Design and analysis of adaptive noise subspace estimation algorithms

Ph.DDOCTOR OF PHILOSOPH

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

Novel algorithms in wireless CDMA systems for estimation and kernel based equalization

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.A powerful technique is presented for joint blind channel estimation and carrier offset method for code- division multiple access (CDMA) communication systems. The new technique combines singular value decomposition (SVD) analysis with carrier offset parameter. Current blind methods sustain a high computational complexity as they require the computation of a large SVD twice, and they are sensitive to accurate knowledge of the noise subspace rank. The proposed method overcomes both problems by computing the SVD only once. Extensive simulations using MatLab demonstrate the robustness of the proposed scheme and its performance is comparable to other existing SVD techniques with significant lower computational as much as 70% cost because it does not require knowledge of the rank of the noise sub-space. Also a kernel based equalization for CDMA communication systems is proposed, designed and simulated using MatLab. The proposed method in CDMA systems overcomes all other methods

Advanced optimization algorithms for sensor arrays and multi-antenna communications

Optimization problems arise frequently in sensor array and multi-channel signal processing applications. Often, optimization needs to be performed subject to a matrix constraint. In particular, unitary matrices play a crucial role in communications and sensor array signal processing. They are involved in almost all modern multi-antenna transceiver techniques, as well as sensor array applications in biomedicine, machine learning and vision, astronomy and radars. In this thesis, algorithms for optimization under unitary matrix constraint stemming from Riemannian geometry are developed. Steepest descent (SD) and conjugate gradient (CG) algorithms operating on the Lie group of unitary matrices are derived. They have the ability to find the optimal solution in a numerically efficient manner and satisfy the constraint accurately. Novel line search methods specially tailored for this type of optimization are also introduced. The proposed approaches exploit the geometrical properties of the constraint space in order to reduce the computational complexity. Array and multi-channel signal processing techniques are key technologies in wireless communication systems. High capacity and link reliability may be achieved by using multiple transmit and receive antennas. Combining multi-antenna techniques with multicarrier transmission leads to high the spectral efficiency and helps to cope with severe multipath propagation. The problem of channel equalization in MIMO-OFDM systems is also addressed in this thesis. A blind algorithm that optimizes of a combined criterion in order to be cancel both inter-symbol and co-channel interference is proposed. The algorithm local converge properties are established as well

Spatio-Temporal processing for Optimum Uplink-Downlink WCDMA Systems

The capacity of a cellular system is limited by two different phenomena, namely multipath fading and multiple access interference (MAl). A Two Dimensional (2-D) receiver combats both of these by processing the signal both in the spatial and temporal domain. An ideal 2-D receiver would perform joint space-time processing, but at the price of high computational complexity. In this research we investigate computationally simpler technique termed as a Beamfom1er-Rake. In a Beamformer-Rake, the output of a beamfom1er is fed into a succeeding temporal processor to take advantage of both the beamformer and Rake receiver. Wireless service providers throughout the world are working to introduce the third generation (3G) and beyond (3G) cellular service that will provide higher data rates and better spectral efficiency. Wideband COMA (WCDMA) has been widely accepted as one of the air interfaces for 3G. A Beamformer-Rake receiver can be an effective solution to provide the receivers enhanced capabilities needed to achieve the required performance of a WCDMA system. We consider three different Pilot Symbol Assisted (PSA) beamforming techniques, Direct Matrix Inversion (DMI), Least-Mean Square (LMS) and Recursive Least Square (RLS) adaptive algorithms. Geometrically Based Single Bounce (GBSB) statistical Circular channel model is considered, which is more suitable for array processing, and conductive to RAKE combining. The performances of the Beam former-Rake receiver are evaluated in this channel model as a function of the number of antenna elements and RAKE fingers, in which are evaluated for the uplink WCDMA system. It is shown that, the Beamformer-Rake receiver outperforms the conventional RAKE receiver and the conventional beamformer by a significant margin. Also, we optimize and develop a mathematical formulation for the output Signal to Interference plus Noise Ratio (SINR) of a Beam former-Rake receiver. In this research, also, we develop, simulate and evaluate the SINR and Signal to Noise Ratio (Et!Nol performances of an adaptive beamforming technique in the WCDMA system for downlink. The performance is then compared with an omnidirectional antenna system. Simulation shows that the best perfom1ance can be achieved when all the mobiles with same Angle-of-Arrival (AOA) and different distance from base station are formed in one beam

Graph-based Methods for Visualization and Clustering

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: it is complex and deprived of semantical context. A common step to address those issues is to embed raw data in lower dimensions, by finding a mapping which preserves the similarity between data points from their original space to a new one. Measuring similarity between large sets of high-dimensional objects is, however, problematic for two main reasons: first, high-dimensional points are subject to the curse of dimensionality and second, the number of pairwise distances between points is quadratic with respect to the amount of data points. Both problems can be addressed by using nearest neighbours graphs to understand the structure in data. As a matter of fact, most dimensionality reduction methods use similarity matrices that can be interpreted as graph adjacency matrices. Yet, despite recent progresses, dimensionality reduction is still very challenging when applied to very large datasets. Indeed, although recent methods specifically address the problem of scaleability, processing datasets of millions of elements remain a very lengthy process. In this thesis, we propose new contributions which address the problem of scaleability using the framework of Graph Signal Processing, which extends traditional signal processing to graphs. We do so motivated by the premise that graphs are well suited to represent the structure of the data. In the first part of this thesis, we look at quantitative measures for the evaluation of dimensionality reduction methods. Using tools from graph theory and Graph Signal Processing, we show that specific characteristics related to quality can be assessed by taking measures on the graph, which indirectly validates the hypothesis relating graph to structure. The second contribution is a new method for a fast eigenspace approximation of the graph Laplacian. Using principles of GSP and random matrices, we show that an approximated eigensubpace can be recovered very efficiently, which be used for fast spectral clustering or visualization. Next, we propose a compressive scheme to accelerate any dimensionality reduction technique. The idea is based on compressive sampling and transductive learning on graphs: after computing the embedding for a small subset of data points, we propagate the information everywhere using transductive inference. The key components of this technique are a good sampling strategy to select the subset and the application of transductive learning on graphs. Finally, we address the problem of over-discriminative feature spaces by proposing a hierarchical clustering structure combined with multi-resolution graphs. Using efficient coarsening and refinement procedures on this structure, we show that dimensionality reduction algorithms can be run on intermediate levels and up-sampled to all points leading to a very fast dimensionality reduction method. For all contributions, we provide extensive experiments on both synthetic and natural datasets, including large-scale problems. This allows us to show the pertinence of our models and the validity of our proposed algorithms. Following reproducible principles, we provide everything needed to repeat the examples and the experiments presented in this work