HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

GEODA-GRUA: Adaptive Multibeam Conformal Antenna for Satellites Communications

The GEODA-GRUA is one conformal adaptive antenna array designed for satellite communications. Operating at 1.7 GHz with circular polarization, it is possible to track and communicate with several satellites at once being able to receive signals in full azimuth and within the range of 5° to broadside elevation thanks to its adaptive beam. The complex structure of the antenna array has 2700 radiating elements based on a set of 60 similar triangular arrays that are divided in 15 subarrays of 3 radiating elements. A control module governs each transmission/receiver (T/R) module associated to each cell in order to manage beam steering by shifting phases.

Red Multihaz de Desfase Escalonado para el Control de un Array de Antenas.

This paper presents a general systems that can be taken into account to control between elements in an antenna array. Because the digital phase shifter devices have become a strategic element and also some steps have been taken for their export by U.S. Government, this element has increased its price to the low supply in the market. Therefore, it is necessary to adopt some solutions that allow us to deal with the design and construction of antenna arrays. system based on a group of a staggered phase shift with external switching is shown, which is extrapolated array.

Study of an electronic steering antenna with a staggered phase shifter configuration

This paper presents a study of three possible solutions that can be taken into account to control the phase shift between elements in an antenna array. Because commercial digital phase shifters have become a strategic element by U.S. Government, these elements have increased their price. For this reason, it is necessary to adopt some solutions that allow us to deal with the design and construction of antenna arrays.

Comparison of different MIMO antenna arrays and user's effect on their performances

Multiple-input multiple-output (MIMO) systems have entailed a great enhancement in wireless communications performances. The use of multiple antennas at each side of the radio link has been included in recent drafts and standards such as WLAN, WIMAX, or DVB-T2. The MIMO performances depend on the antenna array characteristics and thus several aspects have to be taken into account to design MIMO antennas. In the literature, many articles can be found in terms of capacity or antenna design, but in this article, different types of antenna arrays for MIMO systems are measured in a reverberation chamber with and without a phantom as a user's head. As a result, the MIMO performances are degraded by the user in terms of efficiency, diversity gain, and capacity. Omnidirectional antennas such as monopoles with high radiation efficiency offer the highest performance for a rich scattering nonline of sight indoor environment.

Broadband active differential array for the mid-frequency SKA band

This paper presents the design and characterization process of an active array demonstrator for the mid-frequency range (i.e., 300 MHz-1000 MHz) of the future Square Kilometre Array (SKA) radio telescope. This demonstrator, called FIDA3 (FG-IGN: Fundación General Instituto Geográfico Nacional - Differential Active Antenna Array), is part of the Spanish contribution for the SKA project. The main advantages provided by this design include the use of a dielectric-free structure, and the use of a fully-differential receiver in which differential low-noise amplifiers (LNAs) are directly connected to the balanced tapered-slot antennas (TSAs). First, the radiating structure and the differential low-noise amplifiers were separately designed and measured, obtaining good results (antenna elements with low voltage standing-wave ratios, array scanning capabilities up to 45°, and noise temperatures better than 52 K with low-noise amplifiers at room temperature). The potential problems due to the differential nature of the proposed solution are discussed, so some effective methods to overcome such limitations are proposed. Second, the complete active antenna array receiving system was assembled, and a 1 m2 active antenna array tile was characterized.

Probabilistic Approach to Design of Large Antenna Arrays

2000 Mathematics Subject Classification: 78A50

Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Dual-band Filtenna Array for WLAN Applications

This paper presents the design and results of a dual-band antenna array integrated with bandpass filters for WLAN applications. The array is fed with a single 50 Ω port and consists of two radiating elements; thereby having a 1x2 array structure. The two bands of the antenna array correspond to the two WLAN bands of 2.4 GHz and 5.8 GHz. A standalone array has first been designed. Other than the two fundamental resonant frequencies, the standalone array exhibits spurious harmonics at various other frequencies. For the suppression of these harmonics, the array has been integrated with two bandpass filters, centered at 2.4 GHz and 5.8 GHz. The resulting filtenna array was simulated, fabricated and measured. Obtained simulation and measurement results agree well with each other and have been presented to validate the accuracy of the proposed structure. Measured return loss of the structure shows dual-bands at 2.4 GHz and 5.8 GHz of more than 30 dB each and also a successful suppression of the spurious harmonics of the antenna array has been achieved. Radiation patterns have also been simulated and measured and both results shown. The gain and efficiency have also been presented; with the values being 6.7 dBi and 70% for the 2.4 GHz band and 7.4 dBi and 81% for the 5.8 GHz band respectively.

Ultracompact Retrodirective Antenna Arrays With Superdirective Radiation Patterns

It is shown that the direction-of-arrival (DoA) information carried by an incident electromagnetic (EM) wave can be encoded into the evanescent near field of an electrically small resonance antenna array with a spatial rate higher than that of the incident field oscillation rate in free space. Phase conjugation of the received signal leads to the retrodirection of the near field in the antenna array environment, which in turn generates a retrodirected far-field beam toward the original DoA. This EM phenomenon enables electrically small retrodirective antenna arrays with superdirective, angular super-resolution, auto-pointing properties for an arbitrary DoA. A theoretical explanation of the phenomenon based on first principal observations is given and full-wave simulations demonstrate a realizability route for the proposed retrodirective terminal that is comprised of resonance dipole antenna elements. Specifically, it is shown that a three-element disk-loaded retrodirective dipole array with 0.15\lambda spacings can achieve a 3.4-dBi maximal gain, 3-dBi front-to-back ratio, and 13% return loss fractional bandwidth (at the 10-dB level). Then, it is demonstrated that the radiation gain of a three-element array can be improved to approximately 6 dBi at the expense of the return loss fractional bandwidth reduction (2%).

Fast Transforms for Acoustic Imaging-Part I: Theory

The classical approach for acoustic imaging consists of beamforming, and produces the source distribution of interest convolved with the array point spread function. This convolution smears the image of interest, significantly reducing its effective resolution. Deconvolution methods have been proposed to enhance acoustic images and have produced significant improvements. Other proposals involve covariance fitting techniques, which avoid deconvolution altogether. However, in their traditional presentation, these enhanced reconstruction methods have very high computational costs, mostly because they have no means of efficiently transforming back and forth between a hypothetical image and the measured data. In this paper, we propose the Kronecker Array Transform ( KAT), a fast separable transform for array imaging applications. Under the assumption of a separable array, it enables the acceleration of imaging techniques by several orders of magnitude with respect to the fastest previously available methods, and enables the use of state-of-the-art regularized least-squares solvers. Using the KAT, one can reconstruct images with higher resolutions than was previously possible and use more accurate reconstruction techniques, opening new and exciting possibilities for acoustic imaging.

Fast Transforms for Acoustic Imaging-Part II: Applications

In Part I [""Fast Transforms for Acoustic Imaging-Part I: Theory,"" IEEE TRANSACTIONS ON IMAGE PROCESSING], we introduced the Kronecker array transform (KAT), a fast transform for imaging with separable arrays. Given a source distribution, the KAT produces the spectral matrix which would be measured by a separable sensor array. In Part II, we establish connections between the KAT, beamforming and 2-D convolutions, and show how these results can be used to accelerate classical and state of the art array imaging algorithms. We also propose using the KAT to accelerate general purpose regularized least-squares solvers. Using this approach, we avoid ill-conditioned deconvolution steps and obtain more accurate reconstructions than previously possible, while maintaining low computational costs. We also show how the KAT performs when imaging near-field source distributions, and illustrate the trade-off between accuracy and computational complexity. Finally, we show that separable designs can deliver accuracy competitive with multi-arm logarithmic spiral geometries, while having the computational advantages of the KAT.

A Review of antenas for indoor positioning systems

This paper provides a review of antennas applied for indoor positioning or localization systems. The desired requirements of those antennas when integrated in anchor nodes (reference nodes) are discussed, according to different localization techniques and their performance. The described antennas will be subdivided into the following sections according to the nature of measurements: received signal strength (RSS), time of flight (ToF), and direction of arrival (DoA). This paper intends to provide a useful guide for antenna designers who are interested in developing suitable antennas for indoor localization systems.

Agrupación de antenas microstrip para un receptor SAR biestático

El objetivo de este proyecto es el diseño de las antenas para el receptor de un radar de apertura sintética biestáticos (SAR). Estas antenas tendrán que maximizar la ganancia con la restricción de maximizar también el campo de visión del radar. Esto quiere decir, que la antena tendrá que tener un ancho de banda relativamente grande en uno de sus planos principales y relativamente estrecho en el otro plano. Con el propósito de diseñar una agrupación de antenas para un receptor SAR biestático, en este documento se analiza la tecnología microstrip orientada a las antenas y la teoría de las agrupaciones de antenas, se diseñan antenas de doble polarización, se estudian agrupaciones de antenas microstrip que cumplan con las especificaciones, se presentan redes de alimentaciones para dichas agrupaciones y se fabrica y mide una agrupación de antenas con doble polarización.

Conditional maximum likelihood timing recovery: estimators and bounds

This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical low-SNR unconditional ML (UML) formulationthat is systematically applied in the literature for the derivationof non-data-aided (NDA) timing-error-detectors (TEDs). A new CML TED is derived and proved to be self-noise free, in contrast to the conventional low-SNR-UML TED. In addition, the paper provides a derivation of the conditional Cramér–Rao Bound (CRB ), which is higher (less optimistic) than the modified CRB (MCRB)[which is only reached by decision-directed (DD) methods]. It is shown that the CRB is a lower bound on the asymptotic statisticalaccuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained boundis not general, it applies to most NDA synchronizers proposed in the literature. A closed-form expression of the conditional CRBis obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high Eg/No.