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31
Semidefinite relaxation of quadratic optimization problems
 SIGNAL PROCESSING MAGAZINE, IEEE
, 2010
"... n recent years, the semidefinite relaxation (SDR) technique has been at the center of some of very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, computa ..."
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Cited by 161 (11 self)
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n recent years, the semidefinite relaxation (SDR) technique has been at the center of some of very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, computationally efficient approximation technique for a host of very difficult optimization problems. In particular, it can be applied to many nonconvex quadratically constrained quadratic programs (QCQPs) in an almost mechanical fashion, including the following problem: min x[Rn x T
Efficient Soft Demodulation of MIMO QPSK via Semidefinite Relaxation
, 2008
"... We develop a computationally efficient and memory efficient approach to (near) maximum a posteriori probability demodulation for MIMO systems with QPSK signalling, based on semidefinite relaxation. Existing approaches to this problem require either storage of a large list of candidate bitvectors, o ..."
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Cited by 8 (2 self)
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We develop a computationally efficient and memory efficient approach to (near) maximum a posteriori probability demodulation for MIMO systems with QPSK signalling, based on semidefinite relaxation. Existing approaches to this problem require either storage of a large list of candidate bitvectors, or the solution of multiple binary quadratic problems. In contrast, the proposed demodulator does not require the storage of a candidate list, and involves the solution of a single (efficiently solvable) semidefinite program per channel use. Our simulation results show that the resulting computational and memory efficiencies are obtained without incurring a significant degradation in performance.
A linear fractional semidefinite relaxed ML approach to blind detection of 16QAM orthogonal spacetime block codes
 in Proc. IEEE Int. Conf. Commun
, 2008
"... This report considers a discrete fractional quadratic optimization problem motivated by a recent application in blind maximumlikelihood (ML) detection of higherorder QAM orthogonal spacetime block codes (OSTBCs) in wireless multipleinput multipleoutput (MIMO) communications. Since this discrete ..."
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Cited by 5 (3 self)
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This report considers a discrete fractional quadratic optimization problem motivated by a recent application in blind maximumlikelihood (ML) detection of higherorder QAM orthogonal spacetime block codes (OSTBCs) in wireless multipleinput multipleoutput (MIMO) communications. Since this discrete fractional quadratic optimization problem is NPhard in general, we present a suboptimal approach, called linear fractional semidefinite relaxation (LFSDR), for obtaining an accurate approximate solution in polynomial complexity. Three possible relaxation possibilities are presented, namely the boundedconstrained LFSDR (BCLFSDR), the virtuallyantipodal LFSDR (VALFSDR), and the polynomialinspired LFSDR (PILFSDR). We compare the three LFSDR methods in terms of their approximation performances and complexities. Simulation results under the scenario of blind ML higherorder QAM OSTBC detection are presented to show the performance of the three LFSDR methods as well as their computational complexities.
Design of Optimized Radar Codes with a Peak to Average Power Ratio Constraint
 SUBMITTED TO IEEE TRANS. ON SIGNAL PROCESSING
, 2010
"... This paper considers the problem of radar waveform design in the presence of colored Gaussian disturbance under a Peak to Average power Ratio (PAR) and an energy constraint. First of all, we focus on the selection of the radar signal optimizing the Signal to Noise Ratio (SNR) in correspondence of a ..."
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Cited by 5 (1 self)
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This paper considers the problem of radar waveform design in the presence of colored Gaussian disturbance under a Peak to Average power Ratio (PAR) and an energy constraint. First of all, we focus on the selection of the radar signal optimizing the Signal to Noise Ratio (SNR) in correspondence of a given expected target Doppler frequency (Algorithm 1). Then, through a maxmin approach, we make robust the technique with respect to the received Doppler (Algorithm 2), namely we optimize the worst case SNR under the same constraints as in the previous problem. Since Algorithms 1 and 2 do not impose any condition on the waveform phase, we also devise their phase quantized versions (Algorithms 3 and 4 respectively), which force the waveform phase to lie within a finite alphabet. All the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints. We prove that these problems are NPhard and, hence, introduce design techniques, relying on Semidefinite Programming (SDP) relaxation and randomization as well as on the theory of trigonometric polynomials, providing high quality suboptimal solutions with a polynomial time computational complexity. Finally, we analyze the performance of the new waveform design algorithms
BLIND IDENTIFICATION OF MIMOOSTBC CHANNELS COMBINING SECOND AND HIGHER ORDER STATISTICS
"... It has been recently shown that some multipleinput multipleoutput (MIMO) channels under orthogonal spacetime block coding (OSTBC) transmissions can not be unambiguously identified by only exploiting the second order statistics (SOS) of the received signal. This ambiguity, which is due to propertie ..."
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Cited by 4 (2 self)
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It has been recently shown that some multipleinput multipleoutput (MIMO) channels under orthogonal spacetime block coding (OSTBC) transmissions can not be unambiguously identified by only exploiting the second order statistics (SOS) of the received signal. This ambiguity, which is due to properties of the OSTBC, is traduced in the fact that the largest eigenvalue of the associated eigenvalue problem has multiplicity larger than one. Fortunately, for most OSTBCs that produce ambiguity, the multiplicity is two. This means that the channel estimate lies in a rank2 subspace, which can be easily determined applying a first principal component analysis (PCA) step. To eliminate the remaining ambiguity, we propose to apply a constant modulus algorithm (CMA). This combined PCA+CMA approach provides an effective solution for the blind identification of those OSTBCs that can not be identified using only SOS. Some simulation results are presented to show the performance of the proposed method. 1.
Correlation Matching Approaches for Blind OSTBC Channel Estimation
"... Abstract—In this paper, the problem of blind channel estimation under orthogonal space–time block coded (OSTBC) transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations. Specifically, the minimization of the Euclidean ..."
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Cited by 3 (0 self)
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Abstract—In this paper, the problem of blind channel estimation under orthogonal space–time block coded (OSTBC) transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations. Specifically, the minimization of the Euclidean distance and the Kullback–Leibler divergence leads, respectively, to the Euclidean correlation matching (ECM) and Kullback correlation matching (KCM) criteria. The proposed techniques exploit the knowledge of the source correlation matrix to unambiguously recover the multipleinput multipleoutput (MIMO) channel. Furthermore, due to the orthogonality properties of OSTBCs, both the ECM and KCM criteria result in closed form solutions. In particular, the channel estimate is given by the principal eigenvector of a matrix, which is obtained from the estimated correlation matrix of the observations modified by the code matrices and a set of weights. In the ECM case, the weights are fixed and equal to the eigenvalues of the source correlation matrix, whereas the KCM weights depend on both the signaltonoise ratio (SNR) and the source eigenvalues. Additionally, we show that the proposed approaches are equivalent in the low SNR regime, whereas in the high SNR regime the KCM criterion is asymptotically equivalent to the relaxed blind maximumlikelihood (ML) decoder. Finally, the performance of the proposed criteria is illustrated by means of some numerical examples. Index Terms—Blind channel estimation, correlation matching, information geometry, Kullback–Leibler divergence, maximumlikelihood (ML), orthogonal space–time block coding (OSTBC).
Nonconvex Quadratic Optimization, Semidefinite Relaxation, and Applications
, 2009
"... In recent years, the semidefinite relaxation (SDR) technique has been at the center of some of the very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, comp ..."
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Cited by 3 (1 self)
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In recent years, the semidefinite relaxation (SDR) technique has been at the center of some of the very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, computationally efficient approximation technique for a host of very difficult optimization problems. In
Hierarchical SpaceTime Block Code Recognition Using Correlation Matrices
 IEEE Transactions on Wireless Communications
, 2008
"... Abstract—The blind recognition of communication parameters is a key research issue for commercial and military communication systems. The results of numerous investigations about symbol timing estimation, modulation recognition as well as identification of the number of transmitters have been report ..."
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Cited by 3 (1 self)
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Abstract—The blind recognition of communication parameters is a key research issue for commercial and military communication systems. The results of numerous investigations about symbol timing estimation, modulation recognition as well as identification of the number of transmitters have been reported in the literature. But, to our knowledge, none of them have dealt with the recognition of the SpaceTime Block Codes (STBC) used in multiple transmitter communications. In order to blindly recognize the STBC of a wireless communication, this paper proposes a method based on the spacetime correlations of the received signals. Under perfect timing synchronization and under ideal conditions (full rank channel and a number of receivers greater or equal to the number of transmitters), it shows that the Frobenius norms of these statistics present nonnull values whose positions only depend on the STBC at the transmitter side. A classifier for the spacetime code recognition of 5 linear STBC (Spatial Multiplexing, Alamouti Coding, and 3 Orthogonal STBC using 3 antennas) is presented. Simulations show that the proposed method performs well even at low signaltonoise ratios. Index Terms—MIMO, spacetime coding, electronic warfare. I.
Twoway training for discriminatory channel estimation in wireless MIMO systems
 IEEE Trans. Signal Process
, 2013
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MaximumLikelihood Noncoherent OSTBC Detection with Polynomial Complexity
, 2010
"... We prove that maximumlikelihood (ML) noncoherent sequence detection of orthogonal spacetime block coded signals can always be performed in polynomial time with respect to the sequence length for static Rayleigh, correlated (in general) channels. Moreover, using recent results on efficient maximiz ..."
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Cited by 2 (2 self)
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We prove that maximumlikelihood (ML) noncoherent sequence detection of orthogonal spacetime block coded signals can always be performed in polynomial time with respect to the sequence length for static Rayleigh, correlated (in general) channels. Moreover, using recent results on efficient maximization of rankdeficient quadratic forms over finite alphabets, we develop an algorithm that performs ML noncoherent sequence detection with polynomial complexity. The order of the polynomial complexity of the proposed receiver equals two times the rank of the covariance matrix of the vectorized channel matrix. Therefore, the lower the Rayleigh channel covariance rank the lower the receiver complexity. Instead, for Ricean channel distribution, we prove that polynomial complexity is attained through the proposed receiver as long as the mean channel vector is in the range of the covariance matrix of the vectorized channel matrix. Hence, fullrank channel correlation is desired to guarantee polynomial ML noncoherent detection complexity for the case of static Ricean fading. Our results are presented for the general case of blockfading Rayleigh or Ricean channels where we provide conditions under which ML noncoherent sequence detection can be performed in polynomial time through our algorithm.