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28
MIMO Channel Modelling and the Principle of Maximum Entropy
, 2004
"... In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we giv ..."
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Cited by 62 (26 self)
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In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are both useful in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks .
Design of reducedrank MMSE multiuser detectors using random matrix methods
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—Reducedrank minimum meansquared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in longsequence codedivision multipleaccess (CDMA) systems. In this paper, we consider the design of reducedrank M ..."
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Cited by 26 (1 self)
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Abstract—Reducedrank minimum meansquared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in longsequence codedivision multipleaccess (CDMA) systems. In this paper, we consider the design of reducedrank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as directsequence CDMA (DSCDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reducedrank receiver. Index Terms—Codedivision multiple access (CDMA), fading channels, minimum meansquared error (MMSE) receivers, multiantenna systems, multicarrier CDMA, multiuser detection, random matrix theory. I.
MMSE Analysis of Certain Large Isometric Random Precoded Systems
 IEEE Transactions on Information Theory, Volume: 49 Issue: 5, Page(s): 1293 1311
, 2001
"... Linear Precoding consists in multiplying by a N K matrix a Kdimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. In this paper, we analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using ..."
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Cited by 24 (11 self)
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Linear Precoding consists in multiplying by a N K matrix a Kdimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. In this paper, we analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the socalled Free Probability Theory, it can be shown that the Signal to Interference plus Noise Ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N 1. These asymptotic results are used to optimally balance the redundancy introduced between Linear Precoding and classical Convolutional Coding, while preserving a simple MMSE equalization scheme at the receiver.
A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals
, 2008
"... This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio ..."
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Cited by 18 (8 self)
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This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiantenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.
Spectral efficiency of multicarrier CDMA
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—We analyze the spectral efficiency (sumrate per subcarrier) of randomly spread synchronous multicarrier codedivision multiple access (MCCDMA) subject to frequencyselective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio. Both upli ..."
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Cited by 16 (1 self)
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Abstract—We analyze the spectral efficiency (sumrate per subcarrier) of randomly spread synchronous multicarrier codedivision multiple access (MCCDMA) subject to frequencyselective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio. Both uplink and downlink are considered, either conditioned on the subcarrier fading coefficients (for nonergodic channels) or unconditioned thereon (for ergodic channels). The following receivers are analyzed: a) jointly optimum receiver, b) linear minimum meansquare error (MMSE) receiver, c) decorrelator, and d) singleuser matched filter. Index Terms—Channel capacity, multicarrier codedivision multiple access (MCCDMA), random matrix theory, multiuser
Applications of Large Random Matrices in Communications Engineering
"... This work gives an overview of analytic tools to the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools from probability theory, operator algebra, and statistical phy ..."
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Cited by 7 (3 self)
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This work gives an overview of analytic tools to the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools from probability theory, operator algebra, and statistical physics are reviewed. The survey of analytical tools is complemented by examples of applications in communications engineering.
On the System Level Prediction of Joint Time Frequency Spreading Systems with Carrier Phase Noise (†)
, 2010
"... Abstract Phase noise is a topic of theoretical and practical interest in electronic circuits. Although progress has been made in the characterization of its description, there are still considerable gaps in its effects especially on multicarrier spreading systems. In this paper, we investigate t ..."
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Cited by 4 (0 self)
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Abstract Phase noise is a topic of theoretical and practical interest in electronic circuits. Although progress has been made in the characterization of its description, there are still considerable gaps in its effects especially on multicarrier spreading systems. In this paper, we investigate the impact of a local oscillator phase noise on the multicarrier 2 dimensional (2D) spreading systems based on a combination of orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) and known as OFDMCDMA. The contribution of this paper is multifold. First, we use some properties of random matrix and free probability theory to give a simplified expression of signal to interference and noise ratio (SINR) obtained after equalization and despreading. This expression is independent of the actual value of the spreading codes and depends mainly on the complex amplitudes of estimated channel coefficients. Secondly, we use this expression to derive new weighting functions which are very interesting for the radio frequency (RF) engineers when they design the frequency synthesizer. Therefore, based on these asymptotic results, we adapt a new method to predict the bit error rate (BER) at the output of the channel decoder by using an effective SINR value. We show by simulations the validity of our models and that at a given BER, the required signal to noise ratio (SNR) may easily increase due to the carrier phase noise. Index Terms Multicarrier spreading systems, large system analysis, phase noise, SINR, EESM. I.
Unified large system analysis of MMSE and adaptive least squares receivers for a class of random matrix channels
 IEEE TRANS. ON INFO. THEORY
, 2005
"... We present a unified large system analysis of linear receivers for a class of random matrix channels. The technique unifies the analysis of both the minimummeansquarederror (MMSE) receiver and the adaptive leastsquares (ALS) receiver, and also uses a common approach for both random i.i.d. and ra ..."
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Cited by 3 (2 self)
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We present a unified large system analysis of linear receivers for a class of random matrix channels. The technique unifies the analysis of both the minimummeansquarederror (MMSE) receiver and the adaptive leastsquares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. We derive expressions for the asymptotic signaltointerferenceplusnoise (SINR) of the MMSE receiver, and both the transient and steadystate SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steadystate SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.
Random Beamforming over Correlated Fading Channels
, 2011
"... We study a multipleinput multipleoutput (MIMO) multiple access channel (MAC) from several multiantenna transmitters to a multiantenna receiver. The fading channels between the transmitters and the receiver are modeled by random matrices, composed of independent column vectors with zero mean and ..."
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Cited by 2 (2 self)
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We study a multipleinput multipleoutput (MIMO) multiple access channel (MAC) from several multiantenna transmitters to a multiantenna receiver. The fading channels between the transmitters and the receiver are modeled by random matrices, composed of independent column vectors with zero mean and different covariance matrices. Each transmitter is assumed to send multiple data streams with a random precoding matrix extracted from a Haardistributed matrix. For this general channel model, we derive deterministic approximations of the normalized mutual information, the normalized sumrate with minimummeansquareerror (MMSE) detection and the signaltointerferenceplusnoiseratio (SINR) of the MMSE decoder, which become arbitrarily tight as all system parameters grow infinitely large at the same speed. In addition, we derive the asymptotically optimal power allocation under individual or sumpower constraints. Our results allow us to tackle the problem of optimal stream control in interference channels which would be intractable in any finite setting. Numerical results corroborate our analysis and verify its accuracy for realistic system dimensions. Moreover, the techniques applied in this paper constitute a novel contribution to the field of large random matrix theory and could be used to study even more involved channel models.
Sensitivity of MultiCarrier Two Dimensional Spreading Schemes to Synchronization Errors ⊥
, 2008
"... Abstract — This paper presents the impact of synchronization errors on the performance of a downlink multi carrier two dimensional spreading OFDMCDMA system. This impact is measured by the degradation of the Signal to Interference and Noise Ratio (SINR) obtained after despreading and equalization. ..."
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Cited by 1 (1 self)
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Abstract — This paper presents the impact of synchronization errors on the performance of a downlink multi carrier two dimensional spreading OFDMCDMA system. This impact is measured by the degradation of the Signal to Interference and Noise Ratio (SINR) obtained after despreading and equalization. The contribution of this paper is twofold. First, we use some properties of random matrix and free probability theories to derive a new expression of the SINR. This expression is then independent of the actual value of the spreading codes while still accounting for the orthogonality between codes. This model is validated by means of MonteCarlo simulations. Secondly, the model is exploited to derive the SINR degradation of OFDMCDMA systems due to synchronization errors which include a timing error, a carrier frequency offset and a sampling frequency offset. It is also exploited to compare the sensitivities of MCCDMA and MCDSCDMA systems to these errors in a frequency selective channel. This work is carried out for zeroforcing and minimum mean square error equalizers.