Results 1  10
of
29
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 ..."
Abstract

Cited by 172 (20 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 33 (6 self)
 Add to MetaCart
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.
On the distribution of SINR for the MMSE MIMO receiver and performance analysis
 IEEE Trans. Inform. Theory
, 2006
"... Abstract — This paper studies the statistical distribution of the signaltointerferenceplusnoise ratio (SINR) for the minimum mean square error (MMSE) receiver in multipleinputmultipleoutput (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flatf ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
Abstract — This paper studies the statistical distribution of the signaltointerferenceplusnoise ratio (SINR) for the minimum mean square error (MMSE) receiver in multipleinputmultipleoutput (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flatfading with unequal powers. The SINR can be decomposed into two independent random variables: SINR = SINR ZF + T, where SINR ZF corresponds to the SINR for a zeroforcing (ZF) receiver and has an exact Gamma distribution. This paper focuses on characterizing the statistical properties of T using the results from random matrix theory. First three asymptotic moments of T are derived for uncorrelated channels and channels with equicorrelations. For general correlated channels, some limiting upperbounds for the first three moments are also provided. For uncorrelated channels and correlated channels satisfying certain conditions, it is proved that T converges to a Normal random variable. A Gamma distribution and a generalized Gamma distribution are proposed as approximations to the finite sample distribution of T. Simulations suggest that these approximate distributions can be used to accurately estimate the probability of errors even for very small dimensions (e.g., 2 transmit antennas). Index Terms — Multipleinputmultipleoutput system, minimum mean square error receiver, signaltointerferenceplusnoise ratio, channel correlation, random matrix, asymptotic distributions, Gamma approximation, error probability. I.
Multiuser Detection for Overloaded CDMA Systems
 IEEE TRANS. INFORM. THEORY
, 2002
"... Multiuser detection for overloaded CDMA systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of subopt ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
Multiuser detection for overloaded CDMA systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and/or interfering signal subspaces are of reduced rank and/or have a nontrivial intersection. In the process, two new suboptimum detectors are proposed that are especially well suited to overloaded systems, namely the group pseudodecorrelator and the group MMSE detector, and the former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form (in the lownoise regime) of the group MMSE detector. Pseudodecorrelation is also used as a feedforward filter in a new decision feedback scheme. For the particular case of realvalued modulation, it is shown that the recent proposals of the socalled "improved" linear (aka "linearconjugate" or "widely linear") detectors were more simply derived earlier using the idea of minimal sufficiency which we also apply to the new detectors of this paper.
Design of block transceivers with decision feedback detection
 in IEEE Trans. Signal Process
, 2006
"... Abstract—This paper presents a method for jointly designing the transmitter–receiver pair in a blockbyblock communication system that employs (intrablock) decision feedback detection. We provide closedform expressions for transmitter–receiver pairs that simultaneously minimize the arithmetic mean ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
Abstract—This paper presents a method for jointly designing the transmitter–receiver pair in a blockbyblock communication system that employs (intrablock) decision feedback detection. We provide closedform expressions for transmitter–receiver pairs that simultaneously minimize the arithmetic mean squared error (MSE) at the decision point (assuming perfect feedback), the geometric MSE, and the bit error rate of a uniformly bitloaded system at moderatetohigh signaltonoise ratios. Separate expressions apply for the “zeroforcing ” and “minimum MSE” (MMSE) decision feedback structures. In the MMSE case, the proposed design also maximizes the Gaussian mutual information and suggests that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation. Index Terms—Bit error rate, block precoding, channel capacity, decision feedback detection, minimum meansquare error, mutual information, zeroforcing. I.
Multiuser Detection and Statistical Physics
, 2002
"... We present a framework for analyzing multiuser detectors in the context of statistical physics. A multiuser detector is shown to be equivalent to a conditional mean estimator which finds the mean value of the stochastic output of a socalled Bayes retrochannel. The Bayes retrochannel is equivalent t ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
We present a framework for analyzing multiuser detectors in the context of statistical physics. A multiuser detector is shown to be equivalent to a conditional mean estimator which finds the mean value of the stochastic output of a socalled Bayes retrochannel. The Bayes retrochannel is equivalent to a spin glass in the sense that the distribution of its stochastic output conditioned on the received signal is exactly the distribution of the spin glass at thermal equilibrium. In the largesystem limit, the biterrorrate of the multiuser detector is simply determined by the magnetization of the spin glass, which can be obtained using powerful tools developed in statistical mechanics. In particular, we derive the largesystem uncoded biterrorrate of the matched filter, the MMSE detector, the decorrelator and the optimal detectors, as well as the spectral efficiency of the Gaussian CDMA channel. It is found that all users with different received energies share the same multiuser efficiency, which uniquely determines the performance of a multiuser detector. A universal interpretation of multiuser detection relates the multiuser efficiency to the meansquare error of the conditional mean estimator output in the largesystem limit.
Spectral Efficiency of CDMA Downlink Cellular Networks with Matched Filter
, 2006
"... In this contribution, the performance of a downlink code division multiple access (CDMA) system with orthogonal spreading and multicell interference is analyzed. A useful framework is provided in order to determine the optimal base station coverage for wireless frequency selective channels with dens ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
In this contribution, the performance of a downlink code division multiple access (CDMA) system with orthogonal spreading and multicell interference is analyzed. A useful framework is provided in order to determine the optimal base station coverage for wireless frequency selective channels with dense networks where each user is equipped with a matched filter. Using asymptotic arguments, explicit expressions of the spectral efficiency are obtained and provide a simple expression of the network spectral efficiency based only on a few meaningful parameters. Contrarily to a common misconception which asserts that to increase spectral efficiency in a CDMA network, one has to increase the number of cells, we show that, depending on the path loss and the fading channel statistics, the code orthogonal gain (due to the synchronization of all the users at the base station) can compensate and even compete in some cases with the drawbacks due to intercell interference. The results are especially realistic and useful for the design of dense networks.
Asymptotic spectral efficiency of multiuser multisignature CDMA in frequencyselective channels
 IEEE Trans. Inform. Theory
"... Abstract: This paper presents an asymptotic analysis of multisignature CodeDivision Multiple Access (CDMA) in the presence of frequencyselective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and Linear Minimum Mean Squared Error (LMMSE) ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract: This paper presents an asymptotic analysis of multisignature CodeDivision Multiple Access (CDMA) in the presence of frequencyselective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and Linear Minimum Mean Squared Error (LMMSE) multiuser receivers. Both i.i.d. signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the LMMSE receiver is determined from the asymptotic output SignaltoInterferencePlus Noise Ratio (SINR). Our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an ‘incrementalsignature ’ analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal codingspreading tradeoff, which maximizes the LMMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finitesize systems of interest. The resulting expressions are used to highlight and infer properties of the multisignature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate
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 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
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.
A family of likelihood ascent search multiuser detectors: an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency
"... Abstract – Tse and Verdú proved that the global maximum likelihood (GML) detector achieves unit asymptotic multiuser efficiency (AME) in the limit of large random spreading CDMA. In this paper, we show that the widesense sequential likelihood ascent search (WSLAS) detectors achieve unit AME with ch ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Abstract – Tse and Verdú proved that the global maximum likelihood (GML) detector achieves unit asymptotic multiuser efficiency (AME) in the limit of large random spreading CDMA. In this paper, we show that the widesense sequential likelihood ascent search (WSLAS) detectors achieve unit AME with channel load < − 1/(4ln2) bits/s/Hz. In simulations for random multicode equalpower systems, the WSLAS with a linear perbit complexity approaches the GML BER in all SNR with channel load as high as 1.05 bit/s/Hz. Index Terms – Multiaccess communication, nonlinear detection, maximum likelihood detection. I.