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17
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 155 (17 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.
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 30 (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.
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 29 (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.
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 24 (0 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
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.
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 2 (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
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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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
EXTREME OPTICS AND THE SEARCH FOR EARTHLIKE PLANETS
, 2006
"... Abstract. In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earthlike planets around nearby stars. Because of limitations inherent in the wave nature of light, the design problem is one of diffraction co ..."
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Abstract. In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earthlike planets around nearby stars. Because of limitations inherent in the wave nature of light, the design problem is one of diffraction control so as to provide the extremely high contrast needed to image a faint planet positioned very close to its much brighter star. I will describe the mathematics behind the diffraction control problem and explain how modern optimization tools were able to provide unexpected solutions that actually changed NASA’s approach to this problem.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Unitary Linear Dispersion Code Design and 1 Optimisation for MIMO Communication Systems
"... Linear Dispersion Codes (LDCs) have recently attracted numerous research interests. Thanks to their efficient spreading of data across both the time and spatial domains, LDCs are capable of achieving a desired DiversityMultiplexing Tradeoff (DMT) in Multiple Input Multiple Output (MIMO) broadband ..."
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Linear Dispersion Codes (LDCs) have recently attracted numerous research interests. Thanks to their efficient spreading of data across both the time and spatial domains, LDCs are capable of achieving a desired DiversityMultiplexing Tradeoff (DMT) in Multiple Input Multiple Output (MIMO) broadband wireless access systems. This paper proposes a novel LDC design method, which relies on the unitary matrix theory combined with a Genetic Algorithm (GA) aided optimisation procedure. The proposed design provides a flexible framework, where new LDCs attaining higher data rates and better error resilience than a number of classic MIMO schemes can be generated. Index Terms Diversitymultiplexing tradeoff, genetic algorithm, multipleinput multipleoutput, linear dispersion code.
On the average power of multiple subcarrier intensity modulated optical signals: Nehari’s problem and coding bounds
 in Proc. of IEEE International Conference on Communications, May 11–14 2003
"... Abstract — Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is an analogous problem to the high peak to mean envelope power ratio (PMEPR) of m ..."
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Abstract — Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is an analogous problem to the high peak to mean envelope power ratio (PMEPR) of multicarrier signals. In this paper, we consider the achievable average power reduction of MSM signals by using optimized reserved carriers and coding methods. Based on Nehari’s result we present a lower bound for the maximum average power of the signal after adding the reserved carriers. It is shown that the mean value of the average required power behaves very close to √ 2n log log n for a BPSK constellation where n is the number of subcarriers. We then consider finding the optimum values for the carriers and the effect of having finite bandwidth for reserved carriers. In the next section, mainly based on recent coding results for the PMEPR of multicarrier signals, we show the existence of very high rate codes with average power of O ( √ n log n) for large values of n, and furthermore the existence of codes with nonvanishing to zero rate and average power of O ( √ n) asymptotically.