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Asymptotic Spectral Distribution of Crosscorrelation Matrix in Asynchronous CDMA

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Chien-Hwa Hwang

Information Theory · Submitted 13 Sep 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The existence of a nonrandom ASD is proved by moment convergence theorem, where the focus is on the derivation of asymptotic eigenvalue moments (AEM) of the crosscorrelation matrix.

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arXiv IDcs/0609076 (version 3)
Pith IDD4E7KCGS, Pith's permanent record of this paper and its review
CitationChien-Hwa Hwang. "Asymptotic Spectral Distribution of Crosscorrelation Matrix in Asynchronous CDMA." arXiv:cs/0609076 (2006). https://pith.science/paper/D4E7KCGS
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.04 · states quantitative result 0.15 · compares with prior results 0.06 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; .

Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is investigated for a random spreading short/long-code asynchronous direct sequence-code division multiple access (DS-CDMA) system. The discrete-time decision statistics are obtained as the output samples of a bank of symbol matched filters of all users. The crosscorrelation matrix is studied when the number of symbols transmitted by each user tends to infinity. Two levels of asynchronism are considered. One is symbol-asynchronous but chip-synchronous, and the other is chip-asynchronous. The existence of a nonrandom ASD is proved by moment convergence theorem, where the focus is on the derivation of asymptotic eigenvalue moments (AEM) of the crosscorrelation matrix. A combinatorics approach based on noncrossing partition of set partition theory is adopted for AEM computation. The spectral efficiency and the minimum mean-square-error (MMSE) achievable by a linear receiver of asynchronous CDMA are plotted by AEM using a numerical method.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is investigated for a random spreading short/long-code asynchronous direct sequence-code division multiple access (DS-CDMA) system. contribution 0.98 0.86 0.10 asserted 0.97
s1 The discrete-time decision statistics are obtained as the output samples of a bank of symbol matched filters of all users. method 0.97 0.72 0.03 asserted 1.00
s2 The crosscorrelation matrix is studied when the number of symbols transmitted by each user tends to infinity. contribution 0.55 0.84 0.06 asserted 0.97
s3 Two levels of asynchronism are considered. method 0.57 0.74 0.02 asserted 0.97
s4 One is symbol-asynchronous but chip-synchronous, and the other is chip-asynchronous. method 0.61 0.63 0.03 asserted 0.99
s5 The existence of a nonrandom ASD is proved by moment convergence theorem, where the focus is on the derivation of asymptotic eigenvalue moments (AEM) of the crosscorrelation matrix. result 0.53 0.92 0.46 asserted 1.00
s6 A combinatorics approach based on noncrossing partition of set partition theory is adopted for AEM computation. method 0.99 0.91 0.06 asserted 1.00
s7 The spectral efficiency and the minimum mean-square-error (MMSE) achievable by a linear receiver of asynchronous CDMA are plotted by AEM using a numerical method. result 0.74 0.91 0.19 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is investigated for a random spreading short/long-code asynchronous direct sequence-code division multiple access (DS-CDMA) system. The discrete-time decision statistics are obtained as the output samples of a bank of symbol matched filters of all users. The crosscorrelation matrix is studied when the number of symbols transmitted by each user tends to infinity. Two levels of asynchronism are considered. One is symbol-asynchronous but chip-synchronous, and the other is chip-asynchronous. The existence of a nonrandom ASD is proved by moment convergence theorem, where the focus is on the derivation of asymptotic eigenvalue moments (AEM) of the crosscorrelation matrix. A combinatorics approach based on noncrossing partition of set partition theory is adopted for AEM computation. The spectral efficiency and the minimum mean-square-error (MMSE) achievable by a linear receiver of asynchronous CDMA are plotted by AEM using a numerical method.

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