3GPPTSG RAN WG1 #121 R1-2503722
Malta , MT, May 19th – May 23th, 2025
Source: BUPT
Title: An Improved DOA Estimation Method Based on Sparse Reconstruction
Agenda item: 9.2
Document for: Discussion
An Improved DOA Estimation Method Based on Sparse Reconstruction
Jiahao Yang(B), Zhongliang Deng, Zhichao Zang, and Biao Lei
Beijing University of Posts and Telecommunications, BUPT, Beijing, China 1421506726@qq.com
Abstract. With the development of millimeter wave technology and the increasingly complex electromagnetic environment, the traditional method of DOA estimation based on subspace technology can not meet the high-precision position requirements of space-time networks in various application scenarios. For this reason, scholars have introduced compressed sensing and sparse reconstruction technology into the problem of array signal estimation, and used sparse Bayesian (SBL) reconstruction based methods to estimate the angle of arrival (DOA), which often faces the problems of estimation performance and computation adjustment. In this paper, we propose a Bayesian grid iteration algorithm with low computational complexity while ensuring high estimation performance. Firstly, the SBL with the lowest computational complexity is used for rough estimation of the direction of arrival, and the grid is divided unevenly according to the rough estimation results. After the grid division termination condition is reached, the MDL criterion is used to estimate the number of sources, and the signal is decomposed into SVD. Finally, the updated grid division is combined with the SVD decomposition results, and the DOA is fine estimated using Root SBL. Simulation results show that this algorithm has low computational complexity and high estimation performance.
Keywords: Sparse reconstruction · DOA estimate · Dynamic mesh generation
1 |
This contribution is a revision of R1-2503722, which was mistakenly submitted as a paper instead of a contribution. The content remains technically unchanged, but is now properly submitted as a contribution to allow proper discussion and consideration by the WG.
We apologize for the oversight.
3GPPTSG RAN WG1 #121 R1-2504568
Malta , MT, May 19th – May 23th, 2025
Source: BUPT
Title: Discussions on DOA estimation algorithm for MIMO
Agenda item: 9.2
Document for: Discussion
Overall description
The topic of discussion in R1 is the applicability and performance analysis of the dynamic grid-optimised DOA estimation algorithm based on sparse reconstruction (GRSBL)
For millimetre wave signal source DOA estimation in the active state
Need to ensure that the initialised grid interval Δθ satisfies Δθ ≤ preset threshold (initial Δθ = 6° in the text)
For the signal activation process
Dynamic grid optimisation with Root SBL is not directly applied to the signal in the activation phase.
The following steps are enforced in the preprocessing enhancement phase to enhance stability:
SVD downscaling: noise suppression by signal subspace decomposition (Eq. 19).
MDL criterion: adaptive estimation of the number of signal sources K value to avoid dimensional redundancy.
For signal de-activation state
Dynamic mesh optimisation should not be used for DOA estimation of de-activated signal sources.
Principles of de-activated signal processing:
The UE may choose to continue to measure the de-activated signal (FFS measurement method), subject to trade-offs between energy consumption and accuracy requirements.
Disable Root SBL hyperparameter update and retain only the base spectrum analysis (low power mode)
System Model
2.1 Array Signal Receiving Model
Assuming that K far-field narrowband signals are injected, the antenna array is a Uniform Liner Array (ULA) with M elements, and the element spacing is d = λ/2, λ is the wavelength of the signal carrier. At time t, k signals are incident at the angle of θ(θ1,...,θk), and the signals received by the array
a(θk) = [1,..,exp(−i2πfDsin(θk)/c)]T is the array steering vector, D is the wave path difference, s(ti) = [s1,...,sk]T is the incident signal vector. Expand to multi snapshot situation
Y = [y(t1),...,y(tl)]T, A = (a(θ1),...,a(θk)), S = [s(t1),...,s(tl)], N =
(n(t1),...n(tl)) are array output matrix, signal guidance matrix and signal noise matrix respectively.
Proposal 1: The definition of the array output matrix for multi-snapshot signals under sparse Bayesian learning can be represented by Equation 2 .
2.2 DOA Estimation Model Based on Sparse Reconstruction
Millimeter wave MIMO signals have significant sparsity in the angular domain, and can be estimated through sparse signal restoration.
Based on this, the whole signal space [−90◦,90◦] is divided equally in the angle domain to generate N spatial grids θ = [θ1,...,θN]. From this, we can get a super complete dictionary A¯ = [a(θ1),...,a(θN)], Then Eq. (2) can be re expressed as
whereS¯ isasparsesignalrepresentedbyasupercompletedictionary.ForsparseBayesian reconstruction signal model, Y is the observation data, A¯ is the observation matrix, S¯ is the sparse signal to be calculated, N is the Gaussian noise with mean value of 0 and variance of σ2.
It can be seen that the probability density of S¯ and the likelihood function of signal Y obey Gaussian distribution.
Where p (7)
Proposal 2: The sparse signal reconstruction model for DOA estimation, incorporating super-complete dictionary Aˉ, is defined by Equation 3.
Proposal 3: The posterior probability framework for sparse Bayesian learning (SBL)-based DOA estimation, including the joint sparsity modeling of hyperparameters and signals, is formally defined by Equation 7.
Conclusion
Proposal 1: The definition of the array output matrix for multi-snapshot signals under sparse Bayesian learning can be represented by Equation 2 .
Proposal 2: The sparse signal reconstruction model for DOA estimation, incorporating super-complete dictionary Aˉ, is defined by Equation 3.
Proposal 3: The posterior probability framework for sparse Bayesian learning (SBL)-based DOA estimation, including the joint sparsity modeling of hyperparameters and signals, is formally defined by Equation 7.
Reference
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