{
    "identifier": "ark:\/88434\/mds2-3087",
    "accessLevel": "public",
    "contactPoint": {
        "hasEmail": "mailto:[email protected]",
        "fn": "Marc Valdez"
    },
    "programCode": [
        "006:045"
    ],
    "@type": "dcat:Dataset",
    "description": "This dataset contains CSV files for the figures in the paper titled \"Multi-frequency Antenna Metrology with Sparse Measurements\", to be submitted to IEEE Transactions on Antennas and Propagation or IEEE Transactions on Signal Processing. In this paper, we derive and experiment with approaches to use compressive sensing for multifrequency antenna radiation pattern measurements when samples are taken on a spherical domain. In particular, we develop sparsity and low-rank compressive sensing approaches and compare them for a simulated horn antenna. This work has applications in antenna metrology.",
    "language": [
        "en"
    ],
    "title": "Data for \"Multi-frequency Antenna Metrology with Sparse Measurements\", to be submitted to IEEE Transactions on Antennas and Propagation or IEEE Transactions on Signal Processing.",
    "distribution": [
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_5_low_rank_PD_success_rates.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 5, which shows the success rate phase diagrams for low-rank matrix recovery using the B. M. factorized low-rank matrix recovery approach (see Section. 2.1.2 in the paper) with the JBOS, Rademacher JBOS, IBOS, Rademacher IBOS, and Rademacher Fourier sampling operators (see Sections 2.1.2 and 4.3). The CSV data file is organized as described in the header (first row) of the file, copied here:Rank - r - of random matrix to be recovered.,Normalized measurement number (measurement # \/ # of matrix entries) (no relevant units).,Average success rate (relative error < 0.001) (no relevant units) for recovering a randomly selected rank-r matrix using the JBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average success rate (relative error < 0.001) (no relevant units) for recovering a randomly selected rank-r matrix using the Rademacher JBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average success rate (relative error < 0.001) (no relevant units) for recovering a randomly selected rank-r matrix using the IBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average success rate (relative error < 0.001) (no relevant units) for recovering a randomly selected rank-r matrix using the Rademacher IBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average success rate (relative error < 0.001) (no relevant units) for recovering a randomly selected rank-r matrix using the Rademacher Fourier sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.",
            "mediaType": "text\/csv",
            "title": "Figure_5_low_rank_PD_success_rates.csv"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_6_low_rank_PD_rel_errors.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 6, which shows the relative error phase diagrams for low-rank matrix recovery using the B. M. factorized low-rank matrix recovery approach (see Section. 2.1.2 in the paper) with the JBOS, Rademacher JBOS, IBOS, Rademacher IBOS, and Rademacher Fourier sampling operators (see Sections 2.1.2 and 4.3). The CSV data file is organized as described in the header (first row) of the file copied here:Rank - r - of random matrix to be recovered.,Normalized measurement number (measurement # \/ # of matrix entries) (no relevant units).,Average relative error (dB) for recovering a randomly selected rank-r matrix using the JBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher JBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the IBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher IBOS sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher Fourier sampling operator and the B. M. factorized matrix sensing approach -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.",
            "mediaType": "text\/csv",
            "title": "Figure_6_low_rank_PD_rel_errors.csv"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_4_50MHz_step_low_rank_errors.csv",
            "format": "CSV",
            "description": "This file contains part of the data needed for Figure 4, which shows the model representation errors for the sparse model and low-rank model at different frequency step sizes (20 and 50 MHz) as well as with or without windowing the Fourier transform across frequencies. The CSV data file is organized as described in the header (first row) also copied here:Normalized model complexity (rank r \/ max possible rank) - no relevant units.,Relative error of the rank-r truncation of the Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 50 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.",
            "mediaType": "text\/csv",
            "title": "Figure_4_50MHz_step_low_rank_errors"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_4_50MHz_step_sparsity_errors.csv",
            "format": "CSV",
            "description": "This file contains part of the data needed for Figure 4, which shows the model representation errors for the sparse model and low-rank model at different frequency step sizes (20 and 50 MHz) as well as with or without windowing the Fourier transform across frequencies. The CSV data file is organized as described in the header (first row) also copied here:Normalized model complexity (sparsity value s \/ # of matrix entries) - no relevant units.,Relative error (dB) of the s-sparse truncation of the windowed Fourier transformed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The Fourier transformation is across the rows of the Wigner D-function coefficient matrix. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 50 is used for the antenna.,Relative error  (dB) of the s-sparse truncation of the windowed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 50 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.",
            "mediaType": "text\/csv",
            "title": "Figure_4_50MHz_step_sparsity_errors"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_7_noisy_low_rank_PD_rel_errors.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 7, which shows the relative error phase diagrams for low-rank matrix recovery with noisy measurements using the B. M. factorized low-rank matrix recovery approach (see Section. 2.1.2 in the paper) with the JBOS, Rademacher JBOS, IBOS, Rademacher IBOS, and Rademacher Fourier sampling operators (see Sections 2.1.2 and 4.3). The CSV data file is organized as described in the header (first row) of the file copied here:Rank - r - of random matrix to be recovered.,Normalized measurement number (measurement # \/ # of matrix entries) (no relevant units).,Average relative error (dB) for recovering a randomly selected rank-r matrix using the JBOS sampling operator and the B. M. factorized matrix sensing approach and noisy samples -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher JBOS sampling operator and the B. M. factorized matrix sensing approach and noisy samples -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the IBOS sampling operator and the B. M. factorized matrix sensing approach and noisy samples -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher IBOS sampling operator and the B. M. factorized matrix sensing approach and noisy samples -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.,Average relative error (dB) for recovering a randomly selected rank-r matrix using the Rademacher Fourier sampling operator and the B. M. factorized matrix sensing approach and noisy samples -- see Sections 4.3 and 2.1.2 of the paper for further information on this approach.",
            "mediaType": "text\/csv",
            "title": "Figure_7_noisy_low_rank_PD_rel_errors.csv"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_8_horn_PD_errors.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 8, which shows the relative error and success rate phase diagrams for sparse and low-rank matrix recovery with noisy measurements using the for a simulated standard gain horn antenna operating in the 8-12 GHz range. Info on recovery approaches is in Section. 2.1.1 and 2.1.2 in. The CSV data file is organized as described in the header (first row) of the file copied here:Sample density (# of measurements \/ # of coefficient matrix entries) (no relevant units),Relative error (dB) of recovered coefficients using the basis pursuit approach (Theorem 8) with the JBOS sampling operator (Section 2.1.1).,Relative error (dB) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) with the JBOS sampling operator.,Relative error (dB) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) approach with the Rademacher JBOS sampling operator.,Relative error (dB) of recovered coefficients using the basis pursuit approach (Theorem 6) with the IBOS sampling operator (Section 2.1.1).,Relative error (dB) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) with the IBOS sampling operator.,Relative error (dB) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) approach with the Rademacher IBOS sampling operator.,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the basis pursuit approach (Theorem 8) with the JBOS sampling operator (Section 2.1.1).,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) with the JBOS sampling operator.,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) approach with the Rademacher JBOS sampling operator.,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the basis pursuit approach (Theorem 6) with the IBOS sampling operator (Section 2.1.1).,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) with the IBOS sampling operator.,Mean success rate (relative error < 0.01) (no relevant units) of recovered coefficients using the B. M. factorized matrix sensing approach (Section 2.1.2) approach with the Rademacher IBOS sampling operator.",
            "mediaType": "text\/csv",
            "title": "Figure_8_horn_PD_errors.csv"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_1_horn_antenna_WDFC_support.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 1, the support locations for the WDFC matrix of a simulated standard gain horn antenna for the frequency range of 8 GHz to 12 GHz. The band-limit used for the simulated horn is 20 and 201 samples across frequency are used. The support locations are calculated as 1 if the coefficient at a particular row and column location is greater than 10^-6, otherwise the location is given a value of 0. The file is organized so that each row or column of the coefficient matrix corresponds to a given row or column of the CSV file.",
            "mediaType": "text\/csv",
            "title": "Figure_1_horn_antenna_WDFC_support.csv"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/make_plots.m",
            "format": "MATLAB script",
            "description": "This MATLAB script uses the data files to generate the figures used in the paper.",
            "mediaType": "application\/octet-stream",
            "title": "make_plots.m"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/README.md",
            "format": "Plain Text \/ Markdown",
            "description": "This is a README summarizing the dataset.",
            "mediaType": "text\/plain",
            "title": "README.md"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_2_horn_VSWF_coefficients_10GHz_n_mx_20.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 2, which shows the relative magnitude (no relevant units), of the vector spherical wavefunction coefficients for a simulated standard gain horn antenna at 10 GHz. The band limit used is 20. The relative magnitude is Rel. Mag. = |A_{n,s}^m|\/max_{n,m,s} |A_{n,s}^m|. The CSV file is organized so that each column corresponds to the m values in increasing order, i.e., -20, -19, ... , 19, 20. The first 21 rows correspond to n values of 0, 1, ..., 20 for s=1 and the remaining rows are for n values of 0, 1, ..., 20 for s=2.",
            "mediaType": "text\/csv",
            "title": "Figure_2_horn_VSWF_coefficients_10GHz_n_mx_20"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_3_horn_WDF_coefficients_10GHz_n_mx_20.csv",
            "format": "CSV",
            "description": "This file contains the data for Figure 3, which shows the relative magnitude in dB, absolute Phase, and relative magnitude of the Fourier transformed (across rows) of the Wigner D-function coefficients for a simulated standard gain horn antenna at 10 GHz as measured by an x-oriented dipole measured at a distance of 1 m. The band limit used is 20. The relative magnitude is Rel. Mag. = |A_{n,s}^m|\/max_{n,m,s} |A_{n,s}^m|. To get the dB value is then 20 * log10(Rel. Mag). The CSV file is organized so that each row of the Wigner D-function coefficient matrix makes up one row of the CSV, and each column corresponds to a matrix column.",
            "mediaType": "text\/csv",
            "title": "Figure_3_horn_WDF_coefficients_10GHz_n_mx_20"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_4_20MHz_step_low_rank_errors.csv",
            "format": "CSV",
            "description": "This file contains part of the data needed for Figure 4, which shows the model representation errors for the sparse model and low-rank model at different frequency step sizes (20 and 50 MHz) as well as with or without windowing the Fourier transform across frequencies. The CSV data file is organized as described in the header (first row) also copied here:Normalized model complexity (rank r \/ max possible rank) - no relevant units.,Relative error of the rank-r truncation of the windowed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.,Relative error of the rank-r truncation of the Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.",
            "mediaType": "text\/csv",
            "title": "Figure_4_20MHz_step_low_rank_errors"
        },
        {
            "downloadURL": "https:\/\/data.nist.gov\/od\/ds\/mds2-3087\/Figure_4_20MHz_step_sparsity_errors.csv",
            "format": "CSV",
            "description": "This file contains part of the data needed for Figure 4, which shows the model representation errors for the sparse model and low-rank model at different frequency step sizes (20 and 50 MHz) as well as with or without windowing the Fourier transform across frequencies. The CSV data file is organized as described in the header (first row) also copied here:Normalized model complexity (sparsity value s \/ no. of matrix entries) - no relevant units.,Relative error (dB) of the s-sparse truncation of the windowed Fourier transformed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The Fourier transformation is across the rows of the Wigner D-function coefficient matrix. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.,Relative error (dB) of the s-sparse truncation of the non-windowed Fourier transformed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The Fourier transformation is across the rows of the Wigner D-function coefficient matrix. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.,Relative error (dB) of the s-sparse truncation of the windowed Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.,Relative error (dB) of the s-sparse truncation of the Wigner D-function coefficients of a simulated standard gain horn antenna as measured by an x-oriented dipole from a distance of 1 m. The coefficient matrix is such that samples in frequency are spaced at 20 MHz intervals in the 8-12 GHz range and a band limit of 20 is used for the antenna.",
            "mediaType": "text\/csv",
            "title": "Figure_4_20MHz_step_sparsity_errors"
        }
    ],
    "license": "https:\/\/www.nist.gov\/open\/license",
    "bureauCode": [
        "006:55"
    ],
    "modified": "2023-09-29 00:00:00",
    "publisher": {
        "@type": "org:Organization",
        "name": "National Institute of Standards and Technology"
    },
    "theme": [
        "Metrology:Electrical\/electromagnetic metrology",
        "Mathematics and Statistics:Image and signal processing"
    ],
    "issued": "2024-01-09",
    "keyword": [
        "acoustic fields;  antenna characterization; compressive sampling; compressive sensing; far-field pattern  near-field pattern; sparse signal processing; Legendre polynomials; Wigner D-functions; low-rank matrices;"
    ]
}