Capsulization of Existing Space Time Techniques

www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 29
IJEEE, Vol. 1, Spl. Issue 1 (March 2014) e-ISSN: 1694-2310 | p-ISSN: 1694-2426
Capsulization of Existing Space Time Techniques
1
Maninder singh, 2
Dr.Hardeep singh Saini
Indo Global College of Engineering, Punjab, India
1
md_singh1989@yahoo.com, 2
hardeep_saini17@yahoo.co.in
Abstract— In this paper, we explore the fundamental
concepts behind the emerging field of space-time coding for
wireless communication system. A space–time code (STC)
is a method which employed to increase the reliability of
data transmission in the wireless communication
systems using multiple transmit antennas. Space–time
code (STC) depends on transmitting
multiple, redundant copies of a data stream to the receiver in
the hope that at least some of them may live the physical
path between transmission and reception section with
reliable decoding.
Keywords— STC; STTC; BLAST;
1. INTRODUCTION
With the increase in demand of increasingly sophisticated
communication services available any-time, anywhere,
wireless communications has emerged as one of the largest
and most rapid and steadfastness sectors of the global
telecommunications industry. A quick look at the status quo
reveals that second and third generation cellular systems
supporting data rates of 9.6 Kbps to 2 Mbps uses by a 700
million people around the world subscribe to existing. More
recently, in wireless LAN networks IEEE 802.11, which
provided 11 Mbps rate and attracted more than $1.6 billion
(USD) in equipment sales [1]. The capabilities of both of
these technologies over the next ten years, are expected to
move toward the 100 Mbps – 1 Gbps range [2] and
subscriber numbers to over 2 billion [3]. One of the most
significant technological developments of the last decade,
that promises to play a key role in realizing this tremendous
growth, is wireless communication using MIMO antenna
architectures.
A space time code (STC) which is used in the wireless
communication to improve the reliability of data
transmission. Space Time Code depends on transmitting
multiple, redundant copies of a data beam to the receiver.
The receiver which in the hope that at least one of them may
live the physical path between both transmission and
reception section. Space time code may be further divided
according to coherent STC and non coherent STC. When the
receiver section the channel impairment through training
called coherent STC[4] and in the non coherent is totally
opposite to the coherent STC .Coherent STC basically is
used widely and division algebras over for making or
constructing codes[6,5],fig1.1 Space time code diagram.[7]
Fig 1.1Space time code diagram [7]
Space time techniques divide into two main parts (see in the
fig) -:
1) Transmit diversity
2) Spatial multiplexing
Fig 1.2 Classification of space time technique [3]
2.SPACE TIME TECHNIQUES
2.1Transmit diversity
2.1.1 Space time block codes –:
The term Space-Time Code (STC) originally got into
existence in 1998 by Tarokh et al. to describe a new two-

International Journal of Electrical & Electronics Engineering 30 www.ijeee-apm.com
dimensional way of encoding and decoding signals
transmitted over wireless fading channels using multiple
transmit antennas.
In this technique, data stream of a multiple copies are
transmits across the number of antennas (MIMO) and this
technique improves the reliability of data transfer. Also, the
transmitted signal must transverse a potentially difficult
environment with scattering, reflection, refraction and then it
effects by thermal noise which effects the information or
data in the receiver section. So, space- time coding basically
add all the copies of the received signal, so in this way it can
easily get the information.
It is divided into three sections. First one is flat quasi-static
fading channel is used in communication system operating
under narrow band conditions, second is frequency selective
fading channel which is used in wideband communication
system[8].
2.1.1.1 Flat quasi-static channel-:
This is further divided into the first one is the Alamouti code
and second is extended version of Alamouti work on which
accommodates large number of transmit antennas, proposed
by Tarokh et al under the name of orthogonal designs. Lately
is linear depression code of Hassibi et al, which address the
capacity limitation of both of these codes and also support
arbitrary number of transmit antenna.
(a)Almouti Block Code-:
It is introduced to improve link-level performance based on
diversity. It is proposed a simple scheme for a 2*2 matrix
system that achieves a full diversity gain with a simple
maximum likelihood decoding algorithm. It is designed from
the view of diversity gain to increased the multiple antenna
transmission scheme in order to achieve the good
performance. Let in the case where these two transmit
antenna by arranging the input symbols (𝑥1, 𝑥2) and input
their complex conjugates in a special 2*2 matrix.
𝑆 =
𝑥1 −𝑥2
∗
𝑥2 𝑥1
∗
Each column of 𝑆 contains the symbols transmitted from the
pair of antennas during a particular symbol period. We see
that second column is a permutation and a reflection of the
complex conjugate of the first. Then 𝑆 over flat fading
channel, written as: where P is the appropriate permutation
reflection matrix.
ℎ−𝑇
𝑆 = [ℎ−𝑇
x ℎ−𝑇
P𝑥∗
]
[(ℎ−𝑇
𝑆)1 (ℎ−𝑇
𝑆)2
∗
] = ℎ−𝑇
(ℎ−𝑇
P)∗
]x
The principle of space time block coding with 2 transmit
antenna and one receive antenna is explained in the post
on Alamouti STBC. With two receive antenna’s the
system can be modeled as shown in the figure below
(fig2.1).
Fig2.1: Transmit 2 Receive Alamouti STBC
The Alamouti space-time block coding is a simple MIMO
technique which can be used to reduce the BER of a
system with a specific SNR and without any loss on the
data rate/information. The presented decoding technique is
called hard decision-based zero forcing and it is easily to
implement in hardware slot. [9]
(b)STBC based orthogonal design-:
It is basically advanced version of Almouti`s work. It
removes the capacity limitations. It also provides full
diversity gain. Example: the code N=U, transmit antenna is
given by
𝑆 =
𝑥1 −𝑥2
−𝑥3 −𝑥4
𝑥2 𝑥1
𝑥4 −𝑥3
𝑥3
𝑥4
−𝑥4
𝑥3
𝑥2 𝑥2
−𝑥2 𝑥1
We seen that each column of S differ from the first by
permutation reflection. Next, we consider a generalized real
orthogonal design, for N=3 transmit antenna.
𝑆 =
𝑥1 −𝑥2
−𝑥3 −𝑥4
𝑥2 𝑥1
𝑥4 −𝑥3
𝑥3 −𝑥4
𝑥1 𝑥2
It views like a counter intuitive at first complex orthogonal
design only exist for N=2 , namely the Almounti`s STBC .
Therefore generalized complex orthogonal design is derived
and various codes are constructed. So, generalized design for
N=4 is given by
𝑆 =
𝑥1 −𝑥2
𝑥2 𝑥1
−𝑥3 −𝑥4 𝑥1
∗ −𝑥2
∗ −𝑥3
∗
−𝑥4
∗
𝑥4 −𝑥3 𝑥2
∗
𝑥1
∗ 𝑥4
∗
−𝑥3
∗
𝑥3 −𝑥4
𝑥4 𝑥3
𝑥2 𝑥2 𝑥3
∗ −𝑥4
∗ −𝑥2
∗
𝑥2
∗
−𝑥2 𝑥1 𝑥4
∗ 𝑥3
∗ −𝑥2
∗
𝑥1
∗
L=8 symbol periods are required to transmit Q=4 symbols,
resulting in a significantly reduced rate but increased the
capacity offered by competitive MIMO scheme such as
BLAST [10,11]. STBC based on amicable designs, which
provide higher rates than those based orthogonal design for
some numbers of transmit and receive antennas [12] and
quasi-orthogonal STBC, which sacrifice diversity to achieve
rate 1 for some condition with more than two transmit
antennas.[13]
(c)Linear dispersion code-:

This is used to realize rates higher than 1 symshz using
STBC transmission, Hassibi et.al. Study the effective
capacity of code based on orthogonal design. It basically
develops a new class of block code designed to maximize the
mutual information between the transmitted and received
signals. The resulting designs are called linear dispersion
codes. Codes for using a set of 2Q dispersion matrices
𝑆 = (𝑥 𝑅𝑞
𝑄
𝑞=1 𝐴 𝑞 + j𝑥𝐼𝑞 𝐵𝑞 )
(1)
Where R stand for real part of complex valued structure and
it is imaginary part. For instance if Q=2 and
𝐴1 =
1 0
0 1
, 𝐵1 =
1 0
0 −1
, 𝐴2 =
0 −1
1 0
, 𝐵2 =
0 1
1 0
then the linear combination of (1) gives
𝑆 =
𝑥 𝑅1 + 𝑗𝑥𝐼1 −𝑥 𝑅2 + 𝑗𝑥𝐼2
𝑥 𝑅2 + 𝑗𝑥𝐼2 −𝑥 𝑅1 − 𝑗𝑥𝐼1
=
𝑥1 −𝑥2
∗
𝑥2 𝑥1
∗
The limitation of LDC is that good designs are not known to
follow systematic or algebraic rules.[14]
2.1.1.2 Frequency Selective Fading Channel:
It is used in STBC for transmission over frequency selective
or multipath fading channel. In this there are two main parts,
in the first class are those techniques for single-carrier
modulation techniques systems that focus on reducing
equalization complexity and this techniques known as time –
reversal approach by LindsKog et al. that takes benefit of
space- time code structure to decrease the dimensionality of
the equalization step.
The second classes of techniques are built around block
processing operations that effectively convert the frequency
selective channel into a set of flat fading sub-channels. These
may employ OFDM with multi-carrier modulation or
Frequency Domain Equalization with single-carrier
modulation.
(a)Time Reversal (TR) STBC-:
This technique is used for single-carrier modulation system
which focuses on reducing equalization complexity. The
proposal in this area is a time-reversal approach by
Zindskog.et.al that takes advantage of the space time code
structure to decrease the dimension of the equalization step.
It is flat fading channel based on orthogonal design. They
are designed for use with single-carrier modulation in
which it simplifying the equalization by decoupling the
problem from LN dimension to N L-dimensional tasks
which may be executed in parallel. The TR-STRC involves
protecting data symbol columns by enclosing each of them
between guard columns of known symbols.
They will refer to these guard blocks as the prefix and suffix,
both must be of length at least K - 1, and denote by the net
length of the protected data block. It is clear that there is
some rate loss associated with the guard blocks, which can
be reduced by increasing the size of the data block.
However, the maximum size of the data blocks is also
limited by the coherence time of the channel 2 In addition
𝐿 , data columns where complex conjugation is applied in
the underlying code are transmitted in time-reversed order,
hence the name given to the code. The accompanying guard
blocks are also conjugated and time-reversed. The
transmitted signal matrix has the following general structure:
It have seen that channel be slowly fading so that
𝐿 = 𝐿0[𝐿 + 2(K-1)] symbol periods, whereas before 𝐿
denotes the gross block length including guard symbols and
𝐿0 is the block length of the underlying STBC design for flat
fading.
The main limitation of the TR-STBC is its limited rate
compared to the potential multiplexing gain available in the
MIMO channel. [15,16]
(b)STBC with frequency domain processing-:
A number of researchers have also considered extensions of
the Alamouti scheme to systems using frequency domain
processing. One of the first proposals for combining STBC
with OFDM and multi-carrier modulation was put forward
by Mudulodu et al. Subsequently, two works based on
single-carrier transmission systems with frequency domain
processing at the receiver were presented by Al-Dhahir and
Zhou et al. All three approaches share substantially similar
signal matrix structures and thus we will follow [17] here.
In this work STBC over frequency selective fading channels
is proposed in combination with FDE. As we shall see, it
exhibits a structure that bears some resemblance to time-
reversal, and thus shares many properties of the TR-STBC.
The transmitted signal matrix is of the form
We note that the rate achieved by this transmission scheme is
fractionally higher than that of the TR-STBC because it does
not require a guard suffix block. [19, 18]
2.1.2 Space time trellis codes (STTC)-:
It is used in the multiple antenna wireless communication. It

transmits multiple redundant copies of a convolutional code
or trellis code distributed over time and with a number of
antennas (MIMO). Then receivers use these multiple,
'diverse' copies of the data to reconstruct the actual
transmitted data. In space time block code, they are able to
provide both coding gain and a better bit error rate
performance. But in space time trellis code they are more
complex than STBCs to encode and decode. They depend on
a viterbi decoder at the receiver where STBCs need only
linear processing. STTC were proposed by Vahid Tarokh et
al. in 1998. Just as trellis codes impose structure within each
code word (cover the code space) and also between code
words transmitted in sequence (over time) the diversity gain
of STTCs is determined via a PEP argument. The PEP
expresses the probability of transmitting 𝑆𝑐 and deciding in
favour of 𝑆𝜀 at the decoder. Defining the code word
difference matrix
B = 𝑆𝑐 − 𝑆𝜀 with SVD B = U 𝑉+
and r = rank B
P(𝑆𝑐 → 𝑆𝜀) < 𝜋𝑖=1
𝑀
𝜋𝑗 =1
𝑟
(𝜎𝑗
2 𝑝
4
)−1
=(det[𝐵𝐵+
])−𝑀
(
𝑝
4
)−𝑀𝑟
(2)
above equation(2) is coding gain of approximately,
𝛾 = [det⁡(𝐵𝐵+
)]
1
𝑟
is achieved.
Fig 2.2: Space time trellis codes
It has high complexity so this is it main limitation. [20]
Comparison between STBC and STTC-:
STBC STTC
1. It has no coding gain. 1. It has coding gain.
2. Easily decodable by
maximum likelihood
decoding via linear
processing.
2. Conserve capacity
irrespective of the number of
antennas.
3. STBC is simple to design
based on orthogonal
sequences.
3. STTC is difficult to
design.
4.For one receive antenna
and state code, performance
is similar to STTC
4. STTC outperforms with
increasing antennas and
trellis states.
5. Easily lends itself to
industrial applications
because of its simplicity.
5. Complex to organize.
6. Loses capacity with two or
more receive antennas.
6.Conserve capacity
irrespective of the number of
antennas.
2.2 Spatial multiplexing –:
In view of the narrowband nature of the transmission, each
data stream follows only one route to the receiver and there
are no multipath experienced by the individual data streams.
In SM system, the maximum number of modulation symbols
that can be transmitted per symbol, maximum (𝑟𝑠) is given
by
max(𝑟𝑠)) =𝑁𝑡
which implies that the maximum spectral efficiency of an
SM system given by
𝜂 𝑚𝑎𝑥 =𝑁𝑡 𝑟𝑡 𝑙𝑜𝑔2(M)bps/Hz
Where 𝑟𝑡 s the rate of any conventional coding used in the
spatial multiplexing system and M is the modulation order.In
general, spatial multiplexing is achieved using a concept
called layered space-time (LST) coding.[21]
2.2.1 Layered space time (LST)-:
Spatial multiplexing is achieved by raising a concept of
layered space time (LST) coding. Foschini proposed LST
architecture. In LST method, SM can also be achieved using
Eigen beam forming, it is a practical SM technique that is
used in most modern wireless communication system. They
are three main approaches are-:
Bell Laboratory layered space-time (BLAST) family of
techniques-:
a) V-Blast (Vertical-Blast)
b) H- Blast (Horizontal Blast)
c) D-Blast (Diagonal Blast
The type of decoding algorithm that is used is an important
consideration for LST coded SM system. Four decoding
schemes are-:
1) Zero Forcing (ZF)
2) Zero Forcing with interference cancellation (ZF-IC)
3) Linear minimum mean square error estimation
(LMMSE)
4) LMMSE with interference cancellation (LMMSE-IC)
(a) VERTICAL BLAST-:
In V-Blast the information bit stream is processed by an
optional conventional error encoder and then split into 𝑁𝑟
data stream, each of which is separately modulation before
being passed to its respective antenna for transmission. The
use of the adjective vertical in v-blast is a reference to the
fact that the input is split into parallel streams that are
depicted vertically in most diagrams encoder employs its
own modulator the V-blast architecture is capable of
accommodating applications where different data rates are
applied to different layers. Layer with higher data rates
might use higher order modulation schemes so that each
layer would have the same bandwidth (fig 2.2 a).

Fig2.2 (a) V-Blast encoding architecture [21]
Since distinct data stream are applied to each of the 𝑁𝑡 layer,
during each use of the channel there are 𝑁𝑡 different
modulation symbols transmitted. Therefore the space-time
code rate associated with the V-BLAST encoder is 𝑅𝑠=𝑁𝑡
and the spectral efficiency is 𝑁𝑡 𝑅𝑡 (M)bps/HZ; where M is
the modulation order. In the case of V-BLAST, Loyka and
Gagnon prove that the diversity order varies from (𝑁𝑟-𝑁𝑡+1)
up to 𝑁𝑟, depending on which layer is being decoded. We
see that N*N V-BLAST only achieves a maximum diversity
gain equal to 1, compared with 𝑁𝑡 𝑁𝑟 for system with full
diversity. [22, 23]
(b) HORIZONTAL-BLAST (H-BLAST)
The H-BLAST encoding architecture shown in fig 2.2 b , it
is basically similar with V-BLAST but only difference is it
includes separate conventional error encoder on each of the
transmit data stream. In this “horizontal” suggest that the
encoder on each layer perform coding in the time domain,
which can be pictured as being horizontal in the picture,
compared with the space dimension that is depicted being
vertical(fig2.2 b).[24]
Fig 2.2(b) H-Blast encoding architecture[21,25]
(c) DIAGONAL-BLAST (D-BLAST)
The D-BLAST encoding architecture shown in fig 2.2 c, it is
basically similar with H-BLAST but only difference is it
includes a block after the modulator that performs stream
rotation. Let we take a example we assume that 𝑁𝑡=4 and
output are divided into blocks consisting of 𝑁𝑡 consecutive
segments, the output of the four convential encoders are
vectors denoted by a, b, c and d and then output of four
encoded segments out of convential encoder 1 by 𝑎1,𝑎2,𝑎3,
and 𝑎4,the next set of four encoded segments by
a5,a6,a7,anda8 Rather than simply passing the modulated
outputs from each encoder onto its respective antenna, the
stream rotator rotates the modulated segments in a round-
robin fashion by performing two operation: a) it distributes
consecutive sequences of 𝑁𝑡 segments from each encoder
onto each of the antenna; b) the order of the encoders that it
operated on is chosen in a circularly rotated manner rather
than simply sequentially from encoder 1 to 𝑁𝑡.
In D-BLAST, each diagonal layer constitutes a complete
code word then decoding is done layer by layer. The
advantage of this type of BLAST techniques is that the
outputs from each conventional encoder are distributed over
space which provides a grater spatial diversity (fig2.2 c).
[26]
Fig2.2(c) D-Blast encoding architecture [21, 25]
2.2.2 THREADED SPACE-TIME ENCODING (TSTE)-:
TST proposed by El Gamal et al. It was developed to enable
the construction of full rates and full diversity MIMO
transmission by combining layering ideas with constituent
space time codes. it is based on partitioning the space time
signal matrix into non-overlapping threads .In this method
mixes the signal more thoroughly across the antennas than
does the D-BLAST diagonal system. The last block is a
spatial interleave, which interleaves the symbols as shown in
fig2.3 in the space time matrix and each shade shows a
thread. We have one code word per thread, in the first

columns the symbols of each layer are not shifted and in
second columns they are shifted once in a cyclic manner. In
the third column they are shifted twice and so on. The 𝑀𝑡
*matrix A contains the symbols transmitted over the Mt
transmit antennas for l symbol periods. We can describe each
layer in general by specifying a set of elements from A. Let
L= (𝐿1, 𝐿2,.. 𝐿 𝑚𝑡 ) be set of indices specifying the elements of
A. Mathematically LI is defined as[27,28]
𝐿𝑖 = { ([t+i-1]𝑀 𝑇 + 1,l): 0≤ 𝑡 ≤ 𝑙}
Fig2.3Threaded Space-Time encoding architecture [21, 25]
3. CONCLUSION
We have study the various types of the space-time codes
techniques in which every techniques it own advantages and
limitation like generally, in the interest of coding gain, we
prefer to use trellis codes instead of block codes within the
space-time architecture, trellis codes provides higher coding
gain but come at the cost of increased decoding complexity.
We have also study that TLST codes yielded the maximum
transmit diversity. The V-BLAST which has gained a lot of
popularity because of its simplicity.
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AUTHORS
Maninder Singh is following M.Tech
from Indo Global College of
Engineering, India. He has completed
B.Tech from IGCE, Mohali (Punjab),
India in the year 2011. He has two
year of educational expertise.
Working as Assistant Professor (ECE)
at indo global college of Engineering, Abhipur (Mohali) since
June-2012.His areas of interest are wireless and mobile
communication, Optical communication.
Hardeep Singh Saini obtained his
Doctorate degree in Electronics and
Communication Engineering in 2012. He holds Master’s
degree in Electronic and communication from Punjab
technical university, jalandhar passed in 2007. His total
experience is 15 year, presently, working as Professor (ECE)
and Associate Dean Academic at Indo Global college of
Engineering, Abhipur (Mohali), PUNJAB (INDIA) since
June-2007. He is author of 5 books in the field of
communication Engineering. He has presented 21 papers in
international /national conferences and published 30 papers
in international journals. He is a fellow and senior member
of various prestigious societies like IETE (India), IEEE,
UACEE, IACSIT and he is also editorial member of various
international journals.

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