On the explanation of spatial smoothing in MUSIC algorithm for coherent sources

Chen, Qing; Liu, Ruolun

doi:10.1109/icist.2011.5765342

Cited by 18 publications

(10 citation statements)

References 5 publications

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“…The array is perturbed by a combination of three types of imperfections and the strength of the perturbations is set to 0.1. We compare the proposed DNN‐based method with several widely studied subspace‐based alternatives, Akaike information criterion [40], minimum description length [41], Gerschgorin disk estimator (GDE) [42], traditional eigenvalue decomposition (ED) method [43], spatial smoothing rank [44], improved eigenvalue decomposition algorithm [45], and signal subspace matching [46]. In the GDE algorithm, the adjustment factor is set to 0.8.…”

Section: Results and Analysismentioning

confidence: 99%

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

Chen

Mao

Liu

2023

IET Radar Sonar & Navi

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In array signal processing, high‐resolution direction‐of‐arrival (DOA) estimation by eigendecomposition method requires knowledge of the array covariance matrix and an exact characterisation of the array. The dependence of most such methods on the array manifold substantially degrades their array performance when the actual sensors deviate from their assumed nominal values. This article aims at formulating a deep neural network framework for DOA estimation with feasible computational complexity. The two‐stage algorithm is composed of a detection network and a series of parallel DOA estimation networks: the multilayer perceptron is trained to detect the presence of one or more sources in an angular sector at the first stage, the DOA estimation networks then estimate their respective DOAs at the second stage. When a single type of array imperfection is considered, numerical results reveal that the DNN‐based method can obtain DOA estimates with much higher precision than the existing techniques for significant location errors and gain/phase perturbations, they also illustrate the potential usefulness of the proposed algorithm towards better DOA estimation accuracy for mutual coupling as the mutual coupling matrix is not simplified. Moreover, the proposed method is finally extended to deal with the DOA estimation problem when multiple types of array perturbations coexist.

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Section: Results and Analysismentioning

confidence: 99%

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

Chen

Mao

Liu

2023

IET Radar Sonar & Navi

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“…The number of frequency shifts is fixed per bandwidth and subcarrier spacing based on empirical evaluations in indoor environments. The smoothing subarray size for all cases is set as N ≈ K Ds /2 following insights from [63], [70] and preliminary evaluations. The number of MPCs specified is scaled with bandwidth as higher resolution estimation of the MPC ToFs is possible with higher bandwidths [57].…”

Section: Discussionmentioning

confidence: 99%

A Multichannel Approach and Testbed for Centimeter-Level WiFi Ranging

Van Marter,

Ben-Shachar,

Alpert

et al. 2024

J. Ind. Sea. Pos. Nav.

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Latest advancements in WiFi ranging enable the use of both timestamps and channel frequency response (CFR) measurements supporting the recently released IEEE 802.11az Next Generation Positioning standard. However, resolution limitations are imposed by the single-channel bandwidth of operation, and WiFi devices that can only operate using 20 MHz channels on a given time instance suffer from limited ranging capabilities. While devices can frequency hop to multiple channels to obtain CFR measurements across larger bandwidths, changes in local oscillator phase offsets and time offsets per channel prevent direct stitching of the CFR. To overcome these challenges and achieve phase-coherent multi-channel (PCMC) CFR measurements, we propose a two-way CFR approach that embeds timestamp information in the phase. We develop a software-defined radio testbed to evaluate our proposed multi-channel ranging technique and answer hardware implementation challenges. For range estimation, we employ Multiple Signal Classification (MUSIC) and a complexity reduction strategy to accommodate large bandwidths with many subcarriers. Utilizing our proposed PCMC technique with 16 channels, we demonstrate a median error of 2.7 cm and a 90th percentile error of 9.5 cm in indoor lineof-sight conditions.

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“…Typically, preprocessing steps are necessary for estimating the DOA of coherent sources, as the covariance matrix becomes singular and becomes rank deficient, rendering accurate DOA estimation of such signals very difficult [8][9]. Specific approaches, like spatial smoothing, can be employed during the preprocessing phase to enhance the rank of the covariance matrix [10][11][12][13][14][15][16][17], but their performance and computational complexity exhibit much variation. These operations add to the complexity and computation cost of DOA estimation.…”

Section: Figure 1 Some Applications Of Doa Estimationmentioning

confidence: 99%

Low Complexity DOA Estimation of Multiple Coherent Sources Using a Single Direct Data Snapshot

Hussain,

Tayem,

Soliman

2024

IEEE Access

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The direction of arrival (DOA) estimation of multiple radio frequency (RF) coherent signals using conventional algorithms such as Multiple Signal Classification (MUSIC), Estimation of the Signal Parameters via the Rotational Invariance Technique (ESPRIT), and their variants is computationally complex and usually requires a large number of data snapshots for accurate estimation. As the number of antenna elements grows, particularly in massive MIMO systems, the complexity of real-time DOA estimation algorithms significantly rises, placing higher demands on computational power and memory resources. In this paper, we present an efficient approach that operates effectively with just a single snapshot for DOA estimation of multiple coherent and non-coherent signals. The proposed method has the following advantages over existing methods: 1) constructs a Toeplitz structure data matrix from a single data snapshot, 2) applies forward-backward averaging operation to the data matrix instead of the covariance matrix constructed using hundreds of snapshots, 3) resolves the differences in the noise elements of the data matrix, preserving the conjugate symmetry property of the Toeplitz matrix, 4) converts the complex Toeplitz data matrix to a realvalued matrix in an efficient way without unitary transformations, and 5) employs QR decomposition to extract the signal and noise subspaces, eliminating the need for computationally complex eigenvalue (EVD) or singular value decomposition (SVD). Finally, we establish the effectiveness of our proposed method through both MATLAB simulations and real-time experiments. Compared to existing methods like Unitary root-MUSIC, the proposed approach demonstrates significantly reduced complexity and faster estimation times.

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On the explanation of spatial smoothing in MUSIC algorithm for coherent sources

Cited by 18 publications

References 5 publications

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

A Multichannel Approach and Testbed for Centimeter-Level WiFi Ranging

Low Complexity DOA Estimation of Multiple Coherent Sources Using a Single Direct Data Snapshot

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