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32
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
, 2006
"... Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our pr ..."
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Cited by 172 (20 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the sth stage it forms the ‘matched filter ’ Φ T rs−1, identifies all coordinates with amplitudes exceeding a speciallychosen threshold, solves a leastsquares problem using the selected coordinates, and subtracts the leastsquares fit, producing a new residual. After a fixed number of stages (e.g. 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g. 10), while OMP can take many (e.g. n). StOMP runs much faster than competing proposals for sparse solutions, such as ℓ1 minimization and OMP, and so is attractive for solving largescale problems. We use phase diagrams to compare algorithm performance. The problem of recovering a ksparse vector x0 from (y, Φ) where Φ is random n × N and y = Φx0 is represented by a point (n/N, k/n)
Randomly spread CDMA: Asymptotics via statistical physics
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the ..."
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Cited by 33 (6 self)
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Abstract—This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before singleuser decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum meansquare error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically nonGaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a “hidden ” Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent singleuser Gaussian channel, whose signaltonoise ratio (SNR) suffers a degradation due to the multipleaccess interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixedpoint equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multipleinput multipleoutput (MIMO) channels such as in multiantenna systems. Index Terms—Channel capacity, codedivision multiple access (CDMA), free energy, multipleinput multipleoutput (MIMO) channel, multiuser detection, multiuser efficiency, replica method, statistical mechanics. I.
Superposition coding for sideinformation channels
 IEEE Trans. Inform. Theory
, 2006
"... We present simple, practical codes designed for the binary and Gaussian dirtypaper channels. We show that the dirty paper decoding problem can be transformed into an equivalent multipleaccess decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested ..."
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Cited by 20 (2 self)
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We present simple, practical codes designed for the binary and Gaussian dirtypaper channels. We show that the dirty paper decoding problem can be transformed into an equivalent multipleaccess decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximumlikelihood decoding. We also present practical implementations of the constructions, and simulation results for both dirtypaper channels. Our results for the Gaussian dirtypaper channel are on par with the best known results for nestedlattices. We discuss the binary dirtytape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel’fandPinsker channels. Index Terms dirty paper, dirty tape, multipleaccess channel, side information, superposition coding.
Scaling up MIMO: Opportunities and challenges with very large arrays
 IEEE Signal Process. Mag
, 2013
"... N.B.: When citing this work, cite the original article. ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to ..."
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Cited by 20 (9 self)
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N.B.: When citing this work, cite the original article. ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Joint Iterative TimeVariant Channel Estimation and MultiUser Detection for MIMOOFDM Systems
"... Abstract—This paper presents an iterative receiver for ..."
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Cited by 7 (6 self)
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Abstract—This paper presents an iterative receiver for
ANALYSIS OF ITERATIVE SUCCESSIVE INTERFERENCE CANCELLATION IN SCCDMA SYSTEMS
"... This paper analyzes the convergence behavior and performance of iterative successive interference cancellation (SIC) for a CDMA system with random spreading using the socalled multiuser efficiency (MUE). The goal of such an analysis is the optimization of the detection scheme. Moreover, an optimiz ..."
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Cited by 5 (5 self)
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This paper analyzes the convergence behavior and performance of iterative successive interference cancellation (SIC) for a CDMA system with random spreading using the socalled multiuser efficiency (MUE). The goal of such an analysis is the optimization of the detection scheme. Moreover, an optimized power allocation of the users at the transmitter is an important means for enhancing the convergence behavior of the detector and is based on the possibility of prediction. While this analysis has only been applied to parallel interference cancellation (PIC) we will generalize it in this paper also for SIC. It will be shown that the achievable system load can be significantly increased. 1.
Nonlinear MMSE Multiuser Detection Based on Multivariate Gaussian Approximation
 IEEE Trans. Commun
, 2006
"... In this paper, a class of nonlinear MMSE multiuser detectors are derived based on a multivariate Gaussian approximation of the multiple access interference. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternat ..."
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Cited by 5 (3 self)
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In this paper, a class of nonlinear MMSE multiuser detectors are derived based on a multivariate Gaussian approximation of the multiple access interference. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference cancellation scheme. Corresponding multiuser softinput, softoutput detectors delivering extrinsic loglikelihood ratios are derived for application in iterative multiuser decoders. Finally, a large system performance analysis is conducted for the simplified PDA, showing that the bit error rate performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large system prediction. Numerical results demonstrate that for large systems, the bit error rate is accurately predicted by the analysis and found to be close to optimal performance.
Asymptotically Optimal Nonlinear MMSE Multiuser Detection Based on Multivariate Gaussian Approximation
"... Abstract—In this paper, a class of nonlinear minimum meansquared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multipleaccess interference for large systems. This approach leads to expressions identical to those describing the probabilistic data associa ..."
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Cited by 5 (1 self)
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Abstract—In this paper, a class of nonlinear minimum meansquared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multipleaccess interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interferencecancellation scheme. Corresponding multiuser softinput, softoutput detectors delivering extrinsic loglikelihood ratios are derived for application in iterative multiuser decoders. Finally, a largesystem performance analysis is conducted for the simplified PDA, showing that the biterror rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative largesystem prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance. Index Terms—Codedivision multiple access (CDMA), Gaussian approximation (GA), largesystem analysis, multiuser detection, optimum detection. I.
Reduced Complexity Joint Iterative Equalization and Multiuser Detection in Dispersive DSCDMA Channels
, 2005
"... Communications in dispersive directsequence codedivision multipleaccess channels suffer from intersymbol and multipleaccess interference, which can significantly impair performance. Joint maximum a posteriori probability equalization and multiuser detection with error control decoding can be use ..."
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Cited by 2 (0 self)
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Communications in dispersive directsequence codedivision multipleaccess channels suffer from intersymbol and multipleaccess interference, which can significantly impair performance. Joint maximum a posteriori probability equalization and multiuser detection with error control decoding can be used to mitigate this interference and to achieve the optimal bit error rate. Unfortunately, such optimal detection typically requires prohibitive computational complexity. This problem is addressed in this paper through the development of a reduced state trellis search detection algorithm, based on decision feedback from channel decoders. The performance of this algorithm is analyzed in the largesystem limit. This analysis and simulations show that this reduced complexity algorithm can exhibit nearoptimal performance under moderate signaltonoise ratio and attains larger system load capacity than parallel interference cancellation. I.
Belief Propagation for Coded Multiuser Detection
 IEEE Int. Symp. Inform. Theory
, 2006
"... Abstract — In this paper a simplified parallel belief propagation (BP) algorithm is suggested as a suboptimal softinput softoutput multiuser detector in an iterative multiuser decoding scheme. The iterative decoding scheme itself is based on applying an outer BP algorithm for message passing betwee ..."
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Cited by 2 (1 self)
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Abstract — In this paper a simplified parallel belief propagation (BP) algorithm is suggested as a suboptimal softinput softoutput multiuser detector in an iterative multiuser decoding scheme. The iterative decoding scheme itself is based on applying an outer BP algorithm for message passing between the BP multiuser detector and the singleuser decoders. The performance of the iterative decoding process is investigated based on parallel scheduling of the outer BP algorithm. In addition, we analyze the large system BER performance of the corresponding multiuser decoding algorithms. By making Gaussian assumptions on the output of the singleuser decoders and the BP multiuser detector, we derive expressions which describe approximately the BER performance of the algorithms. Finally, numerical examples are presented, demonstrating the accuracy of this approximation. I.