1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
INTERNATIONAL JOURNAL OF ELECTRONICS AND
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 5, September – October, 2013, pp. 207-213
© IAEME: www.iaeme.com/ijecet.asp
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IJECET
©IAEME
A NEW APPROACH IN DISTORTIONLESS TECHNIQUES FOR PAPR
REDUCTION IN MULTICARRIER TRANSMISSION SYSTEMS
Ms. Shraddha R. Waghmare
Electronics and Communication Engineering Department,
Dr. Babasaheb Ambedkar College of Engineering and Research, Nagpur (India)
Prof. Dr. Shripad P. Mohani
Electronics and Telecommunication Engineering Department,
College of Engineering, Pune (India)
ABSTRACT
Orthogonal frequency division multiplexing (OFDM) is a robust and effective multicarrier
transmission technique for high speed communication in wireless mobile environment and
applications. A major challenging issue in application of OFDM is its high peak to average power
ratio (PAPR). Selective mapping (SLM) is one of the promising techniques which offer distortionless PAPR reduction at the cost of bandwidth efficiency and computational complexity. In this work,
SLM is modified by using new phase sequences, which are combinations of Centering matrix along
with Hadamard and Riemann matrices. Simulation results show that the proposed phase sequences
offer improved PAPR reduction and thus outperform some of the previously proposed techniques.
Keywords: Centering operation, Multicarrier Systems, Orthogonal Frequency Division Multiplexing
(OFDM), Peak to average power ratio (PAPR), Selected Mapping (SLM)
I.
INTRODUCTION
Orthogonal Frequency Division Multiplexing is extensively implemented in various high
speed wireless communication standards because of its favorable properties such as high spectral
efficiency, robustness to channel fading, capability of handling multipath fading and immunity to
impulse interference. Interestingly, OFDM is a combination of modulation and multiplexing. ne
major limitation is its large Peak to Average Power Ratio (PAPR). These large peaks cause
saturation in power amplifiers at the transmitting end, leading to inter-modulation among the
subcarriers, which causes an increase in the out of band (OOB) energy of the spectrum. Hence, to
design a cost effective and robust system, it is highly desirable to reduce the PAPR. Reduction of
PAPR is a major challenge for which many techniques are proposed in the literature.
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
Advancement to the existing Selected Mapping technique for PAPR reduction is done by
introducing new set of phase sequences. The proposed phase sequences show enhanced performance
with respect to PAPR reduction.
II.
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM)
The multicarrier modulation techniques employ several carriers, within the allocated
bandwidth, to convey the information from source to destination. Each carrier may utilize one of the
several available digital modulation techniques (BPSK, QPSK or QAM) [1].
Generally, an OFDM signal can be represented as:
cሺtሻ = ∑୒ିଵ
୬ୀ଴
s୬ ሺtሻ sinሺ2πf୬ tሻ
Where: c(t)
s୬ ሺtሻ
(1)
: OFDM signal representation in Time Domain
: Symbols mapped to chosen constellation (BPSK/QPSK/QAM)
f୬
: Represents the orthogonal frequencies
Equation (1) can be thought of as an Inverse Fast Fourier Transform (IFFT) where ‘N’ is the
size of IFFT. The Fourier transform breaks a signal into different frequency bins by multiplying the
signal with a series of sinusoids. Since the OFDM signal is in time domain (refer (1)), IFFT is the
appropriate choice to use at the transmitter. To acquire the original transmitted signal, FFT is
performed at the receiver side [2].
III.
PEAK TO AVERAGE POWER RATIO (PAPR)
The mathematical representation of PAPR of an OFDM signal can be given as –
PAPRሼcሺtሻሽ ൌ
మ
ౣ౗౮
౥ರ౤ರొషభ│ୡሺ୲ሻ│
మ
(2)
୉ቂ│ୡሺ୲ሻ│ ቃ
ଶ
Where E ቄ│cሺtሻ│ ቅ denotes the expectation of c (t).
PAPR can be expressed in ‘dB’ as follows.
PAPR (dB) = 10logଵ଴ PAPR ୡሺ୲ሻ
(3)
Some of the distortion based techniques for PAPR reduction include clipping and filtering,
commanding, coding. Selective mapping (SLM), partial transmit sequence (PTS), tone reservation,
tone injection, constellation extension are Distortion less Techniques for PAPR reduction. SLM
technique improves PAPR statistics of an OFDM signal significantly without any in-band distortion
and out-of-band radiation. The selection of proper phase sequences to achieve good PAPR reduction
is very important in the SLM technique [3].
IV.
SELECTED MAPPING TECHNIQUE (SLM)
SLM method is a distortion less probabilistic technique for PAPR reduction. This technique
is called distortion less because the quantity with which the actual signal is altered is sent as side
information [4] In this method, the original modulated OFDM data block is multiplied element by
element with phase sequences;
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
Bሺ୳ሻ ൌ ሾb୳,଴ , b୳,ଵ , … … b୳,୒ିଵ ሿ୘
u=1, 0, 2…..U
To make the U phase rotated OFDM data blocks
X ሺ୳ሻ ൌ ሾX ୳,଴ , X୳,ଵ , … … X୳,୒ିଵ ሿ୘
The classical definition of SLM refers to a random sequence to be used as phase altering
sequence [3][4].
Where X୳,୫= X୫ . b୳,୫ , m=0, 1 … N െ 1
All phase rotated OFDM data blocks represent the same information as that of the
unmodified OFDM. PAPR is calculated for phase rotated OFDM data blocks by using (2) and (3).
Among the modified data blocks, one with the lowest PAPR is selected and transmitted. The
information about the selected phase sequence should be transmitted to the receiver as side
information. Reverse operation should be performed at the receiver to obtain the original data block
[3], [4].
Fig. 1 Block diagram of the SLM scheme in OFDM
V.
EXISTING PHASE SEQUENCE FOR SLM
The Matrices like Hadamard and Riemann are very popular phase sequence generating
matrices for SLM techniques [5][6]. A newly introduced matrix called Centering matrix has given so
far the best performance as compared to the conventional matrices. [7]
5.1 Centering matrix
The centering matrix is a symmetric and idempotent matrix, which when multiplied with a
vector has the same effect as subtracting the mean of the components of the vector from every
component [7]. The structure of centering matrix (C୬ ) is given by
C୬ ൌ I୬ െ
1
O
n ୬
Where, I୬ - is the n-by-n identity matrix
O୬ - is an n-by-n matrix of all 1's
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
VI.
PROPOSED PHASE SEQUENCE
In this experimentation, combinations of the Centering matrix with the special matrices like
Hadamard and Riemann has been explored. The formulation of the new phase sequence generating
Matrices is explained below.
6.1 Centering of Hadamard and Riemann Matrices
Centering operation on a data matrix is done by multiplying the particular matrix with the
Centering matrix. The values of the newly formed data matrices get close to their respective mean
values after the centering operation [8].
Centered Hadamard matrix:
Centered Riemann matrix:
Where,
H୬ - Hadamard matrix (n-by-n)
C୬ - Centering matrix (n-by-n)
C୦ = C୬ * H୬
C୰ = C୬ * R ୬
6.2 New Phase Matrix
In the quest of finding new phase sequences, another combination of centering matrix with
the special matrices is formed. The proposed phase sequences are generated by performing elementby-element multiplication of Centering matrix with Hadamard and Riemann matrices. This
combination delivers a new set of phase sequences, which offers better results than the other matrices
considered in this experimentation. As there is element-by-element multiplication between the two
matrices, it has fewer computations than the Centered matrices explained earlier. Instead of using
any random sequence as phase sequence, a combination of two standard matrices is being used in
this work. This matrix combination can also be generated at the receiver, leading to a reduction in
side information, as only the row index number can be sent as side information. Modifications in the
existing SLM scheme are introduced by the newly proposed phase sequences.
New Hadamard Cୡ୦ሺ୬ୣ୵ሻ = C୬ .* H୬
New Riemann Cୡ୰ሺ୬ୣ୵ሻ = C୬ .* R ୬
VII.
SIDE INFORMATION
The side information is the most important aspect of the SLM technique. Thus, it is highly
essential to save the side information from getting corrupted while it travels through the channel. In
this experimentation, the side information is sent in the form of row index or row number of the
phase sequence generator matrix, which provides the least PAPR for a particular OFDM symbol [7]
[9]. BCH coding is done on the set of side information collected for all the corresponding OFDM
symbols.
The Bose, Chaudhuri and Hocquenghem (BCH) codes form a large class of powerful random
error-correcting cyclic codes. For any positive integers mሺm ൒ 3ሻ and tሺt ൏ 2୫ିଵ ሻ, there exists a
binary BCH code with the following parameters:
Block Length:
n ൌ 2୫ െ 1
Number of parity-check digits: n െ k ൑ mt
Minimum distance:
d୫୧୬ ൒ 2t ൅ 1
This code is capable of correcting any combination of ‘ ’ or fewer errors in a block of
n ൌ 2୫ െ 1 digits. BCH code of size (7, 4) is used in this experimentation.
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
VIII. RESULTS
Following are the system specifications used commonly for both unmodified OFDM,
conventional SLM and modified SLM scheme [12]. The simulation is performed using MATLAB.
TABLE I
System Specifications
Number of input bits
Modulation
IFFT/FFT size for OFDM s (N)
Oversampling Rate
Phase altering matrix (U)
20,000
16 QAM
64
4
16-by-16
Side information generated is of 4 bits (log ଶ Uሻ for every OFDM symbol. The CCDF plot in
Fig.2 shows the PAPR reduction for each individual phase matrix. It can be observed that the
proposed new Riemann matrix performs exceedingly well than other matrices considered in this
experimentation. The proposed new Hadamard matrix offers PAPR reduction nearly same as that of
the Centering matrix.
CCDF plots of PAPR(dB) values
0
Basic OFDM
Hadamard
Riemann
Centering
Cent. Hadamard
Cent. Riemann
New Hadamard
New Riemann
-1
10
Unmodified
Hadamard
Riemann
Circulant
Circulant. Hadamard
Circulant Riemann
New. Hadamard
New. Riemann
-1
10
B it E rror Rate
P ro b a b ility ,P (P A P R (d B )) > = P A P R o
Bit Error Probability curve
0
10
10
-2
10
-3
10
-2
10
-4
1
2
3
4
5
6
7
PAPRo dB
8
9
10
11
10
12
Fig 2. CCDF plots for Different phase matrices
10
20
30
40
Eb/No, dB
50
60
70
Fig 3. BER plots for different phase matrices
The Centered Hadamard performs better than original Hadamard and Centered Riemann
provides more PAPR reduction than the original Riemann matrix. The proposed New Riemann
matrix shows near elimination of peaks from the OFDM signal. PAPR reduction of around 8 dB to
8.5 dB is obtained. Centering matrix shows PAPR reduction more than Riemann (refer Fig. 2) [7].
From this work, it can be stated that the proposed new Riemann matrix performs even better than the
Centering matrix. The proposed new Riemann matrix was tested for its PAPR performance on a
fixed input bit stream taking different M-QAM constellations and IFFT sizes. Four times
oversampling of the modulated symbols is performed before taking IFFT. Following table
demonstrates the results. An OFDM symbol is generated using the combinations of M-QAM and
IFFT and minimum PAPR (dB) is found.
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME
IFFT
64
128
256
TABLE II
M-QAM
16QAM
32QAM
16QAM
32QAM
16QAM
32QAM
Min. PAPR(dB)
0.1643
0.2000
0.0629
0.0613
0.0250
0.0212
It can be observed from Table. II, as the IFFT size increases, the PAPR of the OFDM signal
reduces by a significant value. For the same IFFT size, if M-QAM constellation is changed, PAPR of
the particular signal does not undergo any major change. The OFDM symbols are transmitted
through AWGN channel i.e. AWGN noise is added to the transmitted signal. The robustness of a
communication system is determined by the performance of the receiver. The BER vs SNR
performance for various phase matrices is compared to that of the unmodified OFDM in Fig. 3. The
unmodified original OFDM and SLM with Hadamard and Centering matrix present almost the same
performance. BER of the system with proposed new Riemann matrix can be reduced by applying
high SNR. As trade-off is usually experienced in communication, here also a trade-off between BER
and PAPR performance in the proposed scheme is seen.
IX.
CONCLUSION
In this paper, a modification in the phase sequence for conventional SLM scheme is
proposed. The proposed new Riemann phase sequence shows PAPR reduction to a greater extent as
compared to that obtained by using other phase altering matrices. It indeed outperforms the already
proposed Centering, Riemann and Hadamard matrices, in terms of amount of PAPR reduction in
OFDM. The side in formation sent along with the individual OFDM data blocks is the row index
number of the selected phase sequence instead of sending the whole of the phase sequence. Thus the
bandwidth efficiency and the power consumption of the system is enhanced. However, the proposed
phase sequences cause an increase in bit error rate (BER). To reduce the BER, highly powerful error
control codes (have the effect of increase in bandwidth) can be used. Use of higher transmit power
can be another alternative for BER reduction. So, either of the two resources, signal-to-noise ratio
(SNR) or bandwidth, can be used to reduce the BER.
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