Marginal Likelihood Maximization Based Fast Array Manifold Matrix Learning for Direction of Arrival Estimation

Mao, Yiwen; Guo, Qinghua; Ding, Jian; Liu, Fei; Yu, Yanguang

doi:10.1109/tsp.2021.3112922

Cited by 7 publications

(4 citation statements)

References 34 publications

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“…with R ¼ XX H =L denoting the sample covariance matrix (SCM). Numerous algorithms are available for solving the above optimisation problem, for example, expectation-maximisation algorithm [23], variational Bayesian inference [39], and marginal likelihood maximisation [40,41] etc. Different from the l 2;0 mixed-norm sparsity metric introduced in the previous section, the log-det term in the SBL cost function ( 23) helps promote sparsity [42].…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Mathematically, the cost function is formulated by minimising the marginal likelihood function with respect to

\boldsymbol{\gamma }

\begin{align*}\tilde{\boldsymbol{\gamma }}=\mathrm{arg}\ \underset{\boldsymbol{\upgamma }}{\min }-\mathrm{ln}\,p\left(\boldsymbol{X}\vert \boldsymbol{\gamma },{\sigma }^{2}\right)\\ \enspace=\,\mathrm{arg}\ \underset{\boldsymbol{\upgamma }}{\min }\ \mathrm{ln}\vert \boldsymbol{\Phi }\boldsymbol{\Gamma }{\boldsymbol{\Phi }}^{H}+{\sigma }^{2}\boldsymbol{I}\vert +\text{Tr}\left({\left(\boldsymbol{\Phi }\boldsymbol{\Gamma }{\boldsymbol{\Phi }}^{H}+{\sigma }^{2}\boldsymbol{I}\right)}^{-1}\widehat{\boldsymbol{R}}\right)\end{align*}

with

\widehat{\boldsymbol{R}}=\mathbf{X}{\mathbf{X}}^{H}/L

denoting the sample covariance matrix (SCM). Numerous algorithms are available for solving the above optimisation problem, for example, expectation‐maximisation algorithm [23], variational Bayesian inference [39], and marginal likelihood maximisation [40, 41] etc. Different from the

{\mathscr{l}}_{2,0}

mixed‐norm sparsity metric introduced in the previous section, the log‐det term in the SBL cost function (23) helps promote sparsity [42].…”

Section: Proposed Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

Cui

Wang

De-gen

et al. 2023

IET Radar Sonar & Navi

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Non‐sidelooking airborne radar encounters significant non‐stationary and heterogeneous clutter environments, resulting in a severe shortage of samples. Sparse recovery‐based space‐time adaptive processing (SR‐STAP) methods can achieve good clutter suppression performance with limited samples. Nonetheless, grid‐based SR‐STAP algorithms encounter off‐grid effects in non‐sidelooking arrays, which can severely degrade the clutter suppression performance. In this study, the authors propose a novel gridless SR‐STAP method in the continuous spatial‐temporal domain to address the issue of off‐grid effects. Inspired by the fact that sparse Bayesian learning (SBL) framework implicitly performs a structured covariance matrix estimation, the authors reparameterise its cost function to directly estimate the block‐Toeplitz structured matrix from the measurements in a gridless manner. Since the proposed cost function is non‐convex, we utilise a majorisation‐minimisation‐based iterative procedure to estimate the clutter covariance matrix. Finally, using the standard concept of semidefinite programming, the authors derive a convex gridless implementation of the SBL cost function for uniformly sampled radar systems. Extensive simulation experiments demonstrate the exceptional clutter suppression and target detection performance of the proposed algorithm.

show abstract

Section: Proposed Algorithmmentioning

confidence: 99%

“…Mathematically, the cost function is formulated by minimising the marginal likelihood function with respect to

\boldsymbol{\gamma }

\begin{align*}\tilde{\boldsymbol{\gamma }}=\mathrm{arg}\ \underset{\boldsymbol{\upgamma }}{\min }-\mathrm{ln}\,p\left(\boldsymbol{X}\vert \boldsymbol{\gamma },{\sigma }^{2}\right)\\ \enspace=\,\mathrm{arg}\ \underset{\boldsymbol{\upgamma }}{\min }\ \mathrm{ln}\vert \boldsymbol{\Phi }\boldsymbol{\Gamma }{\boldsymbol{\Phi }}^{H}+{\sigma }^{2}\boldsymbol{I}\vert +\text{Tr}\left({\left(\boldsymbol{\Phi }\boldsymbol{\Gamma }{\boldsymbol{\Phi }}^{H}+{\sigma }^{2}\boldsymbol{I}\right)}^{-1}\widehat{\boldsymbol{R}}\right)\end{align*}

with

\widehat{\boldsymbol{R}}=\mathbf{X}{\mathbf{X}}^{H}/L

{\mathscr{l}}_{2,0}

mixed‐norm sparsity metric introduced in the previous section, the log‐det term in the SBL cost function (23) helps promote sparsity [42].…”

Section: Proposed Algorithmmentioning

confidence: 99%

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

Cui

Wang

De-gen

et al. 2023

IET Radar Sonar & Navi

View full text Add to dashboard Cite

show abstract

“…Eigenvalues are computed by solving the following equation. (13) where, λ=Eigenvalue, ei=Eigenvector.…”

Section: Computation Of Eigenvaluesmentioning

confidence: 99%

“…Bayesian learning is applied for the linear array to compute the value of array manifold vector, likelihood functionality has the performance parameters such as size complexity and computational complexity which are used for detection of Angle of Arrival [13]. Antenna sensor array performs the signal processing at the Base Station to detect the direction of the incoming electromagnetic wave using Multiple Signal Classification (MUSIC) algorithm [14].…”

Section: Introductionmentioning

confidence: 99%

High Resolution Detection, Estimation and Location Using GTF DoA Method for Smart Antenna System

Morab¹,

Hegde²,

Hegde³

2022

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Accommodating multiple users within the limited available bandwidth and providing the same Quality of Service (QoS) to all the users is a challenging task. Channel capacity can be increased by using the Spatial Division Multiple Access (SDMA) technique. Smart Antenna Systems are used to implement the SDMA technique in Real-Time and it also helps in finding the high-resolution Direction of Arrival (DoA) detection of the desired mobile users. In this paper novel Gaussian Triangular Factor (GTF) method is proposed for the detection of the desired mobile users from the 3-D spatial domain. This method is based on vector subspaces, which perform the triangular decomposition of the entire Eigenspace into the Lower Element Factor (LEF) and Upper Element Factor (UEF). These are then supplied for the computation of the power spectrum where peaks represent the detected locations of the desired mobile users in the 3-D spatial field. The proposed method was able to detect all the desired users, which were spaced nearer or far apart spatially, it provided high-quality detection regardless of the number of antenna elements used at the Base Station (BS). The GTF Method was able to detect all the desired users under the presence of heavy noise, fading, and interference. It was able to suppress the side lobes, back lobes, and grating lobes thus immensely improving the detection quality, detection range, system power consumption, detection efficiency, and effectiveness. The proposed GTF method was compared with several existing methods and it provided the best results for different performance parameters like Detection Error, Resolution, Time Complexity, and Disturbance Error.

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Improved block sparse Bayesian learning based DOA estimation for massive MIMO systems

Liu¹,

Liu²,

Long³

et al. 2023

AEU - International Journal of Electronics and Communications

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Marginal Likelihood Maximization Based Fast Array Manifold Matrix Learning for Direction of Arrival Estimation

Cited by 7 publications

References 34 publications

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

High Resolution Detection, Estimation and Location Using GTF DoA Method for Smart Antenna System

Improved block sparse Bayesian learning based DOA estimation for massive MIMO systems

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