A discrete first-order method for large-scale MIMO detection with provable guarantees

Liu, Huikang; Yue, Man–Chung; So, Anthony Man–Cho; Ma, Wing-Kin

doi:10.1109/spawc.2017.8227768

Cited by 29 publications

(24 citation statements)

References 13 publications

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“…Although there is no theoretical guarantee, the GP algorithm always finds the same solution as the SDP solution in our simulation tests. Some recent theoretical progress on using the GP algorithm to solve a similar non-convex problem has been reported in [22]. It would be interesting to also obtain some convergence and optimality guarantee of the GP algorithm for solving QCQP (5.8).…”

Section: Discussionmentioning

confidence: 99%

Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Liu

Yan

et al. 2018

Math. Program.

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An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors. In this paper, we propose a novel nonlinear least squares (LS) formulation for the problem by assuming the existence of a reference target moving with an (unknown) constant velocity. We also propose an efficient block coordinate decent (BCD) optimization algorithm, with a judicious initialization, to solve the problem. The proposed BCD algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs (SDPs). In the absence of measurement noise, the proposed algorithm is guaranteed to find the global solution of the problem and the true biases. Simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error (RMSE).

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Section: Discussionmentioning

confidence: 99%

Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Liu

Yan

et al. 2018

Math. Program.

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“…In fact, since δ k ≤ δ 2k ≤ δ 3k , we see that ≤ 3δ 3k 1+δ 3k 1−δ 3k +δ 3k < 1 which is ensured by the condition δ 3k ≤ 1/5. The bound (30) immediately follows from (40) and (41).…”

Section: So the Vector [(Umentioning

confidence: 93%

“…These models provide an essential basis for the development of the theory and algorithms for compressed sensing (see, e.g., [12,25,26,32,53]). The problem (1) has also been widely used in the fields of statistical regressions and wireless communications (see, e.g., [45,4,41]). The problems (1) and (2) are NP-hard in general [46].…”

Section: Introductionmentioning

confidence: 99%

Optimal $k$-Thresholding Algorithms for Sparse Optimization Problems

Zhao¹

2020

SIAM J. Optim.

117

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The simulations indicate that the existing hard thresholding technique independent of the residual function may cause a dramatic increase or numerical oscillation of the residual. This inherit drawback of the hard thresholding renders the traditional thresholding algorithms unstable and thus generally inefficient for solving practical sparse optimization problems. How to overcome this weakness and develop a truly efficient thresholding method is a fundamental question in this field. The aim of this paper is to address this question by proposing a new thresholding technique based on the notion of optimal k-thresholding. The central idea for this new development is to connect the k-thresholding directly to the residual reduction during the course of algorithms. This leads to a natural design principle for the efficient thresholding methods. Under the restricted isometry property (RIP), we prove that the optimal thresholding based algorithms are globally convergent to the solution of sparse optimization problems. The numerical experiments demonstrate that when solving sparse optimization problems, the traditional hard thresholding methods have been significantly transcended by the proposed algorithms which can even outperform the classic 1 -minimization method in many situations.

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“…Second, Theorem 4.4 states that the true vector of transmitted signals x * can be recovered by solving appropriate SDPs if condition (1.5) is satisfied. It is worth mentioning a recent related result in [22,Theorem 1] for the general M -PSK modulation case, which shows that x * can be recovered by using the generalized power method (GPM) if the following conditions are satisfied:…”

Section: (Ersdp) Is Tighter Than (Csdp2)mentioning

confidence: 99%

Tightness of a New and Enhanced Semidefinite Relaxation for MIMO Detection

Lü¹,

Liu²,

Zhang³

et al. 2019

SIAM J. Optim.

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In this paper, we consider a fundamental problem in modern digital communications known as multiple-input multiple-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite relaxation (SDR) based algorithms have been proposed to solve the problem in the literature. In this paper, we first show that the conventional SDR is generally not tight for the problem. Then, we propose a new and enhanced SDR and show its tightness under an easily checkable condition, which essentially requires the level of the noise to be below a certain threshold. The above results have answered an open question posed by So in [35]. Numerical simulation results show that our proposed SDR significantly outperforms the conventional SDR in terms of the relaxation gap.

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A discrete first-order method for large-scale MIMO detection with provable guarantees

Cited by 29 publications

References 13 publications

Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Optimal $k$-Thresholding Algorithms for Sparse Optimization Problems

Tightness of a New and Enhanced Semidefinite Relaxation for MIMO Detection

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