Subarrays of phased-array antennas for multiple-input multiple-output radar applications

International Journal of Informatics and Communication Technology (IJ-ICT)
Vol. 11, No. 3, December 2022, pp. 218~228
ISSN: 2252-8776, DOI: 10.11591/ijict.v11i3.pp218-228  218
Journal homepage: http://ijict.iaescore.com
Subarrays of phased-array antennas for multiple-input
multiple-output radar applications
Syahfrizal Tahcfulloh1
, Muttaqin Hardiwansyah2
1
Department of Electrical Engineering, Universitas Borneo Tarakan, Tarakan, Indonesia
2
Department of Electrical Engineering, Universitas Trunojoyo Madura, Bangkalan, Indonesia
Article Info ABSTRACT
Article history:
Received Dec 24, 2021
Revised Jul 24, 2022
Accepted Aug 9, 2022
The subarray MIMO radar (SMIMO) is a multiple-input multiple-output
(MIMO) radar with elements in the form of a sub-array that acts as a phased
array (PAR), so it combines at the same time the key advantage of the PAR
radar, which is high directional gain to increase target range, and the key
advantage of the MIMO radar, i.e., high diversity gains to increase the
maximum number of detected targets. Different schemes for the number of
antenna elements in the transceiver zones, such as uniform and/or variable,
overlapped and non-overlapped, significantly determine the performance of
radars as virtual arrays (VARs), maximum number of detected targets,
accuracy of target angle, detection resolution, SNR detection, and detection
probability. Performance is also compared with the PAR, the MIMO, and the
phased MIMO radars (PMIMO). The SMIMO radar offers great versatility
for radar applications, being able to adapt to different shapes of the multiple
targets to be detected and their environment. For example, for a transmit-
receive with an antenna element number, i.e., M = N = 8, the range of the
number of detected targets for the SMIMO radar is flexible compared to the
other radars. On the other hand, the proposed radar's signal-to-noise ratio
(SNR) detection performance and detection probability (K = 5, L = 3) are
both 1,999 and above 90%, which are better than other radars.
Keywords:
Amount of detected targets
Angular resolution
Detection probability
SNR detector
Subarray MIMO radar
Virtual array
This is an open access article under the CC BY-SA license.
Corresponding Author:
Syahfrizal Tahcfulloh
Department of Electrical Engineering, Universitas Borneo Tarakan
No.1, Jl. Amal Lama No. Kel, Pantai Amal, Tarakan Tim., Kota Tarakan, Kalimantan Utara, Indonesia
Email: rizalubt@gmail.com
1. INTRODUCTION
Along with the development of multi-antenna systems on radar technology that detects multiple
targets at a long distance, it has a detection function and a flexible response to the target state and its
surroundings, supported by high detection accuracy and angle resolution. One of the most important factors
in radar performance is optimal range and tracking angle [1] and multi-target detection [2]. High accuracy
enhances the ability to detect targets, and high angle resolution increases the number of detected targets. Its
implementation requires a radar with high detection accuracy and angle resolution for multiple target
detection, especially as an automotive radar [3]. The phased array (PAR) and multiple-input multiple-output
(MIMO) radars are two common types of multi-antenna radar systems. This array on the radar system is
arranged in order to get a highdirectivity mainlobe [4], [5]. The PAR radar is that all antenna elements are fed
by adjusting the phase difference to provide higher directional gain in certain directions only [6], [7], so that
the number of detected targets is limited by the small resolution of the resulting angle. The number of

Int J Inf & Commun Technol ISSN: 2252-8776 
Subarrays of phased-array antennas for multiple-input multiple-output … (Syahfrizal Tahcfulloh)
219
detected targets is increased by applying the MIMO radar because it exploits all orthogonal transmission
signals to obtain multiple echo signals reflected by multitarget [8]–[11], but has a low directional gain.
Besides, the MIMO system concept has been known to have the advantage of increasing the channel capacity
[12], which is directly proportional to the number of detected targets.
The troubles skilled via way of means of the PAR and the MIMO radars are triumph over via way of
means of the Phased MIMO radar (PMIMO) [13]–[16] via way of means of forming overlapped subarrays
(SAs) at the transmit array side (Tx) in order that this radar can concurrently take gain of the primary gain of
the PAR radar, specifically excessive directional advantage and the primary gain of the MIMO radar is
excessive range advantage to growth the range of goal detection and range. Furthermore, this radar is referred
to as PMIMO_Tx.
In the [17]–[19] study of Full PMIMO radar (FPMIMO), using SAs that overlap both Tx and Rx
actually yielded the maximum amount of detected targets and angle resolution. It turned out to increase. The
amount of SA elements in Tx-Rx array is the same. This radar is also known as the PMIMO_Tx_Rx.
To achieve generalization and flexibility of multi-target detection and high angle resolution, this
paper introduces the Subarray MIMO radar (SMIMO), which allows SAs to have the following conditions: a)
the numeral of SA elements varies and or uniform and b) overlapped and or non-overlapped, on Tx-Rx so
that it can form a PAR, MIMO, PMIMO_Tx, PMIMO_Tx_Rx radar configuration, and other radar
variations. SMIMO radar sub-array conditions provide increased degrees of freedoms (DoFs) compared to
other radar types where traditional radars cannot provide detection accuracy, high angle resolution, high SNR
detection, and high detection probability to adapt to current environmental conditions. While using the
SMIMO radar, all you have to do is adjust the configuration and number of Tx-Rx SAs.
The proposed radar performance is expressed in terms of the number of VAs (NVAR), the maximum
amount of detected targets (max), the angle resolution, the maximum complex amplitude of the target return,
the SNR detection (), and the probability detection (Pd). All of these have not been explained in detail in
previous studies and have not been shown comprehensively. The results of this paper show that the SMIMO
radar is highly flexible in various configurations by adjusting the amount of SA elements, the amount of SAs,
overlapped/non-overlapped, and target detection conditions at that time.
The structure of this paper is as follows. In section 2 shows the SMIMO radar system and signal
model. The formulas used to calculate NVAR, max, the magnitude of the complex amplitude, , and Pd are
described in section 3. Section 4 presents the results and considerations in the form of numerical calculations
and simulations of the SMIMO radar performance parameters, as well as their analysis and verification.
Finally, section 5 contains the conclusions of this research.
2. THE SMIMO RADAR
2.1. System model
The multi-antenna uniform linear array (ULA) radar system in Tx-Rx array consists of a total of M
and N elements, respectively. The distances between the antenna elements of Tx and Rx array are dM and dN,
respectively. The transmitted signal has a non-dispersive and narrowband propagation. As shown in Figure 1,
the Tx and Rx arrays are divided into the numeral of SAs, i.e. K and L. These SAs may follow a combination
of overlapped and/or non-overlapped, and the numeral of elements may vary. The SA numbers for Tx and Rx
are 1 ≤ K ≤ M and 1 ≤ L ≤ N, respectively.
Since each SA of both the Tx array and the Rx array acts as an element of the MIMO radar array
that acts as a directional gain controller like a PAR radar, the subarray acts as an orthogonal Tx-Rx element
of the SMIMO radar and independent of each other. The configuration of these sub-arrays promises a
combination of directional gain and diversity gain that can be used simultaneously with both the MIMO and
the PAR radars.
Figure 1 shows some configurations (such as overlapped and/or non-overlapped) of various SAs
within a Tx-Rx array on a SMIMO radar, and the amount of elements in each subarray that are equal and/or
variable. Figure 1(a) shows an proposed radar scheme called a SA in which the SA terms overlap and the
numeral of elements in each sub-array is equal (OES), or K = 3 and L = 4 overlap in Tx and Rx. This
configuration detects multiple targets by generating three quadrature signals transmitted by three SAs on Tx
and received by four SAs operating independently on Rx. Figure 1(b) shows the conditions between the sub-
arrays on the overlapped SMIMO radars, where the amount of elements in each sub-array changes or the
overlapping unequal SAs (OUS) with K = 3 for Tx and L = 4 for Rx. Three orthogonal signals transmitted by
the three SAs of Tx and received by the four SAs of Rx. The difference between the OES configuration and
the OUS configuration is that the radiation shape (beamforming) of the SAs in the OES configuration is the
same for Tx and Rx of each SA, but different for OUS. This is because the OUS configuration has a variable
amount of antenna elements, and a SA with many elements produces higher directivity.

 ISSN: 2252-8776
Int J Inf & Commun Technol, Vol. 11, No. 3, December 2022: 218-228
220
The configurations of the proposed radar SAs in Figure 1(c) do not overlap, and each SA has a
uniform number of elements (NOES), or Tx has K sub-arrays and Rx has L sub-arrays. In this configuration,
for multi-target capture, K orthogonal signals are generated that are sent by the Tx array and received by the
L independent SAs in the Rx array. Figure 1(d) shows the non-overlapped schemes between the SAs, where
the numeral of elements in each sub-array varies or is called a non-overlapping unequal SAs (NOUS), where
Tx has K SAs and Rx has L SAs. The difference between the NOES configuration and the NOUS
configuration is that the sub-arrays with the NOES scheme have the same radial shape for Tx and Rx of each
SA, whereas the radial shape for NOUS is different. This is because the NOUS scheme has a variable amount
of antenna elements, as described in Figure 1(c).
The distinction among overlapped SA (OS) and non-overlapped SA (NOS) is special in Section 4.1,
i.e. concerning the dimensions of the virtual array (VAR) generated and the sign transmitted through the SAs
is semi-orthogonal. This immediately impacts the accuracy and backbone of the detection attitude of the
target.
(a) (b)
(c) (d)
Figure 1. The configuration of the Tx-Rx antenna array on an SMIMO radar with SA is a subarray with the
following conditions: (a) overlapped-equal number (OES), (b) overlapped-unequal number (OUS), (c) non-
overlapped-equal number (NOES), and (d) non-overlapped-unequal number (NOUS)
2.2. Signal model
The SMIMO radar block diagram is an adaptation of the PMIMO_Tx_Rx radar block diagram
described by [18] see Figure 2. The difference lies in the numeral of elements of the SA and the state of the
SA, i.e. a non-overlapping number. Tx subpartitions transmit orthogonal signals simultaneously to multiple
targets. The k-th SA of the Tx network sends signals k(t) independently of each other. For M elements in the
Tx network, transmit the baseband signal vector through the k-th SA with k = 1, 2, ..., M, i.e.
𝒙𝑘(𝑡) = √𝑀/𝐾𝜙𝑘(𝑡)𝒘𝑘
∗
(1)
where ()* denotes the operator of complex conjugate and (M/K) is the normalized power factor, ensuring that
the energy transmitted by the proposed radar in a pulse is M. Meanwhile wk denotes a complex weight vector
of M unit elements perpendicular to the k-th SA.
The reflected signal with a reflectance coefficient of () from a target  in the distant field is
expressed as follows:
𝑟(𝑡, 𝜃) = √𝑀 𝐾
⁄ 𝛽(𝜃) ∑ 𝑤𝑘
𝐻
𝑎𝑘(𝜃)𝑒−𝑗2𝜋𝑓𝜏𝑘(𝜃)
𝜙𝑘(𝑡)
𝐾
𝑘=1
(2)

221
where (.)H
is the Hermitian displacement operator, ak() denotes the Tx direction vector with M elements in
the k-th SA, f denotes the carrier signal frequency, k() denotes the corresponding delay time of the first
element of the k-th SA to the first element of the first SA.
When the Tx coherent vector and the Tx diversity vector are defined as K-elements, respectively:
𝒄(𝜃) = [𝒘1
𝐻
𝒂1(𝜃) 𝒘2
𝐻
𝒂2(𝜃) ⋯ 𝒘𝐾
𝐻
𝒂𝐾(𝜃)]𝑇
(3)
and
𝒅(𝜃) = [𝑒−𝑗2𝜋𝑓𝜏1(𝜃)
𝑒−𝑗2𝜋𝑓𝜏2(𝜃)
⋯ 𝑒−𝑗2𝜋𝑓𝜏𝐾(𝜃)]𝑇
(4)
So (2) can be stated briefly as
𝒓(𝑡, 𝜃) = √𝑀/𝐾𝛽(𝜃)(𝒄(𝜃) ∘ 𝒅(𝜃))𝑇
𝝍(𝑡) (5)
where ()T
denotes the transpose operator, (t) = [1(t) ... K(t)]T
and  denotes the operator of Hadamard
multiplication. If it is assumed that there are T targets in the direction {t} with t = 1, 2, 3, ...., T, then the
complex of signal received vector by the sub-array L at Rx is
𝒚(𝑡) = √𝑀/𝐾 ∑ 𝛽𝑡(𝜃𝑡)[𝒆(𝜃𝑡) ∘ 𝒇(𝜃𝑡)]
𝑇
𝑡=1 [𝒄(𝜃𝑡) ∘ 𝒅(𝜃𝑡)]𝑇
𝝍(𝑡) + 𝒏(𝑡) (6)
with
𝒆(𝜃) = [𝒗1
𝐻
𝒃1(𝜃) 𝒗2
𝐻
𝒃2(𝜃) ⋯ 𝒗𝐿
𝐻
𝒃𝐿(𝜃)]𝑇
(7)
and
𝒇(𝜃) = [𝑒−𝑗2𝜋𝑓𝜏1(𝜃)
𝑒−𝑗2𝜋𝑓𝜏2(𝜃)
⋯ 𝑒−𝑗2𝜋𝑓𝜏𝐿(𝜃)]𝑇
(8)
where bl() denotes the Rx steering vector with N elements in the k-th sub-array and vl is the complex weight
vector with N-unit elements in the l-th sub-array. Meanwhile e() and f() are the Rx coherent vectors and
the Rx diversity vectors with L element and n(t) denotes the N element vectors of zero mean white Gaussian
noise.
3. VIRTUAL ARRAY, MAXIMUM AMOUNT OF DETECTED TARGETS, COMPLEX
AMPLITUDE OF ECHO SIGNAL, SNR DETECTION, AND DETECTION PROBABILITY
FOR SMIMO RADAR
The advantage of orthogonally transmitted MIMO radar over the PAR radar is the formation of
VAR [11]. Target detection, angular accuracy, detection angle resolution, and maximum numeral of detected
targets are primarily determined by the VAR of the PAR and MIMO radar [11] and the FPMIMO radar [19]
with evenly overlapping SAs.
VAR calculations at the MIMO, the PAR, the PMIMO_Tx_Rx, and the PMIMO_Tx radars had
been supplied through [19], at (14)-(17). For the most wide variety of detectable goals the MIMO and the
PAR radars had been mentioned through [20], whilst for the PMIMO_Tx_Rx and the PMIMO_Tx radars it's
been mentioned through [19]. The calculation of the angular decision acquired through the complicated
amplitude of the goal echo sign at the PMIMO_Tx_Rx, the MIMO, the PMIMO_Tx, and the PAR radars has
been defined through [19]. For the SNR detector on the proposed radar is an extension of the SNR detector
on the MIMO radar by [21]. Meanwhile, to determine the detection probability on the SMIMO radar, we
adapt Pd from the FPMIMO radar by [19].
The calculation of VAR, the maximum amount of targets that can be detected, and the complex
amplitude of the target return signal on the proposed radar is an extension of the study in [19]. The number of
both overlapped and non-overlapped SAs, and/or the number of SMIMO radar VARs that vary uniformly or
have a number of Tx and Rx SAs, is defined by K and L, respectively.
𝐸 ∈ [𝐾 + 𝐿 − 1, 𝐾𝐿] (9)
To calculate the maximum amount of detected targets on the proposed radar is (10)

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𝑇𝑚𝑎𝑥 ∈ [
𝐾+𝐿−2
2
,
𝐾𝐿+1
2
) (10)
The complex amplitude of the SMIMO radar target return signal is expressed by (11)
𝛽̑(𝜃) =
√𝑀/𝐾 ∑ (𝒆(𝜃)∘𝒇(𝜃))𝐻𝑹
̂𝒚𝝍(𝒄(𝜃)∘𝒅(𝜃))∗
𝑄
𝑞=1
‖𝒆(𝜃)∘𝒇(𝜃)‖2(𝒄(𝜃)∘𝒅(𝜃))𝑇𝑹
̂𝝍𝝍(𝒄(𝜃)∘𝒅(𝜃))∗
(11)
with (12) and (13)
𝑹
̂𝒚𝝍 = (1/𝑄) ∑ 𝒚(𝑞)𝝍𝐻
(𝑞)
𝑄
𝑞=1 (12)
𝑹
̂𝝍𝝍 = (1/𝑄) ∑ 𝝍(𝑞)𝝍𝐻
(𝑞)
𝑄
𝑞=1 = 𝑰𝑀×𝑀 (13)
where ‖⋅‖ is the Euclidean norm operator, 𝛽
̂(𝜃) denotes the least squares (LS) estimate of the coeficient
reflectivity of radar or the magnitude of the target's complex amplitude in the direction , and q = 1, 2, 3, ...,
Q denotes the sample data index. The amount of detected targets can be determined from the spatial spectral
peaks in the LS estimate.
Through the same approach by [19] and based on the SNR detector by [21], to calculate the SNR
detector on the proposed radar is expressed by
 =
2(𝑀/𝐾)2𝑀𝐾
2
𝑁𝐿
2
𝐾2𝐿2(𝑆𝑁𝑅)2
(𝑀/𝐾)2𝑀𝐾
2 𝑁𝐿
2𝐾2𝐿2(𝑆𝑁𝑅)2+2(𝑀/𝐾)𝑀𝐾𝑁𝐿𝐾𝐿(𝑆𝑁𝑅)+2
(14)
where MK and NL are M – K + 1 and N – L + 1, respectively.
Meanwhile, to determine the detection probability on the SMIMO radar by developing Pd in [19] for
a certain false alarm probability (Pfa) and the SNR is expressed by
𝑃𝑑 = exp (
𝐾 ln(𝑃𝑓𝑎)
𝐾+𝑀𝑀𝐾𝑁𝐿𝐾𝐿(𝑆𝑁𝑅)
) (15)
4. RESULTS AND DISCUSSION
4.1. Virtual array
Calculating VAR (NVAR) with SMIMO radar allows you to apply the concept of VAR with the
MIMO radar. That is, antenna-shaped elements can be used to radiate orthogonal signals and extend to sub-
array-shaped elements that are not mutually exclusive overlaps or NOES. VAR is the result of the
convolution of the Tx array and Rx [11]. To determine the VAR, the subarray is considered a single antenna
in the site center and emits orthogonal signals according to the scheme shown in [11]. Based on a comparison
with PMIMO_Tx with 4 OES, the following is an example of VAR calculation for proposed radar with
(M = N = 8) and 4 NOES (2 elements per subarray).
𝑇𝑥 𝐴𝑟𝑟𝑎𝑦 = {0 1 0 1 0 1 0 1}; 𝑅𝑥 𝐴𝑟𝑟𝑎𝑦 = {1 1 1 1 1 1 1 1};
𝑉𝐴𝑅 = {1 1 2 2 3 3 4 4 3 3 2 2 1 1 0}
(16)
Since there are four NOES, there is one compelling element position that is displayed in different font colors.
The Rx array is worth one in the position of eight elements. The VAR of the SMIMO radar using NOES is
14, which is near to the VAR amount of the MIMO radar of 15. For comparison of SMIMO radar using 2
NOES (numeral of elements per 4 SAs).
𝑇𝑥 𝐴𝑟𝑟𝑎𝑦 = {0 0 0 1 0 0 0 1 0}; 𝑅𝑥 𝐴𝑟𝑟𝑎𝑦 = {1 1 1 1 1 1 1 1};
𝑉𝐴𝑅 = {0 1 1 1 1 2 2 2 2 1 1 1 1 0 0}
(17)
then the VAR variety for the SMIMO radar with 2 NOES is 13.
For the PMIMO_Tx radar pronounced by [13] which makes use of a radiation detail withinside the
shape of Tx OES, in accordance to [11] every waveform is radiated from the midpoint of the segment or the

223
vicinity of the antenna detail withinside the SA with MK the maximum middle detail can be 1 at the same
time as the others are 0. Here are a few examples of VAR calculations for the PMIMO_Tx radar with the
same amount of Tx-Rx antenna elements. For example, the configuration of K is four then MK is 5. The shape
of Tx-Rx array and VAR are
𝑇𝑥 𝐴𝑟𝑟𝑎𝑦 = {0 1 1 1 1 0 0}; 𝑅𝑥 𝐴𝑟𝑟𝑎𝑦 = {1 1 1 1 1 1 1 1};
𝑉𝐴 = {0 1 1 1 1 2 2 2 2 1 1 1 1 0 0}
(18)
Since there are 4 SAs per SA 5, the element in the center of each SA is worth 1, shown in different
font colors, and the Rx array is worth 1. There are 8 element positions. The PMIMO radar has an VAR
number of 11, which is between two extreme configurations, slightly higher than the PAR radar, i.e. 8, and
lower than the MIMO radar, i.e. 15.
To compare the amount of VARs for proposed radar using OES and NOES, Table 1 shows the
numeral of OES or NOES type SAs, the amount of elements per SA, the amount of OES and NOES, and the
amount of VARs. The numeral of overlapped locations on the SMIMO-OES radar clearly affects the VAR
because there are multiple elements between the shared SAs and the signals are not perfectly orthogonal.
This is shown in the configuration of two OESs, with six element positions in the O state, where NVAR is close
to NVAR on the PAR radar i.e. 9. Meanwhile, if the position of the element in state O is small (like the scheme
of 7 OES with 1 element in state O), NVAR will be one or more of NVAR in the MIMO radar. The OES-based
PMIMO_Tx radars generally have a higher SINR [13] due to the large amount of OES elements, but have a
higher of the directional gain, such as the PAR radars [22], [23]. Therefore, a compromise must be made
between NVAR and the amount of OES, which is proportional to the angle resolution, angle accuracy, and the
numeral of detected targets, to conform to the situations of the desired target of radar.
Table 1. Comparison of the SMIMO radar with NOES and OES for M = N = 8
Amount of
SAs
Amount of elements
per SA
Amount of overlapped locations
between SAs
Amount of non-overlapped locations
between SAs
NVAR
NOES
2 4 0 2 13
4 2 0 4 14
8 1 0 8 15
OES 2 7 6 2 9
3 6 5 2 10
4 5 4 2 11
5 4 3 2 12
6 3 2 2 13
7 2 1 2 14
During the calculation of NVAR on the FPMIMO / PMIMO_Tx_Rx radar reported by [18] and [19],
Tx and Rx are OES, and according to [11] each signal is emitted from the midpoint of the phase or the
position of the antenna element. The Tx subarray with MK has a central element value of 1 and the other
elements 0. The same conditions apply to Rx SAs with many elements. That is, NL. For example, if you
calculate NVAR with K = L = 4 and then MK = NL is 5, the array will be Tx, Rx, and VAR.
𝑇𝑥 𝐴𝑟𝑟𝑎𝑦 = {0 1 1 1 1 0 0}; 𝑅𝑥 𝐴𝑟𝑟𝑎𝑦 = {0 1 1 1 1 0 0};
𝑉𝐴𝑅 = {0 0 0 0 1 2 3 4 3 2 1 0 0 0 0}
(19)
In case there are 4 SAs in Tx and Rx array, the arrangement of the elements is alike. The NVAR of the
PMIMO_Tx_Rx radar is 7 because out of the 15 slots in the VAR element with a value greater than 1, only 7
are available.
The following is a table showing the result NVAR of all configurations formed for K = L = 8 using (9)
as shown in Table 2. Table 2 shows that the NVAR in the SA configuration of proposed radars such as
PMIMO_Tx and PMIMO_Tx_Rx is intermediate between the PAR and the NVAR of the MIMO radar and
gives the NVAR,PAR < NVAR,SMIMO < NVAR,MIMO. These results also show the proposed radar with the numeral of
Tx and Rx SAs. K and L are common forms of radar that emit many orthogonal signals. Special conditions
for proposed radar are the PAR or SMIMO OES radar (M = 1, N = 8), the MIMO or SMIMO NOES
(M = N = 8), and the PMIMO_Tx or SMIMO OES (1 < K < M, L = 8 ).
However, if dM and dN are not equal with d and are greater than d, the resulting NVAR will be greater
than those tabulated in Table 2. Similarly, for the magnitudes dM = LdN and dN = d, the maximum value of
NVAR becomes KL. For example, if K = L = 8, the maximum NVARs for the PAR, the MIMO, the PMIMO_Tx,

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and the PMIMO_Tx_Rx radars are 8, 64, 32, and 16, respectively. However, in reality, M = N, which is
already safe. For example, it is not possible programmatically to set the spacing between the elements of Tx
and Rx in order to get the uppercase NVAR. The antennas on the Tx and Rx arrays are almost always in a
specific location from the beginning.
Table 2. The value of NVAR is of the array Tx-Rx with K = L = 8 and dM = dN is d
NVAR
L
1 2 3 4 5 6 7 8
K
1 1 2 3 4 5 6 7 8
2 2 3 4 5 6 7 8 9
3 3 4 5 6 7 8 9 10
4 4 5 6 7 8 9 10 11
5 5 6 7 8 9 10 11 12
6 6 7 8 9 10 11 12 13
7 7 8 9 10 11 12 13 14
8 8 9 10 11 12 13 14 15
4.2. Angle resolution
The formation of the VAR is due to the Tx array transmitting the quadrature signal, thus forming a
more focused radiation or beam ray. This happens because a large array is formed in the VAR. The output
beam scheme is the product of the Tx and the Rx beam scheme. The Tx beam ray is the power pattern
radiated from the Tx antenna in all directions of the target. Similarly, the Rx beam ray is the received power
pattern from the target as the arrival angle function of the return signal. If the Rx uses only one antenna, it is
difficult to determine the arrival of angle as it will be difficult to distinguish between strong signals from the
top of the beam and weak signals in the sidelobes. However, if Rx is an array, this does not happen and the
beam can be digitally directed to the reach angle of the echo signal.
Figure 2(a) shows the MIMO radar beam schemes for a two-element Tx array and a three-element
Rx array. The spacing between the Tx and the Rx array elements is 0.5λ. Here, λ is wavelenght a carrier
signal. Its output beam ray is similar to the Rx beam ray. However, if you increase the spacing among the
elements of the Tx array to 3 times dN, the resulting beam scheme is shown in Figure 2(b). The resulting
beam pattern has a narrower beamwidth. Also, the grating lobes that appear in the beam scheme do not seem
to appear in the output beam ray. The output beam ray in Figure 2(c) is similar to Figure 2(b), with the
difference that the spacing between the elements of Tx is 0.5λ, while the spacing between the elements of Rx
is twice dM. Therefore, the beam ray can also be represented as a pattern from a 2 × 3 = 6 element Rx array,
or the output beam ray is a VAR beam scheme as shown in Figure 2(d). This shows that calculating the
correct geometry between the correct element of the Tx array and Rx improves the angle resolution of the
radar system without adding the element of antenna to the array.
For PAR transmit signals, a high gain beam is obtained and the SNR is increased M-fold, which
does not occur for quadrature signal transmissions. Therefore, it is necessary to find a compromise between
signal transmission with directional amplification and quadrature signal transmission in order to obtain
angular resolution that meets the target conditions. This guarantees a compromise between the two extreme
configurations and supports the application of the proposed radar concept, which can simultaneously provide
SNR, angle resolution, maximum amount of detected targets, and beam schemes. The use of SAs is a
compromise between Tx-Rx gain, SINR, and maximum range, as described in [22] and [23].
There is capacity for the usage of SAs with extraordinary variety of elements (unequal subarray,
US) to triumph over the restrictions of identical subarray (ES). Especially if it's far adjusted to the situations
for detecting more than one objectives due to the fact usually with excessive directional benefit it's far
appropriate for objectives which have an extended variety and weak or small radar cross section (RCS). If the
goal situations range i.e. varies in variety, RCS, etc., then using a aggregate of various SA schemes (OS/NOS
and ES/US) may be found out as an example in a single time and one Tx array may be found out as a non-
overlapped identical SA (NOES), overlapped identical SA (OES), non-overlapped unequal SA (NOUS), or
overlapped unequal SA (OUS). However, there additionally wishes to be technical issues in its
implementation which decide whether or not it may be implemented practically, particularly to the waveform
generator in Tx and sign processor in Rx for the utility of the SA methods.

225
.
(a) (b)
(c) (d)
Figure 2. The MIMO radar beampatterns with M = 2, N = 3, and d = 0.5λ for: (a) dM = dN is d,
(b) dM = 3d, dN = d, (c) dM = d, dN = 2, and (d) VAR and the whole sample
4.3. Relationship between VAR and maximum amount of discoverable targets
Section 4.1 explained the relationship between the numerical calculation of VAR using (9) reported
in [20]. Since VAR is proportional to angle resolution and accuracy, it is also proportional to the calculation
of the maximum amount of detected targets (max). In calculating the maximum numeral of the MIMO radar
targets formulated in [20], at (22), it is also useful to calculate the maximum amount of detected targets for
PAR, PMIMO_Tx, and PMIMO_Tx_Rx radars i.e. special conditions for proposed radar. Radar uses (10). To
demonstrate this, (11) is used to obtain numerical results as shown in Figure 3. This shows a comparison of
these four parameters for all variations of the proposed radar at K = 4, L = 5, and M = N is about 8.
As shown in Figure 3, the MIMO and the PMIMO_Tx radars can detect the four targets indicated by
the red dotted vertical lines. That is, D = {-25o
, -10o
, 5o
, 15o
}, but only two the PAR radar and the
PMIMO_Tx_Rx radars can detect the target.  = {-25o
, -10o
}. MIMO radar has the highest detection
accuracy of the four radars. Similarly, it detects the magnitude of the complex amplitude of the return signal
most often obtained by MIMO radar. This is related to the amount of VARs in the largest MIMO radar,
which improves angle detection accuracy and angle resolution.
Based on the max equation in (10) of the SMIMO radar, the max value of the PMIMO_Tx and
PMIMO_Tx_Rx radar signal schemes is between the PAR and the max value of the MIMO radar, and they
are related i.e. max,PAR < max,PMIMO < max,MIMO. For example, for Tx-Rx with K = L is 8, get max,PAR,
max,MIMO, max,PMIMO-Tx, and max,PMIMO-Tx-Rx, that is, 4, (7, 32), (5, 16) and (3, 8), respectively. Looking at
Figure 3, the MIMO and the PMIMO radars are within the detectability limits of more than four radars, so
they can properly detect four targets.
-80 -60 -40 -20 0 20 40 60 80
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Angle, (deg)
Power
(dB)
Tx pattern
Rx pattern
Overall pattern
-80 -60 -40 -20 0 20 40 60 80
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Angle, (deg)
Power
(dB)
Tx pattern
Rx pattern
Overall pattern
-80 -60 -40 -20 0 20 40 60 80
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Angle, (deg)
Power
(dB)
Tx pattern
Rx pattern
Overall pattern
-80 -60 -40 -20 0 20 40 60 80
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Angle, (deg)
Power
(dB)
VA pattern
Overall pattern

 ISSN: 2252-8776
226
Figure 3. The magnitude of the complex amplitude as an assessment of the accuracy and resolution of the
goal attitude with D and () = 1 for numerous radar configurations
4.4. SNR detector
The best performance measure of various detectors is Pd which will be presented in section 4.5. So
comparisons of Pd of various radar systems must be made and selected to determine which one is the best.
The comparison is a numerical calculation of a single scalar performance measure such as a function of the
detector's SNR performance [21].
Figure 4 is the result of the evaluation of expression (14) to calculate the SNR detector performance
of the proposed radar. It is assumed that M = N = 8 and the SNR range = {-10:1:15} where the radar
configurations of the PAR, the MIMO, the PMIMO_Tx, and two variations of SMIMO are (K = 1, L = 8),
(K = L = 8), (K = 4, L = 8), (K = 5, L = 3), and (K = 7, L = 6), respectively. It appears that the SNR detector
of the PAR radar is superior to other radar configurations, especially for low SNR, but when the SNR is
above 10 dB, generally the performance of the SNR detector from the proposed radar, namely SMIMO, tends
to reach the same value as the SNR detector from the PAR radar. For example, for an SNR condition of 10
dB, the SNR detector constant value () for PAR, MIMO, PMIMO_Tx radars, and the two proposed radar
variants are 1,998, 1,994, 1,996, 1,999, and 1,995, respectively. The results also show that the variation in the
amount of SAs in Tx-Rx, i.e. K and L, affects the value of  where it is evident that the proposed radar
configuration (K = 5, L = 3) has a high value compared to the special configuration of the proposed radar,
namely the PAR radar. Thus, the SMIMO radar has high flexibility to detect multiple targets by adjusting the
numeral of Tx-Rx SAs, i.e. K and L.
4.5. Detection probability
In the radar detection results according to [21] that the performance of the PAR radar outperforms
compared to the MIMO radar at low SNR but the condition is reversed for high SNR. Based on (15) with
similar assumptions to the previous evaluation, i.e. M = N = 8, the SNR is set to 10 dB, and the range
Pfa = {0:0.1:1} where the configurations of the PAR, the MIMO, the PMIMO_Tx, and the SMIMO radars
respectively are (K = 1, L = 8), (K = L = 8), (K = 4, L = 8), and (K = L = 4), the results are obtained as
presented in Figure 5. The numerical evaluation results in Figure 5 corroborate the results discussed in
section 4.4 and as reported by [21] namely the Pd performance of the PAR radar outperforms the
performance of other radars. While at a low Pfa of about 10-4
, all Pd performances of the SMIMO radar
variation have Pd values above 90%. This shows that detection target is more best for SNR values above
10 dB. It also appears that the variation in the amount of SAs in Tx-Rx namely K and L affects the Pd value.
This is evident because the PAR, the MIMO, and the PMIMO_Tx radars are special conditions of the
proposed radar.
-80 -60 -40 -20 0 20 40 60 80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Angle (deg)
Magnitude
of
Complex
Amplitude
PAR(K=1,L=8)
MIMO(K=L=8)
PMIMO-
Tx(K=4,L=8)
PMIMO-
Tx-
Rx(K=L=4)
(K=L=6)

227
Figure 4. SNR detection of various SMIMO radar
configurations for SNR variations
Figure 5. The detection probability for various
SMIMO radar configurations for Pfa variations
5. CONCLUSION
This article described the number of the VARs, the angle resolution, the maximum number of
detectable targets, the magnitude of the complex amplitude, the SNR detector, and the detection probability
of the SMIMO radar return signal under various SA configurations. The number of VARs strongly
determines the angle resolution and the number of detected targets. These are strongly influenced by SA
schemes like OES, OUS, NOES, and NOUS. For the total amount of Tx-Rx array of antennas, or the
proposed radar with M and N, all parameters of SMIMO radar performance are primarily determined by the
number of Tx-Rx SAs, K and L. The maximum number of targets that can be detected, the SNR detector, the
size of the complex amplitude, and the detection probability turn on the number of SAs of the Tx-Rx
proposed radar, where the PAR, the MIMO, the PMIMO_Tx, and the PMIMO_Tx_Rx radars represent
special schemes. Changing the number of specific K and L Tx-Rx SAs (M and N) is adaptive, flexible, and
programmable with the proposed radar, providing multi-target detection capabilities with multi-antenna radar
systems that increase with target and environment. The condition is more reliable and the design planning
radar is easier.
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-10 -5 0 5 10 15
1.4
1.5
1.6
1.7
1.8
1.9
2
SNR (dB)

PAR(K=1,L=8)
MIMO(K=L=8)
PMIMO-
Tx(K=4,L=8)
(K=5,L=3)
(K=7,L=6)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pfa
P
d
PAR(K=1,L=8)
MIMO(K=L=8)
PMIMO-
Tx(K=4,L=8)
(K=L=4)

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BIOGRAPHIES OF AUTHORS
Syahfrizal Tahcfulloh received the B.Eng. degree from Universitas Gadjah
Mada, Yogyakarta, Indonesia in 2003, and the M.Eng. and Ph.D. degrees from Institut
Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia in 2010 and 2020, respectively, all
in Electrical Engineering. Currently, he is a Lecturer with the Department of Electrical
Engineering of Universitas Borneo Tarakan. His research interests include array signal
processing and MIMO radar. He is a member of IEEE especially the IEEE Antennas and
Propagation Society. He can be contacted at email: rizalubt@gmail.com.
Muttaqin Hardiwansyah is a Lecturer at the Department of Electrical
Engineering of Universitas Trunojoyo Madura. He is received the B.Eng. degree from
Telecommunication Engineering of Politeknik Elektronika Negeri Surabaya (PENS),
Indonesia in 2011, and the M.Eng. degree from Electrical Engineering of Institut Teknologi
Sepuluh Nopember (ITS). His research interests include MIMO radar and internet of thing
(IoT). He can be contacted at email: muttaqin.hardiwansyah@trunojoyo.ac.id.

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