46 research outputs found

    Ultrasound tomography using pyroelectric and piezoelectric sensors

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    Acoustic absorption is one of several quantities which can differentiate healthy breast tissue from cancerous tissue. In order to accurately quantify the acoustic absorption, the sensor system must be able to accurately distinguish acoustic power loss due to absorption from other modes of attenuation. Traditional piezoelectric sensors are susceptible to phase-cancellation artifacts due to their directional signal response, and thus pyroelectric ultrasound sensors, which have a much flatter directional response, have been suggested as an alternate measurement device for improved absorption reconstructions in ultrasound tomography (UST). In this thesis we investigate the use of pyroelectric phase-insensitive sensors in UST — the thesis is divided into two parts. In the first part we present a model for a pyroelectric ultrasound sensor and investigate its directional response and sensitivity properties. The model’s time-series response and directional response are compared to real-world measurements to confirm accuracy. The second part focuses on the inverse problem aspect of ultrasound tomography, where we consider various reconstruction methods and sensor geometries to determine which situations can benefit from phase-insensitive data for acoustic absorption reconstruction. Reconstructions for both phase-insensitive as well as phase-sensitive sensors are analysed, with future work considerations for combined sensor systems

    A Distributed and Secure Algorithm for Computing Dominant SVD Based on Projection Splitting

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    In this paper, we propose and study a distributed and secure algorithm for computing dominant (or truncated) singular value decompositions (SVD) of large and distributed data matrices. We consider the scenario where each node privately holds a subset of columns and only exchanges ''safe'' information with other nodes in a collaborative effort to calculate a dominant SVD for the whole matrix. In the framework of alternating direction methods of multipliers (ADMM), we propose a novel formulation for building consensus by equalizing subspaces spanned by splitting variables instead of equalizing themselves. This technique greatly relaxes feasibility restrictions and accelerates convergence significantly, while at the same time yielding simple subproblems. We design several algorithmic features, including a low-rank multiplier formula and mechanisms for controlling subproblem solution accuracies, to increase the algorithm's computational efficiency and reduce its communication overhead. More importantly, the possibility appears remote, if possible at all, for a malicious node to uncover the data stored in another node through shared quantities available in our algorithm, which is not the case in existing distributed or parallelized algorithms. We present the convergence analysis results, including a worst-case complexity estimate, and extensive experimental results indicating that the proposed algorithm, while safely guarding data privacy, has a strong potential to deliver a cutting-edge performance, especially when communication costs are high

    Enabling Efficient Communications Over Millimeter Wave Massive MIMO Channels Using Hybrid Beamforming

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    The use of massive multiple-input multiple-output (MIMO) over millimeter wave (mmWave) channels is the new frontier for fulfilling the exigent requirements of next-generation wireless systems and solving the wireless network impending crunch. Massive MIMO systems and mmWave channels offer larger numbers of antennas, higher carrier frequencies, and wider signaling bandwidths. Unleashing the full potentials of these tremendous degrees of freedom (dimensions) hinges on the practical deployment of those technologies. Hybrid analog and digital beamforming is considered as a stepping-stone to the practical deployment of mmWave massive MIMO systems since it significantly reduces their operating and implementation costs, energy consumption, and system design complexity. The prevalence of adopting mmWave and massive MIMO technologies in next-generation wireless systems necessitates developing agile and cost-efficient hybrid beamforming solutions that match the various use-cases of these systems. In this thesis, we propose hybrid precoding and combining solutions that are tailored to the needs of these specific cases and account for the main limitations of hybrid processing. The proposed solutions leverage the sparsity and spatial correlation of mmWave massive MIMO channels to reduce the feedback overhead and computational complexity of hybrid processing. Real-time use-cases of next-generation wireless communication, including connected cars, virtual-reality/augmented-reality, and high definition video transmission, require high-capacity and low-latency wireless transmission. On the physical layer level, this entails adopting near capacity-achieving transmission schemes with very low computational delay. Motivated by this, we propose low-complexity hybrid precoding and combining schemes for massive MIMO systems with partially and fully-connected antenna array structures. Leveraging the disparity in the dimensionality of the analog and the digital processing matrices, we develop a two-stage channel diagonalization design approach in order to reduce the computational complexity of the hybrid precoding and combining while maintaining high spectral efficiency. Particularly, the analog processing stage is designed to maximize the antenna array gain in order to avoid performing computationally intensive operations such as matrix inversion and singular value decomposition in high dimensions. On the other hand, the low-dimensional digital processing stage is designed to maximize the spectral efficiency of the systems. Computational complexity analysis shows that the proposed schemes offer significant savings compared to prior works where asymptotic computational complexity reductions ranging between 80%80\% and 98%98\%. Simulation results validate that the spectral efficiency of the proposed schemes is near-optimal where in certain scenarios the signal-to-noise-ratio (SNR) gap to the optimal fully-digital spectral efficiency is less than 11 dB. On the other hand, integrating mmWave and massive MIMO into the cellular use-cases requires adopting hybrid beamforming schemes that utilize limited channel state information at the transmitter (CSIT) in order to adapt the transmitted signals to the current channel. This is so mainly because obtaining perfect CSIT in frequency division duplexing (FDD) architecture, which dominates the cellular systems, poses serious concerns due to its large training and excessive feedback overhead. Motivated by this, we develop low-overhead hybrid precoding algorithms for selecting the baseband digital and radio frequency (RF) analog precoders from statistically skewed DFT-based codebooks. The proposed algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder and the hybrid beamformer and maximizing the signal to interference noise ratio for the single-user and multi-user cases, respectively. Mathematical analysis shows that the proposed algorithms are asymptotically optimal as the number of transmit antennas goes to infinity and the mmWave channel has a limited number of paths. Moreover, it shows that the performance gap between the lower and upper bounds depends heavily on how many DFT columns are aligned to the largest eigenvectors of the transmit antenna array response of the mmWave channel or equivalently the transmit channel covariance matrix when only the statistical channel knowledge is available at the transmitter. Further, we verify the performance of the proposed algorithms numerically where the obtained results illustrate that the spectral efficiency of the proposed algorithms can approach that of the optimal precoder in certain scenarios. Furthermore, these results illustrate that the proposed hybrid precoding schemes have superior spectral efficiency performance while requiring lower (or at most comparable) channel feedback overhead in comparison with the prior art

    Expansions and factorizations of matrices and their applications

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    Abstract. Linear algebra is a foundation to decompositions and algorithms for extracting simple structures from complex data. In this thesis, we investigate and apply modern techniques from linear algebra to solve problems arising in signal processing and computer science. In particular, we focus on data that takes the shape of a matrix and we explore how to represent it as products of circulant and diagonal matrices. To this end, we study matrix decompositions, approximations, and structured matrix expansions whose elements are products of circulant and diagonal matrices. Computationally, we develop a matrix expansion with DCD matrices for approximating a given matrix. Remarkably, DCD matrices, i.e., a product of diagonal matrix, circulant matrix, and another diagonal matrix, give an natural extension to rank-one matrices. Inspired from the singular value decomposition, we introduce a notion of a matrix rank closely related to the expansion and compute the rank of some specific structured matrices. Specifically, Toeplitz matrix is a sum of two DCD matrices. Here, we present a greedy algorithmic framework to devise the expansion numerically. Finally, we show that the practical uses of the DCD expansion can be complemented by the proposed framework and perform two experiments with a view towards applications

    7. Minisymposium on Gauss-type Quadrature Rules: Theory and Applications

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