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Machine Learning for Rectangular Waveguide
Mode-Identification, Using 2D Modal Field Patterns
Brian Guiana and Ata Zadehgol
Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844–1023
Email: bguiana@uidaho.edu and azadehgol@uidaho.edu
Abstract—We apply machine learning (ML) techniques to
identify the modes in rectangular waveguides from images of
2D modal field patterns injected with uniform, exponential, cor-
related exponential, and Gaussian noise distributions. A binary
classifier is used to identify either transverse electric (TE) or
transverse magnetic (TM) modes, and a Multi-class classifier is
used to identify the mode numbers. Signal to noise ratios of 1,
0.1, and 0.01 are used to show the effectiveness of each model.
Results show accuracy scores up to 99.95%. Several examples
demonstrate that noisy modal patterns (unidentifiable to human
eyes) may be successfully classified by the ML model.
I. INTRODUCTION
Rectangular waveguides (RWG) are commonly used in
electromagnetic applications [1]–[3]. In a RWG with perfect
electric conductor (PEC) boundaries, analytical expressions
[1], [2] may be used to obtain the cross-sectional frequency-
domain field components; conversely, given an image of a
2D modal field pattern (magnitude and phase), with minimal
effort one may use the analytical expressions to determine the
modal information; i.e., TEm,n or TMm,n, and mode numbers
{m, n} ∈ Integers. However, if noise (due to measurement
or modeling errors) is added to the image, then the mode-
identification via simple (human) visual inspection may not
be feasible; e.g., Fig 3(c)-(d). We show that although modal-
identification by ML model becomes challenging for small
signal-to-noise ratio (SNR), it still outperforms detection by
visual inspection. In this paper, the modal field patterns are
modulated by random noise sources which are applied as
correlated and uncorrelated [4] noise to data from analytical
field components. We employ the Scikit-Learn [5] and Python
[6] packages and apply methods outlined in [7] to test the ML
classification models (MLCM).
II. METHODOLOGY AND FO RM UL ATIO N
We classify RWG modes into TE and TM modes using
a binary classifier, and identify mode numbers {m, n}with
a multi-class classifier. We use the K-Neighbors classification
model here, as it was shown to function well in [8] for MNIST
image recognition, where the binary classifier has two output
classes (or levels) and the multi-class classifier has ten output
levels. We use the distance option with four neighbors for the
classifier, placing weight on surrounding pixels inverse pro-
portionally to the distance from other pixels. Our experiments
assume typical K-band rectangular waveguides composed of
PEC sidewalls surrounding a good dielectric core (r≈4.0,
σ= 0 (S/m), and µ=µ0(H/m)) width a= 1.07 cm,
height b= 0.43 cm, and source frequency f= 60 GHz.
This setup allows modes above the fundamental to propagate
without loss through the waveguide, where the modes are
limited to TEmn and TMmn with 0≤m, n ≤3, excluding
m=n= 0. Assuming the field components are transverse
to ˆz, the resulting boundary value problem has analytical
solutions for all field components in each mode which may
be found in Table 3.2 in [1, Ch. 3].
A. Noise Figures
We use three uncorrelated noise distributions and one ex-
ponentially correlated noise distribution. Each of these are de-
scribed by their respective probability density function (PDF).
The uncorrelated noise images use uniform, exponential, or
Gaussian PDFs. The correlated noise images are generated
using the exponential PDF and correlation techniques in [9],
where the noise images are two dimensional (2D). Correlation
and spectral data for uncorrelated versus correlated noise
images are shown in Fig. 1.
shift along
x
10075 50 25 025 50 75100
shift along
y
100
75
50
25
025
50
75
100
Autocorrelation
0.0
0.2
0.4
0.6
0.8
1.0
Uncorrelated Noise
(a)
shift along
x
100 50 050 100
shift along
y
100
50
0
50
100
Autocorrelation
0.0
0.2
0.4
0.6
0.8
1.0
Correlated Noise
(b)
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20
Spatial Frequency (1/pixel)
10 1
100
101
102
103
FFT Value
Uncorrelated Noise
(c)
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20
Spatial Frequency (1/pixel)
10 1
100
101
102
103
Correlated Noise
(d)
Fig. 1: (a) Uncorrelated and (b) correlated noise autocorrela-
tion; (c) uncorrelated and (d) correlated noise spectrum.
The correlated noise images are generated automatically
with the Pyspeckle package [9]. The control image (with no
noise) and examples of noisy images are shown in Fig. 2,
where values have been normalized to be in [0,1].
0.00
0.22
0.43
height
(cm)
(a) No Noise
0.00
0.22
0.43
height
(cm)
(b) Uniform Noise
0.00
0.22
0.43
height
(cm)
(c) Exponential Noise
0.00
0.22
0.43
height
(cm)
(d) Gaussian Noise
0.000 0.258 0.553 0.812 1.070
width (cm)
0.00
0.22
0.43
height
(cm)
(e) Correlated Noise 0.2
0.4
0.6
0.8
1.0
|
Ex
| Normalized
Fig. 2: Magnitude of Exin the TE11 mode with each noise
figure at SNR=1.
III. RES ULTS A ND DISCUSSION
A. Data Generation and Selection
We use the Exand Eyfield components with a 30 ×30
pixel resolution. One noisy image is generated for each real
and imaginary component of Exand Ey(4 total per sample),
and each image is injected to have SNR={1,0.1,0.01}, where
smaller SNR values indicate more noise than signal. 10,000
samples were generated with random modes for each corner
plus a noiseless control (130,000 samples total). Magnitude
plots of Exfor each of the noise images at SNR=1 are shown
in Fig. 2, and the correlated noise images are shown at each
SNR target in Fig. 3.
0.00
0.22
0.43
height
(cm)
(a) No Noise: SNR=
0.00
0.22
0.43
height
(cm)
(b) Correlated Noise: SNR=1.0
0.00
0.22
0.43
height
(cm)
(c) Correlated Noise: SNR=0.1
0.000 0.258 0.553 0.812 1.070
width (cm)
0.00
0.22
0.43
height
(cm)
(d) Correlated Noise: SNR=0.01
0.2
0.4
0.6
0.8
1.0
|
Ex
| Normalized
Fig. 3: Magnitude of Exin the TE11 mode with correlated
noise figure at each SNR.
B. Training and Testing Classification Models
The accuracy scores are shown in Table I, where a score
of 1.0 indicates perfect detection, and where a score of 0.5
for the binary classifier and 0.1 for the multi-class classifier
indicates random guessing. The control and the SNR=1 results
show a perfect score, and the results at SNR=0.01 show
random guessing for both models. For example, with the
binary classifier we find the order of goodness with SNR=0.1
is (1) uniform, (2) exponential, (3) correlated, and (4) Gaussian
noise, where uniform noise is almost ignored, Gaussian noise
causes nearly random guessing, and the uncorrelated and cor-
related exponential noise images show scores nearly uniformly
spaced between random guessing and perfect scores. The order
TABLE I: Accuracy Scores of Classification Models
Binary Classifier Multi-class Classifier
SNR 1.0 0.1 0.01 1.0 0.1 0.01
Control 1.0 N/A N/A 1.0 N/A N/A
Uniform Noise 1.0 0.9985 0.4885 1.0 0.9995 0.1165
Exponential Noise 1.0 0.8150 0.5050 1.0 0.7055 0.1190
Gaussian Noise 1.0 0.5470 0.5085 1.0 0.2080 0.1135
Correlated Noise 1.0 0.6540 0.4970 1.0 0.4240 0.1175
of goodness could be the result of spectral composition in
the noise images. The K-neighbors classifier acts as a low-
pass filter (for noise), so low-frequency noise is more likely
passed through. Correlated noise has increased low-frequency
content, so we can expect the uncorrelated exponential noise
to outperform its correlated counterpart. However, the spectral
content of white noise should be nearly uniform across all
frequencies, thus further investigation may be necessary.
IV. CONCLUSION
Machine learning models based on K-neighbors were
trained and tested on RWG modal images with noise injected
at three different SNR levels. The results at SNR = 0.1 showed
that overall MLCM performance was poor for Gaussian noise,
marginally improved for correlated exponential noise, further
improved for uncorrelated exponential noise, and was almost
unaffected by uniform noise. Increasing the noise by two
orders-of-magnitude with SNR=0.01, the MLCM accuracy
was much worse. These SNRs were chosen for emphasis, but it
may not be common to see SNR<0.1in a laboratory environ-
ment. This means that for SNR ≥0.1, the machine learning
model can likely outperform simple visual identification of
RWG modes based on images of 2D modal field patterns.
ACKNOWLEDGMENT
This work was funded, in part, by the National Science
Foundation [10].
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