Performance analysis of negative group delay network using MIMO technique

TELKOMNIKA Telecommunication, Computing, Electronics and Control
Vol. 18, No. 5, October 2020, pp. 2572~2579
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v18i5.13666  2572
Journal homepage: http://journal.uad.ac.id/index.php/TELKOMNIKA
Performance analysis of negative group delay network
using MIMO technique
Yaqeen S. Mezaal1
, Marwah Al-Ogaidi2
1
Department of Medical Instrumentation Engineering, Al-Esraa University College, Baghdad, Iraq
2
Department of Laser and Optoelectronics Engineering, Al-Nahrain University, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Jul 22, 2019
Revised Mar 19, 2020
Accepted Apr 17, 2020
This study introduces comparative consequences that determine the bit error
rate enhancements, resultant from adopting a proposed MIMO wireless model
in this study. The antenna configurations for this model uses new small
microstrip slotted patch antenna with multiple frequency bands at strategic
operating frequencies of 2.4, 4.4, and 5.55 respectively. The S11 response of
the proposed antenna for IEEE802.11 MIMO wireless network has been
highly appropriate to be adopted with MIMO antenna system. The negative
group delay (NGD) response is the most significant feature for projected
MIMO antenna. The NGD stands for a counterintuitive singularity that
interacts time advancement with wave propagation. These improvements are
employed for increasing a reliability of instantly conveyed data streams,
enhance the capacity of the wireless configuration and decrease the bit error
rate (BER) of adopted wireless system. In addition to antenna scattering
response, the enhancements have been analysed in term of BER for different
MIMO topologies.
Keywords:
Bit error rate
MIMO antenna
MIMO wireless networks
Negative group delay
STBC mathematical equations
This is an open access article under the CC BY-SA license.
Corresponding Author:
Yaqeen S. Mezaal,
Medical Instrumentation Engineering Department,
Al-Esraa University College,
Baghdad, Iraq.
Email: yakeen_sbah@yahoo.com
1. INTRODUCTION
Since 1960s, wireless systems have promptly mounting segments with the potential for making
available, swift and super information exchange among convenient devices placed somewhere in the world.
The remarkable growth of wireless communication technology is because of a union of numerous aspects.
Primarily, the requirement of the wireless connection has increased highly. Secondly, the spectacular
advancement of VLSI machinery has activated low-power and compact implementing of complex code and
signal processing. Thirdly, 2nd
generation wireless communication standards, as in GSM, cause it achievable
to broadcast voice with small volume of digital data. In addition, a 3rd
generation of wireless systems has given
clienteles higher service quality which accomplishes greater capacity and spectral efficiency [1].
Prospective applications activated by wireless systems consist of multimedia facilities on cellular
phones, stylish homes, computerized highway systems, video chatting and self-directed sensor networks.
On the other hand, there have been dual major technological challenges in sustaining these appliances: first
challenge includes a fading occurrence, deviation time of the channel in consequence of a small-scale outcome
of multipath fading along with large-scale influence as in pass loss by remote attenuation and obstacles
shadowing. Moreover, as wireless sender and receiver require air communication with noteworthy interference

TELKOMNIKA Telecommun Comput El Control 
Performance analysis of negative group delay network using MIMO technique (Yaqeen S. Mezaal)
2573
among them. All challenges have been mainly due to restricted accessibility of radio frequency range and
the complex time-varying wireless regulating.
At present, a main objective in wireless engineering is for upturning information rate and developing
transmission dependability. Specifically, owing to the growing demand for superior bit rates, better-quality
service quality, less faults, upper network capability and user coverage calls for inventive techniques which
enhance spectral effectiveness and channel reliability, more and more wireless communication technologies
have been initiated, like MIMO techniques [2]. In 1998, Alamouti built up diversity design using dual antennas
in the transmit side and single antenna in the receive end. This design offers the identical diversity order like
the maximal-ratio combining (MRC) in a receiver end, with single sending antenna and dual receiving
antennas. Bandwidth extension in this design hasn’t required. An entire coming response from receiving to
sending antennas and its calculation complexity level have been identical to MRC [3]. Many categories of
NGD network using RLC resonators were, in theory and experiments, proven in reported papers
in [4-6]. Nevertheless, no one of them had employed transmission-type toplogy for NGD network by means of
the parallel RLC resonator with a distributed transmission line due to an application inconveniency.
Wilzeck et al. [7], proposed MIMO test-bed that uses two sending antennas and four receiving antennas
receiver in “offline” mode, in which pre-processed data has been sent over-air and logged for upcoming
processing. The receiving system permits 512 Mbytes of memory for every receive antenna and maximum
sampling frequency of 100 MHz, which causes 2.68 seconds of logging time with 14-bit resolution.
The test-bed has been in relation to Sundance’s modular digital signal processing platform and plug-in radio
frequency constituents produced through Mini-Circuits. Besides, bandpass filters using microstrip technique
at 2.4 GHz resonant frequency have been used to prevent image bands and enhance the operation of adopted
system. Lozano and Jindal [8], offered MIMO wireless network that has diversity principles.
This wireless system is based on the trade-off between spatial multiplexing and transmit antenna
diversity. Bhatnagar et al. [9], showed MIMO OFDM wireless network using space time block coding (STBC)
throughout Rayleigh channels by means of 2PSK as well as 4PSK modulations to conquer sub-channel
interfering. Simulated output graphs showed that there is reduction in bit error rate amounts as SNR raises. On
the other hand, the system throughput increases as SNR decreases. Premnath et al. [10], proposed a new rapid
algorithm for antenna selection in wireless MIMO systems. This technique does comparable capacity as
the most advantageous selection method and the rapid processing at more lessened computational costs.
The applied uncomplicated G-circles process decreases the complication notably with a rational performance
loss. It can be as well efficiently organized in correlation matrix-based on antenna selections. Multi band
antennas for wireless systems have been presented in [11-18]. These devices are very important to operate in
separated strategic bands for front ends of wireless systems especially for MIMO configurations. In this paper,
the MIMO antenna configurations for IEEE802.11 model uses new microstrip slotted patch antenna with
multiple interesting bands and significant NGD values. The return loss of the proposed antenna is suitable to
be adopted with MIMO wireless configuration. By the influence of this antenna, the corresponding BER has
been investigated using MATLAB simulator.
2. SPACE-TIME BLOCK CODES
Assume a wireless configuration has N sending antennas and M receiving antennas in a flat fading
channel with a propagation gain lmnh , . The parameter lmnh , is an independent complex Gaussian with variance
0.5 for every element in Rayleigh distributed random variable. Here, n, m, and l are indicators of sending
antenna, receiving antenna and time, correspondingly. In STBC communication system, the code can be
described by C matrix and STBC period by L. Supposing T is the symbol interval, a collected signal in a receive
antenna m under lT time can be determined by [2, 19, 20]:
=
+=
N
n
lmnllmnlm nchr
1
,,,, (1)
𝑐𝑙,𝑛 represents the (l,n) part of the L by N code matrix C, while 𝑛 𝑚,𝑙 belongs to additive noise with variance 𝜎2
and zero-mean. In the case of quasi-static channel, the time index l in lmnh , is feasibly misplaced. Signify (⋅) 𝐻
,
(⋅)∗
and (⋅) 𝑇
as a Hermitian transpose, a complex conjugate and a transpose, correspondingly. Through
accumulating the vector form of received signal, as shown in (1) for quasi-static channel is expressed as:
𝑅 = 𝐶𝐻 𝑇
+ 𝑁 (2)

 ISSN: 1693-6930
TELKOMNIKA Telecommun Comput El Control, Vol. 18, No. 5, October 2020: 2572 - 2579
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where R, H and N represent the L by M matrix with the (l,m) component lmr , , the M by N channel matrix with
the (m,n) element mnh , and an L by M noise matrix.
It has been hard for implementing signal processing procedures to the matrix depiction in (2), because
a code matrix C has not stated as a linear arrangement of STBC input symbols. Additionally, for not
quasi-static channels, it is not possible to convert as shown in (1) into (2). Therefore, there is necessity to make
an all-purpose expression form irrespective of code constitution or channel state. With the intention of applying
signal processing techniques, linear superposition is required, as in (3);
𝑟̅ = 𝐻̅ 𝑧 + 𝑛̅ (3)
Here, r indicates the LM by 1 received signal vector, z has identified as the K by 1 sent signal vector
[ 𝑧1 ⋯ 𝑧 𝐾] 𝑇
, 𝐻̄ is the LM by K channel matrix, and 𝑛̄ points to the LM by 1 noise vector. Various STBC
schemes are feasibly changed into the linear superposition structure. A code matrix C used for Alamouti
scheme [3] can be written as:
𝑪 = [
𝑧1 𝑧2
−𝑧2
∗
𝑧1
∗]
The code is transformed into the linear superposition representation (LSR) in this following manner.
Through determining the conjugating of 2nd
half of the received signal, the LSR for Alamouti system has
described by:
[
𝑟1
𝑟2
∗] = [
ℎ1,1 ℎ2,1
ℎ2,2
∗
−ℎ1,2
∗ ] [
𝑧1
𝑧2
] + [
𝑛1
𝑛2
∗]
where 𝑟𝑙, lnh , , and 𝑛𝑙 stand for M by 1 column vectors at time lT and have expressed as [𝑟1,𝑙 𝑟2,𝑙 ⋯ 𝑟 𝑀,𝑙] 𝑇
,
T
lMnlnln hhh ][ ,,2,1  and [ 𝑛1,𝑙 𝑛2,𝑙 ⋯ 𝑛 𝑀,𝑙] 𝑇
, correspondingly.
For quasi-static channels, the best possible discovery for the Alamouti method can be done by only
multiplying the vector 𝑟̄ by 𝐻̄ 𝐻
and adjusting the symbol by symbol detector. A complete Maximum Likelihood
(ML) search has denoted as the extensive exploration for equation solution, 𝑚𝑖𝑛‖𝑟̄ − 𝐻̄ 𝑧‖2
, through inspection
every probable sets of sent symbols. However, for wide-ranging STBC systems, it is not viable to generate a
complex LSR for (3). For instance, for N=4 antennas configurations at a rate of 3/4, we assume C matrix [21] as:
𝑪 = [
𝑧1 𝑧2 𝑧3 0
−𝑧2
∗
𝑧1
∗
0 −𝑧3
−𝑧3
∗
0 𝑧1
∗
𝑧2
0 𝑧3
∗
−𝑧2
∗
𝑧1
] (4)
This code matrix is not convertible to a complex LSR as achieved in the Alamouti code. But, if real
and imaginary parts matrix facets are defined separately, the collected vector can be written in a real LSR.
Ordinarily, by separating the real and imaginary components, each block code can be described. This is known
as the lattice version.
3. LATTICE VERTION FOR STBC SCHEMES
A regular form of the lattice (higher orders) version for STBC can be constructed by dividing C matrix
into dual components that are defined as 𝐶̃ = [𝐶 𝑅
𝐶 𝐼
] where 𝐶 𝑅
and 𝐶 𝐼
refer to real and imaginary elements of
the vector or matrix, correspondingly. If 𝑧 𝑘 = 𝑥 𝑘 + 𝑗𝑦 𝑘 has been considered, presume that the (l,n) constituent
of C represents 𝑐𝑙,𝑛 = 𝑐1 𝑥 𝑘 + 𝑗𝑐2 𝑦 𝑘, in which 1c and 2c stand for scalar constants. After that,
the lth row vector of 𝐶 𝑅
and 𝐶 𝐼
has been symbolized by 𝑐𝑙
𝑅
= [⋯ 𝑐1 𝑥 𝑘 ⋯], 𝑐𝑙
𝐼
= [⋯ 𝑐2 𝑦 𝑘 ⋯] where
kxc1 and kyc2 stand for the real and imaginary elements of nlc , , respectively. At this point, kxc1 and kyc2
have been positioned at the nth location in R
lc and I
lc . Such as the 2nd
row vectors of matrix 𝐶 𝑅
and 𝐶 𝐼
as
shown in (4) can be clearly acquired as 𝑐2
𝑅
= [−𝑥2 𝑥1 0 −𝑥3], 𝑐2
𝐼
= [𝑦2 −𝑦1 0 −𝑦3] [19]. By
resembling the depiction lattice to transform a complex channel matrix equation into real lattice channel matrix
𝐻̃ as stated in [14], the formation of 𝐻̃ of the adapted code matrix 𝐶̃ will be:

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𝐻̃ = [
𝐻1
𝑅
−𝐻2
𝐼
𝐻1
𝐼
𝐻2
𝑅 ]
where the facets in 𝐻1 and 𝐻2 are calculated as a result of equivalent constituents of 𝐶 𝑅
and 𝐶 𝐼
. Namely,
the kth column vector in the lth row block of the matrix 𝐻1 (or 𝐻2), lnhc ,1 (or lnhc ,2 ), has been evaluated
using (l,n) part of 𝐶 𝑅
(or 𝐶 𝐼
), kxc1 (or kyc2 ). For instance, the 2nd
row elements of 𝐻1 and 𝐻2 related to the
row vectors 𝑐2
𝑅
and 𝑐2
𝐼
are gotten as ][ 2,42,12,22,1 hhhH −= ][ 2,42,12,22,2 hhhH −−= .
Accordingly, the size of real lattice channel matrix 𝐻̃ has been 2LM by 2K. A lattice representation has lastly
expressed as 𝑟̃ = 𝐻̃ 𝑧̃ + 𝑛̃ where;
𝑟̃ = [ 𝑟 𝑅
𝑟 𝐼
], 𝑧̃ = [ 𝑧 𝑅
𝑧 𝐼
], 𝑛̃ = [ 𝑛 𝑅
𝑛 𝐼
],
here, 𝑟 = [ 𝑟1 𝑟2 ⋯ 𝑟𝐿] 𝑇
and 𝑛 = [ 𝑛1 𝑛2 ⋯ 𝑛 𝐿] 𝑇
. After this representation rule, 𝑯̃ can be defined as:
A different case we take in the consideration here, is the code, where some 𝑧 𝑘's are joint in (l,n) element
of C in the preservative form. Namely, 𝑧 𝑘 comes into view more than once in one row of C. This type of codes
can be defined by adopting the linear superposition criteria. Accordingly, the code matrix will be [14]:
𝐶 =
[
𝑧1 𝑧2
1
√2
𝑧3
1
√2
𝑧3
−𝑧2
∗
𝑧1
∗
1
√2
𝑧3 −
1
√2
𝑧3
1
√2
𝑧3
∗
1
√2
𝑧3
∗
−𝑧1 − 𝑧1
∗
+ 𝑧2 − 𝑧2
∗
2
−𝑧2 − 𝑧2
∗
+ 𝑧1 − 𝑧1
∗
2
1
√2
𝑧3
∗
−
1
√2
𝑧3
∗
𝑧2 + 𝑧2
∗
+ 𝑧1 − 𝑧1
∗
2
−
𝑧1 + 𝑧1
∗
+ 𝑧2 − 𝑧2
∗
2 ]
A lattice channel matrix can be expressed as:
𝐻1 =
[
ℎ1,1 ℎ2,1
1
√2
(ℎ3,1 + ℎ4,1)
ℎ2,2 −ℎ1,2
1
√2
(ℎ3,2 − ℎ4,2)
−ℎ3,3 −ℎ4,3
1
√2
(ℎ1,3 + ℎ2,3)
−ℎ4,4 ℎ3,4
1
√2
(ℎ1,4 − ℎ2,4)
]
and


























−−
−−
−−−−
−−−
−−−
−−−
−−−
=
RRRIII
RRRIII
RRRIII
RRRIII
IIIRRR
IIIRRR
IIIRRR
IIIRRR
4,24,34,44,24,34,4
3,13,43,33,13,43,3
2,42,12,22,42,12,2
1,31,21,11,31,21,1
4,24,34,44,24,34,4
3,13,43,33,13,43,3
2,42,12,22,42,12,2
1,31,21,11,31,21,1
~
hhhhhh
hhhhhh
hhhhhh
hhhhhh
hhhhhh
hhhhhh
hhhhhh
hhhhhh
H

 ISSN: 1693-6930
2576
𝑯2 =
[
ℎ1,1 ℎ2,1
1
√2
(ℎ3,1 + ℎ4,1)
ℎ2,2 ℎ1,2
1
√2
(ℎ3,2 + ℎ4,2)
ℎ4,3 ℎ3,3 −
1
√2
(ℎ1,3 + ℎ2,3)
ℎ3,4 −ℎ4,4
1
√2
(ℎ2,4 − ℎ1,4)
]
In the circumstances of the quasi-static channel response, the equivalent channel matrix has been
orthogonal in a case of orthogonal code matrix [19]. Consequently, a transpose of real lattice channel matrix
𝐻̃ 𝑇
belongs to a matched filter. The symbol by symbol ML detection has been in a highly advantageous case
and optimal after matched filtering. The outcome of the matched filtering for a symbol 𝑧 𝑘 has been:
𝑧̂ 𝑘 = 𝛾𝑧 𝑘 + 𝑛̂ = ∑ ∑|ℎ 𝑚𝑛|2
𝑧 𝑘
𝑁
𝑛=1
+ 𝑛̂
𝑀
𝑚=1
where nˆ represents a new term of additive noise with mean equals to 0 and variance equals to
∑ ∑ |ℎ 𝑚𝑛|2
𝜎2𝑁
𝑛=1
𝑀
𝑚=1 , and 𝛾 is the channel response power. However, more in-depth STBC encoding and
decoding information with the various number of transceiver antennas have given in [20-25].
4. MIMO SYSTEM MODEL OF IEEE 802.11
Alamouti scheme has been employed extensively in MIMO wireless systems. The typical adopted
MIMO block diagram uses STBC signal processing at transmit and receive antennas as in Figure 1. We used
applied wave research (AWR) electromagnetic package in designing and simulation of that MIMO antenna.
This simulation software package provides schematic circuit technology with good performance in accuracy,
capacity, convergence and speed. The microstrip antenna with uniform geometrical slot provides good
performance of the antenna frequency response using dual via ports.
This MIMO antenna, as depicted in Figure 2, has been modelled based on FR4 substrate with dielectric
constant of 4.4 and h of 1.6 mm. Dual via ports are positioned in the main microstrip resonator. The projected
antenna substrate dimensions have overall of 31x31 mm2
. The consequent S11 (return loss) response has clarified
in Figure 3. The S11 response in this graph has band frequencies of 2.4 GHz, 4.4 GHz, and 5.54 GHz.
The subsequent input reflection values are 20.1, 18, and 15.2 dB for each band respectively, while the bandwidth
ranges are 2.389-2.42, 4.314-4.47 and 5.545-5.61 GHz for the same band frequencies respectively. The new
MIMO antenna has compact size and worthy frequency responses and multiple service bands that have been
looked-for features for many MIMO wireless configurations as perceived by Figure 3. Table 1 explains
the dimensions of proposed MIMO antenna.
Figure 1. MIMO model
Table 1. Dimensions of the proposed MIMO antenna
Parameter Value (mm)
Wg, Lg 31, 31
Wp1, Lp1 2.5, 30
p2 5
Wp3, Lp3 1, 5

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Figure 2. The modelled layout of multiband antenna
Figure 3. The S11 frequency responses of proposed MIMO antenna
With the intention of getting close by the angle response of S11 scattering parameter of the suggested
microstrip MIMO antenna, simulation phase response at band resonant frequencies is depicted in Figure 4.
This graph shows that the proposed antenna has good phase response linearity within 1 to 6 GHz sweeping
frequency range. In Figure 5, group delay response of projected antenna has been presented. For this response,
a positive group delay means that the pulse is shifted back in time as it passes through an antenna; whereas
a negative group delay means it is shifted forward in time. The latter case doesn't necessarily violate causality,
it just means that the antenna predicts where the pulse will be in the future, based on where it is now.
The negative group delay (NGO) response is highly interested recently for RF and microwave devices
including antennas [26]. Here, significant NGD values with -14.71, -3.2 and -1.507 ns are found in 2.4, 3.04
and 5.55 GHz. Using a suitable script to interface between AWR and MATLAB simulators, the used
parameters in the simulated channel model have illustrated in Table 2. It has been essential here to reference
that the entire bit error rate results in this paper are done with some transmitted bits of 106
bits and carrier
frequency of fc = 2.4 GHz related to the first band of employed antenna.
The channel code is employed for information encoding, and the encoded data has split into different
data streams, all of them transmitted, based on numerous transmit antennas. The inward signal at every receive
antenna is linear. Figure 6 illustrates BER responses with respect to signal to noise ratio (S/N) for 2PSK digital
modulation in the case of Rayleigh channel. It explains as N and M are increased, the BER remains on declining
and presents superior BER output as a result of spatial diversity. It has been important to indicate that (SIMO)
antenna groupings (1x2 and 1x4) have higher quality BER results unlike (2x1 and 4x1) multiple input single
output (MISO) antenna arrangements. This has been due to the received data from an active link makes antenna
diversity order of 4 and 8, in which diversity order has been generally twofold a number of receiving antennas.
For the number of symbols = 1000000 (transmitted), we can merely measure BER down to 10−5
consistently
as in Figure 6. The most advantageous BER has been found in (4x4) antenna configurations.

 ISSN: 1693-6930
2578
Figure 4. Phase responses of MIMO antenna Figure 5. Group delay response of MIMO antenna
Table 2. The Simulated channel model parameters
Parameter Magnitudes
Carrier
frequency fc
2.4 GHz
Sampling
frequency fs
10 KHz
Sent bits 106
bit
Modulation type BPSK
N , M 1, 2,3,4
Figure 6. Bit error rate results of 2 PSK MIMO System with several antenna arrangements
5. CONCLUSION
The new implementation and characteristic of self-designed MIMO antenna was employed as multi
band device. The proposed device provides frequency band responses at 2.4, 4.4, and 5.55 GHz respectively
within (1-6) GHz frequency sweeping range with low insertion loss and high return loss magnitudes as well as
the compactness property of the projected antenna. This antenna offers significant NGD magnitudes with
-14.71, -3.2 and -1.507 ns at 2.4, 3.04 and 5.55 GHz. Simulation results of BER for 2 PSK MIMO NGD
network with several antenna arrangements are tolerable. The enhanced IEEE802.11 wireless model has very
good error rate performance, since it has the diversity gain by coding across time and space for accomplishing
the reliable transmission.

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