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

1Maninder singh,

2Dr.Hardeep singh Saini

Indo Global College of Engineering, Punjab, India 1md_singh1989@yahoo.com,

2hardeep_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-

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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−𝑇𝑆 = [ℎ−𝑇 x ℎ−𝑇P𝑥∗ ]

[(ℎ−𝑇𝑆 )1 (ℎ−𝑇𝑆 )2

∗] = ℎ−𝑇 (ℎ−𝑇P)∗]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 𝑥1𝑥4 −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 𝑥1𝑥4 −𝑥3

𝑥3 −𝑥4𝑥1 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-:

www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 31

This is used to realize rates higher than 1 sym\s\hz\ 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 = (𝑥𝑅𝑞𝑄𝑞=1 𝐴𝑞 + j𝑥𝐼𝑞𝐵𝑞 )

(1)

Where R stand for real part of complex valued structure and

it is imaginary part. For instance if Q=2 and

𝐴1 = 1 00 1

, 𝐵1 = 1 00 −1

, 𝐴2 = 0 −11 0

, 𝐵2 = 0 11 0

then the linear combination of (1) gives

𝑆 = 𝑥𝑅1 + 𝑗𝑥𝐼1 −𝑥𝑅2 + 𝑗𝑥𝐼2

𝑥𝑅2 + 𝑗𝑥𝐼2 −𝑥𝑅1 − 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

International Journal of Electrical & Electronics Engineering 32 www.ijeee-apm.com

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 (𝜎𝑗2 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

𝜂𝑚𝑎𝑥 =𝑁𝑡𝑟𝑡 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).

www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 33

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 𝑁𝑡𝑅𝑡 (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 𝑁𝑡𝑁𝑟 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

International Journal of Electrical & Electronics Engineering 34 www.ijeee-apm.com

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,.. 𝐿𝑚𝑡 ) be set of indices specifying the elements of

A. Mathematically LI is defined as[27,28]

𝐿𝑖 = { ([t+i-1]𝑀𝑇 + 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.