1. Introduction
Due to random environmental effects, there are multiple factors in signal performance
degradation. The main parameters are inter-symbol interference (ISI), inter-carrier
interference (ICI), multipath fading, and other propagation phenomena. A delay in
the signal at the receiver end causes overlapping of the symbols (time selective),
and the mobility of a user causes carrier frequency offset (CFO) (frequency selective).
Doubly selective channels (DSCs) are characterized by frequency selectivity and time
variations. To mitigate the channel effects and to achieve improved quality of service
(QoS), channel equalization plays a crucial part in eliminating ISI effects [1-4].
Doubly selective channel equalization (DSCE) is an emerging field. Various authors
have been working in this area, and there are various types of algorithms for DSCE.
DSCE can be carried out using adaptive algorithms, neural networks, nature-inspired
algorithms, machine learning, and hybridization of heuristic computational techniques
(HCTs) and neural networks or adaptive algorithms.
An equalizer is basically a filter that updates its weights and generates a desired
response. A channel equalizer is either linear or non-linear, and it depends on the
functionality of the equalizer. Whenever the channel conditions are too bad, non-linear
equalizers are used in place of linear equalizers. Equalization of DSCs is needed
to eliminate ISI and ICI, to meet the ever-growing demand of higher data rates, and
to improve QoS [4-6].
The conventional algorithms for adaptive equalization are classified in Fig. 1. The algorithms are firstly classified as linear and non-linear. The linear algorithms
are further classified as transversal and lattice equalizers. Transversal equalizers
are divided into zero forcing (ZF) equalizers, least mean squares (LMS) equalizers,
recursive least squares (RLS) equalizers, and fractional least mean squares (FLMS)
equalizers. The commonly used types of non-linear equalizers are decision feedback
equalizers (DFEs), maximum likelihood (ML) equalizers, and maximum likelihood sequence
estimators (MLSEs) [7-18].
ZF equalizers are frequently used. They use the pseudoinverse of the channel matrix
as a weight vector. A ZF equalizer has low complexity but reduced performance in bad
channel conditions. Some authors [19] proposed a ZFE for MIMO systems. A new ZF-based equalizer for uplink fractional split
that divides Massive MIMO processing was proposed [20]. A joint low complexity regularized ZF (JLCR-ZF) equalizer for MIMO systems was proposed
to cope the previously mentioned problem [21].
LMS exploits the gradient decent (GD) algorithm in order to estimate the desired
response. The GD algorithm finds minima to minimize the error by adjusting filter
coefficients. Due to the simplicity of the algorithm, researchers frequently work
on the algorithm. There are multiple variants proposed in the literature with little
modifications according to the requirements of the problem [22]. A bi-normalized (BN) data-reusing LMS was proposed to investigate the performance
of a proposed equalizer for indoor and pedestrian MIMO systems [23]. An LMS-based adaptive algorithm was proposed to find the tap weights in order to
estimate the channel conditions for an underwater acoustic channel (UAC) [24].
Other authors proposed a feed-forward software-defined equalization approach using
LMS [25]. A complex improved fractional-order non-linear alternative to the LMS and normalized-LMS
were presented [26]. The performance of the model was evaluated for frequency-selective and flat-fading
channel characteristics. Other authors [27] developed a nonlinear neural structure-based equalizer (wavelet-neural-network (WNN))
for a telephonic channel and trained equalizers’ weights by using the symbiotic organisms
search algorithm (meta-heuristic). Other authors proposed a joint adaptive algorithm
that involves LMS and RLS to suppress the ISI caused by channel impairments [28].
Other authors [30] studied the performance of multiple adaptive filters for blind and non-blind equalization.
The key performance parameters of the RLS algorithm have been discussed [31]. The main reason for the higher convergence rate of the RLS algorithm is due to the
continually minimization weighted linear least squares value of the error. For the
triply selective MIMO-UWA, authors [32] developed a turbo equalization scheme and soft decision-driven sparse channel estimation
method. The fast time variations in MIMO channels were estimated by extending the
conventional approach to RLS-DCD.
In the past few years, a trend of adaptive equalization using evolutionary computing
approaches has been observed. In one study [33], authors proposed artificial fish swarm and DNA encoding sequences based on genetic
optimization to answer the problems in the multi-modulus blind equalization algorithm
(MMA) for large MSE, low convergence rate, and high computational loads. Other authors
[34] proposed a blind equalization algorithm based on a neural network that was based
on ant colony optimization (ACO) in order to enhance the transmission quality.
A simplified cat swarm optimization (SCSO) algorithm was proposed for several
channel conditions for LTE structure in order to update equalizer weights [35]. A hybrid GA-PSO-based trained functional link artificial-neural-network (FLANN)
was used as an equalizer to remove the limitations of an LMS equalizer [36]. Other work [37] used sign regressor FLANN (SR-FLANN) for a QAM modulation scheme, where the equalizer
weights were estimated with a GA. The PSO-DFE showed dominance with a variable constriction
for channels with high eigenvalue spread factor as compared to the PSO-based LE and
LMS/RLS-based DFE [38].
An efficient PSO algorithm-based model was developed for near-field time delay
equalizer meta-surface (TDEM) in order to improve the directivity and radiation patterns
of conventional electromagnetic band gap resonator antennas (ERAs) [39]. A model [40] used a PSO tuned ANN inference system-based channel equalizer. The training data
of the equalizer was used, and fuzzy C-means clustering was adopted to model the channel
without a priori knowledge of channel dynamics.
A neural network-based multilayer perceptron was used to equalize non-linear channels
[41]. A modified firefly algorithm was proposed to improve the equalization process. Authors
examined the impact of fading channels on the performance of ZigBee using the IEEE
802.15.4 PHY layer DSSS technique and OQPSK modulation [42]. The LMS adaptive-linear-equalizer was combined with the system to lessen the channel
effects. In order to reduce MSE and increase the convergence, a PSO algorithm was
presented where the inertia weight (w) and position update method were improved for
PSO in this problem [43]. Authors [44] used an ANN trained with Quantum-PSO to solve the equalization problem. The QPSO
estimates the optimal weights of the equalizer in training of the ANN.
Channel estimation of a doubly selective channel was analyzed for filter-bank-multicarrier
(FBMC) waveforms by means of LMMSE [45]. Authors [46] proposed a novel model for MIMO-OFDM for DSC channels. The proposed model was sub-divided
into two major parts: a) firstly, time domain-based training b) secondly, a GA was
used to find the optimal location. Authors proposed an iterative channel estimation
(ICE) and data detection system with the help of the current compressed sensing (CS)
algorithm of approximate message passing (AMP) for an OFDM-based DSC channel [47]. A low-complexity BEM-based model was adapted for a DSC channel in order to eliminate
ICI [48]. Other authors [49] discuss channel estimation for a DSC channel, and a deep learning-based DSC estimation
method was proposed by employing a deep neural network (DNN).
Fig. 1. Classification of the Equalizers.
2. Contribution & Organization of Paper
HCTs like GA, PSO, DE, CSO, BCO, hybrid GA-PSO, and CSA are used for the weight
updating and optimization of the equalizer structure. Equalization of a channel's
effects using HCTs can significantly reduce the computational time complexity. The
figure of merit (FoM) of the problem is the mean squared error (MSE). The research
objectives are as follows:
· Time complexity comparison for GA, PSO, DE, CSO, BCO, Hybrid GA-PSO and CSA
based DSCE’s
· Different modulated sequences are equalized using considered HCT’s.
· Comparison of FoM for considered algorithms.
The rest of the paper is organized as follows. Section II presents the detailed
system model of the proposed equalizer structure. The cost function for the heuristic
algorithms is also calculated. Section III explains the heuristic algorithms with
the help of a flow chart and pseudocode. In section IV, the proposed equalizer structure
is simulated, and the performance of each algorithm is compared. Section V concludes
the paper and gives some future directions.
Fig. 2. Proposed System Model.
3. The Proposed Scheme
The proposed system model is shown in the form of a block diagram in Fig. 2. The input signal $s\left(n\right)$ is QPSK modulated, and the modulated signal $x\left(n\right)$
is convolved with the impulse response of a doubly selective channel; i.e., $h\left(n,~
l\right)$, where $n~ $and $l$ represent the time and frequency domain, respectively.
The received signal with additive white Gaussian noise $\eta \left(n\right)$ is expressed
as follows:
where $L$ is the length of the multipath channel. The received signal is in a
matrix form:
Table 1. Pseudocode of the GA.
Table 2. Pseudocode of the PSO.
where
$\textit{L=L}_{1}$ $\textit{+L}_{2}$ is the equivalent length, and $\textit{L}_{1}$
and $\textit{L}_{2}$ are the equalizer pre-cursor and post-cursor length, respectively
[15]. If$~ h\left(n,~ l\right)=h\left(n\right)$, the channel only contains ICI, and if$~
h\left(n,~ l\right)=h\left(l\right)$, the channel is frequency selective, which corresponds
to ISI. The output of the feed forward filter of the equalizer block is$~ y\left(n\right)$.
The output of the FF filter is not in a form to yield the estimate of the transmitted
signal. Therefore, there is a need to update the weights of the FF filter. For that
purpose, the error function is calculated to adaptively update the weight vector.
The$~ y\left(n\right)~ $and error signal $e\left(n\right)$ is expressed as:
where $w\left(i\right)$ is the weights of the feed forward filter, and N is the
length of the filter. The goal of the cost function is to minimize the error signal,
and for that, we have utilized famous nature-inspired algorithms, such as GA, PSO,
DE, CSO, and CSA. The goal of the objective function is to update the weights of the
feed forward filter and is defined as:
The fitness function (FF) for the all the heuristic techniques are defined as:
HCTs (meta-heuristics) are algorithms inspired by some natural phenomena and used
to find near-optimal global solutions with little computational cost. HCTs are population-based
algorithms that iteratively search for the optimum solution from the defined objective
function [50,51]. The main theme of the research is to minimize the error function (i.e., Eq. (5)) and to maximize the fitness function using Eq. (7). Numerous nature-inspired algorithms have been employed in this research to equalize
the doubly selective channel effects. A brief discussion of the HCT algorithms adapted
for DSCE is carried out in this section.
3.1 Genetic Algorithm
GAs are the most frequently used heuristic algorithms and works using the behaviors
of natural selection and genetics. The solutions are adaptively improved through crossover
and mutation [52,53]. The steps of the algorithms are described in Table 1.
3.2 Particle Swarm Optimization
In PSO, the velocity and position (solution) are adaptively updated by exploiting
the natural processes of birds flocking and fish schooling. It has a high convergence
rate, which is the main reason for the popularity of the algorithm. The rest of the
information, including velocity and position update equations, can be found in other
studies [54-59]. The pseudocode of the PSO is given in Table 2.
3.3 Differential Evolution
DE is a population based stochastic process [60] where a set of parameters evolve through crossover and mutation. It purely works
based on the behavior of survival of the fittest, where a comparison is carried out
between the preceding and proceeding solutions [61-64]. Table 3 shows a brief explanation of the algorithm.
Table 3. Pseudocode of the DE.
Table 4. Pseudocode of the CSO.
Table 5. Pseudocode for BCO.
Table 6. Pseudocode for Hybrid GA-PSO.
3.4 Cat Swarm Optimization
The natural behavior of the cats is exploited to develop the cat swarm optimization.
The cats are updated in two different methods selected by mixing ratio (MR), the methods
are seeking and tracing mode [65-69]. Both modes have diverse set of steps, and later, the solutions from these steps
are combined. A brief description of the algorithm is presented in Table 4.
3.5 Bee Colony Optimization
BCO adapts the natural behavior process of honeybees. The solutions are updated
by searching the neighboring areas through three different processes done by employer
bees, onlooker bees, and scout bees [70-73]. Table 5 presents the brief steps for the BCO algorithm.
3.6 Hybrid GA-PSO
A GA proves to be good for slowly converging problems, while PSO gives good results
for quickly converging problems. For a mixed problem, the benefits of GA and PSO can
be used by hybridizing these two algorithms. The total population is divided into
two halves, and the best half is fed into a GA, whereas the worst is passed through
PSO [74,75]. The algorithm for hybrid GA-PSO is given in Table 6.
3.7 Cuckoo Search Algorithm
CSA is designed to exploit the natural process of the cuckoo bird for laying
their eggs in host birds’ nests. The following two processes evolve the solutions:
levy flights and alien egg discovery. The detailed description of the algorithm can
be found in other studies [76-78]. Table 7 shows the steps of CSA.
Table 7. Pseudocode for CSA.
Table 8. Simulation Parameters.
|
Parameters
|
Values
|
|
Population Size
|
10 to 100
|
|
Averages
|
10
|
|
Filter Length, N
|
50
|
|
Doppler spread, Q
|
10
|
|
Time delays, L
|
5
|
|
SNR
|
-10dB to 10dB
|
|
Genetic Algorithm
|
|
Selection process
|
Roulette Wheel
|
|
Crossover
|
Single Point
|
|
Particle Swarm Optimization
|
|
Inertial weight, w
|
0.8
|
|
Constants: C1, C2
|
1.1
|
|
Differential Evolution
|
|
Crossover rate, CR
|
0.3
|
|
Cat Swarm Optimization
|
|
Counts of Dimensions to change, CDC
|
30%
|
|
Seeking Range of Dimensions, SRD
|
30%
|
|
Seeking Memory Pool, SMP
|
40% of population
|
|
Constant, C
|
1.2
|
|
Mixing Ration, MR
|
0.8
|
|
Cuckoo Search Algorithm
|
|
Discovery probability, Pa
|
0.3
|
|
Beta, ẞ
|
1.5
|
|
Bee Colony Optimization
|
|
Scaling factor for phi, a
|
0.8
|
4. Performance Evaluation
The simulation parameters for the equalization of a doubly selective channel using
HCTs are shown in Table 8. All the simulations were performed in MATLAB software with the following system
specifications: Intel(R) Core$^{TM}$ i-5-7200U CPU @ 2.50 GHz, 16 GB RAM. FoM means
the square of the error, which is represented in terms of the FF in Eq. (7). The FF of each algorithm is compared with the considered HCTs at different SNRs.
The various types of signals considered for the equalization are QPSK, 16-PSK,
64-PSK, 256-PSK, 512-PSK, and 16-QAM. The time complexity of each algorithm was calculated
and compared. A flow chart of the proposed algorithm is shown in Fig. 3. The population is randomly generated weights that are optimized using HCTs, and
the candidate solutions are selected from the population matrix.
Table 9 shows the quantitative analysis results of the FF for the DSCE of QAM signal using
GA, CSA, PSO, DE, CSO, HGP, and BCO. The candidate solutions vary from 10 to 50. For
a number of candidate solutions, extensive simulations are performed with fixed iterations
(i.e., 500 at SNRs of 0, 5, and 10 dB). The minimum MSE is 0.0012, which is represented
in terms of an FF of 0.9988. From the table, it is evident that PSO performs much
better than the other algorithms, even at lower SNRs. The FF is closer to its maximum
value for 50 candidate solutions and for higher SNRs.
For CSO, FF approximately approaches 1 at lower SNRs for 50 candidate solutions.
For HGP, FF is 0.9988 at an SNR of 10 dB, which is the best one among all considered
HCTs. CSA has the worst performance among all the HCTs with a maximum fitness of 0.9541
at SNR of 10 dB with 50 candidate solutions. The BCO algorithm performs very poorly
for lower SNRs, and the minimum fitness achieved is 0.4892 for the 10 candidate solutions.
The performance of BCO at higher SNRs is acceptable.
Fig. 7 shows the DSCE of a 512-PSK signal using PSO and BCO. From the figure, it is clear
that FF for the PSO is 0.99, while for the BCO, it is 0.97. In the second portion
of Fig. 6, the simulation time is shown in minutes. The time complexity of the BCO is quite
high as compared to PSO. The PSO algorithm takes approximately 112 seconds, and BCO
takes 671 seconds for 200 candidate solutions.
Fig. 4 shows the time complexity of each algorithm for a QAM signal. The computation time
was calculated with 500 iterations and for 150 candidate solutions. The time complexity
of the PSO algorithm is only 16 seconds, while BCO takes around 434 seconds. The PSO’s
FF and time complexity are both much better when compared to other HCTs.
In Table 9 and Fig. 4, the PSO algorithm outperforms in terms of FF and time complexity, so it is recommended
to utilize PSO for DSCE. Fig. 4 shows the FF obtained using PSO for the DSC equalization of the QPSK signal. It is
clear from Fig. 5 that FF approaches 1 as SNR increases and approaches 10 dB. The FF was evaluated
for a lower SNR of -10 dB, and in the graph, the FF is approximately 0.9659.
Table 10 shows the DSCE performance for the 16-PSK signal. The number of candidate solutions
and SNR are fixed at 50 and 10 dB, respectively. The FF of each considered algorithm
is shown for different numbers of iterations (500, 1000, 1500, 2000, and 2500). The
PSO outperforms all the HCTs. The maximum fitness approaches 0.99985 and corresponds
to a minimum MSE of 0.00015 (10-4).
The histogram plot in Fig. 6 shows the comparison of FF at a fixed SNR of 10 dB and 100 candidate solutions. Increasing
the number of candidate solutions increases the time complexity of the algorithm and
affects the MMSE and FF. The number of iterations in Fig. 5 is fixed at 2500, and almost all the HCTs provide acceptable MMSE.
Table 11 shows the performance of algorithms for the DSCE of the 16-QAM signal. The FF is
achieved at SNR of 10 dB. The maximum fitness attained with 100 candidate solutions
is approximately 0.83, which is quite less than that of the 16-PSK signal equalization
on DSC. The overall performance of DSCE using HCTs on PSK signals is much better than
that on the QAM signals. The BCO’s maximum attained fitness for the 16-QAM is 0.750148,
and for the 16-PSK signal, it is 0. 93534. Similarly, for the case of GA, the fitness
values achieved for 16-QAm and 16-PSK are 0.617721 and 0.85199, respectively.
Fig. 7 shows the DSCE of the 512-PSK signal using PSO and BCO. From the figure, it is clear
that FF for the PSO is 0.99, while for the BCO, it is 0.97. In the second portion
of Fig. 6, the simulation time is shown in minutes. The time complexity of the BCO is quite
high as compared to PSO. The PSO algorithm takes approximately 112 seconds, and BCO
takes 671 seconds for 200 candidate solutions.
Figs. 8-11 show the performance at a fixed SNR of 10~dB with 100 candidate solutions
for various types of modulated signals (16-PSK, 64-PSK, 256-PSK, and 16-QAM). The
FF approximately approaches the maximum value for all the considered HCTs. PSO and
BCO perform much better than all other algorithms.
Fig. 3. Flow chart of proposed DSCE.
Fig. 4. Time Complexity of HCT’s for DSCE.
Fig. 5. Fitness Function of PSO algorithm for DSCE.
Fig. 6. Fitness Function for DSCE of 16-PSK signal.
Fig. 7. Time Complexity Comparison for 512-PSK signal Equalization.
Fig. 8. FF for DSCE of 16-PSK signal.
Fig. 9. FF for DSCE of 64-PSK signal.
Fig. 10. FF for DSCE of 256-PSK signal.
Fig. 11. FF for DSCE of 16-QAM signal.
Table 9. DSCE for QAM using various HCT’s.
|
Candidate Solutions
|
10
|
20
|
30
|
40
|
50
|
|
GENETIC ALGORITHM (GA)
|
|
SNR=0dB
|
0.9259
|
0.9387
|
0.9388
|
0.9418
|
0.9518
|
|
SNR=5dB
|
0.9320
|
0.9426
|
0.9426
|
0.9478
|
0.9699
|
|
SNR=10dB
|
0.9479
|
0.9449
|
0.9449
|
0.9480
|
0.9752
|
|
CUCKOO SEARCH ALGORITHM (CSA)
|
|
SNR=0dB
|
0.6697
|
0.8495
|
0.9172
|
0.9297
|
0.9480
|
|
SNR=5dB
|
0.6837
|
0.8563
|
0.9253
|
0.9327
|
0.9493
|
|
SNR=10dB
|
0.7086
|
0.8684
|
0.9390
|
0.9406
|
0.9541
|
|
PARTICLE SWARM OPTIMIZATION (PSO)
|
|
SNR=0dB
|
0.8775
|
0.9522
|
0.9709
|
0.9745
|
0.9830
|
|
SNR=5dB
|
0.8670
|
0.9543
|
0.9748
|
0.9797
|
0.9889
|
|
SNR=10dB
|
0.9008
|
0.9615
|
0.9841
|
0.9954
|
0.9963
|
|
DIFFERENTIAL EVOLUTION (DE)
|
|
SNR=0dB
|
0.8203
|
0.9678
|
0.9773
|
0.9716
|
0.9716
|
|
SNR=5dB
|
0.8311
|
0.9739
|
0.9739
|
0.9749
|
0.9749
|
|
SNR=10dB
|
0.8382
|
0.9775
|
0.9775
|
0.9785
|
0.9785
|
|
CAT SWARM OPTIMIZATION (CSO)
|
|
SNR=0dB
|
0.8184
|
0.8793
|
0.9386
|
0.9624
|
0.9868
|
|
SNR=5dB
|
0.8485
|
0.9437
|
0.9688
|
0.9817
|
0.9946
|
|
SNR=10dB
|
0.8687
|
0.9598
|
0.9788
|
0.9945
|
0.9987
|
|
Hybrid GA-PSO (HGP)
|
|
SNR=0dB
|
0.8464
|
0.9084
|
0.9106
|
0.9286
|
0.9624
|
|
SNR=5dB
|
0.8634
|
0.9868
|
0.9868
|
0.9868
|
0.9881
|
|
SNR=10dB
|
0.8820
|
0.9905
|
0.9988
|
0.9988
|
0.9988
|
|
BEE COLONY OPTIMIZATION (BCO)
|
|
SNR=0dB
|
0.4892
|
0.7186
|
0.7990
|
0.8371
|
0.9031
|
|
SNR=5dB
|
0.6078
|
0.7494
|
0.9144
|
0.9103
|
0.9544
|
|
SNR=10dB
|
0.8011
|
0.9301
|
0.9402
|
0.9486
|
0.9622
|
Table 10. DSCE for 16-PSK signal using various HCT’s.
|
Iterations
|
500
|
1000
|
1500
|
2000
|
2500
|
|
GA
|
0.85199
|
0.852338
|
0.922344
|
0.955308
|
0.961455
|
|
CSA
|
0.855159
|
0.885304
|
0.910866
|
0.937291
|
0.989274
|
|
PSO
|
0.958088
|
0.970436
|
0.988625
|
0.999856
|
0.99985
|
|
DE
|
0.86612
|
0.901309
|
0.903469
|
0.972408
|
0.972408
|
|
CSO
|
0.943592
|
0.961777
|
0.99409
|
0.996017
|
0.997269
|
|
H.GA-PSO
|
0.912178
|
0.932166
|
0.933263
|
0.957857
|
0.987442
|
|
BCO
|
0.93534
|
0.938353
|
0.943155
|
0.977558
|
0.995555
|
Table 11. DSCE for 16-QAM signal.
|
Candidate Solutions
|
10
|
20
|
30
|
50
|
70
|
100
|
|
PSO
|
0.689331
|
0.705914
|
0.732587
|
0.743433
|
0.751481
|
0.818931
|
|
BCO
|
0.676435
|
0.685555
|
0.730182
|
0.750148
|
0.780809
|
0.823379
|
|
GA
|
0.542992
|
0.596464
|
0.600279
|
0.617721
|
0.731647
|
0.763755
|
|
CSA
|
0.095441
|
0.304726
|
0.363071
|
0.601148
|
0.612979
|
0.649249
|
|
DE
|
0.3916
|
0.420681
|
0.577255
|
0.61282
|
0.651194
|
0.758186
|
5. Conclusion
The equalization of a doubly selective channel was comprehensively discussed in
this paper. Several HCTs were employed. Various types of modulated signals were considered
to validate the performance of the HCTs. The simulations were carried out at different
SNRs with variable numbers of candidate solutions and different iterations.
From the extensive simulations, it was shown that PSO performs much better in
approximately all considered scenarios compared to GA, CSA, DE, CSO, HGP, and BCO.
The FF approaches its maximum value with lower time complexity. The PSO convergence
for 100 candidate solutions for the 16-QAM modulated signal was approximately 82%,
and compared to other algorithms, there was a 17% improvement in FF.
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Author
Nooh Bany Muhammad is an Assistant Professor of computer science at the College
of Engineering and Applied Sciences at American University of Kuwait. He received
the Bachelor degree of Computer Science and Information Systems from the Jordan University
of Science and Technology, Jordan, in 2007, the M.Sc. and Ph.D. degrees (with honors)
in Computer Science from the University of Southern Mississippi (USM), Mississippi,
USA, in 2010 and 2015, respectively. His current research interests include Security
in Wireless Sensor Networks, Mobile Security, Routing Protocols, Wireless Sensor Networks
Deployments, Web privacy and Cloud security.
Sajjad A. Ghauri received his B.Sc. and MS (Specialization in Signal Processing
and communication) in 2007 & 2010 respectively. He completed his Ph.D. in Electronic
Engineering from ISRA University, Pakistan in 2015. Currently he has been working
as an Associate Professor in Department of Electrical Engineering, School of Engineering
& Applied Sciences, ISRA University, Islamabad. He has been conducting research
in signal processing, communication, heuristic techniques and neural network for past
14 years. Currently, he is working on modulation classification algorithms, smart
grid-based communication systems and application of fractional algorithms in massive
MIMO communication system. He has more than 50 publications in leading recognized
international journals, international and local conference proceedings. He is a member
of several journal and conference program committees.
Mubashar Sarfraz received the bachelor’s degree in Electrical Engineering with
majors in Telecommunications from the National University of Modern Languages, Islamabad,
Pakistan. He is currently pursuing his MS research from ISRA University, Islamabad
and also working as Lab Engineer in Department of Electrical Engineering, NUML. His
research interest includes cognitive radio networks, smart grid communication and
application of heuristic computation techniques in engineering problems.
Adnan Aftab received his Masters of Science in Electronic Engineering from ISRA
University, Islamabad. His research interest in Massive MIMO based smart antennas.