International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
A High Capacity and Low Decoding Complexity of Multiple Active
Spatial Modulation System over Correlated Channels
Uma.S
Student M.E-communication systems,
Loyola Institute of Technology,
Chennai-600 123.
Suganthi.K
Student M.E- Communication Systems,
Loyola Institute of Technology,
Chennai-600 123.
Abstract:
A generalized spatial modulation (SM) scheme with
multiple active transmit antennas, named as Multiple ActiveSpatial Modulation (MA-SM), is alternative to the STBC
system. It work on the principle of multiple transmission of data
stream from different transmit antennas in multiple time slots.
By allowing multiple transmit antennas in the spatial
modulation system (SM) and high multiplexing gain of Vertical
Bell Lab Layered (V-BLAST) systems to transmit different
symbol at the same time instants. Design of MA-SM for
arbitrary number of transmits antennas and the modulation
scheme was presented and mapped in to the high dimensional
constellation including spatial dimension. Finally to compare
the MA-SM with different MIMO schemes, and implemented in
to the correlated channel (Rayleigh and Nakagami) fading
channels. And by using the spatial correlation to improve the
channel capacity and compare the capacity along with antenna
mutual coupling and also compare the low complexity detection
of MA-SM.
Index terms-Spatial Modulation(SM), vertical-Bell lab layered
Space-Time (V-BLAST), maximum likelihood (ML) detection,
multiple-input multiple-output (MIMO) systems.
I. INTRODUCTION
Multiple Input Multiple Output (MIMO)
multiplexing is a promising technology that could greatly
increase the channel capacity without additional spectral
resources. Many recent research results have concluded that
the multiple-input multiple-output (MIMO) wireless
communication architecture is a promising approach to
achieve high bandwidth efficiencies. MIMO wireless
channels can be simply defined as a link for which both the
transmitting and receiving ends are equipped with multiple
antenna elements. The capacity of a MIMO system not only
depends on the number of channels (N. M), but also depends
on the correlation between the channels. The channel
correlation of a MIMO system is mainly due to two
components (spatial correlation, antenna mutual coupling).
This advanced communication technology has the
potential to resolve the bottleneck in traffic capacity for
future wireless networks.
ISSN: 2231-5381
MIMO is an effective way to improve the capacity and
reliability, comparing with single antenna wireless
systems[1],[2].several MIMO techniques have been
comprehensively studied recently studied among which the
space time block code (STBC) for two transmit antennas.
Offers a low- complexity maximum likelihood (ML) decoding
due to its orthogonal structure. Based on this property of
orthogonality, orthogonal space time block codes (OSTBCs)
was presented in [3],[4].OSTBCs are special class of space time
codes which exploits the spatial diversity and offer low
complexity ML decoding. However ,rate one OSTBC exists for
two transmit antennas only to increase the data rate a new class
of semi-orthogonal codes was proposed in [5],[6] known as
quasi orthogonal space time block codes (QOSTBCs) they are
all full rate codes with pair wise decoding complexity .however
,the QOSTBCs of[5],[6] cannot achieve full diversity. To
achieve full diversity, QOSTBC in [7],[8] was proposed by
talking half of the symbols from rotated constellation.
To further reduce the decoding complexity without
compromising on the data rates, a new and distinct class of
codes were designed using the concept of co-ordinate
interleaving .these codes are popularly known as co-ordinate
interleaved orthogonal designs(CIODs) [9],[10].the CIODs are
full rate codes which achieve single-symbol decidability. In [9],
[10] CIODs for PAM and QAM constellation are discussed.
The existing STBCs retransmit each symbol in space and time
which reduce the capacity of the system. This reduction in
capacity can be improved by using a mapping function for 16QAM constellation in Alamouti STBC [2], in this M-PAM
constellation and extended it to square QAM constellations.
Using this mapping function I proposed an STBC for four
transmit antennas which achieves high coding gain and full
diversity. In this STBC renamed as multiple antenna space
modulation (MASM).
a novel scheme approaching even higher capacity by
combining the amplitude/phase modulation techniques with
antenna index modulation, named Spatial Modulation
(SM), is proposed to extend the constellation into a three
dimension one (both the complex plane and the spatial
dimension are involved) [1].
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
Symbols are emitted from a selected antenna after being
mapped through a traditional modulator. Therefore, the
information is conveyed not only by the amplitude/phase
modulation techniques, but also by the antenna indices. The
ICI and IAI in SM system will also be avoided if only one
antenna is active all over the transmission. Hence the low
complexity decoder is capable of prominent performance.
The Space Time Block Coding-Spatial Modulation
(STBC-SM) scheme, in which SM is combined with Space
Time Block Code (STBC) to exploit high spectral efficiency
from SM and enjoy coding gains from STBC. At the
transmitter side, mapped symbols are emitted from several
chosen antennas after being coded with STBC encoder. At
the receiver side, a demodulator combining ML algorithm
along with the linear STBC decoder is shown to be optimal.
Similar to STBC, STBC-SM suffers from either low
multiplexing gain or high computational complexity when
the block code size extends to more than two. Since the ML
decoder for STBC-SM employs an exhaustive search of
antenna sets, the decoder complexity increases exponentially
as the antenna subset expands. Both the low multiplexing
gain and computational complexity, a multiple active –spatial
modulation (MA-SM) scheme and near optimal decoder with
linear complexity are proposed.
The main contribution of this paper:
1) A novel scheme of multi-antenna transmission for SM,
named MA-SM, is proposed; in which several transmit
antennas carrying different information symbols are active
during each time slot. Similar to traditional SM, information
bits in MA-SM are mapped into both spatial dimension and
traditional complex dimension. As a new approach, we
consider the antenna sets with arbitrary number of active
antennas rather than a single antenna index in spatial
dimension to further explore multiplexing gains.
Antenna
set
deytector
Spatial
Modulator
Demappe
r-1
Mod-1
S/P
H
P/S
Demappe
r-
Mod-
Fig.1, System model.
II. MULTI -ACTIVE SPATIAL MODULATION
A. Proposed MA-SM scheme
The general system model consists of a MIMO wireless link
with
transmit antennas and
receive antennas, which is
illustrated in Figure 1. The source information bits are
transmitted from
of the transmit antennas after being
mapped through an M order Quadrature Amplitude
Modulation (M-QAM). Through the
×
wireless
channel H and the
-dim additive white Gaussian noise
(AWGN) = [ ,
….
] the received signal is given
by (1) where ρ is the average signal to noise ratio (SNR) at
each receive antenna, H and
are independent and
identically distributed (i.i.d) entries according to C (0, 1)
(complex Gaussian zero mean distribution with variance 1)
and S is the constellation set of M -QAM. The transmitted
symbol X is comprised with
QAM symbols emitted from
the antennas
…..
, respectively for denoting
convenience, the antenna group ( ….. ) will be written as
=(0,1,…..1….),j {1,…..[
]2}where
corresponds
stand for the states of
transmit antennas and each 0 and 1
represents the off and on of the corresponding antenna
respectively for example ,in a system where =4, =2,the
possible
antenna
groups
could
be
denoted
as =(1,1,0,0,), =(1,0,1,0), =(1,0,0,1), =(0,1,1,0), =(0,1
,0,1), =(0,0,1,1).
=
≜[0
Where …..
S,
ISSN: 2231-5381
+
…..
…..
(1)
0]
{1.... .
}.
2) A general principle for designing the MA-SM code is
given. By carefully designing over the antenna sets and the
rotation angle applied to symbols, more diversity gains are
available.
3) A near-optimal decoder with low complexity is derived.
In order to reduce the computational complexity, it separates
the antenna set detection from the traditional demodulator.
Compared to the ML detection, the proposed detection
algorithm
reduces
the
computational
complexity
prominently.
4) Theoretical analysis and computer simulations to
substantiate the efficiency of MA-SM. A closed form
expression for the upper bound on the bit error probability
(BEP) is de-rived for the selection of transmission as well as
the detection algorithm. Simulation results demonstrate the
superior performance of MA-SM when applied to several
communication systems by comparing with several widely
used algorithms.
B.System Design and Optimization
In MA-SM system, the information bits are conveyed by
both the complex symbols and the indices of the active
antennas from which those symbols are transmitted. At the
transmitter side, NP antennas are chosen to carry different
symbols during the transmission, which results in the
increase of multiplexing gain. Theoretically, there is no
limitation on , which implies that
could be allowed to
be any number no larger than
to benefit the available
Multiplexing gain. However, this will lead to the
exponentially increasing complexity at the receiver side and
the ICI and IAI would degrade the performance seriously.
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
The constellation set of MA-SM could be denoted as the
Cartesian product of the complex set including both the real
and imaginary parts of the transmit symbols and the antenna
groups with a discrete topology. Besides, the available
antenna groups composed of the
antennas are always
more than2[ ] which means that we can carefully select the
active antenna groups to minimize interference.
Transmitter
Spatial
Modulation
Symbol
Channel
QAM
mapping
Serial
to
parrel
AWGN
QAM
demap
ping
As to the complex symbol optimization, it could be observed from (4) that the minimum distance between symbols
could be maximized by properly choosing the rotation angles.
The 3-dim constellation could be treated as one constituted
by different constellation planes. Each of them is a standard
QAM constellation and planes are distinguished by the
antenna groups. Since the Euclidean distance between
symbols locating on the same complex plane is maximized
with the QAM modulation, rotation angles for them on the
same plane should be exactly the same.
C.Complexity
In this section, the complexity of both the transmitter and
receiver are taken into consideration. The complexity of the
decoder for MA-SM is compared to the complexity of the
ML decoder and some other optimal decoders for SM and
GSM. The number of operations needed is used to estimate
the receiver complexity.
Receiver
Parrel to
serial
means
= 2 selection procedure could be skipped.
Otherwise, the distance definition indicates that we should try
to avoid overlapping antenna indices between different
groups since groups sharing the same antenna indices will
lead to the increase of the linear dependence probability of
channel space, which is the main cause of detection error.
Spatial
demodu
lation
M
R
C
Error
rate
III. T HEORETICAL A NALYSIS
Figure.2. Block Diagram of MA-SM
Since the minimum distance between codewords
dominates the BEP, transmission scheme can be optimized
by maximizing the minimum distance involved. Unlike the
traditional complex space where Euclidean distance could be
applied, the three dimensional space here contains a discrete
dimension that confuses the definition of distance. Referring
to the most widely used distance definition in discrete metric
space as in a similar definition could be derived.
δ(a, b) =
0,
1,
=
≠
We now derive the bit error probability (BEP) for
the proposed decoder in system to estimate its performance.
In this mainly focus on system with N T transmit antennas and
NP active .antennas employing bit phase shift keying
(BPSK).The analysis could easily be extended to other cases.
For our convenience, we assume that the power of the
transmit symbols is normalized and the Gaussian noises
added on all the receive antennas are with same variance
thus the system model could be rewritten as
Y=HX+
(2)
to find the hybrid distance d in which the
Frobinenious Norm equals to the Euclidean distance and
,
denotes the rotation angle applied to QAM symbol
Si∈S emmited from antenna group . is defined as the
number of different indices between two antenna groups, thus
the minimum distance between two codewords X and x is
maximized, the performance gain is achieved.
(4)
An error that can be occurred in the demodulator could be
categories into two scenarios due to the separated steps in
demodulator. First is the error occur in the active antenna
detection (denoted by PAntErr) and the second one is that the
error occurs in traditional demapping when antenna detection
is corrected (denoted by PModErr) thus the overall bit error
probability could be bounded as
Perror=1-(1-PAntErr) (1-PModErr)
d
,
=
{
+||
,
-
,
|| }
⎧
It shows that the optimization could be executed in the
selection of antenna groups and complex symbol respectively
we will first consider the antenna group optimization.
Denoting [
]= q
the number of illegal sets is
The active antennas are detected with a projection operator
that is linear.an explicit formula for the projection for the k-th
antenna could be denoted as
written as
-2 which provides redundancy for antenna
set selection. When no illegal set available which
ISSN: 2231-5381
(5)
(3)
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=
= HX+
(6)
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
IV. N UMERICAL R ESULTS
In this section some simulation results for the MASM system with different numbers of transmit antennas and
make comparisons with other MIMO systems, such as SM,VBLAST,Alamouti’s scheme and STBC-SM.the bit error
rate(BER) performance of these systems was evaluated by
Monte carlo simulations for various spectral efficiencies as a
function of a the average SNR per receive antenna and in
cases the independence of channels is assumed unless
otherwise specified.
In order to be convincing, comparisons are realized
under the same transmission rate without restraint on the
constellations. The SM system uses the optimal decoder
derived in the GSM employs the detection algorithm in the
V-BLAST system uses linear decorrelator detection and the
STBC-SM uses the optimal detector introduced in Rotation
parameters and antenna groups for different transmission
rates in MA-SM are selected.
Fig.4 Transmit vs Receive diversity
C.BER performance qam modulation with masm
A.M-QAM constellation diagram
The transmitted signals must traverse a potentially
difficult environment with scattering reflection and so. In
MIMO transmits the multiple data at the same time so that
the data’s are occurs aliasing, to avoid this aliasing the signal
are mapped and the transmitted to the channel it’s very useful
to find the distance between the data’s and avoid
interference.
Fig.5 BER performance of MASM wit QAM modulation
D.Comparison with Alamouti’s STBC, STBC-SM and VBLAST schemes
Fig .3M-QAM constellation diagram
B.Transmit vs. receive diversity
STBC uses the diversity techniques have they
provide the reliable communication in multi antenna system.
In Fig.1 different diversity techniques are used at the transmit
vs receiver (no diversity –one transmit antenna, one receive
antenna,.Alamouti two transmit antenna , one receive antenna
Maximal ratio combiner one transmit antenna, two receive
antennas and theoretical second order diversity).in that the Xaxis SNR and Y-axis BER, the SNR is increased and BER
are reduced. The maximal ratio combiner provides the better
SNR performance compare to other techniques.
ISSN: 2231-5381
Fig.6.comparison of different MIMO schemes
Comparison with some traditional MIMO schemes
are presented here over different transmission rates.fig.6
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
capacity of rayleigh fading channel using spatial correlation
1
0.9
0.8
0.7
0.6
CDF (C )
gives
comparison
at
6
bit/s/Hz
of
MASM
with =4, =2with 16-QAM modulation,Alamouti’s STBC
uses 1024 QAM modulation,STBC-SM employs 256 QAM
modulation and 8 transmit antennas and V-BLAST uses
=2 and 32 QAM modulation.it shows that MA-SM
provides better SNR gains over V-BKAST,STBC-SM,and
Alamouti’s STBC at BER value of 10 ,respectively.it
shows that MA-SM becomes more efficient at high
transmission rate.
D.Decoding complexity comparison
0.5
0.4
0.3
0.2
Comparison of complex ity among sc hemes
0.1
0.045
r1
r2
1.2
r3
r4
0
0.04
6
8
10
12
C(Bits/Sec/(Hz ))
14
16
18
0.035
1
0.03
Fig.8.capacity of Rayleigh fading channel using spatial
correlation
2. Mutual coupling
0.8
ra tio
ra tio
0.025
0.6
0.02
0.015
0.4
0.01
capacity of rayleigh fading channel using mutual coupling
1
0.2
0.005
0.9
0
6
7
8
9
10
11
R(bits/s/Hz)
12
13
14
15
0
6
7
8
9
10
11
R(bits/s/Hz)
12
13
14
15
0.8
0.7
Fig.7.complexity comparison
The complexity of both the transmitter and receiver are taken
into consideration.the complexity of the decoder MA-SM is
compared to the complexity of the ML decoder and some
other optimal decoders for SM and GSM. The number of
transmit antennas are needed for target transmission has
enormous implication on the on the complexity of the
transmitter .because there are multiple antennas being active
simultaneously conveying different symbols, the number of
antennas needed decreases prominently for a given size of
constellation. In fig 5.1 r1 denotes the complexity ratio of
optimal MA-SM receiver to optimal GSM decoder under the
same target rate R=10, r2 denotes the ratio of optimal MASM decoder to the optimal SM decoder, r3 denotes the ratio
of proposed low complexity MA-SM decoder to optimal
GSM decoder and r4 denotes the ratio of proposed MA-SM
decoder to optimal SM decoder. In this at least 8 transmit
antennas are needed in a GSM scheme and 64 antennas are
needed in SM system while only 4 transmit antennas are
essential in an MA-SM system, so that the complexity is less
compared with SM and GSM.
E. MA-SM over correlated channel
1.
Spatial correlation
In multipath wireless communication environment, the
wireless channels are not independent from each other but
due to scatterings in the propagation paths, the channels are
related to each other with different degrees. This kind of
correlation is called spatial correlation.
ISSN: 2231-5381
C DF (C)
0.6
0.5
0.4
0.3
0.2
0.1
0
4
5
6
7
8
9
C(Bits/Sec/(Hz))
10
11
12
13
14
Fig.9.Capacity of Rayleigh fading channel using antenna
mutual coupling
Comparison between spatial correlation and mutual coupling
Spatial correlation
Mutual coupling
dt=0.2500
dt=0.2000
dr=0.1500
dr=0.1500
Capacity=12.7605
Capacity=9.200
V. CONCLUSION AND DISCUSSIONS
In this a generalized mapping rules for Quadrature
Amplitude Modulation (QAM) constellation .using this
mapping function we propose an STBC for four transmit
antennas and MASM for 4*2 antennas.MA-SM offers
significant improvements of system performance compared
with SM ,STBC and V-BLAST systems and it provides the
better capacity in the spatial correlation compare to antenna
mutual coupling. It concludes that the MA-SM scheme can
be useful for high rate wireless communication systems
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
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