A Study of Comb Beam Transmission on Phased Array Weather Radars

Yoshikawa, Eiichi; Ushio, Tomoo; Kikuchi, Hiroshi

doi:10.1109/tgrs.2020.3029875

“…where x l or its covariance matrix 6 in the communications scenario. In the latter case, if the matrix A is also known, then the covariance matrix R (26) to the DOA estimation for signals x κ,l from point targets [23], where each angle θ κ in ( 13) is estimated as a discretized angle θ m in (15).…”

Section: Mmse Beamformingmentioning

confidence: 99%

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Kitahara¹,

Kuroda²,

Hirabayashi³

et al. 2022

Preprint

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<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group-sparsities. We consider two optimization problems. One problem roughly evaluates the group-sparsities and is relatively easy to solve. The other evaluates the group-sparsities more accurately, but requires more time to solve. Both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using synthetic and real-world PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

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“…Moreover, we evaluated the estimated periodograms (| u k,m | 2 ) by the following normalized mean absolute errors (NMAEs). 6 In this model, the variance…”

Section: Numerical Simulations a Simulation Settingsmentioning

confidence: 99%

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Kitahara¹,

Kuroda²,

Hirabayashi³

et al. 2021

Preprint

Self Cite

1

0

View full text Add to dashboard Cite

<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group- parsities. We consider two optimization problems which evaluate the group-sparsities in slightly different ways, and both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using real PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

show abstract

“…The optimal solution to this problem is given by 26) where x l or its covariance matrix R 6 in the communications scenario. In the latter case, if the matrix A is also known, then the covariance matrix (26) to the DOA estimation for signals x κ,l from point targets [22], where each angle θ κ in ( 13) is estimated as a discretized angle θ m in (15).…”

Section: Mmse Beamformingmentioning

confidence: 99%

“…and the exact optimal solution to this problem is given by 6 In the former case, the observation matrix A is unknown.…”

Section: Mmse Beamformingmentioning

confidence: 99%

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Kitahara¹,

Kuroda²,

Hirabayashi³

et al. 2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group-sparsities. We consider two optimization problems. One problem roughly evaluates the group-sparsities and is relatively easy to solve. The other evaluates the group-sparsities more accurately, but requires more time to solve. Both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using synthetic and real-world PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

show abstract

A Study of Comb Beam Transmission on Phased Array Weather Radars

Cited by 9 publications

References 17 publications

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

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