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IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)

作者： Itzhak, Gal Cohen, Israel Technion Israel Inst Technol Andrew & Erna Viterbi Fac Elect & Comp Engn Haifa Israel

ISBN: (纸本)9798350323726

This paper presents a region-of-interest (ROI) oriented constant-beamwidth (CB) beamforming approach with rectangular arrays. We decompose a global rectangular beamformer into a Kronecker-product (KP) of two linear sub-beamformers: a uniform constant-beamwidth beamformer along the y-axis and a nonuniform robust superdirective (SD) beamformer along the x-axis whose topology is optimized for a broadband array directivity criterion. The KP decomposition allows a flexible tradeoff control between the CB threshold frequency and the array directivity by tuning the number of microphones along each axis. The topology optimization considers a continuous ROI and therefore does not require an accurate desired source direction in space. The proposed approach is compared to uniform rectangular arrays with uniform differential sub-beamformers along the x-axis. We show that the proposed method is advantageous regarding white noise gain and directivity factor measures, especially when the desired source direction differs from the estimated source direction.

关键词： Microphone arrays region-of-interest beamforming constant-beamwidth beamformer rectangular arrays

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Beam Depth Analysis for Large rectangular arrays

Beam Depth Analysis for Large Rectangular Arrays

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IEEE Conference on Global Communications (IEEE GLOBECOM) - Intelligent Communications for Shared Prosperity

作者： Kosasih, Alva Bjornson, Emil KTH Royal Inst Technol Div Commun Syst Stockholm Sweden

ISBN: (纸本)9798350310900

Most wireless communication systems operate in the far-field region of antennas and antenna arrays, where waves are planar and beams have infinite depth. When antenna arrays become electrically large, it is possible that the receiver is in the radiative near-field of the transmitter, and vice versa. Recent works have shown that near-field beamforming exhibits a finite depth, which enables a new depth-based spatial multiplexing paradigm. In this paper, we explore how the shape and size of a rectangular array determine the near-field beam behaviors. In particular, we investigate the 3 dB beam depth (BD), defined as the range of distances where the gain is greater than half of the peak gain. We derive analytical gain and BD expressions and prove how they depend on the aperture area and length. The largest BD is obtained for a square array while the smallest BD is obtained by a uniform linear array.

关键词： Beam depth active arrays Fresnel region finite-depth near-field beamforming rectangular arrays

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Successive Standardization of rectangular arrays

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ALGORITHMS 2012年第1期5卷 98-112页

作者： Olshen, Richard A. Rajaratnam, Bala Stanford Univ Sch Med Dept Hlth Res & Policy Biostat HRP Redwood Bldg Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Stat Stanford CA 94305 USA Yang & Yamazaki Environm & Energy Bldg Dept Environm Earth Syst Sci Stanford CA 94305 USA Woods Inst Environm Stanford CA 94305 USA

In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column;then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again, ... In [1] it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in [I] is true, though the argument in [1] is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in [1] suggest that except for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it "Efron's algorithm". More importantly, the rapidity of convergence is illustrated by numerical examples.

关键词： rectangular arrays successive iterations exponentially fast convergence

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Symmetry-Imposed rectangular Coprime and Nested arrays for Direction of Arrival Estimation With Multiple Signal Classification

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IEEE ACCESS 2019年 7卷 153217-153229页

作者： Adhikari, Kaushallya Drozdenko, Benjamin Louisiana Tech Univ Elect Engn Dept Ruston LA 71272 USA Louisiana Tech Univ Cyber Engn Dept Ruston LA 71272 USA

Linear sparse arrays (coprime and nested arrays) have been studied extensively as a means of performing direction of arrival (DoA) estimation while bypassing Nyquist sampling theorem. However, rectangular sparse arrays have few studies, most of which are based in lattice theory. Although the multiple signal classification (MUSIC) alogrithm can be applied to lattice theory-based sparse arrays, fewer DoAs can be estimated for these arrays than for a full array with the same aperture. One contribution of this paper is the formulation of symmetry-imposed rectangular coprime and nested array designs that have wider contiguous lags than lattice-based arrays. Also, existing algorithms for rectangular arrays employ the direct sample covariance matrix estimate, which has low accuracy. Another contribution of this paper is an alternate method for estimating the covariance matrix that ensures the matrix is block-Toeplitz. Using the proposed covariance matrix estimate, we integrate a MUSIC-based DoA estimation method that applies to both full arrays and sparse arrays. The results show that the covariance estimates produced by the proposed method have higher accuracy than the traditional sample covariance estimates. The results also demonstrate that symmetry-imposed sparse arrays have higher resolution than full rectangular arrays with the same number of sensors.

关键词： Covariance matrices Sensor arrays Direction-of-arrival estimation Multiple signal classification Estimation Apertures Coarray coprime arrays DoA estimation MUSIC nested arrays planar arrays rectangular arrays sparse arrays

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Expressiveness and complexity of regular pure two-dimensional context-free languages

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2013年第8期90卷 1708-1733页

作者： Bersani, Marcello M. Frigeri, Achille Cherubini, Alessandra Politecn Milan Dipartimento Elettron Informaz & Bioingn I-20133 Milan Italy Politecn Milan Dipartimento Matemat I-20133 Milan Italy

Picture languages generalize classical string languages to two-dimensional arrays. Several approaches have been proposed during the years;consequently, a general classification and a detailed comparison of the proposed classes turn to be necessary. In this paper, we study some closure properties of (regularly controlled) pure two-dimensional context-free grammars, for which we also prove that the parsing is NP-hard. Moreover, we draw some comparisons with other interesting picture grammars like (regional) tile grammars, Prua grammars and local languages, clarifying, in some cases, their mutual relationship with respect to expressiveness.

关键词： picture languages pure grammars rectangular arrays two-dimensional grammars

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Parallel splicing on images

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2004年第6期18卷 1071-1091页

作者： Chandra, PH Subramanian, KG Thomas, DC Jayaraj Annapackiam Coll Women Dept Math Periyakulam Theni India Madras Christian Coll Dept Math Madras 600059 Tamil Nadu India

In this paper, splicing on images of rectangular arrays is introduced as a simple and effective extension of the operation of splicing on strings extensively studied in the context of DNA computing. A comparison of the resulting class of splicing array languages with the local two-dimensional array languages and two-dimensional right linear languages is made. Certain closure properties are obtained. Furthermore, the notion of self cross-over of strings is extended to arrays with respect to the splicing of arrays introduced here.

关键词： two-dimensional languages rectangular arrays dominoes splicing operation self cross-over operation

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Wideband smart antenna theory using rectangular array structures

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2002年第9期50卷 2143-2151页

作者： Ghavami, M Sony Comp Sci Labs Inc Tokyo Japan

Smart antenna techniques at the base station can dramatically improve the performance of the mobile radio system by employing spatial filtering. The design of a fully spatial signal processor using rectangular array configuration, is proposed in this paper. Two-dimensional (2-D) spatial filters that can be implemented by microstrip technology are capable of filtering the received signal in the angular domain as well as the frequency domain. Furthermore, it has wideband properties and, hence, eliminates the requirement, of different antenna, spacing for applications including various carrier frequencies. The desired frequency selectivity of the smart antenna can be combined with compensation of the undesired frequency performance of a single antenna element, and the result is quite satisfactory for practical implementation. In addition, if the elements of the array are not perfectly onmidirectional or frequency independent, we can compensate for these deficiencies in the design algorithm. Two different algorithms for calculating the real-valued weights of the antenna elements are proposed. The first algorithm is more complex but leads to sharper beams and controlled performance. The second method is simpler but has wider beam and lower fractional bandwidth. Some computer simulation results demonstrating the directional beam patterns of the designed beamformers are presented at the end of this paper.

关键词： formation rectangular arrays spatial filtering wideband beam

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Pure 2D picture grammars and languages

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DISCRETE APPLIED MATHEMATICS 2009年第16期157卷 3401-3411页

作者： Subramanian, K. G. Ali, Rosihan M. Geethalakshmi, M. Nagar, Atulya K. Univ Sains Malaysia Sch Math Sci George Town 11800 Malaysia Dr MGR Janaki Coll Dept Math Madras 600028 Tamil Nadu India Liverpool Hope Univ Dept Comp Sci Intelligent & Distributed Syst Lab Liverpool L16 9JD England

Anew syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Pure grammars Two-dimensional grammars Picture languages rectangular arrays Hexagonal arrays

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Finite Beam Depth Analysis for Large arrays

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第8期23卷 10015-10029页

作者： Kosasih, Alva Bjornson, Emil KTH Royal Inst Technol Div Commun Syst Stockholm 16440 Sweden

Most wireless communication systems operate in the far-field region of antennas and antenna arrays, where waves are planar and beams have infinite depth. When antenna arrays become electrically large, it is possible that the receiver is in the radiative near-field of the transmitter, and vice versa. Recent works have shown that near-field beamforming exhibits a finite depth, which enables a new depth-based spatial multiplexing paradigm. In this paper, we explore how the shape and size of an array determine the near-field beam behaviors. In particular, we investigate the 3 dB beam depth (BD), defined as the range of distances where the gain is greater than half of the peak gain. We derive analytical gain and BD expressions and prove how they depend on the aperture area and length. For non-broadside transmissions, we find that the BD increases as the transmitter approaches the end-fire direction of the array. Furthermore, it is sufficient to characterize the BD for a broadside transmitter, as the beam pattern with a non-broadside transmitter can be approximated by that of a smaller/projected array with a broadside transmitter. Our analysis demonstrates that the BD can be ordered from smallest to largest as ULA, circular, and square arrays.

关键词： Array signal processing Transmitters Gain Antennas Behavioral sciences Phased arrays Wireless communication Beam depth beam width radiative near-field Fresnel region finite-depth beamforming rectangular arrays circular arrays

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Computing with membranes and picture arrays

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JOURNAL OF DISCRETE ALGORITHMS 2015年 33卷 31-42页

作者： Venkatesan, A. S. Prasanna Thomas, D. G. Robinson, T. Nagar, Atulya K. BS Abdur Rahman Univ Dept Math Madras 600048 Tamil Nadu India Madras Christian Coll Tambaram Dept Math Madras 600059 Tamil Nadu India Liverpool Hope Univ Dept Comp Sci Liverpool L16 9JD Merseyside England

Splicing systems were introduced by Tom Head [3,4] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Membrane computing P system rectangular arrays Hexagonal arrays Parallel splicing

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