Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 13, No. 3, June 2023, pp. 2865~2875
ISSN: 2088-8708, DOI: 10.11591/ijece.v13i3.pp2865-2875  2865
Journal homepage: http://ijece.iaescore.com
Indexed-channel estimation under frequency and time-selective
fading channels in high-mobility systems
Ali Alqatawneh1
, Luae Al-Tarawneh2
, Ziyad Almajali3
1
Computer Engineering and Communication Department, Tafila Technical University, Tafila, Jordan
2
Communications Engineering Department, Princess Sumaya University for Technology, Amman, Jordan
3
Electrical Engineering Department, Mu’tah University, Al-Karak, Jordan
Article Info ABSTRACT
Article history:
Received Jun 10, 2022
Revised Oct 24, 2022
Accepted Dec 2, 2022
Index modulation (IM) techniques have been employed in different
communication systems to improve bandwidth efficiency by carrying
additional information bits. In high-mobility communication systems and
under both time-selective and frequency-selective fading channels with
Doppler spread, channel variations can be tracked by employing pilot-aided
channel estimation with minimum mean-squared error estimation. However,
inserting pilot symbols among information symbols reduces the system's
spectral efficiency in pilot-aided channel estimation schemes. We propose
pilot-aided channel estimation with zero-pilot symbols and an energy
detection scheme to tackle this issue. Part of the information bit-stream is
conveyed by the indices of zero-pilot symbols leading to an increase in the
system's spectral efficiency. We used an energy detector at the receiver to
detect the transmitted zero-pilot symbols. This paper examines the impacts
of diversity order on the zero-pilot symbol detection error probability and
the mean-squared of error estimation. The impacts of pilot symbols number
and the zero-pilot symbol number on the mean-squared error of the
minimum mean-squared error (MMSE) estimator and the system error
performance are also investigated in this paper.
Keywords:
Diversity order
Doppler spread
Energy detection
Index modulation
Pilot symbols
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ali Alqatawneh
Computer Engineering and Communication Department, Faculty of Engineering, Tafila Technical
University
Tafila, Jordan
Email: ali.qatawneh@ttu.edu.jo
1. INTRODUCTION
The availability of high-speed broadband wireless communication services such as online video
streaming and gaming, internet of things applications, and multimedia transmission [1] has become necessary
in high-speed transport such as aircraft, trains, and unmanned aerial vehicles (UAV) [2]. In high-mobility
wireless communication systems, Doppler spread is a critical design parameter that should be considered to
maximize the system's performance. High mobility of vehicles, such as high-speed trains (HST), produces a
large Doppler spread that can destroy orthogonality among subcarriers in multi-carrier systems leading to
intercarrier interference (ICI) [3], [4]. Furthermore, these variations result in channel estimate errors.
It is shown in [5] that the error performance of a communication system with perfectly known
channel state information (PNCSI) consistently outperforms an identical system with channel estimation
errors, and the performance gap increases with Doppler spread. However, channel variations can provide
significant Doppler diversity, leading to performance enhancement [6], [7]. The tradeoff between channel
estimation errors and Doppler diversity is investigated in [8]. Results show that a system with imperfect

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 13, No. 3, June 2023: 2865-2875
2866
channel estimation can achieve the same diversity order as a system with PNCSI if the signal-to-noise ratio
(SNR) of data and pilot symbols have a linear relationship with each other [9]. The authors of [10] show that
at low pilot percentage, the benefits of Doppler diversity might be reduced due to channel estimation errors.
If the pilot samples the channel at a rate greater or equal to the Nyquist rate of the time-variant channel, the
mean squared of channel estimation at pilot and data symbols is equal [11]. The optimum pilot percentage
that maximizes the system spectral efficiency is examined in [12], where the results reveal that the pilot
symbols should be assigned more energy with Doppler spread increase. Pilot estimation based on sending
pilot symbols is examined in [13] for bad urban, typical urban and rural areas. In adaptive filter-based
channel estimation, combining channel estimation and space-time coding can improve channel estimation
process [14]. Pilot-assisted channel estimation techniques with least-square (LS) or minimum mean-squared
error (MMSE) are widely used [15], [16]. In the Rayleigh and Rician channels, the MMSE estimator
outperforms the LS estimator. The MMSE estimator, on the other hand, is more complex than the LS
[17]–[19].
Sending pilot symbols among data symbols for channel estimation reduced the spectral efficiency of
the wireless system. Spectral efficiency reduction in systems with pilot-assisted based channel estimation
schemes can be compensated using index modulation. The primary goal of index modulation is to improve
the spectral efficiency of the communication system by sending extra bits using: the indices of the active
subcarriers in multi-carrier communication system [20]–[22], indices of Hermite Gaussian pulses [23],
indices of pilot positions [24], indices of transmit antennas of multiple input multiple output (MIMO)
systems [25], and impedance matching between transmitter and receiver [26]. In [27], the performance of an
energy detector for an unknown signal transmitted over fading channels and additive white Gaussian noise
(AWGN) is studied. The findings indicate that improving the detection probability considerably improves the
detection error performance. Energy detection is commonly used for spectrum sensing in cognitive
communication due to its simplicity, and it does not require prior knowledge about the targeted signal [28],
[29]; the detection is performed by comparing the energy of the received signal with a predefined threshold.
This paper studies the performance of channel estimations with pilot symbol selection technique in
high mobility wireless communications under frequency and time selective fading channels. In the studied
system, pilot symbols are inserted among data symbols and then transmitted for channel estimation purposes.
Some inserted pilot symbols are zero-pilot symbols; the positions of zero-pilot symbols and their numbers are
chosen according to a part of the transmitted data bits. Based on the channel length, extra zeros are added
between data and pilot symbols to maintain non-zero pilot symbols from inter-symbol interference. Energy
detection is employed at the receiver to detect the zero pilot symbols, and then the transmitted pilot sequence
can be determined. From a look-up table, the assigned data bits sent using zero pilot symbols positions can be
determined. The detected pilot symbols are then used for channel estimation at pilot and data symbol
locations with the help of the MMSE estimator.
This paper also investigates the impact of channel length, number of total pilot symbols, number of
zero-pilot symbols, signal-to-noise ratio, and Doppler spread on the mean squared error of channel
estimation. The rest of this paper is organized as follows: section 2 presents the system model. Section 3
presents results and discussion, and finally, section 4 concludes the paper.
2. RESEARCH METHOD
2.1. System model
Consider a wireless communication system that operates on frequency and time-selective fading
channels and uses pilot-aided channel estimation with pilot symbol selection technique. In this system, the
transmitted bit stream is split into two groups: group 𝐴, with 𝑝1binary bits, is converted to M-array phase
shift keying (PSK) symbols, and group 𝐵, with 𝑝2 bits, which is transmitted through zero-value primary pilot
symbol selection technique. In this technique, a pilot-slot is added after every 𝐾-length M-array PSK
symbols. Each pilot slot contains 2𝐿 − 1 symbols, where 𝐿 is the length of the multipath fading channel. The
primary pilot symbol is the middle of the pilot slot, which is selected as 1 or 0 based on bits in the group 𝐵.
The rest of the pilot-slot contains 2𝐿 − 1 zeros or secondary pilots located before and after each primary pilot
symbol to prevent the primary pilot symbol from inter-symbol interference (ISI) problems due to frequency
and time selective fading channels. The data symbols along with primary and secondary pilot symbols are
transmitted as one segment of length 𝑁 + 𝑁𝐾, where 𝑁 is the number of the primary pilot symbols and 𝑁𝐾
is the number of data symbols. The relationship between the number of bits in group 𝐵 and the number of the
primary pilot with zero symbols and the number of inserted primary pilots can be expressed as
𝑝2 = ⌊log2(𝐶(𝑁, 𝑚)) ⌋ with 𝐶 being the binomial operation and ⌊ ⌋ being the floor function. The number of
primary pilot symbols with 0s and their locations are determined based on data bits in group 𝐵.

Int J Elec & Comp Eng ISSN: 2088-8708 
Indexed-channel estimation under frequency and time-selective fading channels … (Ali Alqatawneh)
2867
For each transmitted pilot slot there will an 𝐿 ISI-free received signals. The l-th
received signal of the
n-th
transmitted pilot symbol 𝑥𝑝(𝑛) ∈ {−1,1,0} is given as (1):
𝑦𝑝(𝑛) = √𝐸𝑝ℎ𝑝 (𝑛, 𝑙)𝑥𝑝(𝑛) + 𝑤𝑝(𝑛 + 𝑙) (1)
for
𝑛 = 0, ⋯ , (𝑁 − 1), 𝑙 = 0, ⋯ , 𝐿 − 1
where 𝑦𝑝(𝑛) is the n-th
received signal at pilot-symbol position, h(n,l) is the discrete-time impulse response of
the transmission channel, 𝐸𝑝 is the energy of the transmitted non-zero pilot symbol, and 𝑤𝑝(𝑛 + 𝑙) is the
corresponding AWGN with noise power N0. We set 𝐸𝑝 = 𝐸𝑠(2𝐿 − 1) with 𝐸𝑠 being the energy of each data
symbol due to fixed transmission power assumption. Vector format can be used to represent the 𝐿 ISI-free
received signals from the n-th
transmitted pilot symbol as (2):
[
𝑦𝑝(𝑛)
𝑦𝑝(𝑛 + 1)
⋮
𝑦𝑝(𝑛 + 𝐿 − 1)]
=
[
ℎ𝑝(𝑛, 0)
ℎ𝑝(𝑛, 1)
⋮
ℎ𝑝(𝑛, 𝐿 − 1)]
𝑥𝑝(𝑛) +
[
𝑤𝑝(𝑛)
𝑤𝑝(𝑛 + 1)
⋮
𝑤𝑝(𝑛 + 𝐿 − 1)]
(2)
or equivalently (2) can be written as (3):
𝑦𝑝
𝑛
= √𝐸𝑝ℎ𝑝
𝑛
𝑥𝑝(𝑛) + 𝑤𝑝
𝑛
(3)
where
𝑦𝑝
𝑛
=
[
𝑦𝑝(𝑛)
𝑦𝑝(𝑛 + 1)
⋮
𝑦𝑝(𝑛 + 𝐿 − 1)]
, ℎ𝑝
𝑛
=
[
ℎ𝑝(𝑛, 0)
ℎ𝑝(𝑛, 1)
⋮
ℎ𝑝(𝑛, 𝐿 − 1)]
, 𝑤𝑝
𝑛
=
[
𝑤𝑝(𝑛)
𝑤𝑝(𝑛 + 1)
⋮
𝑤𝑝(𝑛 + 𝐿 − 1)]
As shown in (3) for every transmitted pilot symbol there would be an L observed signals at the receiver.
2.2. Energy detection of transmitted pilot symbols
In this sub-section, we discuss the application of an energy detector in pilot symbol detection at the
receiver side. Depending on the pilot symbol whether zero or non-zero pilot symbol, the observed signals at
the receiver for pilot symbols can indicate one of two states that can be modeled as (4) [30]:
𝑦𝑝
𝑛
= √𝐸𝑝ℎ𝑝
𝑛
𝑥𝑝(𝑛) + 𝑤𝑝
𝑛
for non zero pilot (4)
𝑦𝑝
𝑛
= 𝑤𝑝
𝑛
(5)
So, according to (5), the noise signal is the only signal observed at the receiver when the transmitted pilot is
zero-pilot symbol. Energy detection can be employed to determine whether the transmitted pilot is a zero-
pilot or a non-zero pilot by computing the energy of the received pilot signals; the computed energy is then
compared with a predefined threshold. The energy of the n-th
pilot symbol can be computed as (6):
𝐸𝑛 =
1
𝐿
̄
∑ |𝑦𝑝(𝑛 + 𝑙)|
2
𝐿
̄ −1
𝑙=0 (6)
where 𝐿
̄ is the number of pilot-signal arrival paths that have been taken into consideration when computing
the energy of the observed pilot signal; 𝐿
̄ also represents the diversity order. To collect all benefits from full
diversity offered by multipath fading, all observed signal for the n-th
transmitted pilot symbol should be
considered in (6), i.e., 𝐿
̄ = 𝐿. After energy calculation, the transmitted pilot symbol can then be determined
as (8):
𝑥
̂𝑝(𝑛) = {
1, If 𝐸𝑛 > 𝑁𝑜
0, If 𝐸𝑛 ≤ 𝑁𝑜
} (7)

 ISSN: 2088-8708
2868
where =𝑁𝑜 is considered as the detection threshold. The detected pilot symbols can be expressed in vector
format as 𝑥
̂𝑝(𝑛) = [𝑥
̂𝑝(1), 𝑥
̂𝑝(2), ⋯ , 𝑥
̂𝑝(𝑁)]. After detecting all the transmitted pilot symbols, the
transmitted bits sent over the indices of zero-pilot symbols can then be specified using a predetermined
lookup table.
2.3. Pilot-based channel estimation
After detecting the pilot symbols, the detected pilot symbols are used for channel estimation. This
sub-section presents channel estimation based on the detected pilot symbols. After detecting all pilot
symbols, the observed signals from all pilot symbols can be approximately expressed in vector format as (8):
𝑦
̂𝑝 = √𝐸𝑝ℎ𝑝𝑋
̂𝑝 + 𝑤𝑝 (8)
where
ℎ𝑝 =
[
ℎ𝑝
0
ℎ𝑝
1
⋮
ℎ𝑝
𝑁𝑝−1
]
, 𝑋
̂𝑝 = diag(x
̂𝑝 ⊗ 1𝐿×1),and w𝑝 =
[
𝑤𝑝
0
𝑤𝑝
1
⋮
𝑤𝑝
𝑁𝑝−1
]
with  being the Kronecker tensor product. The channel coefficients at pilot positions can be estimated as
ℎ
̂𝑝 = 𝐷𝑝
𝐻
𝑦𝑝, where 𝐷𝑝 denotes the channel estimation matrix. By minimizing the mean-squared error (MSE)
between the estimated channel coefficients and the true ones, and based on the orthogonal principle 𝐸[(ℎ
̂𝑝 −
ℎ𝑝)𝑦
̂𝑝
𝐻
], with 𝐸 being the mathematical expectation. The estimation channel matrix can be obtained as [15]:
𝐸[(ℎ
̂𝑝𝑦𝑝
𝐻
− ℎ𝑝𝑦𝑝
𝐻
)] = 𝐸[(𝐷𝑝
𝐻
𝑦𝑝𝑦𝑝
𝐻
− ℎ𝑝𝑦𝑝
𝐻
)] = 0 (9)
where
𝐸[𝐷𝑝
𝐻
𝑦𝑝𝑦𝑝
𝐻
] = 𝐷𝑝
𝐻
(𝐸𝑝𝑋
̂𝑝𝐷𝑝𝑝𝑋
̂𝑝
𝐻
+ 𝑁𝑜𝐼𝐿𝑁𝑝
)−1
(10)
and
𝐸[ℎ𝑝𝑦𝑝
𝐻
] = √𝐸𝑝𝐸[ℎ𝑝(ℎ𝑝
𝐻
𝑋𝑝
𝐻
+ 𝑤𝑝
𝐻
)] = √𝐸𝑝𝐷𝑝𝑝𝑋
̂𝑝
𝐻
(11)
where 𝐷𝑝𝑝 = 𝐸[ℎ𝑝ℎ𝑝
𝐻
].
From (9)-(11) we can find the minimum MSE (MMSE) estimation matrix as (12):
𝐷𝑝 = √𝐸𝑝(𝐸𝑝𝑋
̂𝑝
𝐻
)−1
𝑋
̂𝑝𝑅𝑝𝑝 (12)
Following the procedure above, the pilot symbols at data positions can be estimated as ℎ
̂𝑑 = 𝐷𝑑 ℎ
̂𝑝, where 𝐷𝑑
represents the estimation matrix. By minimizing the mean-squared error between the estimated channel
coefficient and the real ones, and based on the orthogonal principle, the estimation channel matrix can be
obtained as 𝐸 [(ℎ
̂𝑑 − ℎ𝑑)ℎ
̂𝑝
𝐻
] = 𝐸 [(ℎ
̂𝑑ℎ
̂𝑝
𝐻
− ℎ𝑑ℎ
̂𝑝
𝐻
)] = 𝐸[𝐷𝑑 ℎ
̂𝑝ℎ
̂𝑝 − ℎ𝑑(𝐷𝑑 𝑦𝑝)𝐻
], from which we can find 𝐷𝑑
as (13).
𝐷𝑑 = √𝐸𝑝𝐷𝑑𝑝𝑋
̂𝑝
𝐻
𝐷𝑝 (𝐷𝑝
𝐻
(𝐸𝑝𝑋
̂𝑝
𝐻
)𝐷𝑝)
−1
(13)
Where 𝐷𝑑𝑝 = 𝐸[ℎ𝑑ℎ𝑝
𝐻
]. The channel coefficients at data-symbols locations are then estimated as (14) [15]:
ℎ
̂𝑑 = √𝐸𝑝𝐷𝑑𝑝𝑋𝑝
𝐻
(𝐸𝑝𝑋
̂𝑝
𝐻
)−1
𝑦
̂𝑝 (14)
2.4. Channel estimation mean-squared error
To calculate the MSE of channel estimation associated with pilot symbols, let 𝑒𝑝 = ℎ
̂𝑝 − ℎ𝑝, then
the auto-correlation matrix of channel estimation error, 𝑃𝑒, can be defined as 𝑃𝑒 = 𝐸[𝑒𝑝𝑒𝑝
𝐻
] = 𝐸[(ℎ
̂𝑝 −
ℎ𝑝)(ℎ
̂𝑝 − ℎ𝑝)𝐻
and can be obtained as (15).

2869
𝑃𝑒 = 𝐷𝑝𝑝 − 𝐷𝑝𝑝𝑋
̂𝑝
𝐻
(𝐸𝑝𝑋
̂𝑝
𝐻
+
𝑁0
𝐸𝑠(2𝐿−1)
𝐼𝐿𝑁𝑝
)−1
𝑋
̂𝑝𝐷𝑝𝑝
𝐻
(15)
Furthermore, the MSE of channel estimation of channel coefficients at the data positions can be obtained as
𝜎𝑝 =
1
𝐾𝑁
∑ 𝜙𝑘
𝐾𝑁
𝑘=1 , where 𝜙𝑘is the eigenvalues of the matrix 𝑃𝑒. Likewise, to calculate the MSE estimation of
channel coefficients at data symbols positions, let 𝑒𝑑 = ℎ
̂𝑑 − ℎ𝑑, then the auto-correlation noise matrix
𝛹𝑒 = 𝐸[𝑒𝑑𝑒𝑑
𝐻
] can be found as
𝛹𝑒 = 𝐷𝑑𝑑 − 𝐷𝑑𝑝𝑋
̂𝑝
𝐻
(𝐸𝑝𝑋
̂𝑝
𝐻
+
𝑁0
𝐸𝑠(2𝐿−1)
𝐼𝐿𝑁)−1
𝑋
̂𝑝𝐷𝑑𝑝
𝐻
(16)
The MSE of channel estimation of channel coefficients at the data positions can be calculated as
𝜎𝑑 =
1
𝐾𝑁
∑ 𝜆𝑘
𝐾𝑁
𝑘=1 ,
where 𝜆𝑘 is the eigenvalues of the matrix 𝛹𝑒 [31].
3. RESULTS AND DISCUSSION
In this section, we present the performance and the mean-squared error of channel estimation for a
system with an energy detection-based pilot channel estimation operating under frequency and time-selective
fading channels. In the simulation, we consider a multipath fading model with equal power taps. Also, we
assume that the data symbol energy is 𝐸𝑠 = 1 and the data slot length is 𝐾 = 1. In Figure 1, the simulated
primary-pilot symbol energy detection probability of error (PE) is shown for three different levels of
diversities under a channel of length 𝐿 = 3. The curves were obtained for systems with 𝑁 = 8,
𝑚 = 2, and 𝑓𝐷𝑇𝑠 = 0.003. As expected, the best performance occurs at the full diversity with diversity order
equals 𝐿
̅ = 3. As an illustration, the detection probability of error at 𝐸𝑏/𝑁o= 20 dB is 1.14 × 10−2
at
diversity order 𝐿
̅ = 1, while, the detection probability of error reduces to 2.906 × 10−4
, and 5 × 10−6
at
𝐿
̅ = 2 and 𝐿
̅ = 3, respectively.
Figure 1. Presenting the simulated primary pilot-symbols detection error probability as a function of the
signal-to-noise ratio, 𝐸𝑏/𝑁o, under different diversity orders
The detection error probabilities for the transmitted primary-pilot symbols and bits transmitted
through a primary-pilot symbol selection under different channel lengths are presented in Figure 2.
Simulations were performed under the full-diversity assumption. Furthermore, all error probability curves
were obtained for systems with 𝑁 = 8, 𝑚 = 3, 𝑓𝐷𝑇𝑠 = 0.003, and 𝑇𝑠 = 3.69 μs. According to Figure 2, the
detection error probabilities for both primary-pilot symbols and bits transmitted via zero-primary-pilot
symbol selection show improvement with channel length increase. This improvement is due to an
enhancement in a multipath diversity gain caused by the rise in the channel length.

 ISSN: 2088-8708
2870
Figure 2. Illustrating the probability of error of the primary-pilot symbol detection and the probability of
error for bits transmitted via indices of zero-primary pilot symbols as a function of signal-to-noise ratio,
𝐸𝑏/𝑁o, under different channel lengths
Figure 3 shows plots the mean-squared error (MSE) of channel estimation at pilot-symbol positions
as a function of 𝐸𝑏/𝑁o and under different channel lengths. We assume 𝑁 = 16, 𝑓𝐷𝑇𝑠 = 0.002, 𝑚 = 2 and
full diversity for all systems. Perfect matching between simulation and analytical results can be easily seen
from the figure. As expected and due to the enhancement in multipath-diversity gain, the mean-squared error
of channel estimation for the proposed system decreases as channel length increases. As an example, at
𝐸𝑏/𝑁o=10 dB, the MSE is 2.3 × 10−3
when L=4; however, it increases to 3 × 10−3
, and 4.5 × 10−3
when
L=3, and L=2, respectively.
Figure 3. Presenting the MSE of channel estimation at pilot positions as a function of signal-to-noise ratio,
𝐸𝑏/𝑁o, for various values of 𝐿
In Figure 4, we plot the simulated and the numerical mean-squared error of channel estimation at
pilot and data symbol locations. The mean-squared error curves were plotted as a function of 𝐸𝑏/𝑁o under
various numbers of pilot symbols. The system parameters used in simulations are m=2, 𝑓𝐷𝑇𝑠 = 0.002, 𝐿 = 2,
and diversity order 𝐿
̅ = 2. We can see an excellent agreement between simulation and numerical results. As
predicted, at a given number of zero-primary pilot symbols, m, a larger value of primary pilot symbols, N,
can reduce the mean-squared error of channel estimation. Thus, a longer transmitted sequence can provide
better channel estimation.

2871
Figure 4. plotting the MSE of channel coefficient estimation as a function of signal-to-noise ratio, 𝐸𝑏/𝑁o,
and under different pilot numbers, 𝑁
In Figure 5, we compare the simulated MSE of the proposed system with the simulated MSE of a
system with a conventional channel estimation scheme at which 𝑚 = 0. In the figure, we plot the MSEs as a
function of 𝐸𝑏/𝑁o under different numbers of zero-primary pilot symbols, 𝑚. The systems parameters are set
as 𝑇𝑠 = 3.69 μs, 𝑓𝐷𝑇𝑠 = 0.001, and 𝐿 = 2 with full diversity order. As expected, the MSE is a decreasing
function of the zero-primary pilot symbol percentage 𝑚/𝑁, rising this percentage leads to channel estimation
error reduction. Figure 5 shows that, at 𝑁 = 16 increasing 𝑚 from 2 to 5 leads to an increase in MSE over its
counterpart in the classical system. However, the MSE difference between the proposed and the conventional
systems becomes very small when the number of primary pilots increases to 𝑁 = 48. For example, at
𝑁 = 48 and 𝑚 = 0, an MSE of 10−4
can be reached at a signal-to-noise ratio of 23.25 dB; however, we
need extra 0.75 dB to reach the same MSE value when 𝑚 = 5. On the other hand, at 𝑁 = 16, the MSE of
10−4
is reached at a signal-to-noise ratio of 26.5 dB when 𝑚 = 0, the required signal-to-noise ratio increases
to 28.5 dB to reach the same MSE value when 𝑚 = 5.
Figure 5. Presenting the MSE of channel estimation for the proposed system as a function of signal-to-noise
ratio, 𝐸𝑏/𝑁o and under different system configurations
In Figure 6, the MSE of the proposed system is plotted as a function of the number of zero-pilot
symbols, m, under different values of inserted pilot symbols N. The system parameters are set as
𝐸𝑏/𝑁o=15 dB, L=2, 𝑇𝑠 = 66.7 μs, 𝑓𝐷𝑇𝑠 = 0.001, and full diversity. From Figure 6, we can see that
increasing the number of zero-pilot symbols leads to an increase in the MSE of the proposed system. This

 ISSN: 2088-8708
2872
increase widens the channel estimation error gap between the proposed system and an equivalent system with
the classical channel estimation at which m=0. However, this gap can be reduced by increasing the number of
pilot symbols. For example, at 𝑚 =6, the MSE percentage difference between the two systems is 55.45% at
𝑁 = 16; fortunately, it becomes 14.45% when 𝑁 = 48.
Figure 7 shows the MSE of channel estimation for the proposed system at both pilot and data
symbols positions versus 𝑓𝐷𝑇𝑠 for different values of 𝐸𝑏/𝑁o. We set the simulation parameters as
𝑁 = 32, 𝑚 = 2, 𝐿 = 2, 𝑇𝑠 = 3.69μs, and full diversity order. From the figure we note that there are
agreements between simulated and analytical results. Furthermore, the figure shows that the mean-squared
error for channel estimations increases with Doppler diversity rise. However, at the same value of Doppler
spread 𝑓𝐷, increasing 𝐸𝑏/𝑁o leads to a reduction in the mean-squared error of channel estimation.
Figure 6. Illustrating the MSE of channel estimation at pilot and data positions as a function of the number of
zero-primary pilot symbols m
Figure 7. Presenting the MSE of channel estimation at both pilot and data positions versus 𝑓𝐷𝑇𝑠. The curves
obtained at different values of signal-to-noise ratio, 𝐸𝑏/𝑁o
Finally, Figure 8 presents the MSE of channel estimation at pilot-symbol locations for the proposed
system as a function of 𝑓𝐷𝑇𝑠. The Results are obtained under different values of 𝐸𝑏/𝑁o, and number of
primary-pilot symbols 𝑁. The system configurations are set as 𝑚 = 2, 𝐿 = 2, and full diversity order. As
expected, at fixed Doppler spread and zero-primary pilot symbols, the channel estimation errors can be
reduced either by increasing the number of pilot symbols or by increasing the signal-to-noise ratio 𝐸𝑏/𝑁o.
For example, at 𝑓𝐷𝑇𝑠 = 0.005 the value of the MSE is 4.4 × 10−3
when 𝐸𝑏/𝑁o equals to 10 dB, while at the
same value of 𝑓𝐷𝑇𝑠 the MSE value reduces to 1.57 × 10−4
when 𝐸𝑏/𝑁o equals to 25 dB. Moreover, at

2873
𝑓𝐷𝑇𝑠 = 0.004 and 𝐸𝑏/𝑁o = 25 dB the values of MSE are 4.6 × 10−3
, 2.45 × 10−4
, and 1.44 × 10−4
when
𝑁 = 8, 16 and 32, respectively.
Figure 8. Presenting the MSE of channel estimation at both pilot and data positions versus 𝑓𝐷𝑇𝑠. The curves
obtained at different pilot numbers
4. CONCLUSION
This paper presents a pilot-aided channel estimation system with zero-primary pilot symbol
selection. In this system, we set some selected primary pilot symbols to zero. The locations of these zero-
pilot symbols are employed to transmit extra data bits over frequency and time-selective fading channels.
Energy detection has been used at the receiver to detect the transmitted zero-pilot symbols. In this paper, we
examine the impacts of diversity order on both the zero-pilot symbol detection error probability and the mean
squared error of channel estimation. We have also studied channel length's effect on the collected diversity
and the overall system performance. Our results showed that increasing the number of zero-primary pilot
symbols can improve system throughput and increase channel estimation errors. It turns out that, at a fixed
number of zero-primary pilot symbols, increasing the number of primary pilot symbols inserted among the
data symbol can significantly reduce channel estimation errors.
REFERENCES
[1] A. Rafay, S. M. Idrus, K. M. Yusof, and S. H. Mohammad, “A survey on advanced transmission technologies for high bandwidth
and good signal quality for high-speed railways,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS),
vol. 23, no. 1, pp. 293–301, Jul. 2021, doi: 10.11591/ijeecs.v23.i1.pp293-301.
[2] V. A. Aalo, P. S. Bithas, and G. P. Efthymoglou, “On the impact of user mobility on the performance of wireless receivers,” IEEE
Access, vol. 8, pp. 197300–197311, 2020, doi: 10.1109/ACCESS.2020.3034450.
[3] H. Zhang, W. Li, and Y. Xu, “EM-based channel estimation with index modulation for high speed train communication,” in 2019
International Conference on Communications, Information System and Computer Engineering (CISCE), Jul. 2019, pp. 390–394,
doi: 10.1109/CISCE.2019.00092.
[4] Z. Sheng, H. D. Tuan, H. H. Nguyen, and Y. Fang, “Pilot optimization for estimation of high-mobility OFDM channels,” IEEE
Transactions on Vehicular Technology, vol. 66, no. 10, pp. 8795–8806, Oct. 2017, doi: 10.1109/TVT.2017.2694821.
[5] W. Zhou, J. Wu, and P. Fan, “On the maximum Doppler diversity of high mobility systems with imperfect channel state
information,” in 2015 IEEE International Conference on Communications (ICC), Jun. 2015, pp. 4431–4436, doi:
10.1109/ICC.2015.7249020.
[6] X. Hou, J. Ling, and D. Wang, “Performance of high-mobility MIMO communications with Doppler diversity,” IEEE Access,
vol. 8, pp. 31574–31585, 2020, doi: 10.1109/ACCESS.2020.2973268.
[7] W. Zhou, J. Wu, and P. Fan, “High mobility wireless communications with doppler diversity: fundamental performance limits,”
IEEE Transactions on Wireless Communications, vol. 14, no. 12, pp. 6981–6992, Dec. 2015, doi: 10.1109/TWC.2015.2463276.
[8] M. A. Mahamadu, J. Wu, Z. Ma, W. Zhou, Y. Tang, and P. Fan, “Fundamental tradeoff between doppler diversity and channel
estimation errors in SIMO high mobility communication systems,” IEEE Access, vol. 6, pp. 21867–21878, 2018, doi:
10.1109/ACCESS.2018.2826438.
[9] M. A. Mahamadu, J. Wu, Z. Ma, W. Zhou, and P. Fan, “Maximum diversity order of SIMO high mobility systems with imperfect
channel state information,” in 2017 IEEE 17th
International Conference on Communication Technology (ICCT), Oct. 2017,
pp. 212–217, doi: 10.1109/ICCT.2017.8359633.
[10] W. Zhou, J. Wu, and P. Fan, “Spectral efficient doppler diversity transmissions in high mobility systems with channel estimation
errors,” in 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), May 2015, vol. 2015, no. 1, pp. 1–6, doi:
10.1109/VTCSpring.2015.7146098.

 ISSN: 2088-8708
2874
[11] N. Sun and J. X. Wu, “Maximizing spectral efficiency with imperfect channel information in high mobility systems,” in 2013
IEEE Global Communications Conference (GLOBECOM), Dec. 2013, pp. 3359–3364, doi: 10.1109/GLOCOM.2013.6831591.
[12] N. Sun, J. Wu, and P. Fan, “Optimum designs of high mobility wireless systems with channel estimation errors,” IET
Communications, vol. 9, no. 13, pp. 1677–1682, Sep. 2015, doi: 10.1049/iet-com.2014.0952.
[13] H. A.-J. Al-Asady, H. F. Fakhruldeen, and M. Q. Alsudani, “Channel estimation of OFDM in C-band communication systems
under different distribution conditions,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 23,
no. 3, pp. 1778–1782, Sep. 2021, doi: 10.11591/ijeecs.v23.i3.pp1778-1782.
[14] S. Pyla, K. Padma Raju, and N. B. Subrahmanyam, “Performance analysis of adaptive filter channel estimated MIMO OFDM
communication system,” International Journal of Electrical and Computer Engineering (IJECE), vol. 8, no. 5, pp. 3829-3838,
Oct. 2018, doi: 10.11591/ijece.v8i5.pp3829-3838.
[15] A. Alqatawneh and L. Tarawneh, “OFDM system with half-symbol-spaced receiver and channel acquisition error over multipath
fading channels,” Jordan Journal of Electrical Engineering, vol. 7, no. 2, 2021, doi: 10.5455/jjee.204-1613432117.
[16] J.-W. Choi and Y.-H. Lee, “Optimum pilot pattern for channel estimation in OFDM systems,” IEEE Transactions on Wireless
Communications, vol. 4, no. 5, pp. 2083–2088, Sep. 2005, doi: 10.1109/TWC.2005.853891.
[17] M. B. Sutar and V. S. Patil, “LS and MMSE estimation with different fading channels for OFDM system,” in 2017 International
Conference of Electronics, Communication and Aerospace Technology (ICECA), Apr. 2017, pp. 740–745, doi:
10.1109/ICECA.2017.8203641.
[18] M. K. Abboud and B. M. Sabbar, “Performance evaluation of high mobility OFDM channel estimation techniques,” International
Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 3, pp. 2562–2568, Jun. 2020, doi:
10.11591/ijece.v10i3.pp2562-2568.
[19] J. A. Sam and A. K. Nair, “Analysis and implementation of channel estimation in OFDM system using pilot symbols,” in 2016
International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT), Dec. 2016,
pp. 725–728, doi: 10.1109/ICCICCT.2016.7988047.
[20] J. Li, S. Dang, M. Wen, X.-Q. Jiang, Y. Peng, and H. Hai, “Layered orthogonal frequency division multiplexing with index
modulation,” IEEE Systems Journal, vol. 13, no. 4, pp. 3793–3802, Dec. 2019, doi: 10.1109/JSYST.2019.2918068.
[21] P. Wei, C. Zhou, Y. Xiao, and S. Q. Li, “GFDM with interleaved subcarrier-index modulation,” Dianzi Keji Daxue
Xuebao/Journal of the University of Electronic Science and Technology of China, vol. 46, no. 3, pp. 516–521, 2017, doi:
10.3969/j.issn.1001-0548.2017.03.007.
[22] S. Althunibat, R. Mesleh, and E. Basar, “Differential subcarrier index modulation,” IEEE Transactions on Vehicular Technology,
vol. 67, no. 8, pp. 7429–7436, Aug. 2018, doi: 10.1109/TVT.2018.2837691.
[23] S. Aldirmaz-Colak, E. Aydin, Y. Celik, Y. Acar, and E. Basar, “Pulse index modulation,” IEEE Communications Letters, vol. 25,
no. 7, pp. 2309–2313, Jul. 2021, doi: 10.1109/LCOMM.2021.3073753.
[24] Q. Li, M. Wen, Y. Zhang, J. Li, F. Chen, and F. Ji, “Pilot insertion with index modulation for OFDM-based vehicular
communications,” in 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Nov. 2018,
pp. 1204–1208, doi: 10.1109/GlobalSIP.2018.8646384.
[25] E. Basar, M. Wen, R. Mesleh, M. Di Renzo, Y. Xiao, and H. Haas, “Index modulation techniques for next-generation wireless
networks,” IEEE Access, vol. 5, pp. 16693–16746, 2017, doi: 10.1109/ACCESS.2017.2737528.
[26] H. Y. LEE and S. Y. Shin, “A novel index modulation scheme with impedance matching,” Indonesian Journal of Electrical
Engineering and Computer Science (IJEECS), vol. 14, no. 3, pp. 1203–1209, Jun. 2019, doi: 10.11591/ijeecs.v14.i3.pp1203-1209.
[27] R. Agarwal, N. Srivastava, and H. Katiyar, “On the energy detection of unknown signals over fading channel for different
diversity combining techniques,” in Proceedings of the International Conference on Industrial Engineering and Operations
Management, 2016, no. 1.
[28] S. Rodriguez-Parera, V. Ramon, A. Bourdoux, F. Horlin, and R. Lauwereins, “Spectrum sensing over SIMO multi-path fading
channels based on energy detection,” in IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference, 2008,
pp. 1–6, doi: 10.1109/GLOCOM.2008.ECP.571.
[29] G. M. Salama and S. A. Taha, “Cooperative spectrum sensing and hard decision rules for cognitive radio network,” in 2020 3rd
International Conference on Computer Applications and Information Security (ICCAIS), Mar. 2020, pp. 1–6, doi:
10.1109/ICCAIS48893.2020.9096740.
[30] S. Atapattu, C. Tellambura, and H. Jiang, “Performance of an energy detector over channels with both multipath fading and
shadowing,” IEEE Transactions on Wireless Communications, vol. 9, no. 12, pp. 3662–3670, Dec. 2010, doi:
10.1109/TWC.2010.100110.091042.
[31] S. M. Blinder, “Guide to essential math: a review for physics, chemistry and engineering students,” Choice Reviews Online,
vol. 46, no. 7, pp. 46-3902-46–3902, Mar. 2009, doi: 10.5860/CHOICE.46-3902.
BIOGRAPHIES OF AUTHORS
Ali Alqatawneh is an Assistant Professor at Computer Engineering and
Communication Department at Tafila Technical University, Jordan. He received a B.Sc.
degree in communication engineering from Mu’tah University, Jordan, an M.Sc. degree in
communication engineering from Mu’tah University, and a Ph.D. degree in Electrical
Engineering with a specialization in wireless communication from the University of Arkansas,
USA. His research experience covers various topics in wireless communications, such as
multicarrier multiple access techniques, channel estimation techniques, high mobility wireless
communications, cognitive radio networks, and orthogonal frequency division multiplexing
with index modulation. He can be contacted at email: ali.qatawneh@ttu.edu.jo.

2875
Luae Al-Tarawneh received his Ph.D. degree in electrical and computer
engineering from Southern Illinois University (SIU), Carbondale, Illinois in 2016, USA, M.Sc.
degree in communications engineering from the University of Jordan, Amman, Jordan in
2008, and B.Sc. degree in communications engineering from Mu’tah University,
Al-Karak, in 1999. Dr. Al-Tarawneh has been with the department of communications
engineering at Princess Sumaya University for Technology (PSUT) since January 2019. He
currently serves as an assistant professor of communications engineering at PSUT. Dr. Al-
Tarawneh’s current research interests are in optical communication networks, wireless
communications and related fields. He can be contacted at email: l.altarawneh@psut.edu.jo.
Ziyad Almajali is an Assistant Professor at Electrical Engineering Department,
Mu’tah University, Al-Karak, Jordan. since 2015. Received his Ph.D. degree in electrical and
electronic engineering from Liverpool University in 2016, UK, M.Sc. degree in electrical and
computer engineering from New York Institute of Technology, Amman, Jordan in 2004, and
B.Sc. degree in electrical engineering from Mu’tah University, Al-Karak, in 1997. His
research interests are in Smart Grids challenges in Electrical Power Systems and its related
fields. He can be contacted at email: ziyad@mutah.edu.jo.

Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems

More Related Content

Similar to Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems (20)

More from IJECEIAES (20)

Recently uploaded (20)

Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems