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IEEE INTERNET OF THINGS JOURNAL,XX,XX 1
Single Sensor to Estimate DOA with Programmable
Metasurface
Mingtuan Lin, Ming Xu, Xiang Wan, Hanbing Liu, Zhaofeng Wu,
Jibin Liu, Bowen Deng, Dongfang Guan, Senior Member, IEEE, Song Zha
Abstract—With small sampling length, a novel direction of ar-
rival (DOA) estimation method based on a single programmable
metasurface sensor is proposed in this paper. Serving as a physi-
cal random sampling receiver, a dynamic metasurface generates
series of random radiation patterns to sense the incident signals,
which is subsequently processed by the compressive sensing
orthogonal matching pursuit (OMP) algorithm to recover the
DOA information. Mathematical model of DOA estimation is
firstly built for theoretical analyses. Furthermore, numerical
simulations are investigated with extensive performance analyses.
In comparison with metasuface-based beam-scanning method,
metasurface-based compressive sensing for DOA estimation has
superior performance with smaller sampling length. Finally, a
proof-of-concept experiment is made to verify the feasibility
of programmable metasurface for DOA estimation. Compared
to other traditional estimation techniques that require multiple
channels, the programmable metasurface can achieve estimation
with only a single channel and small sampling length.
Index Terms—Compressive sensing (CS), direction of arrival
(DOA), internet of things (IoT), metamaterial, metasurface, or-
thogonal matching pursuit (OMP), programmable metasurface.
I. INT ROD UC TI ON
Direction of arrival (DOA) estimation, as one of the impor-
tant techniques for array signal processing, has been always
an important topic for the industrial and academic communi-
ties. For example, the satellite communications on-the-move
(SOTM) [1], providing seamless connectivity in both civilian
and tactic communications, requires the DOA estimation as
the prior information for forming a highly directive beam in
the direction of source to strengthen the weak signals from
hundreds of kilometers distance. Also, DOA estimation is
crucial for smart antenna technology [2] to facilitate steering
beamforming and achieve a large capacity of communication.
Especially, as the rapid development of internet of things (IoT)
and the fifth generation (5G) communication or beyond 5G
(B5G), communication with smart beamforming [3], [4], low
power consumption, high data speed is in demand, which
would further increase the demand of DOA estimation or beam
localization techniques.
This work was supported in part by the National Natural Science Foundation
of China under grant 61901491, and in part by National Natural Science
Foundation of Hunan Province under grant 2020J5665.
M. Lin, M. Xu, H. Liu, Z. Wu, J. Liu, B. Deng, D. Guan, S. Zha
are with College of Electronic Science, National University of Defense
Technology, Changsha 410073, China. (Corresponding author: Song Zha :
zhasong0551@163.com)
X. Wan is with the State Key Laboratory of Millimeter Waves, Southeast
University, Nanjing 210096, China.
Array signal processing methods based on multiple sensors
or channels are the most common techniques to estimate DOA.
Minimum variance distortionless response (MVDR) algorithm
[5] is the classic estimation method, which is based on the
minimization of the output power, subject to the constraint that
the gain in the steering direction is unity. To further increase
the estimation resolution, sub-space methods such as multiple
signal classification (MUSIC) [6] and estimation of signal
parameters via a rotational invariant (ESPRIT) algorithms [7]
perform an eigenvalue-decomposition on the covariance matrix
of the received signal samples to achieve DOA estimation.
However, an antenna array consisting of multiple antennas or
channels suffers from high hardware complexity, high cost and
low energy efficiency. Each antenna in the array is connected
to a separate receiver channel in radio frequency front (RF) end
which is then performed by amplifying, down-converting, fil-
tering, analog-to-digital convertor (ADC) sampling and finally
processed by the digital baseband signal processing. Multi-
sensor-based DOA estimation can be only used for important
applications such as radar system or base stations, which
is not suitable for general IoT applications requiring cost-
effective devices. With manually or mechanically steerable
ability, high gain directional antennas [8] can also be used
for DOA estimation by comparing the received power at each
scanning direction. Manually steerable antennas need to be
mounted on a rotatable platform, which takes a long time to
estimate DOA and is bulky. Electrically reconfigurable phased
arrays, with flexible feeding of the elements to achieve beam
scanning, can substantially reduce the hardware complexity
and the estimation time. However, it requires large quantities
of scanning beams to cover the whole space. In addition, the
continuous control of the phase or amplitude in each element
increases the cost and hardware complexity of the channel,
which is not suitable for massive antenna elements to achieve
high performance.
Meanwhile, the artificial metamaterial especially for meta-
surface with unprecedented property, attracted much atten-
tion from researchers of multi-discipline, which provides a
new perspective for traditional engineering applications. By
employing metasurface technology, the electromagnetic prop-
erties such as the phase, amplitude and polarization can be
manipulated to realize different functions: radar absorber [9],
generation of radio vortex [10], energy selective surface (ESS)
[11], computational imaging system [12], etc. By integrating a
tuning device into each metamaterial element, programmable
metasurface can have a further control over the radio waves,
which had been widely investigated for satellite communi-
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Things Journal
IEEE INTERNET OF THINGS JOURNAL,XX,XX 2
Fig. 1. Programmable metasurface antenna for smart communication.
cation on-the-move [13], near-field computational imaging
[14], synthetic aperture radar (SAR) system [15] and security
screen technology [16], to name a few. In comparison with
the phased array or electrical scanned antenna (ESA) [17],
programmable metasurface fabricated by printed circuit board
(PCB) techniques can provide comparable performance with
extreme low cost and complexity. Approaches to achieve the
tuning performance include the employment of liquid crystal
[18], micro-electro-mechanical system (MEMS) switch [19],
positive-intrinsic-negative (PIN) diode [20] or varactor diode
[21], among which the liquid crystal and MEMS have high
fabrication cost and processing complexity while varactor
diode has a high loss.
Using the space-time modulated metasurface [22], a nov-
el DOA estimation method was recently proposed in [23],
which uses the time-delay principle. The method only requires
one sensor. However, it can only achieve 1D DOA estima-
tion and has a narrow working bandwidth. Inspired by the
programmable metasurface and compressive sensing (CS), a
method of DOA estimation with small estimation samples is
proposed in this paper. It is well known that CS is for acqui-
sition of sparse signals and reconstruction with compressed
sampling. DOA estimation in a whole space is a spatially
sparse problem, therefore, it can be solved with CS techniques.
Compressed sampling such as random sampling is the key
part of CS techniques. However, the random sampling in time
domain is not easy to be implemented in practical application.
In spatial domain, single programmable metasurface sensor
with random radiation patterns can be regarded as a naturally
physical random sampling device that can be easily employed
in DOA estimation. Benefiting from the low cost and low
complexity of the metasurface fabrication, the proposed DOA
estimation can be used in specific IoT applications that need
high data transmission throughput and smart communication,
such as the image or video collection IoT terminal, the
central IoT communication node, .etc. The proposed technique
can be utilized in the smart IoT communication as shown
in Fig.1, which includes sensing and beam steering stages.
During sensing stage, programmable metasurface sensor in
the collecting terminal is configured at sensing mode which
generates a series of random radiation samples to estimate
DOA of the user terminal. Based on the obtained DOA
information, the metasurface is then set at steering mode that
smartly steer the beam to the direction of interest to ensure a
high-efficiency communication link. Traditional beamforming
techniques use the continuous phase and amplitude weight,
while in programmable metasurface antenna the element can
only achieve discrete phase or amplitude weight. The com-
mon metasurface technology uses the discrete weights to
approximate the continuous weights and achieve beamforming.
Even though the spacetime-modulated metasurface can achieve
DOA estimation with less complexity, it can neither achieve
2D DOA estimation nor estimate multiple sources, with a
narrow bandwidth. On contrast, the proposed method has
advantages over the spacetime-modulated metasurface-based
DOA estimation in terms of 2D DOA estimation, multiple
sources estimation and wider bandwidth.
The remain parts of paper are organized as follows. The
proposed method is elaborated in Section II, with the deriva-
tion of mathematical model and the reconstruction of DOA
estimation. Subsequently, simulation results are made in sec-
tion III, with extensive performance analyses. Section IV
presents the realization of space-fed metasurface antenna and
the proof-of-concept experiment of DOA estimation, with the
final conclusions drawn in Section V.
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Things Journal
IEEE INTERNET OF THINGS JOURNAL,XX,XX 3
Fig. 2. (a) The space-fed programmable metasurface sensor for DOA estimation. (b) The sparse representation of incident
signals.
II. PRO PO SE D DOA ESTIMATION TECHNIQUE
In this section, the mathematical model of space-fed pro-
gramable metasurface sensor for DOA estimation is illustrated
firstly. Subsequently, classical OMP algorithm is introduced
for the DOA information recovery. Please note that here the
novelty of our paper is about the programmable metasurface to
genenrate random radiation pattern for compressive sensing,
which only requires only one sensor. Hence, any other CS
algorithms are also applicable for this method. Here we just
choose the typical OMP for verification.
A. Mathematical Model
The proposed DOA estimation employs a space-fed pro-
grammable metasurface antenna as the receiver sensor, which
is shown in Fig.2 (a). It is noted that, for simplicity and
clarity, here a model of 1D metasurface rather than a 2D
metasuface is plotted. The receiving antenna consists of a horn
antenna feeder and a programable metasurface which utilizes
PIN diodes to achieve the tuning performance between ’0’ and
’1’ states with two discrete phase responses of 0◦and 180◦.
Both states have the same amplitude response. By coding the
metasurface synthetically, a specific radiation pattern such as
steering beam or random beam can be achieved. Assume that
at the ith sampling time tithere are Nsignals (s1, s2, ...sN)
from different directions (θ1, θ2, ...θN) imping on the M-
element metasurface. The configuration code matrix of the
metasurface is B∈Z1xM. By applying a control voltage to
a PIN diode through field programmable gate array (FPGA),
the element of Bcan be set to either 0 (low) or 1 (high)
so that two states of phases can be configured. Based on
the above assumptions, the received signal by the space-fed
metasurface antenna at time tifor a given coding matrix B
can be formulated as:
x(ti) = n(ti)+
N
P
n=1
M
P
m=1
sne−jφni (−1)Bme−j2π
λxmsin θn+j2π
λqz2
f+(xf−xm)2
(1)
φni is phase of nth signal at time tiand λis the central
wavelength. ni(t)is the gaussian noise with power intensity
σ2.xmis the position of the mth element, while (xf, zf)
refers to the position of the feeder. (−1)Bmrepresents the
reflection coefficient of element m. It is assumed that the
reflection amplitudes of two states are the same. At state ’0’ ,
Bmis configured to 0 and the normalized reflection phase is
0◦, hence the reflection coefficient of the element is 1. While
at state ’1’, the reflection coefficient of the element is −1
with 180◦phase response. The reason why a 2-bit or 3-bit
element is not used in our design is that more bits does not
mean a better estimation performance, since the determined
factor is the orthogonality of the measurement matrix, which
will be discussed in the following part, has no relation with
the number of bits. But more bits entitle better beam scanning
performance. Besides, the design complexity of 2-bit or 3-
bit metasurface is high. If we design a 2-bit or 3-bit meta-
atom using varactor diodes to form a 20 ×20 elements array,
400 digital-to-analog-convertors (DACs) are required, which
increases the complexity and the cost of the controlling board.
Hence, 1-bit element is employed in our design. Based on
the formulation (1), the mean power intensity of the received
signal of 1-bit metasurface sensor can be then expressed as
E[x(ti)x(ti)∗] = σ2+
N
X
n=1
Rn|FE(θn)|2
| {z }
Part1
+
N
X
n=1
N
X
k=1,k6=nRnk e−jφni +jφki FE(θn)F∗
E(θk)
| {z }
Part2(2)
Derivations of (2) can be seen in Appendix, which are also
the novelty of our work since we use the theory to verify
the feasibility of metasurface-based-CS to estimate DOA.
FE(θ)denotes the far-field pattern of θ.Rnindicates the
power intensity of the nth signal, while Rnk is the correlation
coefficient of nth signal and kth signal. From the formulation
(2), it can be concluded that the received power is determined
by two parts, of which Part 1 is the scalar energy superposition
of the incident signals at corresponding directions, while Part
2 further considers the mutual phase effect of different sig-
nals. Specifically, when calculating how much energy coming
through a specific direction θ, we mainly consider the signal
with direction θand ignore the mutual effect of the other
signals with other directions which contributes to Part 2.
For typical applications, either the correlation coefficient or
FE(θn)F∗
E(θk)is small, hence the influence of Part 2 is
marginal which can be ignored.
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Things Journal
IEEE INTERNET OF THINGS JOURNAL,XX,XX 4
Suppose that the DOAs during the short sensing time are
approximately constant. By generating Lcode matrixes {B}to
sense the incident signals, then according to formulation (2),
the received power matrix of Lsamples can be formulated as:
Y=HRS+n
=
H1(θ1)H1(θ2)· · · H1(θN)
H2(θ1)H2(θ2)· · · H2(θN)
.
.
..
.
..
.
..
.
.
HL(θ1)HL(θ2)· · · HL(θN)
| {z }
H(H(θ)=|FE(θ)|2)
Rs1
Rs2
.
.
.
RsN
| {z }
RS
+
σ2
1
σ2
2
.
.
.
σ2
L
| {z }
n
(3)
where Y= [y1, y2, ..., yL]T∈RL×1is the total received
power of Lsamples , Rs∈RN×1is the source power of the
incident signals and H(θ)is the far-field (power) radiation
pattern under specific coding formulation.
B. Sparse Representation And DOA Information Recovery
Divide the whole space equally into K(K >> N )parts
as shown in Fig.2 (b), it is easy to conclude that the N
incident signals are sparse in the space. Consequently, the
estimation of ˆ
Θ = [ˆ
θ1,ˆ
θ2, ..., ˆ
θN]Tcan be solved through
compressive sensing techniques, which can help greatly reduce
the sampling times. Using the sparse representation approach,
the model has a similar formulation with (3):
Y=HRS+n
=
H1(θ1)H1(θ2)· · · H1(θN)
H2(θ1)H2(θ2)· · · H2(θN)
.
.
..
.
..
.
..
.
.
HL(θ1)HL(θ2)· · · HL(θK)
| {z }
H∈RL×K
Rs1
Rs2
.
.
.
RsK
| {z }
RS∈RK×1
+
σ2
1
σ2
2
.
.
.
σ2
L
| {z }
n
(4)
where RShas Nelements that are not zero i.e. there are K-N
elements equal to zero, while His the measurement matrix
according to the CS theory. This kind of typical compressive
sensing problem can be tackled through the solution of L1-
norm model:
ˆ
RS= arg min kRSk1s.t. kY−HRSk ≤ δ(5)
where δrepresents the error caused by the total noise level.
From the index of non-zero elements RS, the DOA informa-
tion can be obtained.
In CS application, a common measurement matrix is the
random matrix. Here a 1-bit random matrix was programmed
by FPGA to achieve random radiation patterns, based on which
the measurement matrix Hcan be obtained. An OMP algo-
rithm is used in this paper to recover the DOA information, as
shown in Algorithm 1. Specifically, Hcan be conceived as
the initial residual error reat the very beginning. Ωurefers to
the indices that remain to make calculation at uth iteration. Dc
is a matrix that consists of deleted columns of measurement
matrix. ID contains the column indices of measurement matrix
corresponding to the estimation results ˆ
Θthrough function fΘ.
For IoT application, the receiver terminals can connect the net
through one or two terminals that have high power radiations.
Hence, there is no necessaries to estimate all the DOAs. Hence
the source number Nin the Algorithm 1 can be set to 1 or 2.
Also, we can use sparsity adaptive matching pursuit (SAMPT)
to estimate the DOAs without the prior information of N.
Here we uses the OMP algorithm with known source number
Nto verify the proposed method for simplicity. In the future
practical application, FPGA can be also used to achieve OMP
algorithm [24].
Algorithm 1 OMP algorithm for DOA estimation
1: Initialization:re(1) = H,Ω1= [1, K],Dc ={},ID={ }.
2: for u= 1 to Ndo
3: begin
4: Compute uth inner-products <re(u),H>
5: Update m= arg max
u∈Ωu
{<re(u),H>}
6: Renew
Dc = [Dc,Hm],ID ={ID, m},Ωu+1 = Ωu\ {m}
7: Update re(u) = H−(DcHDc)−1DcDcHH
8: end
9: Obtain estimation of DOA:ˆ
Θ=fΘ(ID)
III. SIM UL ATIO N RES ULTS AND PERFORMANC E
ANALYSES
In this section, simulations are conducted to verify the fea-
sibility of metasurface-based compressive sensing technique
to estimate DOA. Subsequently, comparisons between the
metasurface-based beam scanning and compressive sensing
techniques are made, showing superior performance of the
proposed method.
A. Simulation Results
According to the mutual incoherence property (MIP) of the
compressive sensing theory, the smaller the correlation coef-
ficients of the measurement matrix the better reconstruction
performance it has. Here we use the average correlation coef-
ficient µ= avg
i6=j
|< Hi, Hj>|to evaluate the MIP performance.
Fig.3 (a) shows the correlations of measurement matrix H
(H∈RL×K) which is generated by a 32-element (M=32)
1D space-fed metasurface antenna with half wavelength of
element distance. The sampling length Lis 50, while K= 181
denotes the number of the directions to be estimated. It can be
observed that the self-correlation of each column is larger than
the mutual correlation coefficients. Specifically, the correlation
coefficients of other columns with the column corresponding
to 0◦is shown in Fig.3 (b), from which it can be seen that the
average mutual correlation is around 0.5. Also, we can observe
a smaller fluctuation of correlation for larger size with more
samples (M= 100, L = 200). Based on the CS theory, for
a given µ, the signal can be reconstructed accurately if the
sparsity of the signal satisfies the following condition:
N < 0.368( 1
µ+ 1) µ=0.5
≈1.1041 (6)
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IEEE INTERNET OF THINGS JOURNAL,XX,XX 5
Fig. 3. Simulation results. (a) The correlation coefficients of matrix H. (b) The correlation coefficients at 0◦.(c) Four selected
radiation patterns. The 2nd row figures (d)-(f) show the simulation results of single incident signal with θ= 20◦, while the
3rd row figures (g)-(i) plot the results under two signals of θ= 20◦and θ=−30◦. The 4th row figures (j)-(l) correspond
to simulation results for 2D metasurface with 20 ×20 elements under two incident signals. For row 2 to 4, the 1st column
figures are the received signals, while the 2nd and 3rd columns figures are the estimation results by projection method and
OMP algorithm, respectively.
When µ= 0.5, the signal sparsity should be smaller than
1.1041. In other word, an accurate reconstruction including the
DOA and the amplitude can be ensured for one incidence of
signal. If the signal number is larger than 2, the reconstruction
performance may not be ensured. For DOA estimation, what
we concern most is the direction, while the accuracy of the
amplitude estimation is not the key concern. As a result, the
proposed DOA estimation of multiple sources is still feasible,
which will be verified in this subsection. Fig.3 (c) plots four
selected random samples i.e. random radiation patterns.
Fig.3 (d)-(f) show the estimation simulation under the
incidence of θ= 20◦. After random sampling as shown in
Fig.3 (d), the DOA information can be recovered by direct
projection and the OMP algorithm as shown in Fig.3 (e)
and (f), respectively. Both the projection and OMP algorithm
can estimate the DOA accurately. However, OMP algorithm
has a sharp spectrum that can be easily identified. Fig.3 (g)-
(i) present the simulation results under two indicant signals
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IEEE INTERNET OF THINGS JOURNAL,XX,XX 6
Fig. 4. The estimation accuracy against the SNR for different (a) metasurface antenna size and (b) sampling length. (c) The
estimation resolution and (d) resolution example. (CS is for compressive sensing and B.S. is for beam scanning.)
with θ= 20◦and θ=−30◦. It can observed that several
side lobes appear in the spectrum of the projection method
which hinders the identification of the DOA information.
While for OMP algorithm, it can achieve the estimation results
accurately. Similar results for 2D metasurface sensor with
20×20 elements to estimate DOA can be seen in the Fig.3 (j)-
(l). Please note that when referring to 2D metasruface, it means
that each element can be configured with an independent state,
which is different from the supercells in spacetime-modulated
metasurface. From the comparison, it can be concluded that the
OMP algorithm has superior estimation performance over the
projection method. Please note that here the aim of comparing
the OMP algorithm with projection method is not to show
the novelty of OMP. What we want to highlight is that using
compressive sensing techniques and the random sampling have
good DOA estimation. Hence, other CS algorithms are also
applicable.
B. Performance Analyses
Beam scanning technique is one of the traditional way to
estimate DOA, which is often used in the phased antenna array.
For 1-bit dynamic metasurface antenna [25]–[27], steering
beam has been investigated extensively, which can also be
used for DOA estimation. Traditional beamforming uses the
continuous phase and amplitude weight, while in 1-bit meta-
surface the element can only achieve discrete phase. Therefore,
it uses the discrete weights to approximate the continuous
weights and achieve beamforming performance by coding all
the element in a specific formulation. However, beam steering
error, resulting from 1-bit discrete phase quantization, leads
the estimation error. Besides, it requires a large quantity of
sampling beams to scan the whole space, resulting in a long
estimating time. While for the metasurface-based compressive
sensing for DOA estimation, small radiation samples are
required, therefore, short estimation time can be ensured.
Fig.4 compares the beam scanning and compressive sensing
for metasurfaee-based DOA estimation. Fig.4 (a) plots the
estimation accuracy against the signal-to-noise-ratio (SNR) for
different number of elements in a 1D metasurface antenna. The
element spacing is half wavelength and the sampling length
is 50. It can be observed that the accuracy of both the beam
scanning (B.S.) and compressive sensing (CS) method increase
with the number of the elements. Specifically for SNR >−20
dB, compressive sensing method with 16 elements has a higher
estimation accuracy more than 80%, which is better than the
beam scanning with 32 elements. Compressive sensing can
achieve a higher estimation accuracy with fewer elements. For
SNR <−20 dB, the accuracies of both methods are low and
the compressive sensing method has comparable performance
with the beam scanning. The estimation accuracies for differ-
ent sampling length are given in Fig.4 (b). It can be seen that
accuracy of the compressive sensing method increases with the
sampling length. From the comparison of both methods, it can
be found that with only 50 samples the proposed method can
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IEEE INTERNET OF THINGS JOURNAL,XX,XX 7
Fig. 5. (a) The space-fed metasurface antenna and its unit, (b) and (c) correspond to the amplitude and phase of reflection
coefficient, (d) and (e) are the electric field distribution of the element at on and off state.
achieve a higher accuracy than the beams scanning method
with 181 samples, demonstrating the sampling advantage.
Furthermore, the resolution performance is simulated as shown
in Fig.4 (c), from which it can be observed that for SNR
>−10 dB high estimation resolution 1◦can be obtained for
compressive sensing method with only 50 samples. While for
the beam scanning method with 181 samples, the estimation
resolution is 2◦. Specifically, Fig.4 (d) gives an example for
estimation of two DOAs with only 1◦difference. From the
inset, we can find that the compressive sensing method with
fewer samples can discriminate these two DOAs, which can
not be achieved by the beam scanning method with more
samples. Overall, the proposed metasurface-based compressive
sensing for DOA estimation has superior performance over
the beam scanning technique, with higher estimation accuracy,
smaller sample length and better resolution.
IV. PROGRAMMABLE METAS UR FACE SE NS OR A ND
MEA SU RE ME NT RE SU LTS
A. Programmable Space-fed Metasurface Antenna
The DOA estimation performance is mainly affected by the
measurement matrix, which is determined by the size of the
metasurface antenna and the bandwidth. A better resolution
can be ensured for a larger size antenna. However, larger
size would cause the increase of the design complexity. To
trade off, we used a fabricated 20×20 metasurface antenna as
the receiver [28], which can be controlled by a single FPGA
board. As for the bandwidth, it is determined by the element,
which can be further studied to have a wider bandwidth.
The fabricated programmable metasurface antenna is shown
in Fig.5 (a). The central working frequency is 10 GHz.
The element spacing is 10 mm, which is smaller than half
wavelength for avoiding grating lobes. The coding element is
composed of three metallic layers and two dielectric layers.
The first dielectric layer has a height of 1.6 mm with a
2.65 relative permittivity, while the relative permittivity of
the second dielectric layer is 3 with height of 0.2 mm. A
PIN diode is integrated in the element structure of the top
metallic layer, while the middle metallic layer serves as a
reflective surface and also as ground of DC signals. A fan-
shaped structure is patterned in the bottom metallic layer to
choke the high-frequency signals from the DC signals. Two
metallic cylinders are used to drive the PIN diode, one of
which is connected to the middle metallic layer, and the other
penetrates the middle metallic layer to load the DC voltages.
A horn antenna is placed 15 cm far from the metasurface as
the feeder.
The used pin diode is skyworks1320-079, which can be
modeled as an inductance 0.75 nH and a shunt impedance
0.5 Ωat diode-ON state, or an inductance 0.75 nH and a
series capacitor 0.24 pF at diode-OFF state as shown in Fig.5
(b). By applying different voltages, the PIN diode will be
switched on and off which affect the resonance of the element,
hence leading to phase difference. As can be observed from
the simulated results in Fig.5 (b) and (c), opposite reflection
phases (180◦difference) and similar reflection amplitudes of
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Fig. 6. (a) and (b) refer to the measured correlation coefficients of two selected columns of measurement matrix, while (c)
and (d) correspond to two sampling radiation patterns.
the element can be achieved. The electric field distribution of
the element at on and off state are shown in Fig.5 (d) and
(e), from which oppose phase can be observed. Specifically,
the coding element is represented by code ’0’ when the PIN
diode is switched off, and code ’1’ when it is switched on.
The whole coding of the metasurface is configured by the
backpacked FPGA board according to specific formulation to
form the radiation patterns of interest.
B. Radiation Pattern Measurement
The programmable metasurface antenna generates a series
of random radiation patterns i.e. random sampling, to construct
the measurement matrix H. Hence, for DOA estimation the
random patterns and the matrix Hshould be measured as
the priori information for DOA reconstruction. For simplicity,
near-field radiation patterns are recoded by a near-field system
in a microwave anechoic chamber rather than by a far-field
measurement system. A waveguide probe in front of the
antenna with a distance of 350 mm was used to record the
values at 10 GHz. The measured area has a size of 450 ×450
mm2, containing 31 ×31 points with a step of 15 mm. For
DOA estimation experiment, a total of 100 random radiation
patterns are used to build the H. For direct observation of
correlation and estimation result, here we use an u−vaxis
rather than θ−φaxis, where u=sinθcosφ, v =sinθsinφ.
Based on the 100 radiation patterns, matrix Hcan be obtained,
among which two pairs of columns are then selected to
evaluate the correlation of matrix as shown in Fig.6 (a) and
(b). The first pair contains 31 columns for u=−0.2, while
the second pairs are for u= 0.14. It can be observed that
the self-correlations are significantly larger than the cross-
correlations as the shown dark read value in the diagonal
area. The measured average correlation coefficient is about
0.5, showing the orthogonality to some extent. Fig.6 (c) and
(d) give two of measured radiation patterns, which exhibit the
random property.
C. DOA Estimation Experiment
For verification of the proposed DOA estimation, a proof-
of-concept experiment is made at 10 GHz. The dynamic
metasurface works as the receiver while a standard horn
antenna at a distance of 6 m is used as a transmitter source
as shown in Fig.7 (a). The transmitter and receiver with a low
noise amplifier (LNA) are connected by two ports of the vector
network. 100 random samples are experimentally recorded in
the lab, while the data is processed by an OMP algorithm in a
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Fig. 7. Experimental DOA estimation results. (a) and (d) correspond to the DOA estimation set-up in the farfield and nearfield,
respectively. (b), (c) and (e), (f) are the estimation results for different directions in the farfield and nearfield, respectively.
laptop to give the estimation spectrum. To briefly evaluate the
computational complexity, processing time by a laptop with
configuration of intel-i7 8550 core is recorded, which is about
0.058 second . With FPGA hardware, the computational time
can be even shorter. Fig.7 (b) shows the estimation of a single
source with θ1= 11◦, φ1= 180◦i.e u=−0.2, v = 0.
The target of the source can be estimated from the measured
spectrum. However, false estimation appears in other direction
as the cross marker shows, which hinders accurate estimation
of the real target source. Similar results can be observed from
Fig.7 (c) for estimation of source with θ1= 0◦, φ1= 0◦.
From the far-field measurement results, it can be concluded
that the proposed DOA estimation can obtain the DOA es-
timation of real target, however with other false estimations
that should be further eliminated. The false estimation may be
due to the employment of near-field measurement matrix H
to the far-field DOA estimation. To test this hypothesis, DOA
estimations in the near-field area are conducted. A waveguide
probe in the near-field area with a distance 0.5 m far from
the receiver is used as a transmitter source. From this point,
the measurement matrix used in the reconstruction of DOA
is approximately equal to the measured near-field H. Fig.7
(e) and (f) show the estimation spectrum of a single source
with θ1= 35◦, φ1= 158◦(u=−0.5408, v = 0.216)
and θ1= 12◦, φ1= 99◦(u=−0.036, v =−0.216),
respectively, from which clear peak spectrum without false
peak can be achieved at the target portions. This further verifies
the feasibility of the proposed metasurface-based compressive
sensing method for DOA estimation. In this case, using 100
samples can estimate the source among 31 ×31 points, which
is beneficial for the smart communication of IoT application
that requires fast DOA estimation and beam steering.
V. CONCLUSIONS
Based on the programmable metasurface and the compres-
sive sensing, a novel DOA estimation method was proposed
in this paper, which employs a single metasurface sensor as
the receiver to sample the incident signals randomly. The
orthogonal matching pursuit algorithm was used to reconstruct
the DOA information. According to the compressive sensing
theory, the orthogonality of the measurement matrix was
evaluated, showing an average correlation of 0.5. Simulations
of 1D and 2D metasurface to estimate DOA were made. In
addition, comparison between beam-scanning and compressive
sensing for DOA estimation were made, implying that the
compressive sensing method with smaller sampling length
can obtain higher estimation accuracy and resolution. Finally,
a metasurface antenna with 20 ×20 elements was used to
conduct proof-of-concept experiments of DOA estimation in
the far-field and near-field, verifying the feasibility of the
proposed method.
Compared to other traditional DOA estimation techniques
that require multiple sensors or channels, the proposed method
only requires a single sensor with lower hardware complexity
and cost. The programmable metasurface can also be used
for beam steering. Therefore, employment of the cost-effective
programmable metasurface antenna in IoT application entitles
its smart communication capacity which has functions of
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DOA estimation and beam steering. Overall, the proposed
metasurface-based DOA estimation is beneficial for IoT ap-
plications.
APP EN DI X
The detailed derivation of mean power intensity formulation
(2) of the received signal in Section II is calculated as follows:
E[x(ti)x(ti)∗] = E[n(ti)n(ti)∗]+A+B+C;(7)
A=
N
P
n=1
M
P
m=1 nE[n(ti)s∗
ne−jφni ](−1)Bm
ej2π
λxmsin θn−j2π
λqz2
f+(xf−xm)2= 0;
(8)
B=
N
P
n=1
M
P
m=1 nE[n∗(ti)snejφni ](−1)Bm
e−j2π
λxmsin θn+j2π
λqz2
f+(xf−xm)2= 0;
(9)
C=
N
P
n=1
N
P
k=1
M
P
m=1
M
P
l=1
{E[sks∗
ne−jφni +j φki ](−1)Bm+Bl×
ej2π
λxmsin θn−j2π
λqz2
f+(xf−xm)2
e−j2π
λxlsin θk+j2π
λqz2
f+(xf−xl)2
}
=D+E;
(10)
The terms A and B consist of the correlation of noise and the
incident signals, therefore are equal to zero. The calculation
of term Ccan be further divided to two parts Dand E, which
can be formulated as
Dk=n
=
N
P
n=1
[
M
P
m=1
M
P
l=1
{ej2π
λxmsin θn−j2π
λqz2
f+(xf−xm)2
×
e−j2π
λxlsin θn+j2π
λqz2
f+(xf−xl)2
}E[sns∗
n]( −1)Bm+Bl]
=
N
P
n=1
FE(θn)
z }| {
M
X
m=1
(−1)Bme−j2π
λxmsin θn+j2π
λqz2
f+(xf−xm)2
×
F∗
E(θn)
z}| {
M
X
l=1
(−1)Blej2π
λxlsin θn−j2π
λqz2
f+(xf−xl)2
E[sns∗
n]
=
N
X
n=1
Rn|FE(θn)|2
| {z }
Part1(11)
Ek6=n
=N
P
n=1
N
P
k=1
M
P
m=1
M
P
l=1 nE[sks∗
ne−jφni +j φki ](−1)Bm+Bl×
ej2π
λxmsin θn−j2π
λqz2
f+(xf−xm)2
×
e−j2π
λxlsin θk+j2π
λqz2
f+(xf−xl)2
}
=
N
P
n=1
N
P
k=1
FE(θn)
z }| {
M
X
m=1
(−1)Bme−j2π
λxmsin θn+j2π
λqz2
f+(xf−xm)2
×
F∗
E(θk)
z }| {
M
X
l=1
(−1)Blej2π
λxlsin θk−j2π
λqz2
f+(xf−xl)2
E[sks∗
ne−jφni +j φki ]
=
N
X
n=1
N
X
k=1,k6=nRnk e−jφni +jφki FE(θn)F∗
E(θk)
| {z }
P art2(12)
Based on the above derivations, the formulation (2) in Section
II can be obtained.
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2021.3051014, IEEE Internet of
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Mingtuan Lin received the B.Sc., M.Sc. and PhD.
degrees in electronic science and technology from
the National University of Defense Technology,
Changsha, China, in 2012, 2014 and 2018, respec-
tively, under the supervision of Prof. P.G. Liu. He
had been a Visiting Ph.D. Student with the Queen
Mary University of London, London, U.K., since
2015, under the guidance of Dr. Y. Gao. He is
currently a Associate Professor in National Univer-
sity of Defense Technology. His current research in-
terests include dynamic-metamaterial-based antenna,
array signal processing, and monolithic microwave integrated circuit (MMIC)
design.
Ming Xu received a Bachelor degree in Electronic
Countermeasures Command and Engineering from
Air Force Early Warning Academy, Wuhan, China,
in 2015. He is currently pursuing the master de-
gree in Electronics and Communications Engineer-
ing from National University of Defense Technology
(NUDT), Changsha, China, under the supervision of
Prof. P. G. Liu. His research interests include high-
intensity radiation fields protection, electromagnetic
metamaterials, metamaterial antennas.
Xiang Wan was born in Hubei, China, in 1986.
He received the B.E. degree in electrical and in-
formation engineering and the M.E. degree in elec-
tromagnetic field and microwave technology from
Wuhan University, Wuhan, China, in 2007 and 2010,
respectively, and the Ph.D. degree in electromagnet-
ic field and microwave technology from Southeast
University, Nanjing, China, in 2014. Since 2014,
he has been a Faculty Member with the School
of Information Science and Engineering, Southeast
University. His current research interests include
programmable metasurfaces and antenna arrays.
Hanbing Liu was born in Hunan, China, in 1991.
He received his bachelor’s degree in communica-
tion engineering from Beijing Jiaotong University
in 2013. He received a Msc degree in electronic
and communication engineering from the National
University of Defense Technology in 2020. His
research interests include array signal processing and
single-channel anti-saturation technology.
Zhaofeng Wu received the B.Eng. and M.E. degree
in electronic science and engineering from the Na-
tional University of Defense Technology, Changsha,
China, in 2017 and 2019, where he is currently
pursuing the Ph.D degree in electronic science and
technology under the supervision of Prof. P.G. Liu.
His research interests include millimeter wave an-
tenna, microwave components, and electromagnetic
protection.
Jibin Liu received the BSc degree in electronics
and information system, and MSc and PhD degrees
in electromagnetic field and microwave technology
from National University of Defense Technology
(NUDT), Changsha, China, in 1995, 1998 and 2007,
respectively. He is currently a professor of NUDT.
His current research interests include electromagnet-
ic compatibility and protection, electromagnetic field
and microwave technology.
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Bowen Deng received a Bachelor degree in Elec-
tronic Engineering from National University of De-
fense Technology (NUDT), Changsha, China, in
2018, where he is currently pursuing the Ph.D.
degree in electronic science and technology under
the supervision of Prof. P. G. Liu. His research
interests include high-intensity radiation fields pro-
tection, electromagnetic metamaterials, metamaterial
antennas.
Dongfang Guan was born in Henan Province,
China, in 1988. He received the B.S. and Ph.D.
degrees from the College of Communications Engi-
neering, PLA University of Science and Technology,
Nanjing, China, in 2011 and 2016. He is now a
Associate Professor in the National University of
Defense Technology, Changsha, China. His current
research interests include microstrip antennas, array
antenna, SIW technology, spoof surface plasmons
and metamaterials.
Song Zha was born in 1987. He received the
B.S. degree in communication engineering and M.S.
degree in signal and information processing from
the Electronic Engineering institute (EEI), Hefei,
China, in 2007 and 2010 respectively, and received
the Ph.D. degree in electronic science and tech-
nology from National University of Defense Tech-
nology(NUDT), Changsha, China, in 2014. He is
currently an Associate Professor in NUDT. His
current research interests include electromagnetic
compatibility and protection, antennas theory and
electromagnetic environmental effect.
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