Correlation-Matrix Approaches for Testing Wireless Devices in Reverberation Chambers

Description

The data correspond to the paper Practical Correlation-Matrix Approaches for Standardized Testing of Wireless Devices in Reverberation Chambers. Abstract: We extend the autocorrelation-based approaches currently used in standards to full correlation matrix-based approaches in order to identify correlation between both spatially adjacent and non-adjacent samples in reverberation-chamber measurements. We employ a scalar metric that allows users to identify the number of effectively uncorrelated samples in new types of stirring sequences. To make these approaches practical and enhance their accuracy, we implement a thresholding technique that retains correlation related to important aspects of chamber configuration such as loading and undermoded conditions. We develop a method to propagate uncertainty in the complex correlation coefficients through to the number of effective samples for a given reverberation-chamber set-up by use of a bootstrap technique that is accurate even for highly skewed distributions of correlation coefficients. We further apply this method in a sensitivity studyregarding the choice threshold value. Agreement with existing approaches in determining the number of effectively uncorrelated samples is presented for a measurement example where spatially adjacent samples are utilized. Examples are then illustrated for non-spatially-adjacent correlated samples at microwave and millimeter-wave frequencies.

Resources

Name Format Description Link
0 Data from one row of the correlation matrix of |r^corr_ij |^2 for Case 1, the unswitched case. https://data.nist.gov/od/ds/mds2-2868/Fig12_CorrMatrix_1Row_AbsSq_Dir1_650MHzFc_500MHzBW.xlsx
47 2868_README.txt https://data.nist.gov/od/ds/mds2-2868/2868_README.txt
0 Bootstrapping approach illustrating the sensitivity of Neff to choice of threshold. The 10,000 bootstrap samples were randomized with choices of threshold ranging from 0.34 to 0.40, along with the randomization as in Fig. 5, with a center frequency of 3.55 GHz. The data for the histograms are included along with the bootstrap metrics at several center frequencies. https://data.nist.gov/od/ds/mds2-2868/Fig7_Neff_Boot_w_replace_wthresh_Nb10000_fc3550_HistData.zip
0 360 × 360 correlation matrices of |r_ij|^2 and zoom-in on 50 × 50 segments prior to thresholding, computed over two different frequency ranges with the Full Correlation Matrix approach (a) 750 MHz - 1.15 GHz and (b) 5.55 GHz - 5.95 GHz. There are more significantly correlated samples in the lower bands, resulting in a smaller value of Neff. https://data.nist.gov/od/ds/mds2-2868/Fig8_CorrelationMatrices_950MHz_5550MHz.zip
0 The number of effective samples as a function of frequency for the IEC/3GPP approach, Circular-Shift Matrix approach and Full Correlation Matrix approach. Plots show three switching cases. Data include four switching cases from Table 2 in the paper: Case 1 (not switched), Case 3 (200 ms switching time), Case 4 (500 ms switching time) and Case 5 (1 s switching time). The IEC/3GPP overestimates the number of effective samples for the unswitched case because it cannot assess the non-spatially adjacent samples. https://data.nist.gov/od/ds/mds2-2868/Fig13_Neff_4Cases.zip
0 The number of effective samples Nind computed with the IEC/3GPP approach as a function of frequency for an unloaded chamber. One file has the values at individual frequencies. The other file has the values averaged over 400 MHz. https://data.nist.gov/od/ds/mds2-2868/Fig11_NeffvsFreq_3GPP_0Abs.zip
0 The link between the distribution of correlation coefficients, the threshold value and Neff. Left axis: Histogram of |rij |^2. Right axis: Neff as a function of threshold value. (a) Unloaded chamber (CBW = 613 kHz); (b) chamber loaded with five RF absorbers (CBW = 3.3 MHz); (c) chamber loaded with eleven RF absorbers (CBW = 6.7 MHz); (d) five absorber case with 180 stirring-sequence samples obtained with a wider spatial step. https://data.nist.gov/od/ds/mds2-2868/Fig6_Histogram_rij_And_NeffwThr_fc5550_HistData.zip
0 Number of effective samples Neff for the three methods discussed in Section II for the case where correlation between stirring-sequence samples is adjacent or near-adjacent. Three rotational stirring mechanisms were moved simultaneously in 1-degree steps. Measurements were performed with three different amounts of RF absorber present in the chamber. The threshold value was rlim = 0.3082. Data in the attached files includes Neff values for the Circular-Shift Correlation Matrix approach and the Full Correlation Matrix approach with and without thresholding. https://data.nist.gov/od/ds/mds2-2868/Fig9_NISTData_Neff_AllAbs_5550MHzMax_400MHzBW.zip
0 Estimate of Neff using all three approaches and the bootstrap 95% confidence interval for the Full Correlation Matrix approach as a function of frequency for a millimeter-wave-band measurement. File "Fig14_Neff_mmWave_AllMethods_2Abs_600MHzBW.xlsx": Neff for two-absorber case averaged or computed over 600 MHz. File "Fig14_Boot_fc28GHzto39p9GHz_601from601_Nb1000_Metrics.xlsx": Bootstrap metrics including the 95% confidence interval for N^corr_eff with 1000 bootstrap samples. https://data.nist.gov/od/ds/mds2-2868/Fig14_Neff_And_Uncert_mmWave_AllMethods_2Abs_600MHzBW.zip
8 Autocorrelation for a stirring sequence with an antenna switch and mechanical mode stirrers. https://data.nist.gov/od/ds/mds2-2868/Fig2b_spiky_autocorrelation.csv
0 Bootstrapping approach to approximate the uncertainty in the estimation of Neff. 10,000 bootstrap samples computed from 400 complex S-parameter measurements of the stirring sequence are given for center frequencies between 1.55 GHz and 5.55 GHz. The center frequency of 3.55 GHz is shown in Fig. 5. Data include Excel files with the histogram data and the bootstrap metrics. https://data.nist.gov/od/ds/mds2-2868/Fig5_Boot_w_replace_Nb10000_1550To5550_HistData.zip
53 Thresholded (top black curves) and unthresholded (bottom red curves) values of Neff plotted as a function of frequency. Curves were computed using the Full Correlation Matrix approach for three correlation-matrix calculation bandwidths. The unthresholded values significantly underestimate Neff. https://data.nist.gov/od/ds/mds2-2868/Fig4b_NeffvsFreq_NoThr_WThr_FullCorr_0Abs.xlsx
0 Thresholded (top black/blue curves) and unthresholded (bottom red/black curves) values of Neff plotted as a function of frequency. Curves were computed using the Circular-Shift Matrix approach. The thin (blue and red) lines represent the computed value of Neff at each frequency, and the thicker (black) line is the average taken over 400 MHz. https://data.nist.gov/od/ds/mds2-2868/Fig4a_NeffvsFreq_NoThr_WThr_CircShiftCorr_0Abs.zip
0 IEC/3GPP threshold rlim that compensates for the use of a finite number of samples in determining the number of uncorrelated samples in reverberation-chamber measurements. https://data.nist.gov/od/ds/mds2-2868/Fig3_rlim_variation.csv
0 Number of effective samples N^corr_eff and the 95% confidence interval as a function of frequency for the data from Fig. 9, as determined from the bootstrap method described in Section II.D. 10,000 bootstrap samples were used to generate the data. The confidence intervals are below 10 samples except for the rapid change in N^corr_eff for the zero-absorber case. https://data.nist.gov/od/ds/mds2-2868/Fig10_Boot_w_replace_Nb10000_1050To5550_Metrics.zip
8 Autocorrelation curves for a stirring sequence with only mechanical mode stirrers, measured at three different frequencies. https://data.nist.gov/od/ds/mds2-2868/Fig2a_normal_autocorrelation_different_peak_widths_diff_freqs.csv
0 Unthresholded correlation matrix for a large reverberation chamber loaded with two RF absorbers (CBW = 4.0 MHz): File Fig15a: Correlation matrix and zoom-in on 100 samples of the correlation matrix of |r^corr_ij |^2 computed over a 600 MHz bandwidth. Files Fig15b: One row of the correlation matrix of |r^circ_ij |^2 computed at three individual frequencies. Files Fig15c: One row of the correlation matrix of |r^corr_ij |^2 computed at three center frequencies over a 600 MHz bandwidth. https://data.nist.gov/od/ds/mds2-2868/Fig15abc_CorrMatrix_mmWave_2Abs_28p4GHz.zip
0 Matlab script and NIST-measured complex S-parameter data used to compute the results in Fig. 9 with the Full Correlation Matrix approach. The script plots Neff as a function of frequency, the correlation matrix, and a histogram of the correlation coefficients. The script can be modified by users for their own data. https://data.nist.gov/od/ds/mds2-2868/Fig9_MatlabScript_FullCorrMatrix.zip

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  • cellular-device-measurements-metrology-for-wireless-systems-millimeter-wave-metrology-millimete

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