A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors

Tanaka, Toshiyuki

doi:10.1109/tit.2002.804053

Cited by 521 publications

(731 citation statements)

References 46 publications

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“…From the practical point of view, this can be explained by the sparsity of the QPSK constellation, which helps to identify symbols perfectly once the SNR is sufficiently high. Similar behavior was also observed in [6] and [12]. Note also here that for the SD scheme with α SR , α RD > 1, Gaussian signaling is no longer optimal and is outperformed by a discrete constellation, as was previously observed in [14].…”

Section: Simulation Resultssupporting

confidence: 85%

“…Our analysis is based on the RS ansatz of the replica method [12] from statistical physics and provides a framework for efficient performance analysis of AF MIMO relay systems under general conditions. The analysis leads to large-system approximations for the achievable ergodic rate and uncoded average BER, which become exact when the numbers of antennas at all terminals grow large without bound at constant ratios.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic properties of dual-hop AF relay MIMO communication systems

Girnyk

Vehkaperä

Rasmussen

2014

2014 IEEE International Symposium on Information Theory

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Abstract-The present paper studies the asymptotic performance of dual-hop amplify-and-forward multiple-input multipleoutput relay communication systems. In the corresponding setup, a relay amplifies the signal received from a source, retransmitting it towards a destination, while the direct source-destination link is absent. Ergodic achievable rates under separate decoding, along with the average bit error rate under various detection schemes are derived in the regime where the number of antennas at each terminal grows without bound. To overcome the mathematical difficulty of averaging over both channel realizations and input signals we apply large-system analysis based on the replica method from statistical physics. The validity of the large-system analysis is further verified through Monte Carlo simulations, providing particularly good accuracy at low SNR. I. INTRODUCTIONMultiple-input multiple-output (MIMO) relaying has been proved a promising technology that allows for reliable communication at increased coverage and data rates [1]. Understanding the fundamental limits of the relay channel has therefore become one of the recent research challenges. The relay MIMO channel (depicted in Fig. 1) -consisting of a source (S), a relay (R) and a destination (D) -is a fundamental building block for complex cooperative networks [2], [3]. It has therefore been regarded as an important milestone in the research efforts within the field.The relays in a cooperative network may realize different cooperative strategies. For instance, a regenerative strategy (e.g., decode-and-forward [4]) involves decoding of the noisy signal from the source, re-encoding the underlying message and retransmitting it upstream. A non-regenerative strategy (e.g., amplify-and-forward (AF) [2]) involves simple amplification of the received noisy signal and subsequent retransmission towards the destination. Non-regenerative relaying, being simple in implementation and independent of the modulation schemes at the source terminal, is of particular interest.In fading environment, the achievable data rate of such cooperative communication systems is measured by the endto-end ergodic mutual information (MI). Hence, performance evaluation requires averaging over the channel randomness. This, in general, prevents one from having closed-form expressions and motivates the need for alternative approaches to

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Section: Simulation Resultssupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of dual-hop AF relay MIMO communication systems

Girnyk

Vehkaperä

Rasmussen

2014

2014 IEEE International Symposium on Information Theory

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“…measurement matrices. When the compression rate is larger than the so-called BP threshold [7], the BP-based algorithm was numerically shown to achieve the Bayes-optimal performance in the large system limit, which was originally conjectured by Tanaka [8] via the replica method-a nonrigorous tool in statistical physics, and proved in [9], [10] for i.i.d. Gaussian measurements.…”

Section: Introductionmentioning

confidence: 93%

Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements

Takeuchi

2017

2017 IEEE International Symposium on Information Theory (ISIT)

104

202

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Abstract-Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm in the large system limit, where both input and output dimensions tend to infinity while the compression rate is kept constant. The main result is the justification of state evolution (SE) equations conjectured by Ma and Ping. This result implies that the EPbased algorithm achieves the Bayes-optimal performance derived by Takeda et al. in 2006 via a non-rigorous tool in statistical physics, when the compression rate is larger than a threshold. The proof is based on an extension of a conventional conditioning technique for the standard Gaussian matrix to the case of the Haar matrix.

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“…In recent years, spin glass theory has been applied to analysis of wireless communication systems, such as code-division multiple-access (CDMA) and multiple-input multiple-output (MIMO) systems, by mapping these systems onto disordered spin systems [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A mean field theory of coded CDMA systems

Yano¹,

Tanaka²,

Saad³

2008

J. Phys. A: Math. Theor.

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Abstract. We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density paritycheck (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

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A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors

Cited by 521 publications

References 46 publications

Asymptotic properties of dual-hop AF relay MIMO communication systems

Asymptotic properties of dual-hop AF relay MIMO communication systems

Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements

A mean field theory of coded CDMA systems

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