Widely Linear Sphere Decoder in MIMO Systems by Exploiting the Conjugate Symmetry of Linearly Modulated Signals

Ding, Yuehua; Li, Nanxi; Wang, Yide; Chen, Hongbin

doi:10.1109/tsp.2016.2598317

“…Now we consider the high SNR regime. Using the fact that lim ρ→∞ P(s ML = s MMSE ) = 1, we have P(K r = 0) = 1, and according to (23), we obtain lim ρ→∞ C min LSR = 0.…”

Section: Appendix a The Proof Of Lemmamentioning

confidence: 98%

Lossless Size Reduction for Integer Least Squares with Application to Sphere Decoding

Neinavaie,

Derakhtian,

Vorobyov

2019

Preprint

0

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Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE point has a vital difference at low SNRs. By exploiting the information provided by the MMSE method, we prove the existence of a lossless size reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless size reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.

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“…3, to compare the complexity of the proposed method with that of the SD algorithm presented in [21] with R H . For comparison, the performance and the computational complexity of the widely linear SD in [23] is also plotted. It can be seen that the proposed algorithm achieves a lower complexity and, unlike the other SD algorithms, is as complex as the MMSE algorithm at low and high SNRs.…”

Section: B Frequency Flat Rayleigh Fading Mimo Channelmentioning

confidence: 99%

“…This minimum complexity is described via introducing the SD complexity exponent. Aiming for reducing the computational complexity, there are a number of other variants of the SD algorithm which can be divided according to the error performance into optimal and suboptimal SD algorithms [15]- [23].…”

Section: Introductionmentioning

confidence: 99%

Lossless Dimension Reduction for Integer Least Squares With Application to Sphere Decoding

Neinavaie

¹

,

Derakhtian

²

,

Vorobyov

³

2020

IEEE Trans. Signal Process.

2

0

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Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE point has a vital difference at low SNRs. By exploiting the information provided by the MMSE method, we prove the existence of a lossless size reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless size reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.

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“…For rigor, the simulations were conducted within a widely linear quaternion framework which has found its potential in MIMO channel identification [30]. Here, a widely linear quaternion moving average of order 3 -WLQMA(3) was used, where the input x n was drawn from 1000 samples of the same distribution N (0, 1) for each component of x n , with a moderate SNR of 40dB.…”

Section: Numerical Experimentsmentioning

confidence: 99%

On an RLS-like LMS adaptive filter

Variddhisai

¹

,

Mandic

²

2017

2017 22nd International Conference on Digital Signal Processing (DSP)

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A unified and generalized framework for a recursive least squares (RLS)-like least mean square (LMS) algorithm is proposed, which adopts the cost function of the RLS to minimize the mean square error. This paper aims to explore, in a systematic way, the corresponding ideas scattered and multiple-time re-invented in the literature, and introduces a unified approach in the same spirit as in [1], which relates LMS with the Kalman filter. The proposed alternative to the RLS is favored when the matrix inversion lemma is not useful, such as the case of multivariate or multichannel data where the input is not a vector. Furthermore, all the derivations are conducted in the quaternion domain and are hence generalizable to complexand real-valued models. The resulting algorithm has a neat form and a similar complexity to the RLS. Through experiments, the method is shown to exhibit performance close to or even better than the RLS algorithm. Other aspects, such as the choice of descent directions and variable stepsizes, are also discussed to support the analysis.

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Widely Linear Sphere Decoder in MIMO Systems by Exploiting the Conjugate Symmetry of Linearly Modulated Signals

Cited by 12 publications

References 37 publications

Lossless Size Reduction for Integer Least Squares with Application to Sphere Decoding

Lossless Size Reduction for Integer Least Squares with Application to Sphere Decoding

Lossless Dimension Reduction for Integer Least Squares With Application to Sphere Decoding

On an RLS-like LMS adaptive filter

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