Matrix Pencil Method (MPM) instead of conventional methods based on the eigen-structure of the input covariance matrix. MPM offers excellent resolution compared to conventional methods.

The objective of this research is to compare the performance of the Matrix Pencil Method (MPM) and well known root-MUSIC algorithm for high resolution DOA estimation. Performance of each technique in terms of the probability of resolution and SNR in the presence of noise is investigated. Simulation results show that the MPM has a superior resolution to the root-MUSIC algorithm.