A NUMERICAL COMPARISON BETWEEN LSSTC AND VBLAST IN

WIRELESS SYSTEMS

Ahmad S. Salim, Salam A. Zummo and Samir N. Al-Ghadhban

Electrical Eng. Dept., King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia

Keywords:

Layered steered space-time codes, LSSTC, VBLAST, Capacity, Symbol error rate.

Abstract:

In this work we evaluate a recently proposed multiple-input multiple-output (MIMO) system called the

Layered Steered Space-Time Codes (LSSTC) that combines the beneﬁts of vertical Bell Labs space-time

(VBLAST) scheme, space-time block codes (STBC) and beamforming. This evaluation is done by comparing

the capacity and the error rate of LSSTC to the well-known MIMO system, known as VBLAST. For that, we

derive a formula for the instantaneous capacity of single-user LSSTC. In addition, an adaptive scheme that is

based on LSSTC and VBLAST systems is proposed. This scheme selects the conﬁguration and the modulation

scheme in order to improve the performance.

1 INTRODUCTION

Various techniques have been proposed to counter the

problem of propagation conditions, and to achieve

data rates that are very close to the Shannon limit.

One of these techniques is using MIMO systems

which uses antenna arrays at both the transmitter and

the receiver. Wolniansky et al. has proposed in (Wol-

niansky et al., 1998) the well-known MIMO scheme,

known as VBLAST. In VBLAST architecture, paral-

lel data streams are sent via the transmit antennas at

the same carrier frequency.

While MIMO systems as VBLAST can improve

the system capacity greatly, it is difﬁcult to imple-

ment antenna arrays on hand-held terminals due to

size, cost and hardware limitation(Alamouti, 1998),

also it has poor energy performance and doesnt fully

exploit the available diversity. In order to overcome

these problems, Alamouti has presented in (Alamouti,

1998) a new scheme called STBC with two trans-

mit and one receive antennas that provides the same

diversity order as maximal-ratio receiver combining

(MRRC) with one transmit and two receive anten-

nas. With the tempting advantages of VBLAST and

STBC, many researchers has attempted to combine

these two schemes to result in a multilayered architec-

ture called MLSTBC (Mohammad et al., 2004) with

each layer being composed of antennas that corre-

sponds to a speciﬁc STBC. This combined scheme

arises as a solution to jointly achieve spatial multi-

plexing and diversitygains simultaneously. With ML-

STBC scheme, it is possible to increase the data rate

while keeping a satisfactory link quality in terms of

symbol error rate (SER).

In (El-Hajjar and Hanzo, 2007) beamforming was

combined with MLSTBC to produce a hybrid system

called the layered steered space time codes(LSSTC).

The addition of beamforming to MLSTBC further im-

proves the performance of the system by increasing

the antenna gain in the direction of the desired user,

while reducing it towards the interfering users. In

this paper, we show the superiority of LSSTC over

VBLAST by comparing their capacity and SER. Also

wee derive a formula for the instantaneous capacity of

a single-user LSSTC system. In addition, an adaptive

scheme based on LSSTC and VBLAST systems is

proposed. This scheme selects the conﬁguration and

the modulation scheme to improve the performance.

2 SYSTEM MODEL OF LSSTC

Figure 1 shows the block diagram of a single-user

LSSTC system proposed in (El-Hajjar and Hanzo,

2007). The system has N

total transmitting anten-

nas and N

receiving antennas and is denoted by an

× N

LSSTC. The antenna architecture employed

in Figure 1 has M transmit adaptive antenna arrays

(AAs) spaced sufﬁciently far apart in order to experi-

ence independent fading and hence achieve transmit

diversity. Each of the AAs consists of L elements that

are spaced at a distance of d = λ/2 to ensure achiev-

161

S. Salim A., A. Zummo S. and N. Al-Ghadhban S. (2010).

A NUMERICAL COMPARISON BETWEEN LSSTC AND VBLAST IN WIRELESS SYSTEMS.

In Proceedings of the International Conference on Wireless Infor mation Networks and Systems, pages 161-164

DOI: 10.5220/0002970401610164

 SciTePress

ing beamforming. A block of B input information bits

LSSTC

processing:

estimate a

and decode

STC 1

é ù

ê ú

ë û

Rich

scattering

environment

Beamformer

DOA

STC K

Vector Encoder:

Serial to Parallel

Converter

Tx data

of length B

Rx data

Beamformer

DOA

( 1)

M m

- +

Figure 1: Block diagram of a single user LSSTC system.

is sent to the vector encoder of LSSTC and serial-to-

parallel converted to produce K streams (layers) of

length B

,...,B

, where B

+ B

+ ··· + B

= B.

Each group of B

bits, k ∈ [1,K], is then encoded by

a component space-time code STC

associated with

transmit AAs, where m

+ m

+ ··· + m

= M.

The output of the k

STC encoder is a m

× l code-

word, c

, that is sent over l time intervals. The space-

time coded symbols from all layers can be written as

C = [c

,...,c

]

, where C is an M × l matrix.

The coded symbols from C are then processed by

the corresponding beamformers, and then transmitted

simultaneously over the wireless channels. The trans-

mit antennas of all the groups are synchronized and

allocated equal power. Moreover, the total transmis-

sion power is ﬁxed, where the transmitted symbols

have an average power of P

= 1, where the average is

taken across all codewords over both spatial and tem-

poral components. For the LSSTC system to operate

properly, the number of receive antennas N

should

be at least equal to the number of layers K.

We formulate the system model as follows. The

channel model is a MIMO quasi-static Rayleigh ﬂat-

fading channel with N

transmit antennas and N

re-

ceive antennas. The quasi-static assumption indicates

that the channel gain coefﬁcients remain constant for

the duration of the STBC block and change inde-

pendently for each STBC block. The ﬂat-fading as-

sumption allows each transmitted symbol to be rep-

resented by a single-tap in the discrete-time model

with no inter-symbol interference (ISI). We assume

independent Rayleigh coefﬁcients, i.e.,fading coef-

ﬁcients are independent and identically distributed

(i.i.d.) circular-complex normal random variables

with zero-mean and 0.5 variance per dimension, ab-

breviated as C N (0, 1). The correlation caused by the

small distance separation is approximately removed

using the beamforming processing as we will show in

this Section..

The system model can be described in matrix no-

tation, where the received baseband data matrix Y can

be expressed as

Y = HWC+ N, (1)

where Y is the received signal over l time intervals

and has a dimension of N

× l, H is an N

× M ma-

trix whose entries are h

n,m

, and N is an N

× l matrix

that characterizes the additive white Gaussian noise

(AWGN). The n

row of N denoted as z

, where

n ∈ [1,...,N

], is a row vector of l columns, the i

en-

try of z

is a spatially uncorrelated circular-complex

normal random variable, and can be written as z

I,n

+ jz

Q,n

, where z

I,n

and z

Q,n

are two independent

zero-mean Gaussian random variables having a vari-

ance of N

/2, we will represent z

as C N (0,N

Furthermore, W is an M × M diagonal weight ma-

trix, whose diagonal entry w

m,m

is the L-dimensional

beamforming weight vector for the m

beamformer

AA and the n

receive antenna, and can be written as

m,m

= [b

,··· ,b

], where b

, i ∈ [1, . . . , L], is the

weighting gain of the m

AA. The received signal

Y can be written in matrix form as



















1,1

·· · h

1,M

M,M

2,1

1,1

·· · h

2,M

M,M

1,1

·· · h

M,M































. (2)

The beamforming vector w

m,m

is given by (Shu et al.,

2007) as w

m,m

= d

∗

n,m

, where the superscript

∗

repre-

sents the conjugate of the matrix. Refering to (2), a

modiﬁed channel matrix is deﬁned as

H =







1,1

··· h

1,M

M,M

2,1

1,1

··· h

2,M

M,M

1,1

··· h

M,M







, (3)

where

H is the reconstructed channel matrix compris-

ing the MIMO fading channel and the DOA informa-

tion. Note that we assumed that the nulling vector

for all the paths corresponding to one AA (w

m,m

) is

the same. This follows from the assumption that the

separation between the receive antennas is much less

than the distance between the AA and the receiver,

then roughly speaking, they will have the same direc-

tion of arrival, which will result in having the same

nulling vector.

According to Equation (2) Y can be rewritten as:

Y =

HC+ N. (4)

The channel coefﬁcient

n,m

can roughly ex-

WINSYS 2010 - International Conference on Wireless Information Networks and Systems

162

pressed as

n,m

= h

n,m

m,m

= α

n,m

· [d

n,m

]

n,m

]

∗

(5)

= L· α

n,m

Therefore the received signal can be expressed as in

(El-Hajjar and Hanzo, 2007):

Y = L

HC+ N, (6)

where

H is an (N

× M) matrix whose entries are

n,m

. Looking at (6), the effect of beamforming can

be clearly seen, which is a direct SNR gain.

3 CAPACITY OF LSSTC

The system capacity of VBLAST is given by (Mo-

hammad et al., 2004) as

VBLAST

= N

min

i=1,2,...,N



log



SNR

ZF,i



(7)

where SNR is the average signal-to-noise ratio, and

ZF,i

is the squared Frobenius norm of the zero-

forcing projection row for the i

layer.

To derive a formula for the capacity of LSSTC per

user, we will follow the derivation of (Al-Ghadhban

et al., 2005). First, the instantaneous capacity was

found in (Sandhu and Paulraj, 2000) for an orthogonal

STBC with M

transmit antennas and R

code rate,

STBC

= R

· log



kHk



(8)

In MLSTBC which is a combination of VBLAST

and STBC, an outage occurs if an outage happens

in any layer because all the STBC encoders (layers)

are transmitting at the same rate. The layer that is

the most probable to fall in an outage is the weakest

layer, i.e. the one that has the least value of kH

i = 1,2, . . . ,K, where H

is the i

matrix of H. There-

fore, the instantaneous capacity of a K layered STBC

system with a sub-stream SNR of ρ can be written as:

C = K · R

· log



1+ ρ· min

k=1,2,...,K







= K · R

· min

k=1,2,...,K



log



1+ ρ·kH



.(9)

Extending the last results, the instantaneous capacity

of LSSTC can be expressed as:

LSSTC

= KR

min

k=1,2,...,K



log



· P

M · N

· kH

PP,k



(10)

where H

PP,k

is the Post-Processing (PP) matrix cor-

responding to the k

layer after nulling out the in-

terference from the yet-to-be-detected layers. It is

clear that the LSSTC capacity is dominated by the

worst group which has the minimum value of H

PP,k

k = 1, 2,...,K.

4 NUMERICAL RESULTS

In all the Monte-Carlo simulations conducted in this

work, we used Alamouti’s STBC matrix of unity rate

for the STBC encoders in each layer. In addition, un-

less otherwise mentioned, non-ordered serial group

interference cancelation (SGIC) detector is used.

Figure 2 shows a fair comparison between LSSTC

and VBLAST in terms of the symbol error rate. The

two systems use a total number of transmit anten-

nas, N

= 8, and the receiver is equipped with 4 an-

tennas. In this comparison we have also compared

many transmitter conﬁgurations, in each a different

modulation scheme is used such that the spectral ef-

ﬁciency would be the same for all of them, which is

set to 4 bps/Hz. From Figure 2 it can be clearly seen

that VBLAST outperforms LSSTC in the low range

of SNR, whereas for values of SNR that exceed 9

dB, the LSSTC outperforms VBLAST because it has

a higher diversity order resulting from using STBC,

which drives the SER to decay sharply. Next, we pro-

0 2 4 6 8 10 12 14 16

−9

−8

−7

−6

−5

−4

−3

−2

−1

↑

(1)

↑

(2)

(dB)

SER

LSSTC (BPSK K= 4, L= 1)

LSSTC (QPSK K= 2, L= 2)

LSSTC (16 QAM K= 1, L= 4)

VBLAST (BPSK K= 4, L= 2)

VBLAST (QPSK K= 2, L= 4)

VBLAST (16 QAM K= 1, L= 8)

Figure 2: SER of LSSTC employing non-ordered SGIC

at 4 bps/Hz and different modulation schemes with N

8 & N

= 4 (comparing VBLAST to LSSTC fairly).

pose an adaptive transmission scheme that selects the

conﬁguration and the modulation scheme in order to

improve the performance. Table 1 lists the proposed

transmitter conﬁguration and modulation scheme de-

pending on the SNR level. The adaptive scheme can

be designed using an antenna array with the capability

A NUMERICAL COMPARISON BETWEEN LSSTC AND VBLAST IN WIRELESS SYSTEMS

163

Table 1: Proposed Tx. and modulation conﬁguration.

SNR level (dB) conﬁguration Modulation

< 6.6 VBLAST QPSK

6.6− 9.2 VBLAST 16-QAM

> 9.2 LSSTC 16-QAM

−15 −10 −5 0 5 10 15 20 25 30

(dB)

Capacity (bits/s/Hz)

LSSTC (K= 4 L= 1)

LSSTC (K= 2 L= 2)

LSSTC (K= 1 L= 4)

VBLAST (K= 4 L= 2)

VBLAST (K= 2 L= 4)

VBLAST (K= 1 L= 8)

Figure 3: Outage Capacity vs. E

for an 8× 4 MIMO at

10% Outage probability, and 15 dB average SNR (compar-

ing VBLAST to LSSTC fairly).

of electronically activating speciﬁc antenna elements

and deactivating the remaining ones. This is done to

meet the antenna separation conditions of each mode

in the multi-conﬁguration system. In LSSTC, there

are two conditions for the antenna element separation.

(1) The AAs should be sufﬁciently far apart in order

to experience independent fading. (2) Beamforming

elements within each AA should be spaced at small

distance (less than λ/2) to achieve beamforming. On

the other hand, VBLAST requires all the antennas to

be spaced sufﬁciently far from each other.

Figure 3 fairly compares LSSTC to VBLAST in

terms of the outage capacity of an 8 × 4 MIMO us-

ing non-ordered SGIC at 15 dB average SNR. Sev-

eral conﬁguration are considered, and the capacity is

plotted versus E

. As it can be seen from the ﬁg-

ure, the capacity is approximately linearly increas-

ing with increasing E

. It is clear to see that

VBLAST outperforms LSSTC, which is actually ex-

pected, since VBLAST is a pure spatial multiplexing

unlike LSSTC, where some antennas are assigned for

diversity. An adaptivesystem can be designed to max-

imize the capacity for all values of SNR. For the fore-

mentioned conﬁguration we choose the single-layer

VBLAST system for the ﬁrst range (-15 dB up to 1

dB), and for the second range (1 dB up to 20 dB) the

dual-layer VBLAST system gives the highest capac-

ity. If the SNR lies in the last range(>20 dB), then

using either LSSTC or VBLAST with 4 layers will

have approximately the same capacity. However, Fig-

ure 2 shows that LSSTC has a lower SER in the last

range, and therefore, choosing LSSTC is better.

5 CONCLUSIONS

In this paper,we evaluated the performanceof LSSTC

by comparing it to VBLAST. Also an adaptive sys-

tem that selects between LSSTC and VBLAST was

proposed. This study showed that combining beam-

forming, STBC, and VBLAST in LSSTC has better

performance than VBLAST at high SNR range.

ACKNOWLEDGEMENTS

The authors like to thank King Fahd University of

Petroleum and Minerals and KACST for their support

under grant no. SB070005 and NSTIP grant no. 08-

ELE39-4.

REFERENCES

Al-Ghadhban, S., Buehrer, R., and Woerner, B. (2005).

Outage Capacity Comparison of Multi-Layered STBC

and V-BLAST Systems. Vehicular Technology Con-

ference, IEEE 62nd, 1:24–27.

Alamouti, S. (1998). A Simple Transmit Diversity Tech-

nique for Wireless Communications. Selected Areas

in Communications, IEEE Journal on, 16(8):1451–

1458.

El-Hajjar, M. and Hanzo, L. (2007). Layered steered space-

time codes and their capacity. IEEE Electronics Let-

ters, pages 680–682.

Mohammad, M., Al-Ghadhban, S., Woerner, B., and Tran-

ter, W. (2004). Comparing Decoding Algorithms

for Multi-Layered Space-Time Block Codes. IEEE

SoutheastCon Proceedings, pages 147–152.

Sandhu, S. and Paulraj, A. (2000). Space-Time Block

Codes: a Capacity Perspective. Communications Let-

ters, IEEE, 4(12):384–386.

Shu, F., Lihua, L., Xiaofeng, T., and Ping, Z. (2007). A Spa-

tial Multiplexing MIMO Scheme with Beamforming

for Downlink Transmission. IEEE Vehicular Technol-

ogy Conference, pages 700–704.

Wolniansky, P. W., Foschini, G. J., Golden, G. D., and

Valenzuela, R. A. (1998). V-BLAST : An Architec-

ture for Realizing Very High Data Rates Over the

Rich-Scattering Wireless Channel. URSI Interna-

tional Symposium on Signals, Systems and Electron-

ics, pages 295–300.

WINSYS 2010 - International Conference on Wireless Information Networks and Systems

164