Results 1  10
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40
On probing signal design for MIMO radar
 IEEE Trans. Signal Process
, 2007
"... Abstract—A multipleinput multipleoutput (MIMO) radar system, unlike a standard phasedarray radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern ..."
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Cited by 43 (2 self)
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Abstract—A multipleinput multipleoutput (MIMO) radar system, unlike a standard phasedarray radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern, and also to minimize the crosscorrelation of the signals reflected back to the radar by the targets of interest. In this paper, we show how the above desirable features can be achieved by designing the covariance matrix of the probing signal vector transmitted by the radar. Moreover, in a numerical study, we show that the proper choice of the probing signals can significantly improve the performance of adaptive MIMO radar techniques. Additionally, we demonstrate the advantages of several MIMO transmit beampattern designs, including a beampattern matching design and a minimum sidelobe beampattern design, over their phasedarray counterparts. Index Terms—Beampattern matching design, multipleinput multipleoutput (MIMO) radar, minimum sidelobe beampattern design, probing signal design, transmit beampattern. I.
Convex Optimization Problems Involving Finite autocorrelation sequences
, 2001
"... We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in opt ..."
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Cited by 40 (0 self)
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We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in a set of linear inequalities. They can also be cast as linear matrix inequalities via the KalmanYakubovichPopov lemma. The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interiorpoint methods for semidefinite programming. However, it has an important drawback: to represent an autocorrelation sequence of length n, it requires the introduction of a large number (n(n + 1)/2) of auxiliary variables. This results in a high computational cost when generalpurpose semidefinite programming solvers are used. We present a more efficient implementation based on duality and on interiorpoint methods for convex problems with generalized linear inequalities.
Optimal waveform design for UWB radios
 George Mason University
, 2004
"... Abstract—With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultrawideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless service ..."
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Cited by 22 (4 self)
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Abstract—With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultrawideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply highrate multidimensional modulation and (carrierfree) orthogonal frequencydivision multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives. Index Terms—Digital pulse design, finite impulse response (FIR) filter, ultrawideband communications. I.
Multivariate nonnegative quadratic mappings
 SIAM J. Optim
, 2002
"... Abstract. In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a prespecified conic order. In particular, we consider the set (cone) of nonnegative quadrat ..."
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Cited by 16 (5 self)
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Abstract. In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a prespecified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone, and study when it can be represented by linear matrix inequalities. We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models. In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semidefinite program. Key words. Linear matrix inequalities, convex cone, robust optimization, biquadratic functions AMS subject classifications. 15A48, 90C22
Efficient Design of Oversampled NPR GDFT Filter Banks
, 2003
"... In this paper, we present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems which are sensit ..."
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Cited by 15 (0 self)
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In this paper, we present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems which are sensitive to aliasing, such as subband adaptive filters. Our design criteria for the prototype filter are explicit bounds (derived herein) on the aliased components in the subbands and the output, the distortion induced by the filter bank, and the imaged subband errors in the output. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved. Our design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter, including the tradeoff between aliasing in the subbands and the distortion induced by the filter bank. In our examples we calculate several of these tradeoffs and demonstrate that our method can generate filters with significantly better performance than filters obtained using current design methods.
Convex Optimization Theory Applied to Joint TransmitterReceiver Design in MIMO Channels
 in SpaceTime Processing for MIMO Communications, Chapter 8
, 2005
"... Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wirelin ..."
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Cited by 7 (1 self)
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Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wireline digital subscriber line (DSL) systems [5] and singleantenna
Positivity and Linear Matrix Inequalities
 EUR. J. CONTROL
, 2002
"... In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for various problems in systems and control. Finally, we indicate h ..."
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Cited by 7 (3 self)
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In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for various problems in systems and control. Finally, we indicate how these problems can be solved numerically and what specific numerical difficulties can be encountered.
Efficient largescale filter/filterbank design via LMI characterization of trigonometric curves
 in Proc. of IEEE Inter. Conf. on Acoustics, Speech and Signal Processing (ICASSP 05
"... Abstract—Many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semiinfinite constraints. Recent advances in design methodology are based on various linear matrix inequality (LMI) characterizations of the semiinfinite ..."
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Cited by 5 (4 self)
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Abstract—Many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semiinfinite constraints. Recent advances in design methodology are based on various linear matrix inequality (LMI) characterizations of the semiinfinite constraints, and semidefinite programming (SDP) solutions. Despite these advances, the design of filters of several hundredth order, which typically arise in multicarrier communication and signal compression, cannot be accommodated. This hurdle is due mainly to the large number of additional variables incurred in the LMI characterizations. This paper proposes a novel LMI characterization of the semiinfinite constraints that involves additional variables of miminal dimensions. Consequently, the design of highorder filters required in practical applications can be achieved. Examples of designs of up to 1200tap filters are presented to verify the viability of the proposed approach. Index Terms—Filter and filter bank, semidefinite programming, trigonometric polynomial. a linear TSIC in the filter coefficients [19], [32] (more precisely, (2) leads to two linear TSICs [16]). More general constraints [1], [2], [37] involving bounds on the frequency response of the FIR filter are also expressible in terms of linear TSIC. Imposing a passband ripple of in the passband, and a stopband attenuation of in the stopband is equivalent to the following linear TSICs (2) I.
Optimized analog filter designs with flat responses by semidefinite programming
 IEEE Trans. Signal Processing
"... Abstract—Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. Allpole filters have maximally flat passband, so our design minimizes their passband distortion. Analogous ..."
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Cited by 3 (1 self)
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Abstract—Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. Allpole filters have maximally flat passband, so our design minimizes their passband distortion. Analogously, maximally flat filters have maximally flat passband, so our design maximizes their stopband attenuation. Its particular cases provide flexible alternatives to the classical counterparts. Semidefinite program (SDP) formulations for the posed filter design problems are presented, which are efficiently solved by existing optimization software. Several examples and comparisons are provided to validate the viability of our design. Index Terms—Analog filter, convex analysis, global optimization, semidefinite programming (SDP). I.
Beampattern synthesis via a matrix approach for signal power estimation
 IEEE Trans. Signal Process
, 2007
"... Abstract—We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight ..."
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Abstract—We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight matrices at the array output, which leads to matrix approaches (MA). We consider several versions of MA, including a (data) adaptive MA (AMA), as well as several dataindependent MA designs. For all of these MA designs, globally optimal solutions can be determined efficiently due to the convex optimization formulations obtained by SDR. Numerical examples as well as theoretical evidence are presented to show that the optimal weight matrix obtained via SDR has few dominant eigenvalues, and often only one. When the number of dominant eigenvalues of the optimal weight matrix is equal to one, MA reduces to VA, and the main advantage offered by SDR in this case is to determine the globally optimal solution efficiently. Moreover, we show that the AMA allows for strict control of mainbeam shape and peak sidelobe level while retaining the capability of adaptively nulling strong interferences and jammers. Numerical examples are also used to demonstrate that better beampattern designs can be achieved via the dataindependent MA than via its VA counterpart. Index Terms—Beamforming, beampattern synthesis, convex optimization, mainbeam shape control, sidelobe control. I.