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22
Joint TxRx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization
 IEEE TRANS. SIGNAL PROCESSING
, 2003
"... This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of consid ..."
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Cited by 224 (19 self)
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This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schurconcave and Schurconvex functions. Once the optimal structure of the transmitreceive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closedform expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peaktoaverage ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel waterfilling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.
MIMO Transceiver Design via Majorization Theory
, 2007
"... and unified representation of different physical communication systems, ranging from multiantenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established. In general, the design of communication systems f ..."
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Cited by 45 (1 self)
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and unified representation of different physical communication systems, ranging from multiantenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established. In general, the design of communication systems for MIMO channels is quite involved (if one can assume the use of sufficiently long and good codes, then the problem formulation simplifies drastically). The first difficulty lies on how to measure the global performance of such systems given the tradeoff on the performance among the different data streams. Once the problem formulation is defined, the resulting mathematical problem is typically too complicated to be optimally solved as it is a matrixvalued nonconvex optimization problem. This design problem has been studied for the past three decades (the first papers
Linear Matrix Inequality Formulation of Spectral Mask Constraints
, 2000
"... The design of a finite impulse response filter often involves a spectral 'mask' which the mag nitude spectrum must satisfy. This constraint can be awkward because it is semiinfinite, since it yields two inequality constraints for each frequency point. In current practice, spectral mask ..."
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Cited by 37 (7 self)
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The design of a finite impulse response filter often involves a spectral 'mask' which the mag nitude spectrum must satisfy. This constraint can be awkward because it is semiinfinite, since it yields two inequality constraints for each frequency point. In current practice, spectral masks are often approximated by discretization, but in this paper we will show that piecewise constant masks can be precisely enforced in a finite and convex manner via linear matrix inequalities.
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 36 (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.
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 35 (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.
Handling nonnegative constraints in spectral estimation
 in Proceedings of the 34th Asilomar Conference on Signals, Systems, and Computers
, 2000
"... We consider convex optimization problems with the constraint that the variables form a finite autocorrelation sequence, or equivalently, that the corresponding power spectral density is nonnegative. This constraint is often approximated by sampling the power spectral density, which results in a set ..."
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Cited by 5 (0 self)
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We consider convex optimization problems with the constraint that the variables form a finite autocorrelation sequence, or equivalently, that the corresponding power spectral density is nonnegative. This constraint is often approximated by sampling the power spectral density, which results in a set of linear inequalities. It can also be cast as a linear matrix inequality via the positivereal 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, these methods require O(n^6) floating point operations per iteration, if a generalpurpose implementation is used. We introduce a much more efficient method with a complexity of O(n³) flops per iteration.
Identification for Control of Multivariable Systems: Controller Validation and Experiment Design via LMIs
, 2008
"... ..."
Connections Between SemiInfinite and Semidefinite Programming
"... We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T ..."
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Cited by 4 (1 self)
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We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T
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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Cited by 3 (0 self)
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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.
Filter Design with Low Complexity Coefficients
"... We introduce a heuristic for designing filters that have low complexity coefficients, as measured by the total number of nonzeros digits in the binary or canonic signed digit (CSD) representations of the filter coefficients, while still meeting a set of design specifications, such as limits on frequ ..."
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Cited by 2 (0 self)
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We introduce a heuristic for designing filters that have low complexity coefficients, as measured by the total number of nonzeros digits in the binary or canonic signed digit (CSD) representations of the filter coefficients, while still meeting a set of design specifications, such as limits on frequency response magnitude, phase, and group delay. Numerical examples show that the method is able to attain very low complexity designs with only modest relaxation of the specifications. 1