<p>To counter radio signal reconnaissance, an efficient way of covert communication is to use subsecond duration burst transmissions in the congested HF band. Against this background, the present thesis treats fast direction finding (DF) using antenna arrays with known response only in a few calibration directions. In such scenarios the known method of array mapping (interpolation) may be used to transform the output data vectors from the existing array onto the corresponding output vectors of another (virtual) array that is mathematically defined and optimally chosen. But in signal reconnaissance the emitters are initially unknown and the mapping matrix must be designed as a compromise over a wide sector of DOAs. This compromise may result in large DOA estimate errors, both deterministic and random. Analyzing, analytically describing, and minimizing these DOA errors, is the main theme of the present thesis. The first part of the thesis analyzes the deterministic mapping errors, the DOA estimate bias, that is caused by dissimilarity between the two array geometries. It is shown that in a typical signal reconnaissance application DOA estimate bias can dominate over DOA estimate variance. Using a Taylor series expansion of the DOA estimator cost function an analytical expression for the bias is derived and a first order zero bias condition is identified. This condition is general, estimator independent, and can be applied to any type of data pre-processing. A design algorithm for the mapping matrix is thereafter presented that notably reduces mapped DOA estimate bias. A special version is also given with the additional property of reducing the higher order Taylor terms and thus the residual bias. Simulations demonstrate a bias reduction factor exceeding 100 in some scenarios. A version based on signal subspace mapping rather than array manifold mapping is also given. This version is of large practical interest since the mapping matrix can be designed directly from calibration data. In the second part of the thesis the derived bias minimization theory is extended into Mean Square Error (MSE) minimization, i.e. measurement noise is introduced. Expressions for DOA error variance and DOA MSE under general pre-processing are derived, and a design algorithm for the mapping matrix is formulated by which mapped DOA estimate MSE can be minimized. Simulations demonstrate improved robustness and performance for this algorithm, especially in low SNR scenarios. In the third and final part of the thesis the theoretical results are supported by experimental data. For an 8 element circular array mapped onto a virtual ULA across a 600 sector it is shown that the mapped DOA estimate errors can be suppressed down to the Cramér-Rao level.</p>

To counter radio signal reconnaissance, an efficient way of covert communication is to use subsecond duration burst transmissions in the congested HF band. Against this background, the present thesis treats fast direction finding (DF) using antenna arrays with known response only in a few calibration directions. In such scenarios the known method of array mapping (interpolation) may be used to transform the output data vectors from the existing array onto the corresponding output vectors of another (virtual) array that is mathematically defined and optimally chosen. But in signal reconnaissance the emitters are initially unknown and the mapping matrix must be designed as a compromise over a wide sector of DOAs. This compromise may result in large DOA estimate errors, both deterministic and random. Analyzing, analytically describing, and minimizing these DOA errors, is the main theme of the present thesis. The first part of the thesis analyzes the deterministic mapping errors, the DOA estimate bias, that is caused by dissimilarity between the two array geometries. It is shown that in a typical signal reconnaissance application DOA estimate bias can dominate over DOA estimate variance. Using a Taylor series expansion of the DOA estimator cost function an analytical expression for the bias is derived and a first order zero bias condition is identified. This condition is general, estimator independent, and can be applied to any type of data pre-processing. A design algorithm for the mapping matrix is thereafter presented that notably reduces mapped DOA estimate bias. A special version is also given with the additional property of reducing the higher order Taylor terms and thus the residual bias. Simulations demonstrate a bias reduction factor exceeding 100 in some scenarios. A version based on signal subspace mapping rather than array manifold mapping is also given. This version is of large practical interest since the mapping matrix can be designed directly from calibration data. In the second part of the thesis the derived bias minimization theory is extended into Mean Square Error (MSE) minimization, i.e. measurement noise is introduced. Expressions for DOA error variance and DOA MSE under general pre-processing are derived, and a design algorithm for the mapping matrix is formulated by which mapped DOA estimate MSE can be minimized. Simulations demonstrate improved robustness and performance for this algorithm, especially in low SNR scenarios. In the third and final part of the thesis the theoretical results are supported by experimental data. For an 8 element circular array mapped onto a virtual ULA across a 600 sector it is shown that the mapped DOA estimate errors can be suppressed down to the Cramér-Rao level. / QC 20101022

In this thesis a new approach is proposed for non-uniform linear arrays (NLA) which employs conventional subspace methods to improve the direction of arrival (DOA) estimation performance. Uniform linear arrays (ULA) are composed of evenly spaced sensor elements located on a straight line. ULA&#039 / s covariance matrix have a Vandermonde matrix structure, which is required by fast subspace DOA estimation algorithms. NLA differ from ULA only by some missing sensor elements. These missing elements cause some gaps in covariance matrix and Vandermonde structure is lost. Therefore fast subspace DOA algorithms can not be applied in this case. Linear programming methods and array interpolation methods can be used to solve this problem. However linear programming is computationally expensive and array interpolation is angular sector dependent and requires the same number of sensor in the virtual array. In this thesis, a covariance matrix augmentation method is developed by using the array interpolation technique and initial DOA estimates. An initial DOA estimate is obtained by Toeplitz completion of the covariance matrix. This initial DOA estimates eliminates the sector dependency and reduces the least square mapping error of array interpolation. A Wiener formulation is developed which allows more sensors in the virtual array than the real array. In addition, it leads to better estimates at low SNR. The new covariance matrix is used in the root-MUSIC algorithm to obtain a better DOA estimate. Several computer simulations are done and it is shown that the proposed approach improves the DOA estimation accuracy significantly compared to the same number of sensor ULA. This approach also increases the number of sources that can be identifed.

The objective of the proposed research is to develop high performance, low computational complexity resolution enhancement and demosaicing algorithms. Our approach to both problems is to find creative ways to incorporate edge information into the algorithm design. However, in contrast with the usual edge directed approaches, we do not try to detect edge presence and orientation explicitly. For the image interpolation problem, we study the relationship between low resolution and high resolution pixels, and derive a general interpolation formula to be used on all pixels. This simple interpolation algorithm is able to generate sharp edges in any orientation. We also propose a simple 3 by 3 filter that quantifies local luminance transition and apply it to the demosaicing problem. Additionally, we propose a gradient based directional demosaicing method that does not require setting any thresholds. We show that the performance of this algorithm can be improved by using multiscale gradients. Finally, we address the low spectral correlation demosaicing problem by proposing a new family of hybrid color filter array (CFA) patterns and a local algorithm that is two orders of magnitude faster than a comparable non-local solution while offering the same level of performance.

In this thesis, DOA estimation using array interpolation in randomly distributed sensor arrays is considered. Array interpolation is a technique in which a virtual array is obtained from the real array and the outputs of the virtual array, computed from the real array using a linear transformation, is used for direction of arrival estimation. The idea of array interpolation techniques is to make simplified and computationally less demanding high resolution direction finding methods applicable to the general class of non-structured arrays.In this study,we apply an interpolation technique for arbitrary array geometries in an attempt to extend root-MUSIC algorithm to arbitrary array geometries.Another issue of array interpolation related to direction finding is spatial smoothing in the presence of multipath sources.It is shown that due to the Vandermonde structure of virtual array manifold vector obtained from the proposed interpolation method, it is possible to use spatial smoothing algorithms for the case of multipath sources.

In this thesis, two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is considered. Usually, DOA estimation is considered in one dimension assuming a fixed elevation angle. While this assumption simplifies the problem, both the azimuth and elevation angles, namely, the 2-D DOA estimates are required in practical scenarios. In this thesis, planar array structures are considered for 2-D DOA estimation. In this context, V-shaped arrays are discussed and some of the important features of these arrays are outlined. A new method for the design of V-shaped arrays is presented for both isotropic and directional beam patterns. The design procedure is simple and can be applied for both uniform and nonuniform V-shaped sensor arrays. Closed form expressions are presented for the V-angle in order to obtain isotropic angle performance. While circular arrays have the isotropic characteristics, V-shaped arrays present certain advantages due to their large aperture for the same number of sensors and inter-sensor distance. The comparison of circular and V-shaped arrays is done by considering the azimuth and elevation Cramer-Rao Bounds (CRB). It is shown that V-shaped and circular arrays have similar characteristics for the sensor position errors while the uniform isotropic (UI) V-array performs better when there is mutual coupling and the sources are correlated. In the literature, there are several techniques for 2-D DOA estimation. Usually, fast algorithms are desired for this purpose since a search in two dimensions is a costly process. These algorithms have a major problem, namely, the pairing of the azimuth-elevation couples for multiple sources. In this thesis, a new fast and effective technique for this purpose is proposed. In this technique, a virtual array output is generated such that when the ESPRIT algorithm is used, the eigenvalues of the rotational transformation matrix have the 2-D angle information in both magnitude and phase. This idea is applied in different scenarios and three methods are presented for these cases. In one case, given an arbitrary array structure, array interpolation is used to generate the appropriate virtual arrays. When the antenna mutual coupling is taken into account, a special type of array structure, such as circular, should be used in order to apply the array interpolation. In general, the array mutual coupling matrix (MCM) should have a symmetric Toeplitz form. It is shown that the 2-D DOA performance of the proposed method approaches to the CRB by using minimum number of antennas in case of mutual coupling. This method does not require the estimation of the mutual coupling coefficients. While this technique is effective, it has problems especially when the number of sources increases. In order to improve the performance, MCM is estimated in the third approach. This new approach performs better, but it cannot be used satisfactorily in case of multipath signals. In this thesis, the proposed idea for fast 2-D DOA estimation is further developed in order to solve the problem when mutual coupling and multipath signals jointly exist. In this case, real arrays with some auxiliary sensors are used to generate a structured mutual coupling matrix. It is shown that the problem can be effectively solved when the array structure has a special form. Specifically, parallel uniform linear arrays (PULA) are employed for this purpose. When auxiliary sensors are used, a symmetric banded Toeplitz MCM is obtained for the PULA. This allows the application of spatial smoothing and ESPRIT algorithm for 2-D DOA estimation. The proposed algorithm uses triplets and presents closed form paired 2-D DOA estimates in case of unknown mutual coupling and multipath signals. Several simulations are done and it is shown that the proposed array structure and the method effectively solve the problem.

To reduce cost, many digital cameras use a single sensor array instead of using three arrays for the red, green and blue. Thus at each pixel location only the red, green or blue intensity value is available. And to generate a complete color image, the camera must estimate the missing two values at each pixel location .Color filter arrays are used to capture only one portion of the spectrum (Red, Green or Blue) at each location. Various arrangements of the Color Filter Array (CFA) are possible, but the Bayer array is the most commonly used arrangement and we will deal exclusively with the Bayer array in this thesis. Since each of the three colors channels are effectively downsampled, it leads to aliasing artifacts. This thesis will analyze the effects of aliasing in the frequency- domain and present a method to reduce the deterioration in image quality due to aliasing artifacts. Two reference algorithms, AH-POCS (Adams and Hamilton - Projection Onto Convex Sets) and Adaptive Homogeneity-Directed interpolation, are discussed in de- tail. Both algorithms use the assumption that there is high correlation in the high- frequency regions to reduce aliasing. AH-POCS uses alias cancellation technique to reduce aliasing in the red and blue images, while the Adaptive Homogeneity-Directed interpolation algorithm is an edge-directed algorithm. We present here an algorithm that combines these two techniques and provides a better result on average when compared to the reference algorithms.