About this Dataset

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.

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.
Organization: Department of Commerce
Last updated: 2025-09-30T05:25:56.719134
Tags: acoustic-fields-antenna-characterization-compressive-sampling-compressive-sensing-far-field-pat

Tables

Figure 1 Horn Antenna WDFC Support

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_1_horn_antenna_wdfc_support

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201 columns

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Figure 2 Horn VSWF Coefficients 10GHz N Mx 20

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_2_horn_vswf_coefficients_10ghz_n_mx_20

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CREATE TABLE figure_2_horn_vswf_coefficients_10ghz_n_mx_20 (
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Figure 3 Horn WDF Coefficients 10GHz N Mx 20

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_3_horn_wdf_coefficients_10ghz_n_mx_20

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CREATE TABLE figure_3_horn_wdf_coefficients_10ghz_n_mx_20 (
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  "n_2_0586e_18_1_647e_18i" VARCHAR  -- 2.0586e-18-1.647e-18i
);

Figure 4–20MHz Step Low Rank Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_4_20mhz_step_low_rank_errors

8.21 kB
201 rows
3 columns

CREATE TABLE figure_4_20mhz_step_low_rank_errors (
  "normalized_model_complexity_rank_r_max_possible_rank_n_9cc4a062" DOUBLE  -- Normalized Model Complexity (rank R / Max Possible Rank) - No Relevant Units.,
  "relative_error_of_the_rank_r_truncation_of_the_windowe_cadc013a" DOUBLE  -- 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__29a0a12c" DOUBLE  -- 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.
);

Figure 4–20MHz Step Sparsity Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_4_20mhz_step_sparsity_errors

10.1 kB
84 rows
5 columns

CREATE TABLE figure_4_20mhz_step_sparsity_errors (
  "normalized_model_complexity_sparsity_value_s_no_of_mat_8a9ce399" DOUBLE  -- Normalized Model Complexity (sparsity Value S / No. Of Matrix Entries) - No Relevant Units.,
  "relative_error_db_of_the_s_sparse_truncation_of_the_wi_cbfc0994" DOUBLE  -- 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_no_3b3f3e91" DOUBLE  -- 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_wi_e65ec643" DOUBLE  -- 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_wi_4c40e488" DOUBLE  -- 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.
);

Figure 4–50MHz Step Low Rank Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_4_50mhz_step_low_rank_errors

4.5 kB
81 rows
2 columns

CREATE TABLE figure_4_50mhz_step_low_rank_errors (
  "normalized_model_complexity_rank_r_max_possible_rank_n_9cc4a062" DOUBLE  -- Normalized Model Complexity (rank R / Max Possible Rank) - No Relevant Units.,
  "relative_error_of_the_rank_r_truncation_of_the_wigner__5de00a0f" DOUBLE  -- 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.
);

Figure 4–50MHz Step Sparsity Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_4_50mhz_step_sparsity_errors

6.48 kB
84 rows
3 columns

CREATE TABLE figure_4_50mhz_step_sparsity_errors (
  "normalized_model_complexity_sparsity_value_s_of_matrix_4eb68f44" DOUBLE  -- Normalized Model Complexity (sparsity Value S / # Of Matrix Entries) - No Relevant Units.,
  "relative_error_db_of_the_s_sparse_truncation_of_the_wi_8a88fcae" DOUBLE  -- 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_wi_6b08c735" DOUBLE  -- 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.
);

Figure 5 Low Rank PD Success Rates

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_5_low_rank_pd_success_rates

9.99 kB
100 rows
7 columns

CREATE TABLE figure_5_low_rank_pd_success_rates (
  "rank_r_of_random_matrix_to_be_recovered" BIGINT  -- Rank - R - Of Random Matrix To Be Recovered.,
  "normalized_measurement_number_measurement_of_matrix_en_9d0e0fdd" DOUBLE  -- Normalized Measurement Number (measurement # / # Of Matrix Entries) (no Relevant Units).,
  "average_success_rate_relative_error_0_001_no_relevant__7fa4029a" DOUBLE  -- 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__12f74844" DOUBLE  -- 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__95fb666d" DOUBLE  -- 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__daf26523" DOUBLE  -- 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__c63d787f" DOUBLE  -- 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.
);

Figure 6 Low Rank PD Rel Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_6_low_rank_pd_rel_errors

13.48 kB
100 rows
7 columns

CREATE TABLE figure_6_low_rank_pd_rel_errors (
  "rank_r_of_random_matrix_to_be_recovered" BIGINT  -- Rank - R - Of Random Matrix To Be Recovered.,
  "normalized_measurement_number_measurement_of_matrix_en_9d0e0fdd" DOUBLE  -- Normalized Measurement Number (measurement # / # Of Matrix Entries) (no Relevant Units).,
  "average_relative_error_db_for_recovering_a_randomly_se_a8dffcad" DOUBLE  -- 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_se_eb44fec8" DOUBLE  -- 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_se_9fa74fd7" DOUBLE  -- 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_se_0cae7f3a" DOUBLE  -- 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_se_9e60c018" DOUBLE  -- 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.
);

Figure 7 Noisy Low Rank PD Rel Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_7_noisy_low_rank_pd_rel_errors

13.45 kB
100 rows
7 columns

CREATE TABLE figure_7_noisy_low_rank_pd_rel_errors (
  "rank_r_of_random_matrix_to_be_recovered" BIGINT  -- Rank - R - Of Random Matrix To Be Recovered.,
  "normalized_measurement_number_measurement_of_matrix_en_9d0e0fdd" DOUBLE  -- Normalized Measurement Number (measurement # / # Of Matrix Entries) (no Relevant Units).,
  "average_relative_error_db_for_recovering_a_randomly_se_03213871" DOUBLE  -- 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_se_af4c4897" DOUBLE  -- 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_se_b476aeff" DOUBLE  -- 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_se_820da43a" DOUBLE  -- 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_se_7fdec8db" DOUBLE  -- 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.
);

Figure 8 Horn PD Errors

@usgov.doc_gov_data_for_multi_frequency_antenna_metrology_wit_f22825c4.figure_8_horn_pd_errors

18.32 kB
40 rows
13 columns

CREATE TABLE figure_8_horn_pd_errors (
  "sample_density_of_measurements_of_coefficient_matrix_e_cb5680c4" DOUBLE  -- Sample Density (# Of Measurements / # Of Coefficient Matrix Entries) (no Relevant Units),
  "relative_error_db_of_recovered_coefficients_using_the__b90ec398" DOUBLE  -- 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__de2d8ac9" DOUBLE  -- 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__ca68258d" DOUBLE  -- 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__e244b75e" DOUBLE  -- 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__0b441f62" DOUBLE  -- 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__c8687577" DOUBLE  -- 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_unit_283f9433" BIGINT  -- 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_unit_5eae09f0" DOUBLE  -- 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_unit_906fcbf9" DOUBLE  -- 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_unit_7c8caef1" DOUBLE  -- 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_unit_48705af0" DOUBLE  -- 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_unit_438eef56" DOUBLE  -- 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.
);