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13
Asymptotic normality of linear multiuser receiver outputs
 IEEE TRANS. INFORM. THEORY
, 2002
"... This paper proves largesystem asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the singleuser matched filter, the decorrelator, the minimum mean square error (MMSE) ..."
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Cited by 38 (7 self)
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This paper proves largesystem asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the singleuser matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signaltointerference ratio (SIR) for large linear systems.
Large System Analysis of Linear Multistage Parallel Interference Cancellation
 IEEE Transactions on Communications
, 2002
"... In this paper, we derive an expression for the signal to interferenceplusnoise ratio of a linear multistage parallel interference cancellation receiver. We focus on a linear multistage receiver which converges to the linear minimum meansquared error receiver as the number of stages increases. The ..."
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Cited by 8 (3 self)
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In this paper, we derive an expression for the signal to interferenceplusnoise ratio of a linear multistage parallel interference cancellation receiver. We focus on a linear multistage receiver which converges to the linear minimum meansquared error receiver as the number of stages increases. The signal to interference plusnoise ratio is given in terms of the system loading, the partial cancellation factor, the number of stages, and the signaltonoise ratio. Our expression also allows a simple approximation for the bit error rate at each stage. Finally, we perform a numerical optimization to maximize the signal to interferenceplusnoise ratio expression with respect to the partial cancellation factor of the resulting linear multistage receiver.
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.
Large system transient analysis of adaptive least squares filtering
 IEEE Trans. on Information Theory
, 2005
"... Abstract—The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multipleaccess interference. Both fullrank LS filters and reducedrank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with know ..."
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Cited by 4 (1 self)
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Abstract—The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multipleaccess interference. Both fullrank LS filters and reducedrank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signaltointerferenceplusnoise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users, the degrees of freedom, and the number of training symbols or observations all tend to infinity with fixed ratios and. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent illconditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically aQP). Given a fixed, short training length, the relative performance of full and reducedrank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full and reducedrank filters are similar. However, fullrank performance is generally much more sensitive to the choice of diagonal loading factor than reducedrank performance. Index Terms—Adaptive filter, large system analysis, least squares (LS), reducedrank filters. I.
Multiuser detection based on Gaussian approximation
 in Proc. Workshop on Telecomm. Internet and Signal Proc
, 2004
"... Abstract—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 identical expressions as describing the probabilistic data association (PDA) detector, thus providing an altern ..."
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Cited by 1 (0 self)
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Abstract—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 identical expressions as 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. 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. Keywords — Codedivision multiple access, multiuser detection, optimum detection, Gaussian approximation, large system analysis. I.
Optimal Multistage Linear Multiuser Receivers
"... Abstract—In this paper, we analyze a linear multiuser receiver for codedivision multipleaccess systems that is based on a matrix polynomial expansion. We focus on the receiver where the polynomial coefficients are chosen to minimize the mean squared error at the output and observe that the resulta ..."
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Cited by 1 (0 self)
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Abstract—In this paper, we analyze a linear multiuser receiver for codedivision multipleaccess systems that is based on a matrix polynomial expansion. We focus on the receiver where the polynomial coefficients are chosen to minimize the mean squared error at the output and observe that the resultant coefficients are also signaltointerference ratio maximizing. We present a simple derivation for the (known) large system coefficients and signaltointerference ratio of this optimal multistage receiver and make a significant step toward a direct derivation of Honig and Xiao’s recursive expression for this large system signaltointerference ratio. Finally, we extend these results to take into account arbitrary power distributions. Index Terms—Large system analysis, multistage receivers, multiuser detection, random spreading, reducedrank filtering. I.
Coded Random CDMA with Partitioned Spreading
 44th Allerton Conference on Communication, Computing and Control
, 2006
"... is considered, where a number of concurrent users, distinguished by random spreading waveforms, access the common additive white Gaussian noise (AWGN) channel. All users employ a regular lowdensity paritycheck (LDPC) error control code (ECC). Additionally, a method, called Partitioned Spreading (P ..."
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Cited by 1 (1 self)
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is considered, where a number of concurrent users, distinguished by random spreading waveforms, access the common additive white Gaussian noise (AWGN) channel. All users employ a regular lowdensity paritycheck (LDPC) error control code (ECC). Additionally, a method, called Partitioned Spreading (PS) is used. Each user’s spreading waveform is divided into M partitions which are interleaved and spread in time. Asymptotic performance of the proposed system is studied for two different decoding schedules. In the first schedule, called twostage schedule, iterative multiple access (MA) detection and LDPC decoding are executed separately. The second schedule, named full decoding allows to exchange information between MA and LDPC sides. Supportable system loads are derived as functions of the users ’ signaltonoise ratio (SNR). It is shown that significantly higher system loads can be achieved compared to the traditional LDPC coded random CDMA. I.
Distributed Linear Multiuser Detection in Cellular
 in Proc. IEEE Global Telecommunications Conference
, 2004
"... We design a robust and computationally efficient iterative implementation of the Linear Minimum Mean Square Error (LMMSE) receiver for Wyner's model of a linear cellular array. An important property of the the iterative LMMSE receiver is that each base station requires only local information to esti ..."
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We design a robust and computationally efficient iterative implementation of the Linear Minimum Mean Square Error (LMMSE) receiver for Wyner's model of a linear cellular array. An important property of the the iterative LMMSE receiver is that each base station requires only local information to estimate its user's signal. Analysis of the convergence of the iterative algorithm reveals a convergence rate that is insensitive to the array size, an important property for practical implementation. Conditions of convergence and the optimal step size to ensure fastest convergence are also determined.
Optimized Power Distributions for Partitioned Signaling on Random Linear Matrix Channels
"... Iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo CDMA, has traditionally been studied as the concatenation of conventional error control codes with the linear (matrix) channel. However, in several situation, such as CDMA, the channel itself contai ..."
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Iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo CDMA, has traditionally been studied as the concatenation of conventional error control codes with the linear (matrix) channel. However, in several situation, such as CDMA, the channel itself contains inherent redundancy, such as a repetition code contained in the directspread signature sequences of CDMA. For such systems, iterative demodulation of the linear channel exploiting the inherent code structure, followed by feedforward conventional error control coding provides an efficient and powerful alternative, and outperform the more complex turbo CDMA methods for equal power modes (users). However, such equalpower systems are spectrally limited. In this paper optimized power distributions are derived and studied which allow arbitrary spectral efficiencies to be achieved with simple twostage receivers. I.