On the performance of code word diversity based quasi orthogonal space time block codes in multiple-input- multiple-output systems

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 3, June 2020, pp. 2535~2542
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i3.pp2535-2542  2535
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
On the performance of code word diversity based quasi
orthogonal space time block codes in multiple-input-
multiple-output systems
Senthilkumar Kumaraswamy1
, Palanivelan Manickavelu2
, Noormohammed Valimohamad3
,
Helanvidhya Thankaraj4
, Yogalakshmi Venkatesan5
, Bakyalakshmi Veeraragavan6
1,2,4,5,6
Department of Electronics and Communication Engineering, Rajalakshmi Engineering College, Chennai, India
3
School of Electronics Engineering, Vellore Institute of Technology, Vellore, TN, India
Article Info ABSTRACT
Article history:
Received Jun 12, 2019
Revised Nov 13, 2019
Accepted Nov 22, 2019
In the recent past, a lot of researches have been put into designing a Multiple-
Input-Multiple-Output (MIMO) system to provide multimedia services with
higher quality and at higher data rate. On par with these requirements,
a novel Quasi Orthogonal Space Time Block Code (QOSTBC) scheme based
on code word diversity is proposed, which is a multi-dimensional approach,
in this paper. The term code word diversity is coined, since the information
symbols were spread across many code words in addition to traditional time
and spatial spreading, without increasing transmission power and bandwidth.
The receiver with perfect channel state information estimates the transmitted
symbols with less probability of error, as more number of samples is available
to estimate given number of symbols due to the extra diversity due to code
words. The simulation results show a significant improvement in the Bit Error
Rate (BER) performance of the proposed scheme when compared with
the conventional schemes.
Keywords:
Bit error rate
Diversity
Multiple-input-multiple-output
Quasi orthogonal space time
block code
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Senthilkumar Kumaraswamy,
Department of Electronics and Communication Engineering,
Rajalakshmi Engineering College,
Rajalakshmi Nagar, Thandalam, Chennai, Tamil Nadu 602105, India.
Email: senthilkumar.kumaraswamy@rajalakshmi.edu.in
1. INTRODUCTION
Higher data rate and reliability are the demands of the modern day applications and are met by
Multiple-Input-Multiple-Output (MIMO) technique. Exhaustive research was carried out in the past and still it
is a field of interest. MIMO systems have become the field of attraction in recent times, as they support high
speed applications without demanding extra communication resources like power and bandwidth [1, 2].
Space-Time Block Coding (STBC) is a scheme developed for MIMO systems to provide higher diversity gain
and coding gain [3]. The subcarrier power allocation algorithms to meet the requirements of next generation
wireless technology are proposed in [4-6]. In [7], a multipath diversity scheme in conjunction with OFDM is
proposed to improve the BER performance of a MIMO system. Orthogonal Space Time Block Code (OSTBC)
is a kind of STBC, having faster Maximum Likelihood (ML) decoding ability due to its orthogonal
property [8], however, suffers a drawback of ability to offer full rate only for two antennas, for complex
constellations [9] and [10]. QOSTBC has gained the attention as an alternative to overcome this drawback with
a compromise in orthogonality, which in turn compromises with diversity order and decoding complexity [11].
To improve Bit Error Rate (BER) performance of QOSTBC, optimum constellation rotation is proposed
in [12]. In [13], a receive antenna selection scheme without feedback requirement for exploiting the advantages
of MIMO is proposed. Cooperative diversity schemes for exploiting advantages of MIMO are proposed
in [14-20]. In contrast to the open loop QOSTBCs mentioned above, several closed loop QOSTBC schemes

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 3, June 2020 : 2535 - 2542
2536
are presented in [21-24] for better performance. The drawbacks of these schemes are higher cost and
complexity due to the feedback. In [25, 26], the channel state information is computed at the receiver and fed
back to the transmitter via single bit of information. Based on the feedback, the transmitter selects one of its
two code words for transmission, which suits better for the present channel conditions. In [27], a scheme that
selects best code word for a given channel condition is presented. All these works are based on the truth that
the channels respond differently for different spatial locations (i.e. spatial diversity), at different instances of
time (i.e. temporal diversity), for different frequencies (i.e. frequency diversity) and for different polarizations
(i.e. polarization diversity).
Similarly, the channels respond differently for different QOSTBC code words, for one code word,
the performance may be good at one instant of time and the same may yield a poor performance later.
A multidimensional approach for space-time coding is proposed in [28], which combined spatial and temporal
diversity with spatial multiplexing. The three dimensional tensor coding considered transmitting antenna, time
and data stream as its dimensions. In [29], the authors have proposed Multiple Khatri-Rao Space-Time
(MKRST) code for improving the performance of MIMO systems by providing additional diversity either in
time or space. In [30], the authors have proposed Double Orthogonal Vandermonde constrained Alternating
Least Square (DOVALS) algorithm to utilize the orthogonal structures in the factored matrices.
From the literature, it is understood that increasing the number of received signals without increasing
the frequency, time and power requirement is still an open problem. It is also clear that the full potential of
diversity is not fully exploited. The idea of the proposed work is that all the code words that are transmitted
will not suffer the same channel impairments and with a hope that at least one will be received in good
condition, similar to the concepts of time, space and frequency diversity. But, the proposed work makes use of
code word diversity, in addition to space and time diversity for improving the BER performance of the system.
To the best of our knowledge, this is the first work on multidimensional approach for code word diversity with
QOSTBC. The proposed work makes use of code word diversity in addition to the space and time diversity.
The proposed work transmits multiple code words simultaneously with the same power and bandwidth, without
requiring feedback. Thus, the performance of the proposed work is better than the conventional schemes, thanks
to the extra code word diversity.
The main contribution of the proposed scheme is the increase in the number of received signals by
increasing the number of code words for a fixed number of symbols to be estimated. The following are
the notations used in this paper. The superscripts  .

, .
T
and  .
H
denotes complex conjugate, transpose and
transconjugate (i.e. Hermitian transpose) respectively. Extraction of diagonal elements from a matrix is denoted
by  .diag . The Moore Penrose pseudo inverse of a matrix and Frobenius norm are denoted by (.)†
and . F
respectively. The rest of the paper is organized as follows. System model is described in section 2. Performance
analysis is presented in section 3. Results and discussions are presented in section 4. Finally, section 5
concludes the paper.
2. SYSTEM MODEL
We have considered quasi-static, flat fading Rayleigh channel which remains constant during
transmission of one block and changes for next. The transmitter of the proposed system consists of a Code
word-Space-Time (CST) encoder, which spreads the complex information symbols from the symbol mapper,
across three dimensions i.e. in space, time and code words. There are A transmitting antennas at the transmitter,
which simultaneously transmits C QOSTBC code words in N time slots. The receiver consists of K antennas,
which adds one more dimension and hence the received signal is a four dimensional signal. With the perfect
channel state information at the receiver, the Code word-Space-Time decoder estimates the transmitted
symbols. The block diagram of the transmitter and receiver of proposed code word diversity based QOSTBC
scheme is given in Figure 1 and Figure 2.
Figure 1. Transmitter of the proposed code word diversity based QOSTBC scheme

Int J Elec & Comp Eng ISSN: 2088-8708 
On the performance of code word diversity based quasi orthogonal… (Senthilkumar Kumaraswamy)
2537
Figure 2. Receiver of the proposed code word diversity based QOSTBC scheme
The incoming bit stream (i.e. 2N bits per block) is mapped onto a complex constellation like QAM or
QPSK and a symbol sequence S of length N is obtained and is given by (1) as
S = [s1,s2,….,sN] 𝒞 1×N
(1)
These information symbols are spread across time, space and code words (3-D) by multiplying with a 3-
dimensional information spreading matrix W and is given by (2) as
W = ej2πanc|ANC 𝒞A×N×C
(2)
where A is the number of transmitting antennas, N is the number of time slots required for transmitting a code
word, C is the number of code words that are simultaneously transmitted. The information spread matrix G is
obtained by element wise product of W in (2) and S in (1) along the dimension N and is given by (3)
𝐺𝐴𝐶
𝑁
= 𝑊𝐴𝐶
𝑁
𝑆 𝐴×N×C
(3)
The information spread matrix G is transmitted through A transmit antennas in N successive time slots.
The transmitted signal X is obtained by element wise product of G and H along the dimension N and is given
by (4) as
XAC
N
= GAC
N
HACK
N (4)
where H  𝒞 A×N×C×K
is the channel matrix whose entries are independent and identically distributed with zero
mean and unit variance. The received signal R is given by (5) as
R = X+Z  𝒞A×N×C×K
(5)
where the noise Z 𝒞A×N×C×K
, whose entries are independent samples of a circularly symmetric complex
Gaussian random variable with zero mean and unit variance. The symbols are decoded at the receiver by
making use of matrix unfolding as follows. The unfolding is done across the plane C. For better understanding
about the unfolding of a matrix, [25] can be referred. The unfolded received signal Runfolded and the unfolded
spreading matrix is Wunfolded given by (6) as
Runfolded = [
R..1
⋮
R..c
] and
Wunfolded = [
W..1
⋮
W..c
] 𝒞ACK×N
(6)
The unfolded channel Hunfolded matrix is given by (7) as
𝑅 𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑 = [
𝐻..1
⋮
𝐻..𝑐
] 𝒞 ACK×N (7)
The unfolded received signal Xunfolded is represented by (8) as
Xunfolded = Gunfolded.* Hunfolded (8)

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2538
=[𝑊𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑 .∗ 𝑆].∗ 𝐻 𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑 (9)
= [𝑊𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑 .∗ 𝐻 𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑].∗ 𝑆 (10)
The transmitted symbols Ŝ can be estimated at the receiver using (10) and it is given by (11) as
Ŝ=diag[[𝑊𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑.∗ 𝐻 𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑]†
.∗ 𝑋 𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑] (11)
From (11), it can be understood that a blind joint symbol and channel estimation is possible using Alternate
Least Square (ALS) technique.
3. PERFORMANCE ANALYSIS
In this section, we have analyzed the performance of the proposed scheme and presented the equation
for maximum diversity gain. In general, the Pair wise Error Probability (PEP) of the Maximum Likelihood
(ML) estimator of the code word matrix is used as a measure of performance. The equation for the maximum
diversity gain can be derived from PEP. The PEP of the ML estimator is as follows.
P(S → Ŝ|H) = Q (‖ 𝑋 − 𝑋‖F / 2√𝑁𝑜/2) (12)
Due to space constraints, we skip the intermediate steps and present the final result of the derivation for
maximum diversity gain maxd in (13) as
dmax = A× C × K × N (13)
The performance comparison between the conventional schemes and the proposed scheme is presented in
Table 1.
Table 1 Comparison of diversity gain and code rate of the proposed code word diversity
based QOSTBC with conventional schemes
Scheme Diversity gain Code rate
Zhu Chen code [25] Full diversity
(M × N)
Full rate
(Unity)
Gerard code [28] Full diversity
(K×P×J×min(M, R))
< Full rate
(
𝑃
𝑅
)
Proposed code word diversity Full diversity
( A×C×K×N)
Full rate
(Unity)
4. RESULTS AND DISCUSSIONS
In this section, we have evaluated the error performance of the proposed code word diversity scheme
in a quasi static flat fading channel by means of Monte Carlo simulations. The receiver is assumed to have
perfect channel state information. The simulation parameters are shown in Table 2. Figure 3 compares
the proposed code word diversity scheme with conventional unrotated QOSTBC, rotated QOSTBC, Zhu Chen
code [25], Gerard code [28], MKRST [29] and DOVALS [30]. We adopt QPSK constellation for simulating
the BER over SNR. The BER for paper [21] is evaluated for a block length of four (P=4), spreading length of
one (J=1), with two transmitting (M=2) and two receiving antennas (K=2). For simulating paper [25], unrotated
QOSTBC and rotated QOSTBC, we have considered four transmitting antennas and one receiving antenna as
mentioned in the original papers. For simulating the proposed code word diversity scheme, we have assumed
four transmitting antennas (A=4) for transmitting three code words (C=3) simultaneously and one receiving
antenna (K=1). From the Figure 3, it is observed that BER of all the schemes decreases with increase in SNR.
It is also clear that the proposed scheme outperforms the schemes of [25] and [28], due to spreading across
code words in addition to time and space. The proposed scheme achieves a SNR gain of 6.7 dB at the BER of
10-5
over [25] and around 2 dB over [28]. The proposed scheme achieves a SNR gain of 2 dB at the BER of
10-5
over [29] and around 1.4 dB over [30].

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In Figure 4, we show the effect of number of code words on the BER performance of the proposed
code word diversity scheme. From the figure, it is observed that BER of all the schemes decreases with increase
in SNR. For a given number of receive antenna, the BER decreases with increase in number of code words.
Also, for a given number of code words, the BER decreases with increase in number of receive antenna.
We found that the proposed scheme with C=3, K=3 outperforms proposed scheme with other values of C
and K, due to increase in number of samples for estimating the same number of symbols, but at the cost of
increase in computational complexity. The effect of constellation size on the BER performance of the proposed
scheme is investigated for various values of M, with single receive antenna.
Table 2. Simulation parameters
Parameter Value
Modulation QAM and QPSK
Noise AWGN
Channel quasi static flat fading
Number of receive antennas 1, 2, 3 and 4
Number of receive antennas 1, 2, 3 and 4
Figure 3. Comparison of BER performance of
proposed code word diversity based QOSTBC with
conventional schemes
Figure 4. Influence of the number of code words C
and number of receive antennas K on the BER
performance of the proposed code word diversity
based QOSTBC
Figure 5 depicts the influence of 128-QAM on BER with C = 1, 2 and 3. It is observed that the BER
performance of the proposed scheme with 128-QAM improves with increase in SNR for all the C values
considered. At a SNR of 10 dB, the BER values for C = 1, 2 and 3 are 9x10-2
, 4x10-2
and 2.8x10-2
respectively.
From the figure, it is evident that the BER performance of a MIMO system improves with code word diversity
(i.e. C = 2 and C = 3) when compared to the scheme without code word diversity (i.e. C = 1).
Figure 6 shows the impact of 64-QAM on BER with C = 1, 2 and 3. It is observed that the BER
, 2.8x10-2
and 2x10-2
respectively.
(i.e. C = 2 and C = 3) when compared to the scheme without code word diversity (i.e. C = 1). On comparing
Figure 5 and Figure 6, it is observed that the BER for C=3 with 128-QAM is 2.8x10-2
at 10 dB, whereas it is
2x10-2
for C=3 with 64-QAM. Therefore, it is clear that the BER performance of the proposed scheme improves
with reduction in constellation size.
Figure 7 illustrates the effect of 16-QAM on BER with C = 1, 2 and 3. It is observed that the BER
, 1x10-2
and 3.5x10-3
respectively.
Figure 6 and Figure 7, it is observed that the BER for C=3 with 64-QAM is 20x10-3
at 10 dB, whereas it is
3.5x10-3
for C=3 with 16-QAM. Therefore, it is clear that the BER performance of the proposed scheme
improves with reduction in constellation size.
0 2 4 6 8 10 12 14 16 18 20
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR in dB
BER
Rotated QOSTBC
Unrotated QOSTBC
Zhu Chen Code
Gerard Code
MKRST
DOVALS
Proposed Code Word Diversity
0 2 4 6 8 10 12 14 16 18 20
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
SNR in dB
BER
C=1; K=1
C=1; K=2
C=1; K=3
C=2; K=1
C=2; K=2
C=2; K=3
C=3; K=1
C=3; K=2
C=3; K=3

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2540
Figure 8 depicts the influence of 4-QAM on BER with C = 1, 2 and 3. It is observed that the BER
, 2.5x10-4
and 4x10-5
respectively.
Figure 7 and Figure 8, it is observed that the BER for C=3 with 4-QAM is 3.5x10-5
at 10 dB, whereas it is 4x10-
5
for C=3 with 16-QAM. Therefore, it is clear that the BER performance of the proposed scheme improves
with reduction in constellation size. From the figures, it is clear that the BER performance of the proposed
scheme degrades with increase in constellation size for given number of code words. Also it is observed that
the BER performance improves with increase in number of code words for a given constellation size. From the
figures it is clear that larger number of code words with smaller constellation size would be beneficial.
Figure 5. Influence of 128-QAM on the BER
based QOSTBC for various values of C
Figure 8 Influence of 4-QAM on the BER
performance of the proposed codeword diversity
5. CONCLUSION
We have presented a novel code word diversity scheme for QOSTBC in this paper. From the simulated
results, it is evident that the addition of code word diversity to the conventional space and time diversity,
achieves a SNR gain of 6.7 dB at the BER of 10-5
over Zhu Chen code and around 2 dB over Gerard code and
MKRST scheme, and around 1.4 dB over DOVALS scheme without increasing transmission power and
bandwidth. The BER performance of the proposed code improves with increase in the number of code words,
0 2 4 6 8 10 12 14 16 18 20
10
-4
10
-3
10
-2
10
-1
10
0
SNR in dB
BER
C=1; 128-QAM
C=2; 128-QAM
C=3; 128-QAM
0 2 4 6 8 10 12 14 16 18 20
10
-4
10
-3
10
-2
10
-1
10
0
SNR in dB
BER
C=1; 64-QAM
C=2; 64-QAM
C=3; 64-QAM
0 2 4 6 8 10 12 14 16 18 20
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR in dB
BER
C=1; 16-QAM
C=2; 16-QAM
C=3; 16-QAM
0 2 4 6 8 10 12 14 16 18 20
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR in dB
BER
C=1; 4-QAM
C=2; 4-QAM
C=3; 4-QAM

2541
across which the information symbols are spread, at the cost of increase in computational complexity. In future,
the proposed work can be extended by considering frequency diversity as quasi orthogonal space-time-
frequency code along with code word diversity. Also the performance of the proposed work can be improved
by incorporating error correcting codes such as turbo and low density parity check codes.
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BIOGRAPHIES OF AUTHORS
K. Senthil Kumar obtained his Ph.D. at Anna University, Chennai, India in the year 2018.
He received his Master Degree from Rajalakshmi Engineering College, Chennai in 2009. In the year
2002, he received his bachelor's degree in Engineering from Bharath Niketan Engineering College,
Theni. He is working as an Associate Professor in the department of ECE, Rajalakshmi Engineering
College, India. His research interests include wireless communications, information & coding theory
and MIMO wireless communication systems.
M. Palanivelan is currently working as a Professor & Head, Department of ECE, Rajalakshmi
Engineering College, Chennai. He received his Ph.D at Anna University in the year 2015 and Master
Degree from College of Engineering, Guindy, Anna University, in the year 2001. His research
interests include Wireless communications, Information and coding theory, Optical Networks and
Multiple antenna wireless communication
Noor Mohammed Vali Mohamad received his B.E., Degree in Electronics and Communication
Engineering from Madras University, Tamil Nadu, India, in 1999 and M.E., Degree in
Communication Systems from Madurai Kamarj University, Tamil Nadu, India in 2003. He received
his Ph.D in Wireless Communication and Networking from Vellore Institute of Technology (VIT),
Vellore, Tamil Nadu, India. Currently he is Associate Professor in School of Electronics
Engineering, VIT, Vellore, Tamil Nadu India. He is a member in IEEE and life member in ISTE.
He has published more than fifty papers, in reputed journals and conferences. His research interests
include Resource allocation in next generation, wireless networks, Massive MIMO and Green
Communication.
T. Helan Vidhya is a member of ISTE and IACSIT. She completed B.E (Electronics and
communication engineering) in Bhajarang Engineering College in 2009 and M.E (Applied
Electronics) in St. Joseph's college of Engineering in 2011. Currently, working as an Assistant
Professor in the Department of Electronics and Communication Engineering, Rajalakshmi
Engineering College, Thandalam and having teaching experience of 8.3 years. Her area of interests
are communication engineering and image processing.
V. Yogalakshmi obtained her Master Degree in Applied Electronics from Arunai Engineering
College in the year of 2012. Currently, she is working as an Assistant professor in the Department
of Electronics and Communication Engineering, Rajalakshmi Engineering College with 6 years of
experience. Her research interest includes wireless communication, speech processing and signal
processing.
V. Bakyalakshmi obtained her Master Degree in communication systems from Rajalakshmi
Engineering College, Chennai in 2016. In the year 2014, she received her bachelor's degree in
Electronics and Communication Engineering from Adhiparasakthi College of Engineering, Kalavai.
She is working as an assistant professor in the department of ECE, Rajalakshmi Engineering College,
India. Her research interests include wireless communication and optical communication.

On the performance of code word diversity based quasi orthogonal space time block codes in multiple-input- multiple-output systems

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On the performance of code word diversity based quasi orthogonal space time block codes in multiple-input- multiple-output systems