When Magnitude Suffices: Reconstructing Time-Domain-Gated Microwave Signals Without Phase on a Thoracic Phantom
Authors: Maciej Cichoń, Patrycja Gołaś, Maksymilian Bartosik, Angelika Walczak, Agata Bielecka-Dąbrowa, Maciej Ślot
Organizations: Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź, Poland · Polish Mother’s Memorial Hospital Research Institute, Rzgowska 281/289, 93-338 Łódź, Poland
Time-domain gating separates the arrivals that form a microwave S-parameter measurement. It requires the measurement of complex values, so this application almost always uses a vector network analyzer (VNA). We show that, on one calibrated measurement configuration, the gated magnitude the VNA would give can be reconstructed from a magnitude-only sweep of a spectrum analyzer with a tracking generator (SA). We select the gate center for separability of the measured states, correct each instrument once by a per-bin subtraction of a reference state, and train a fully connected network on sweeps from both instruments. The test object is a torso phantom with lung-shaped compartments whose filling takes eleven dielectric states, each held out in turn. On S11 the reconstruction from SA input reaches a shape error of 0.08 dB2 with a state ordering of 0.81. This matches the reconstruction from VNA input. On S21 it reaches 0.82 dB2 and keeps the ordered groups of the states. An explicit phase prediction performs much worse, because gating needs the phase to about 0.2 rad RMS. Across eleven measurement configurations the dependence of phase on magnitude is strong for reflection and weak for transmission. This explains the difference between S11 and S21. Where the magnitude carries enough of the phase, a scalar instrument gives the gated response without any phase measurement after installation. On the open UM-BMID breast data set, with whole phantoms held out, the shape error of the network is 30 percent lower than that of a per-bin linear map.
Figures & tables
Fig. 1: Measurement phantom and setup. (a) Schematic of the phantom, top view. (b) Prepared measurement phantom, top view. (c) Measurement system, side view. (d) Lung-shaped compartments with positioning elements.
Step
Exchanged (mL)
ε′ at 2 GHz
0
0
78.0
1
100
72.9
2
200
68.4
3
300
64.5
4
400
61.0
5
500
58.0
Table 1: Lung-compartment filling steps and nominal real permittivity at 2 GHz.
Fig. 2: S21 , gated shape error when the true magnitude is gated with a substitute phase, against gating with the true phase. The dashed line marks the direct magnitude-to-gated model at its within-VNA median over the held-out states.
Fig. 3: S11 , gated shape error when the true magnitude is gated with a substitute phase, against gating with the true phase, as in Fig. 2 . The dashed line marks the direct magnitude-to-gated model at its within-VNA median over the held-out states (0.017 dB 2 ).
Fig. 4: S11 per-state means. The left panel is the VNA-gated target; the right panel is the reconstruction from SA input with the full method (training on both instruments, ordering loss, smoothed).
Fig. 5: S21 per-state means, same display as Fig. 4 . The three groups of dielectric states and their order are preserved across the change of instrument.
Fig. 6: S21 per-state means, same display as Fig. 5 ; VNA-gated target left, reconstruction from SA input under training on VNA sweeps only right, ordering −0.01 .
Fig. 7: S11 per-state means, same display as Fig. 4 ; VNA-gated target left, reconstruction from SA input under training on VNA sweeps only right, ordering 0.59.
S-param.
Training
VNA shape
VNA ρ
SA shape
SA ρ
S11
VNA only
0.037
0.90
0.243
0.59
S11
both, plain loss
0.047
0.87
0.076
0.82
S11
both, ordering loss
0.047
0.88
0.082
0.81
S21
VNA only
0.052
0.86
0.78
−0.01
S21
both, plain loss
0.069
0.84
0.99
0.25
S21
both, ordering loss
0.061
0.86
0.82
0.28
Table 2: Results with one dielectric state held out at a time. Shape error in dB 2 and ordering as Spearman ρ , evaluated on VNA input and on SA input. The plain loss is per-bin mean-squared error alone.
Method
0.5 ns gate
1.0 ns gate
Ordering ρ
reference curve
8.7
13.1
−0.8
per-bin linear map
2.5
4.6
1.0
network (this work)
1.8
3.8
1.0
minimum phase, then gate
67
66
−0.8
stored reference, learned quadrature, then gate
2.2
4.6
1.0
Table 3: Open breast data set with whole phantoms held out. Median shape error in dB 2 of the held-out sweeps of UM-BMID generation two, five folds over 66 phantoms, for two gate widths. Ordering of the four density classes as Spearman ρ at the 0.5 ns gate.
S-param.
Regime
n
dCor
CV R2
S11
within (1 config.)
275
1.00
0.95
S11
across, combined
6776
0.83
0.97
S11
across, mean removed
6776
0.56
0.86
S21
within (1 config.)
275
0.75
0.64
S21
across, combined
6776
0.68
0.52
S21
across, mean removed
6776
0.60
0.47
Table 4: Magnitude-phase dependence. Distance correlation (dCor) and mean cross-validated R2 of phase on magnitude, with detrended phase. Rows per S-parameter: the single configuration; ten configurations combined; ten configurations combined with each configuration’s per-bin mean subtracted.
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Ene Meco, Ahmet Enis Cetin
Dept. of Electrical and Computer Engineering, University of Illinois at Chicago, IL, 60607, USA
Neural networks outperform classical GCC-PHAT for Time-Difference-of-Arrival (TDOA) estimation in noise and reverberation, yet their internal strategy remains unexplored. To uncover it, we turn GCC-PHAT's mathematical steps into diagnostic targets, probing hidden layers of three architectures (MLP, CNN, Transformer) and complementing with gradient attribution and causal frequency masking. We find that cross-power computation consistently emerges across all architectures and conditions, while PHAT whitening, the defining step of GCC-PHAT, fails to emerge. Instead, networks learn a magnitude-aware frequency weighting that preserves per-frequency reliability information discarded by PHAT. This makes PHAT an information bottleneck: removing it from both classical and neural GCC pipelines improves performance under additive noise. On real-world reverberant data, PHAT remains the best classical weighting, but end-to-end networks achieve lower error by learning data-adaptive weighting.
Yaozhong Kang, Jiang Wang, Runwu Shi +3
Department of Systems and Control Engineering, Institute of Science Tokyo, Japan
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