Symbol Error Rate Performance of Box-Relaxation Decoders in Massive MIMO

Thrampoulidis, Christos; Xu, Weiyu; Hassibi, Babak

doi:10.1109/tsp.2018.2831622

Cited by 53 publications

(99 citation statements)

References 42 publications

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“…where p(x) = 1 √ 2π e −x 2 /2 is the pdf of a standard Gaussain random variable and Q(x) is its associated Q-function. The expectation in (19) can be found in a similar way.…”

Section: Resultsmentioning

confidence: 53%

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Precise Performance Analysis of the Box-Elastic Net Under Matrix Uncertainties

Alrashdi

Atitallah

Al-Naffouri

2019

IEEE Signal Process. Lett.

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In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) real Gaussian measurement matrix with additive Gaussian noise. In many practical situations, the measurement matrix is not perfectly known, and so we only have a noisy estimate of it. In this work, we precisely characterize the mean squared error and the probability of support recovery of the Box-Elastic Net in the high-dimensional asymptotic regime. Numerical simulations validate the theoretical predictions derived in the paper and also show that the boxed variant outperforms the standard EN.Index Terms-Elastic Net, squared error, measurement matrix uncertainties, probability of support recovery, box-constraint.

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“…where p(x) = 1 √ 2π e −x 2 /2 is the pdf of a standard Gaussain random variable and Q(x) is its associated Q-function. The expectation in (19) can be found in a similar way.…”

Section: Resultsmentioning

confidence: 53%

“…The proof of Theorem 2 is also based on the CGMT and largely follows the proof of Theorem 1 but is omitted for space limitations (see [19] for a similarly detailed treatment). Remark 1 (Small/Large Regularizers).…”

Section: Resultsmentioning

confidence: 99%

Precise Performance Analysis of the Box-Elastic Net Under Matrix Uncertainties

Alrashdi

Atitallah

Al-Naffouri

2019

IEEE Signal Process. Lett.

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“…The BRO is a relaxation of (1) to an efficient convex quadratic program, namelyx = sign arg min x∈[−1,1] n y − Ax 2 . Its performance in the large-system limit has been recently analyzed in [10]. Regarding the performance of (1), Tse and Verdu [14] have shown that the BER approaches zero at high-SNR.…”

Section: Settingmentioning

confidence: 99%

“…In particular, the MFB corresponds to the probability of error in detecting (say) x0,1 ∈ {±1} from y = x0,1a1 + z, where y = y − n i=2 x0,iai is assumed known, and ai is the i th column of A (eqv., the MFB is the error probability of an isolated transmission of only the first bit over the channel). It can be shown (e.g., [10]) that the MFB is given by Q( √ δ SNR). Combining this with (a straightforward re-parametrization of) Theorem 3.1 it follows that the BER of (1) satisfies…”

Section: Upper Boundmentioning

confidence: 99%

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A Simple Bound on the BER of the Map Decoder for Massive MIMO Systems

Thrampoulidis

Zadik

Polyanskiy

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The deployment of massive MIMO systems has revived much of the interest in the study of the large-system performance of multiuser detection systems. In this paper, we prove a non-trivial upper bound on the bit-error rate (BER) of the MAP detector for BPSK signal transmission and equal-power condition. In particular, our bound is approximately tight at high-SNR. The proof is simple and relies on Gordon's comparison inequality. Interestingly, we show that under the assumption that Gordon's inequality is tight, the resulting BER prediction matches that of the replica method under the replica symmetry (RS) ansatz. Also, we prove that, when the ratio of receive to transmit antennas exceeds 0.9251, the replica prediction matches the matched filter lower bound (MFB) at high-SNR. We corroborate our results by numerical evidence.Index Termsmassive mimo, large-system analysis, JO detector, Gaussian process inequalities, replica method.

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Likelihood ascent search‐aided low complexity improved performance massive MIMO detection in perfect and imperfect channel state information

Chakraborty

Sinha²,

Mitra

2022

Int J Communication

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Summary Massive multiple‐input multiple‐output (MIMO) systems improve spectral efficiency and link reliability. Linear minimum mean‐squared error (MMSE) detectors can achieve optimal performance in massive MIMO detection but require large dimension matrix inversion, which is computationally intensive. Therefore, low complexity iterative detection schemes are proposed in the literature as an alternative to the exact MMSE method. However, the performance of these schemes is greatly influenced by the choice of the initial solution. Therefore, to improve the detection performance in this paper, we proposed three hybrid detection schemes, which are Newton–Schultz–Richardson (NS‐RI), Newton–Schultz–Chebyshev (NS‐Cheby), and Newton–Schultz–Gauss–Seidel (NS‐GS). The proposed hybrid schemes show significant performance improvement and a higher convergence rate compared to their original counterpart. The performance of the proposed detectors is further improved by the likelihood ascent search (LAS) stage, which corrects the detected symbols obtained from iterative MMSE methods through a neighborhood search. However, the complexity of the LAS algorithm primarily depends on the initialization step. In this work, we introduce an efficient Gram matrix computation in the real domain. Additionally, we have applied a band approximation of the Gram matrix for the LAS initialization, which reduces the order of computational complexity of the Gram matrix from Ofalse(NT2NRfalse) to O(ωNTNR) where ω < <2NT.

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Symbol Error Rate Performance of Box-Relaxation Decoders in Massive MIMO

Cited by 53 publications

References 42 publications

Precise Performance Analysis of the Box-Elastic Net Under Matrix Uncertainties

Precise Performance Analysis of the Box-Elastic Net Under Matrix Uncertainties

A Simple Bound on the BER of the Map Decoder for Massive MIMO Systems

Likelihood ascent search‐aided low complexity improved performance massive MIMO detection in perfect and imperfect channel state information

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