Hand Gesture Recognition based on Radar
Micro-Doppler Signature Envelopes
Moeness G. Amin
Center for Advanced Communications
Villanova, PA 19085, USA
Zhengxin Zeng, Tao Shan
School of Information and Electronics
Beijing Institute of Technology
Abstract—We introduce a simple but effective technique in
automatic hand gesture recognition using radar. The proposed
technique classiﬁes hand gestures based on the envelopes of
their micro-Doppler signatures. These envelopes capture the
distinctions among different hand movements and their corre-
sponding positive and negative Doppler frequencies which are
generated during each gesture act. We detect the positive and
negative envelopes separately, and form a feature vector of their
augmentation. We use the k-nearest neighbor (kNN) classiﬁer and
Manhattan distance (L1) measure, in lieu of Euclidean distance
(L2), so as not to diminish small but critical envelope values.
It is shown that this method outperforms both low-dimension
representation techniques based on principal component anal-
ysis (PCA) and sparse reconstruction using Gaussian-windowed
Fourier dictionary, and can achieve very high classiﬁcation rates.
Keywords—Hand gesture recognition; time-frequency repre-
sentations; micro-Doppler signature envelope.
Radar systems assume an important role in several areas of
our daily life, such as air trafﬁc control, speed enforcement
systems, and advanced driver assistance systems [1–3]. Re-
cently, radar has also become of increased interest for indoor
applications. In particular, human activity monitoring radar
systems are rapidly evolving with application that include gait
recognition, fall motion detection for elderly care and aging-
in-place technologies [4, 5].
Over the past decade, much work has been done in hu-
man motion classiﬁcations which include daily activities of
walking, kneeling, sitting, standing, bending, falling, etc. [6–
16]. Distinguishing among the different motions is viewed
as an inter-class classiﬁcation [6–13], whereas the intra-class
classiﬁcation amounts to identifying the different members of
the same class, e.g., classifying normal and abnormal gaits
[14–16]. There are two main approaches of human motion
classiﬁcations, namely those relying on handcrafted features
that relate to human motion kinematics [7–9, 14], and others
which are data driven and include low-dimension represen-
tations [6, 15], frequency-warped cepstral analysis , and
neural networks [10–12, 16].
The work of Mr. Zhengxin is funded by the International Graduate
Exchange Program of Beijing Institute of Technology, and was performed
while he was a Visiting Scholar at the Center for Advanced Communications,
In addition to classifying human motions, radars have been
recently used for gesture recognition which is an important
problem in a variety of applications that involve smart homes
and human-machine interface for intelligent devices [17–21].
The latter is considered vital in aiding the physically impaired
who might be wheelchair conﬁned or bed-ridden patients.
The goal is to enable these individuals to be self-supported
and independently functioning. In essence, automatic hand
gesture recognition is poised to make our homes more user
friendly and most efﬁcient through the use of contactless
radio frequency (RF) sensors that can identify different hand
gestures for instrument and household appliance control.
The same approaches employed for classifying human daily
activities can be applied for recognition of hand gestures using
the electromagnetic (EM) sensing modality. However, there is
an apparent difference between micro-Doppler signatures of
hand gestures and those associated with motion activities that
involve human body. Depending on the experiment and data
collection radar specs and setting, Micro-Doppler representa-
tions of hand gestures can be simple, limited to short time
duration and small bandwidth, and are mainly characterized
by their conﬁned power concentrations in the time-frequency
domain. On the other hand, the micro-Doppler signatures of
body motions are intricate, of multi-component signals, span
relatively longer time periods and assume higher Doppler
In this paper, we present a method to discriminate ﬁve
classes of dynamic hand gestures using radar micro-Doppler
sensor. These classes are swiping hand, hand rotation, ﬂip-
ping ﬁngers, calling and snapping ﬁngers. We begin with
many types of hand motions, and use the canonical angle
metric to assess the subspace similarities constructed from
their respective time-frequency distributions [22, 23]. Based
on the results, we group these motions into the ﬁve most
dissimilar classes. Two micro-Doppler features are extracted
from the data spectrograms. They correspond to the upper and
lower envelopes of the hand gesture micro-Doppler signatures.
The two envelopes implicitly capture, for each motion, the
positive-negative frequency differences, the time alignments
and misalignments of the peak positive and negative Doppler
frequencies, and the signature extent and occupancy over the
joint time and frequency variables.
We compare the proposed approach with that based on
PCA [6, 15] and on sparse reconstruction employing Gaussian-
windowed Fourier dictionary . In the latter, the classiﬁer
was applied to hand gesture data showing signatures com-
prising rather detached power concentrated time-frequency
regions The experimental results applied to our measured data
demonstrate that the proposed method outperform the above
two methods, and achieve a classiﬁcation accuracy higher than
The remainder of this paper is organized as follows. In Sec-
tion II, we present the extraction method of micro-Doppler sig-
nature envelopes and discusses the employed classiﬁer. Section
III describes the radar data collection and pre-processing of
hand gestures. Section IV gives the experimental results based
on the real data measurements. Section V is the conclusion of
II. HA ND GE ST UR E RECOGNITION ALGORITHM
A. Time-frequency Representations
Hand gestures generate non-stationary radar back-scattering
signals. Time-frequency representations (TFRs) are typically
employed to analyze these signals in the joint-variable do-
mains, revealing what is referred to as micro-Doppler signa-
tures. A typical technique of TFRs is the spectrogram. For a
discrete-time signal s(n)of length N, the spectrogram can be
obtained by taking the short-time Fourier transform (STFT)
S(n, k) =
where n= 0,· · · , N −1is the time index, k= 0,· · · K−1
is the discrete frequency index, and Lis the length of the
window function h(·).
B. Extraction of the Micro-Doppler Signature Envelopes
We select features speciﬁc to the nominal hand gesture
local frequency behavior and power concentrations. These
features are the upper and lower envelope in the spectrograms.
The envelopes attempt to capture, among other things, the
maximum positive frequency and negative frequencies, length
of the event and its bandwidth, the relative emphases of the
motion towards and away from the radar, i.e., positive and
negative Doppler frequencies. In essence, the envelopes of
the signal power concentration in the time-frequency domain
may uniquely characterize the different hand motions. The
envelopes of the micro-Doppler signature can be determined
by an energy-based thresholding algorithm . First, the
effective bandwidth of each gesture frequency spectrum is
computed. This deﬁnes the maximum positive and negative
Doppler frequencies. Second, the spectrogram S(n, k)is di-
vided into two parts, the positive frequency part and the
negative frequency part. The corresponding energies of the two
parts, EU(n)and EL(n), at slow-time are computed separately
These energies are then scaled to deﬁne the respective thresh-
olds, TUand TL,
TU(n) = EU(n)·σU(4)
TL(n) = EL(n)·σL(5)
where σUand σLrepresent the scale factors, both are less
than 1. These scalars can be chosen empirically. However, an
effective way for their selections is to maintain the ratio of
the energy value to the threshold value constant over all time
samples. For the upper envelope, this ratio can be computed
by ﬁnding both values at the maximum positive Doppler
frequency. Once the threshold is computed per equation (4),
the upper envelope is then found by locating the Doppler
frequency for which the spectrogram assumes equal or higher
value. Similar procedure can be followed for the lower enve-
lope. The upper envelope eU(n)and lower envelope eL(n),
are concatenated to form a long feature vector e= [eU, eL].
We apply proper classiﬁers based on the envelope features
extracted from the spectrograms. The kNN and Support vector
Machine (SVM) are among the most commonly used classi-
ﬁers in pattern recognition which are used in this paper. In
particular, the kNN is a simple machine learning classiﬁcation
algorithm. For each test sample, the algorithm calculates the
distance to all the training samples, and selects the kclosest
training samples. Classiﬁcation is performed by assigning the
label that is most frequent among these samples . Clearly,
the best choice of kwould depend on the data. In this work,
kis set to 1. Four different distance metrics are considered,
namely, the Euclidean distance, the Manhattan distance ,
the Earth Mover’s distance (EMD)  and the modiﬁed
Hausdorff distance (MHD) .
SVM is a supervised learning algorithm . It exhibits
clear advantages in nonlinear and high dimension problems.
III. HAND GES TU RE SUBCLASSES
The data analyzed in this paper was collected in the Radar
Imaging Lab at the Center for Advanced Communications,
Villanova University. The radar system used in the experi-
ment generates continuous wave, with carrier frequency and
sampling rate equal to 25 GHz and 12.8 kHz, respectively.
The radar was placed at the edge of a table. The hand was
approximately 20 cm away from radar at zero angle, and the
arm remained ﬁxed as much as possible during each gesture
As depicted in Fig.1. The following 15 hand gestures were
conducted: (a) Swiping hand from left to right, (b) Swiping
hand from right to left, (c) Swiping hand from up to down,
(d) Swiping hand from down to up, (e) Horizontal rotating
hand clockwise, (f) Horizontal rotating hand counterclockwise,
(g) Vertical rotating hand clockwise, (h) Vertical rotating
hand counterclockwise, (i) Opening hand, (j) Flipping ﬁngers,
(k) Clenching hand, (l) Calling, (m) Swipe left with two
ﬁngers, (n) Snapping ﬁngers, (o) Pinching index. Four persons
participated in the experiment. Each hand gesture was recorded
over 8 seconds to generate one data segment. The recording
was repeated for 5 times. Each data segment contained 2 or
3 individual hand motions, and a 1 second time window is
applied to capture the individual motions. As such, repetitive
motions and associated duty cycles were not considered in
classiﬁcations. In total, 755 segments of data for 15 hand
gestures were generated.
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
(k) (l) (m) (n) (o)
Fig. 1. Illustrations of 15 different hand gestures.
Fig. 2 shows examples of spectrograms and corresponding
envelopes for different hand gestures. The employed sliding
window h(·)is rectangular with length L=2048 (0.16 s),
and Kis set to 4096. It is clear that the envelopes can well
capture the salient features of the respective spectrograms. It
is also evident that the micro-Doppler characteristics of the
spectrograms are in agreement and consistent with each hand
motion kinematics. For example, for the hand gesture ‘Swiping
hand’, the hand moves closer to the radar at the beginning
which causes the positive frequency, and then moving away
from the radar which induces the negative frequency.
Observing the spectrograms in Fig. 2, it is noticeable that
similar motions generate similar signatures. To mathematically
conﬁrm these resemblances, we consider sub-grouping the 15
hand gestures using the Canonical correlation measure . In
this case, the spectrograms are converted to gray-scale images
with the size 100 ×100, and then vectorized with the size
Deﬁne matrix Xcontains Mvectorized images Si, i =
1,· · · , M of a speciﬁc hand gesture,
The d-dimensional subspace of a speciﬁc hand gesture can
be obtained by taking PCA of X. Suppose Φ1and Φ2are
two d-dimensional linear subspaces, the canonical correlations
of the two subspaces are the cosines of principal angles, and
are deﬁned as :
cos θi= max
(a) (b) (c) (d)
(e) (f) (g) (h)
(k) (l) (m)
Fig. 2. Spectrograms and corresponding envelopes of 15 different hand
subject to ||u|| =||v|| = 1, uiTuj=viTvj= 0, i 6=j. Let U
and Vdenote unitary orthogonal bases for two subspaces, Φ1
and Φ2. The singular value decomposition (SVD) of UTVis
The canonical correlations are the singular values Λ, i.e.,
cos(θi) = λi, i = 1,· · · , d. The minimum angle is used
to measure the closeness of two subspaces. Table I shows
the canonical correlations coefﬁcients, from which we can
clearly see the similarities between the different hand gestures;
larger coefﬁcient indicates the two hand gestures are more
similar. The red part of the table indicates the coefﬁcient
exceeds 0.9, and the yellow part means the coefﬁcient is over
0.85. According to the Table numbers, we group the 15 hand
gestures into 5 Class. Class I is the gesture ‘Swiping hand’
which contains motions (a), (b), (c) and (d). Class II represents
the gestures ‘Hand rotation’ which contains motions (e), (f),
(g) and (h). The gesture ‘Flipping ﬁngers,’ which involves
motions (i) and (j), makes Class III. Class IV is the gesture
‘Calling,’ which has motions (k), (l) and (m). The last Class
V is the gesture ‘Snapping ﬁngers’; it has motions (n) and
(o). It is important to note that other similarity measures [*]
can be applied, in lieu of the canonical correlation. However,
we found the canonical correlation most consistent with the
IV. EXPERIMENTAL RESU LTS
In this section, all 755 data segments are used to validate the
proposed method where 70% of the data are used for training
and 30% for testing. The classiﬁcation results are obtained
TABLE I. CANONICAL CORRELATIONS COEFFI CIE NT S
b c d e f g h i j k l m n o
a0.79 0.83 0.91 0.70 0.75 0.79 0.84 0.69 0.66 0.78 0.77 0.76 0.77 0.81
b0 0.92 0.80 0.70 0.68 0.82 0.82 0.65 0.61 0.78 0.82 0.83 0.73 0.60
c0 0 0.76 0.64 0.59 0.85 0.88 0.72 0.65 0.80 0.80 0.82 0.76 0.69
d0 0 0 0.61 0.68 0.81 0.75 0.57 0.55 0.78 0.67 0.60 0.63 0.64
e0 0 0 0 0.86 0.70 0.75 0.59 0.66 0.56 0.72 0.66 0.72 0.71
f0 0 0 0 0 0.78 0.83 0.70 0.70 0.67 0.73 0.70 0.78 0.79
g0 0 0 0 0 0 0.85 0.67 0.67 0.78 0.66 0.71 0.74 0.73
h0 0 0 0 0 0 0 0.55 0.60 0.72 0.67 0.61 0.71 0.71
i0 0 0 0 0 0 0 0 0.87 0.75 0.61 0.67 0.76 0.74
j0 0 0 0 0 0 0 0 0 0.68 0.61 0.68 0.83 0.73
k0 0 0 0 0 0 0 0 0 0 0.94 0.94 0.83 0.76
l0 0 0 0 0 0 0 0 0 0 0 0.93 0.73 0.66
m0 0 0 0 0 0 0 0 0 0 0 0 0.77 0.63
n0 0 0 0 0 0 0 0 0 0 0 0 0 0.82
by 1000 Monte Carlo trials. Three different automatic hand
gesture approaches are compared with the proposed method.
These are: 1) the empirical feature extraction method; 2) the
PCA-based method ; 3) the sparse reconstruction-based
A. Empirical Feature Extraction Method
Three empirical features are extracted from the spectro-
grams to describe the hand gestures motions, namely the
length of the event, the ratio of positive-negative frequency
and the signal bandwidth. Fig. 3 is an example showing these
Fig. 3. Empirical feature extraction.
1) Length of the event T:This describes the effective time
duration to perform each hand gesture,
where tsand terepresent the start time and the end time of a
single hand gesture, respectively.
2) Ratio of positive-to-negative peak frequencies R:This
feature is obtained by ﬁnding ratio of the maximum positive
frequency value,fp, and maximum negative frequency value,
where |·| is the absolute function.
3) Bandwidth Bw:This is a measure of the the signal
The scatter plot of the above extracted features is shown in
Fig. 4. Table II depicts the nominal behavior of these values
over the different classes considered. When using kNN-L1 as
the classiﬁer, the recognition accuracy based on these features
is only 68% with the confusion matrix shown in Table II.
Fig. 4. Scatter plot of three extracted empirical features.
TABLE II. CONFUSION MATRIX YIE LDE D BY EMPIRICAL FE ATURE EX-
TR ACTI ON ME THO D
I II III IV V
I66.79% 13.80% 4.08% 9.18% 6.15%
II 20.04% 64.65% 3.53% 4.88% 6.90%
III 9.94% 5.59% 76.53% 0.03% 7.91%
IV 19.04% 6.74% 0.65% 71.79% 1.78%
V12.03% 10.96% 12.28% 11.59% 53.14%
B. Proposed Envelope-based Method
As discussed in Section II, the extracted envelopes are fed
into the kNN classiﬁer, with different distance measures, and
SVM classiﬁer. The recognition accuracy are presented in
Table III. It is cleat that the kNN classiﬁer based on L1
distance achieves the highest accuracy, over 96%, followed
by those employing the modiﬁed Hausdorff distance and
the Euclidean distance. Different from other distances, the
L1 distance attempts to properly account for small envelope
values. The confusion matrix of the kNN classiﬁer based on
the L1 distance is shown in Table IV, from which we can ﬁnd
that Class III and Class IV are most distinguishable with the
accuracy over 98%.
TABLE III. RECOGNITION AC CUR ACY W ITH DI FFE REN T TYP ES OF CL AS -
TABLE IV. CONFUSION MATRIX YIE LD ED BY ENVELOPE ME THO D
BAS ED O N kNN-L1 CLAS SI FIER
I II III IV V
I95.23% 3.17% 0.14% 1.46% 0
II 3.03% 95.39% 0.01% 0.06% 1.51%
III 0.07% 0 99.01% 0.28% 0.64%
IV 0.61% 0 1.16% 98.21% 0.02%
V0 2.31% 2.61% 2.83% 92.25%
C. PCA-based Method
For the PCA-based method, each sample represents a spec-
trogram image of 100 ×100 pixels. The number of principal
TABLE V. C ONFUSION MATRI X YIEL DE D BY PCA-BA SED ME THO D WI TH
I II III IV V
I89.50% 3.02% 0.67% 6.80% 0.01%
II 2.92% 94.83% 0 1.45% 0.80%
III 2.85% 1.23% 94.42% 0 1.50%
IV 5.24% 0.25% 1.37% 93.14% 0
V3.24% 8.14% 5.03% 1.83% 81.76%
components dis determined by the eigenvalues. Fig.5 shows
how the classiﬁcation accuracy changes with d, with the
recognition rate increases as dincreases. However, there is
no signiﬁcant improvement of the recognition accuracy past
d= 30. Table V is the confusion matrix using 30 eigenvalues.
Although the PCA method can achieve an overall accuracy of
92.71%, it is clearly outperformed by the proposed method.
Fig. 5. Performance of PCA with different number of principal components.
D. Sparsity-based Method
The features used for this method are the time-frequency
trajectories. Details of the sparsity-based method can be found
in . The trajectory consists of three parameters, namely
the time-frequency position (ti, fi), i = 1,· · · , whereP and
the intensity Ai,Pis the sparsity level that is set to 10
in this paper. Hence, each sample contains 30 features. The
spectrograms of reconstructed signals and the Plocations
of time-frequency trajectory are plotted in Fig. 6 and Fig.
7. In the training process, the K-means algorithm is used
to cluster a central time-frequency trajectory . In the
testing process, the kNN classiﬁer based on the modiﬁed
Hausdorff distance is applied to measure the distance between
the testing samples and central time-frequency trajectories.
The corresponding confusion matrix is presented in Table VI.
The overall recognition accuracy was found to be only about
70% when applied to our data.
TABLE VI. C ONFUSION MATRIX YIELD ED BY SPARSITY-BASED ME TH OD
I II III IV V
I71.72% 11.36% 1.45% 11.74% 3.73%
II 10.95% 81.29% 2.57% 0.28% 4.91%
III 7.40% 2.10% 83.63% 0.69% 6.18%
IV 16.04% 6.52% 1.22% 74.14% 2.08%
V6.65% 15.05% 9.96% 10.02% 58.32%
We introduced a simple but effective technique for auto-
matic hand gesture recognition based on radar micro-Doppler
(a) (b) (c) (d)
(e) (f) (g) (h)
(k) (l) (m)
Fig. 6. Spectrograms of reconstructed signals with P= 10.
(a) (b) (c) (d)
(e) (f) (g) (h)
(k) (l) (m)
Fig. 7. Locations of time−frequency trajectories with P= 10.
signature envelopes. An energy-based thresholding algorithm
was applied to separately extract the upper (positive) envelope
and the lower (negative) envelope of the signal spectrogram.
We used the canonical correlation coefﬁcient to group 15
hand gestures into ﬁve different classes. The members of
each class have close signature behavior. The extracted en-
velopes were concatenated and inputted to different types
of classiﬁers. It was shown that the kNN classiﬁer based
on L1 distance achieves the highest accuracy and provided
over 96 percent classiﬁcation rate. The experimental results
also demonstrated that the proposed method outperformed
the lower dimensional PCA-based method, the sparsity-based
approach using Gaussian-windowed Fourier dictionary, and
existing techniques based on handcrafted features.
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