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All figures (14)
Fig. 5: Plot of the energy function W (f) for measurements derived from a noisy Doppler tone at 1.4567 GHz over (a) the entire range of allowable frequencies and (b) frequencies close to the true CF. In (a) we see that the energy functional is clearly maximized in an area near the true CF, and (b) shows that the maximum of the energy function occurs at 1.4571 GHz. For this example, we used a total of 3315 Nyquist samples with a sampling rate of 5 GHz, so our intrinsic frequency resolution is on the order of 5 GHz/3315 ≈ 1.5 MHz. The estimate of the carrier frequency is well within this resolution.
TABLE II: Detection performance as a function of the interferer strength (1 RMPI Samp. = 1/fADC = 10.4 ns).
TABLE IV: Detection rate and standard deviation of the parameter estimate errors as a function of pulse lengths (1 Frame = 1/fADC = 10.4 ns).
Fig. 13: Parameter estimation errors for (a) CF, (b) TOA, and (c) TOD over 686 trials.
TABLE III: Detection rate and standard deviation of the parameter estimate errors as a function of pulse amplitudes (1 Frame = 1/fADC = 10.4 ns).
Fig. 6: Plot of the energy function E(τ) for measurements derived from a noisy Doppler tone at 1.4567 GHz arriving at Nyquist sample n = 3028 over (a) the entire range of sample indices and (b) sample indices close to the true TOA. In (a) we see that the energy functional is clearly maximized in an area near the true TOA, and (b) shows that the maximum of the energy function occurs at n = 3030. Since the sampling rate for this example is 5 GHz, this corresponds to an error of 400 ps.
Fig. 7: Fraction of measurement energies that are explained by frequencies up to 2.5 GHz for the case where (a) there is a 1.581 GHz tone and noise present and (b) there is only noise present. The noise energy is equally spread out over the band, where the tone energy is concentrated at one frequency.
Fig. 11: Assembled RMPI IC/Digitizer Interface. The board is 5 inches × 5 inches. The ADC board has 4 12 bit ADCs with output bits routed to 4 data-connectors that are acquired with a Logic Analyzer
TABLE I: Maximum, minimum, and standard deviation of estimation errors for CF, TOA, and TOD over 686 trials (1 Frame = 1/fADC = 10.4 ns is the length of one integration window).
Fig. 12: Block Diagram of RMPI Test Setup
Fig. 10: Stages of the pulse detection and parameter estimation algorithm for overlapping pulse data: (a) source pulses; the pulse heights indicate their amplitude and the color of the pulse is reflective of the CF of the pulse, with red closer to 2.5 GHz and blue closer to 0 Hz; (b) CF estimates for blocks using 5 RMPI samples; (c) segments detected based on consistent CF estimates for blocks of size 5 with no phase or amplitude estimation; (d) CF estimates for blocks of size 9; (e) segments detected based on consistent CF estimates for blocks of size 9 with no phase or amplitude estimation; (f) the merged segments; (g) the merged segments after the second pass is completed; (h) the detected pulses with refined estimates of their parameters.
Fig. 8: Carrier frequency estimates and measurement energy percentages for block shifts of RMPI measurements. In this simulation, several puretone pulses are present at various times. The blocks corresponding to RMPI samples that cover the time support of the pulse contain consistent CF estimates which account for a reasonably large portion of the RMPI measurement energy. When pulses are absent, the CF estimates are erratic and account for considerably less energy in the measurements.
Fig. 9: Fraction of measurement energies that are explained by frequencies up to 2.5 GHz for the case where (a) no nulling is used and there is strong interfering signal between 1.976 and 2.026 GHz and (b) the nulling operator is used to cancel out the interfering band. The nulling operator allows us to estimate the CF of the underlying tone, which is 1.367 GHz. In (b) the energy in the interfering band has virtually disappeared.
Fig. 4: RMPI IC die photo. Die size is 4.0 mm ×4.4 mm.
Journal Article
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DOI
•
A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition
[...]
Juhwan Yoo
1
,
C. Turnes
2
,
E. B. Nakamura
3
,
C. K. Le
3
,
Stephen Becker
1
,
Emilio A. Sovero
3
,
Michael B. Wakin
4
,
Michael C. Grant
1
,
Justin Romberg
2
,
Azita Emami-Neyestanak
1
,
Emmanuel J. Candès
5
- Show less
+7 more
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Institutions (5)
California Institute of Technology
1
,
Georgia Institute of Technology
2
,
Northrop Grumman Corporation
3
,
Colorado School of Mines
4
,
Stanford University
5
24 Sep 2012
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IEEE Journal on Emerging and Selected Topics in Circuits and Systems