Randomly spread CDMA: asymptotics via statistical physics

By Dongning Guo, Sergio Verdú. IEEE Transactions on Information Theory, 2005

398 citations recorded by the source corpus.

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system 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 single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum mean-square 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 non-Gaussian 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 single-user Gaussian channel, whose signal-to-noise ratio (SNR) suffers a degradation due to the multiple-access 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 fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multiple-input multiple-output (MIMO) channels such as in multiantenna systems.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/25282ed3b1ff891fb6994379b35b16ee5b1c47c1

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Citations in the corpus

Generalized approximate message passing for estimation with random linear mixing (2010, result): “The fixed point of the updates (28) are precisely the equations given by Guo and Verdú in their replica analysis of MMSE estimation with AWGN outputs and non-Gaussian priors [18], which generalized several earlier analyses in [19]–[21].”
Optimal errors and phase transitions in high-dimensional generalized linear models (2017, methodology): “Random instances of GLMs describe both the setting of code-division multiple access—a multiuser access method used in communication technologies (34, 35)—and an error correction scheme called sparse superposition codes, which have been shown to achieve the Shannon capacity for any type of noisy…”
Orthogonal AMP (2016, methodology): “(The latter can be obtained using the replica method [8]–[11].”
Statistical Mechanics of Optimal Convex Inference in High Dimensions (2016, background): “the number of unknowns, for example, in neural network memory capacity [12], perceptron learning theory [13,14], communication theory [15], compressed sensing [16–19],”
Polar Codes for Channel and Source Coding (2009, background): “The analysis is extended in [99] to include the case of unequal powers and other constellations.”
A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm (2008, background): “showed that the marginal posterior finding is exact if the matrix Φ is a sparse matrix and N → ∞ [8],[9],[10].”
A perspective on massive random-access (2017, background): “Optimal MUD results in each user seeing an effective single-user BI-AWGN channel with SNR found from Tanaka’s formula [29], [30].”
Statistical physics-based reconstruction in compressed sensing (2011, methodology): “The replica method is a standard method in statistical physics [7], which has been applied successfully to several problems of information theory [17,28,36,37], including compressed sensing [12–14].”
Mutual information and minimum mean-square error in Gaussian channels (2004, background): “1) Some Applications of Theorems 1 and 2:The newly discovered relationship between the mutual information and MMSE finds one of its first uses in relating CDMA channel spectral efficiencies (mutual information per dimension) uder joint and separate decoding in the large-system limit [30],[31].”
Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory (2013, result): “We limit ourselves to the main steps, since analogous calculations can be found in several earlier works [40], [41], [48].”
Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO With Low-Precision ADCs (2015, background): “The major difﬁculty in computing (29) is the expectation of the logarithm of P ( (cid:101) Y ) , which, nevertheless, can be facilitated by rewriting F as [33] Note that the expectation operator is now moved inside the log-function.”