International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2341
Reduction of PAPR Performance in Alamouti Coded
MIMO-OFDM System using Selected Mapping
Techniques with BPSK Modulation
Tincy Mary Mathew
ME Scholar, Electronics and Telecommunication
Department
Shri Shankaracharya Technical Campus
Bhilai, Chhattisgarh, India.
Ekant Sharma
Assistant Professor, Electronics and
Telecommunication Department
Shri Shankaracharya Technical Campus
Bhilai, Chhattisgarh, India.
.
Abstract—Orthogonal frequency division Multiplexing
(OFDM) is one of the most popular multicarrier or
multiplexing modulation techniques in high speed
wireless communication. The main principle of OFDM
system is to transmit multiple numbers of signals
simultaneously over a single transmission path. OFDM
convert high data rate stream in to smaller data rate
stream. Due to this high data rate and ability to combat
frequency selective fading, OFDM has a strong
candidate for 4G wireless networks. OFDM combined
with multiple-input multiple-output (MIMO) to increase
system capacity over the time variant frequency-selective
channels and the diversity gain. The main idea of MIMO
system is to use multiple antennas at both the
transmitter and receiver end in order to improve
communication performance. MIMO-OFDM system has
a major drawback that might exhibit high peak-to-
average power ratio (PAPR). In this paper, we present
Selected Mapping scheme (SLM) based on alamouti
coded MIMO OFDM system with reduced PAPR using
BPSK modulation schemes for N=128, 256 and 512.
Simulation results show that MIMO OFDM system
using SLM in alamouti code has low PAPR when
compared to conventional MIMO OFDM system.
MATLAB simulations show that our proposed SLM
modification significantly improves the PAPR reduction.
Index Terms— Alamoutic code, MIMO, OFDM, PAPR,
SLM.
I. INTRODUCTION
Orthogonal Frequency Division multiplexing is also
known as Multicarrier modulation (MCM) techniques or
Multiplexing technique because of its increasing demand of
high speed data rates, robustness to channel fading, flexibility and easy equalization. MCM will transmit signals
through multiple carriers where these carriers (subcarriers)
will have different frequencies and they are orthogonal to
each other. As an effective technique OFDM have been
widely adopted by many wireless communication systems,
such as Digital Audio Broadcasting (DAB), Digital Video
Broadcasting (DVB) and Wireless Metropolitan Area
Networks (WMAN) for IEEE 802.16a standard and Wireless Local Area Networks (WLAN), for IEEE 802.11a
standard.
In high-speed wireless communication, an arrangement of
using multiple antennas at transmitter and receiver of
OFDM system is called as (MIMO-OFDM) multiple input
multiple output OFDM. OFDM combined with MIMO
technology using alamouti code of space time block coding
(STBC) for mobile communication systems due to its ability
to achieve high data rate robust transmission. Therefore,
MIMO-OFDM systems achieve coding gain and diversity
gain by space-time coding (STBC). MIMO-OFDM System takes advantages of multipath interference effect to increase
user and data capacity. Like single-input-single-output
OFDM (SISO OFDM), one of the major drawbacks of
MIMO-OFDM is the high peak to average power ratio
(PAPR) of the signal transmitted to different antenna. In
order to reduced the high PAPR in alamouti MIMO-OFDM
system we would have to apply the PAPR reduction scheme
[2-6].
However, there is one major problem associated with
OFDM signals that is its inherent drawback of high peak-to-
average power ratio (PAPR). High PAPR causes signal distortions such as the in-band distortion and out-of-band
radiation and induces the degradation of bit error rate
performance due to the nonlinearity effects [1]. There are
several reduction technique that have been proposed to
reduce the PAPR problem such as Clipping And
Filtering[2], Partial Transmit Sequences (PTS)[3], Selected
Mapping Technique[4], tone reservation (TR) and
tone injection (TI)[5], Zadoff-Chu matrix Transform
(ZCT)[6].
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2342
In this paper, we proposed to use the property of space-
time block coded (STBC) coding technique (Alamouti) in
MIMO-OFDM system, with reduction techniques by which
better PAPR performance is achieved by the most widely
used methods are selective mapping (SLM) and the
modulation techniques used is BPSK for different number of
subcarriers. And we proved that by using the Alamouti
scheme, the conjugate symbols transmitted on two antennas
has same PAPR property .Section II explains MIMO
system. Section III explains Alamouti MIMO OFDM
system and their PAPR. The proposed system model for PAPR reduction of SLM Alamouti MIMO OFDM system is
explained in section IV. Section V presents the simulation
result and section VI describes the conclusion.
II. MIMO SYSTEM
MIMO stands for Multiple Input Multiple Output system
that means MIMO system has two antennas at both the
transmitter and receiver side. Multiple transmitting and
receiving antennas will achieve antenna diversity without
reducing the spectral efficiency. MIMO system has
disadvantages like complexity, power consumption and size
of the mobile device.
A. System Model
MIMO system consists of basically three components
transmitter (TX), channel (H) and the receiver (RX). Let us
consider 𝑛𝑡 be the no. of transmitter antenna, 𝑛𝑟 be the no.
of receiving antennas and ℎ𝑖 ,𝑗 represent the complex value
of the channel for transmitter antenna i and receiver antenna
j respectively. Let 𝑥𝑖 = {𝑥1 ,𝑥2 ,…… .𝑥𝑛𝑡 } be the complex
signals transmitted via 𝑛𝑡 antennas. Then the receiving
antenna can be expressed as:
𝑦𝑗 = ℎ𝑖 ,𝑗 𝑥𝑖 + 𝑛𝑖𝑛𝑡𝑖=1 (1)
𝑛𝑖 = noise term
Fig.1 MIMO System with 𝑛𝑡 x 𝑛𝑟 antennas.
The received signal of Eq (1) can be written as:
𝑦 = 𝐻𝑥 + 𝑛 (2)
Where 𝐻 =
ℎ1,1 … ℎ1,𝑛𝑡
⋮ ⋱ ⋮ℎ𝑛𝑡 ,1 ⋯ ℎ𝑛𝑡 ,𝑛𝑟
(3)
y is the received vector of size 𝑁𝑟 ∗ 1, 𝑥 is the transmitted
vector of size 𝑁𝑡 ∗ 1, H is channel matrix of size 𝑁𝑟 ∗ 𝑁𝑡 and n is the noise vector.
B. Alamouti Space-Time Block Code (STBC)
The first space time block code (STBC) is the alamouti
code that provides full diversity to data rate for the two
transmit antennas. Fig.2 represents the block diagram of
alamouti code.
Fig.2 Block diagram of Alamouti code
Firstly the input data source X is passed through the
modulator using a digital modulation schemes in this case
BPSK modulation is used. After the process of modulation it
is passed through the STBC encoder which generate two
modulated symbols 𝑥1 and 𝑥2 in each precoding operation.
𝑋 = 𝑥1 −𝑥2
∗
𝑥2 𝑥1∗ (4)
The first row represents the first transmission period and
the second row represents the second transmission period.
During the first time slot, the symbols 𝑥1 and 𝑥2 are
transmitted simultaneously from 1st and 2nd antenna
respectively. In the second time slot, the symbol −𝑥2∗ and
𝑥1∗ are transmitted from 1st and 2nd antenna respectively.
III. ALAMOUTI MIMO OFDM SYSTEM AND THEIR
PAPR
Fig.3 shows the general block diagram of a STBC
Alamouti MIMO-OFDM system. Let us consider the MIMO-OFDM systems with M transmit antennas that use N
subcarriers. The complex vector of size N can be expressed
as 𝑋 = [𝑋1 ,𝑋2 ,…… . ,𝑋𝑁]. These modulated baseband signal
are passed through serial to parallel converter such that each
modulated signal has different subcarrier and form a set of 𝑓𝑛 , 𝑛 = 0,1,… . ,𝑁 − 1 . The N subcarriers are orthogonal
to each other i.e. 𝑓𝑛 = 𝑛∆𝑓 where ∆f =1
𝑁𝑇 and T is the
symbol period. The complex vector, X is the passed through
space time encoder which generate two sequences.
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2343
Fig.3 Block diagram of STBC Alamouti MIMO-OFDM system
From the 1st antenna 𝑋1 is generated
𝑋1 = [𝑥1 ,−𝑥2∗,𝑥3 ,−𝑥4
∗,………… , 𝑥𝑁−1 ,−𝑥𝑁∗] (5)
And for 2nd antenna 𝑋2 is generated
𝑋2 = [𝑥2 ,𝑥1∗,𝑥4 ,𝑥3
∗,………… , 𝑥𝑁 ,𝑥𝑁−1∗] (6)
Eq (5) and (6) means that in the 1st time slot signal 𝑥1 and
𝑥2 are transmitted from the 1st and 2nd antennas respectively,
in 2nd time slot signal −𝑥2∗ and 𝑥1
∗ are transmitted from the
two antennas, in the 3rd time slot signal 𝑥3 and 𝑥4 are
transmitted from the two antennas and in the 4th time slot
signal −𝑥4∗ and 𝑥3
∗ are transmitted respectively from the
two antennas and so on. Both of these sequences are then
passed through each IFFT block for antenna 1 and antenna 2
respectively. After the process of IFFT it is then passed
through cyclic prefix where the last part of an MIMO
OFDM symbol is inserted into the front of an MIMO
OFDM symbol. The resulting baseband STBC MIMO-
OFDM signal for antenna i with N subcarriers can be written as:-
𝑥𝑖(𝑘) =1
𝑁 𝑋𝑖(𝑘)𝑒 𝑗2𝜋
𝑛
𝑁𝑘 𝑁
𝑛=1 (7)
Where 𝑘 = 1,2,… .𝑁, 𝑖 = 1,2 and 𝑗 = −1 .PAPR of the STBC MIMO-OFDM signal for antenna i can be written as:
𝑃𝐴𝑃𝑅 =max 1≤n≤N | 𝑥𝑖 𝑘 |²
𝐸[ 𝑥𝑖(𝑘) 2] (8)
E[.] denotes expectation value. Complementary
cumulative distribution function (CCDF), define the
probability that the PAPR of an OFDM symbol exceeds the
given threshold 𝑃𝐴𝑃𝑅0 can be written as:
𝐶𝐶𝐷𝐹 = 𝑃𝑟(𝑃𝐴𝑃𝑅 > 𝑃𝐴𝑃𝑅0) (9)
For MIMO OFDM, the CCDF of PAPR can be written as:
𝐶𝐶𝐷𝐹 = 1 − (1 − 𝑒−𝑃𝐴𝑃𝑅0 )𝑀𝑁 (10)
IV. SLM ALAMOUTI MIMO OFDM SYSTEM
Selected Mapping (SLM) technique is one of the most
promising reduction techniques to reduce Peak to Average
Power Ratio (PAPR) in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO
OFDM). The main principle of SLM technique is to
generate a number of MIMO OFDM symbols as candidates
and then select the one with the lowest PAPR for actual
transmission that have the same information the main idea
of SLM technique is based on the phase rotation. Fig.4
shows the block diagram of SLM STBC Alamouti MIMO-
OFDM system.
The input sequence X are mapped with BPSK modulation
and passed through serial to parallel converter which
generate complex vector of size N is 𝑋 = [𝑋1 ,𝑋2 , . . ,𝑋𝑁]. The modulated data are then passed through the space time
encoder (2x2) which generates two sequences 𝑋1 =[𝑋1 ,−𝑋2
∗,… .𝑋𝑁−1 ,−𝑋𝑁∗] for antenna 1 and 𝑋2 =
[𝑋2 ,𝑋1∗,… .𝑋𝑁 ,𝑋𝑁−1
∗] for antenna 2. Both of these
sequence is then multiplied by the U different phase
sequence vector 𝑃𝑚𝑢 = [𝑃1
𝑢 ,𝑃2𝑢 ,… . .𝑃𝑁
𝑢 ] where m=1,2
and u=1,2,....,U. The output of phase sequence vector is
written as:
𝑋𝑚𝑢 = 𝑋𝑚𝑃𝑚
𝑢 (11)
Fig.4 Block diagram of SLM STBC Alamouti MIMO-OFDM system.
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2344
For antenna 1 and 2 𝑋1𝑢 and 𝑋2
𝑢 can be written as:
𝑋1𝑢 = [𝑋1𝑃1
𝑢 ,−𝑋2∗𝑃2
𝑢∗. . . . ,𝑋𝑁−1𝑃𝑁−1𝑢 ,−𝑋𝑁
∗𝑃𝑁𝑢∗ ] (12)
𝑋2𝑢 = [𝑋2𝑃2
𝑢 ,𝑋1∗𝑃1
𝑢∗. . . . ,𝑋𝑁𝑃𝑁𝑢 ,𝑋𝑁−1
∗𝑃𝑁−1𝑢∗] (13)
These frequency domain signals 𝑋𝑚𝑢 are transformed into
time domain signals 𝑥𝑚𝑢 via the IFFT operation.
𝑥𝑚𝑢 = 𝐼𝐹𝐹𝑇 (𝑋𝑚
𝑢 ) (14)
𝑥𝑚𝑢 =
1
𝑁 𝑋𝑚
𝑢 (𝑘)𝑒 𝑗2𝜋𝑚𝑘
𝑁𝑁𝑘=1 (15)
The PAPR of an SLM MIMO OFDM signal of Eq(15)
can be written as:
𝑃𝐴𝑃𝑅 =max |𝑥𝑚
𝑢 |²
𝐸[ 𝑥𝑚𝑢 2]
(16)
The optimal set with the minimum PAPR of the two
signals is chosen as.
𝑢 = arg min1≤𝑢≤𝑈(max𝑚=1,2 max1≤𝑛≤𝑁 | 𝑥𝑚𝑢 |) (17)
The U phase rotation sequences 𝑃𝑚𝑢 should be transmitted
to the receiver as the SI with log2 𝑈 bits.
V. SIMULATION RESULT
In this section, we present some simulation results
showing the PAPR performance of the proposed SLM
Alamouti MIMO OFDM system. To show the effect of our
proposed SLM Alamouti MIMO OFDM system we use two
transmitting antenna M= 2 using BPSK modulations. We
also compared our results with Alamouti MIMO OFDM
system with and without adding cyclic prefix for N = 128,
256 and 512
Fig.5. CCDF Vs PAPR for Alamouti MIMO OFDM System with System
subcarriers N=128 using BPSK Modulation.
Fig.6. CCDF Vs PAPR for Alamouti MIMO OFDM System with System
subcarriers N=256 using BPSK Modulation.
Fig.5 shows the CCDF comparisons of PAPR of Alamouti
MIMO OFDM systems with N = 128 using BPSK
modulation. At clip rate of 10−3, the PAPR is to 10 dB for
Original MIMO OFDM systems and 10 dB for MIMO
OFDM CP.
Fig.6 shows the CCDF comparisons of PAPR of Alamouti
MIMO OFDM systems with N = 256 using BPSK
modulation. At clip rate of 10−3, the PAPR is to 10.6 dB for Original MIMO OFDM systems and 10.6 dB for MIMO
OFDM CP.
Fig.7 shows the CCDF comparisons of PAPR of Alamouti
MIMO OFDM systems with N = 512 using BPSK
modulation. At clip rate of 10−3, the PAPR is to 11 dB for Original MIMO OFDM systems and 11 dB for MIMO
OFDM CP.
\
Fig.7. CCDF Vs PAPR for Alamouti MIMO OFDM System with System
subcarriers N=512 using BPSK Modulation
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2345
Fig.8. CCDF Vs PAPR for SLM Alamouti MIMO OFDM System with
System subcarriers N=128 using BPSK Modulation.
Fig.8 shows the CCDF comparisons of PAPR of SLM
Alamouti MIMO OFDM systems with N = 128 using BPSK
modulation. At clip rate of 10−3 , the PAPR is to 9.7 dB for Alamouti MIMO OFDM systems, 9.7 dB for Alamouti
MIMO OFDM CP and 8.5 dB for SLM Alamouti MIMO OFDM.
Fig.9 shows the CCDF comparisons of PAPR of SLM
Alamouti MIMO OFDM systems with N = 256 using BPSK
modulation. At clip rate of 10−3, the PAPR is to 9.9 dB for Alamouti MIMO OFDM systems, 9.9 dB for Alamouti
MIMO OFDM CP and 8.8 dB for SLM Alamouti MIMO
OFDM.
Fig.9 CCDF Vs PAPR for SLM Alamouti MIMO OFDM System with
System subcarriers N=256 using BPSK Modulation
Fig.10 CCDF Vs PAPR for SLM Alamouti MIMO OFDM System with
System subcarriers N=512 using BPSK Modulation
Fig.10 shows the CCDF comparisons of PAPR of SLM
Alamouti MIMO OFDM systems with N = 512 using BPSK
modulation. At clip rate of 10−3, the PAPR is to 10.6 dB for Alamouti MIMO OFDM systems, 10.6 dB for Alamouti
MIMO OFDM CP and 9 dB for SLM Alamouti MIMO
OFDM.
TABLE I PAPR ANALYSIS
Systems
PAPR in dB
(BPSK)
Number of
subcarriers (N) 128 256 512
Original MIMO
OFDM
10 10.6 11
MIMO OFDM CP 10 a. 10.6 11
Alamouti MIMO
OFDM
9.7 9.9 10.6
Alamouti MIMO
OFDM CP
9.7 9.9 10.6
Alamouti SLM
MIMO OFDM
8.5 8.8 9
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 3 Issue 7, July 2014
ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET 2346
VI. CONCLUSIONS
In this paper, we present an analysis of the PAPR for the
SLM Alamouti MIMO OFDM system especially space time
block encoder alamouti schemes has been used. In the
proposed method we multiply the space time encoder value
with the phase rotation vector. Therefore it reduce the PAPR
more than the conventional SLM OFDM and have higher data rate And compare this SLM Alamouti MIMO OFDM
system with the original Alamouti MIMO OFDM system.
Simulation results have shown that the SLM Alamouti
MIMO OFDM system has much lower PAPR than original
MIMO OFDM system. Thus the proposed system does not
require any complex optimization, side information and
power increase.
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