1. International Journal of ElectronicsJOURNAL OF ELECTRONICS AND
INTERNATIONAL and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 1, January (2014), pp. 130-137
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IJECET
©IAEME
PAPR REDUCTION BY USING COMPLEMENTARY DUMMY SEQUENCE
INSERTION IN OFDM
Shirish L. Kotgire1,
Shankar B. Deosarkar2
1
(Electronics & Telecommunication Department, Dr. Babasaheb Ambedkar Technological
University Lonere, India)
2
(Electronics & Telecommunication Department, Dr. Babasaheb Ambedkar Technological
University Lonere, India)
ABSTRACT
In this paper a new low complexity distortion-less technique is proposed to reduce the Peak
to Average Power Ratio (PAPR) and to overcome problem of large envelope variation in OFDM
symbol by adding redundancy in the form of dummy sequence. This dummy sequence is determined
by performing number of iterations in such a way that the PAPR of the signal is reduced.
Combinations of dummy sequence along with partial transmit sequence results in reduced peaks and
lowers BER. As compared to conventional PTS technique the proposed technique requires lesser
IFFT operations. Complementary sequence is used as dummy and this sequence does not work as the
side information unlike the PTS and SLM methods. Two null symbols can also be added at regular
spacing in the OFDM symbol synchronization purpose. BER Performance of DSI is better than the
PTS and SLM since there is no degradation due to error in side information. If the PAPR of IFFT
output is lower than a certain prescribed PAPR threshold level, the IFFT output data is transmitted.
Otherwise, dummy sequence is inserted to lower the PAPR. This simplifies design of transmitter
amplifier and escalates the processing speed [1].
Keywords: Bit Error Rate (BER), Dummy Sequences, Orthogonal Frequency Division Multiplexing
(OFDM), Peak to Average Power Ratio (PAPR), Partial Transmit Sequence (PTS).
1. INTRODUCTION
Multi-carrier communication systems have several advantages over conventional single
carrier communication, such as high speed data transmission, better spectral efficiency, better noise
performance and insensitive to multi-path propagation. Due to this, multi-carrier communication is
being widely used in various wireless applications such as Digital Audio Broadcasting (DAB),
Digital Video Broadcasting (DVB), Various Wireless Local Area Networks (WLANs), personal and
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
mobile communications. Moreover the available frequency spectrum can also be shared for digital
transmissions. However, a major drawback of multi-carrier signal is large peak to average power
ratio (PAPR) that results due to superimposition of large number of sub-carriers. Since the
transmitter power amplifiers are peak power limited, the large PAPR leads to in-band noise and outof-band radiation. Although the problem of large amplitude variation can be solved by increasing
the transmit power amplifier backoff, it comes with a side effect of reducing transmit power
amplifier efficiency. Achieving lower PAPR with acceptable Bit Error Rate (BER) is a challenging
task. Therefore, it is essential to propose multi-carrier techniques that result in low PAPR, lower
complexity, and lower noise while maintaining spectral efficiency [2].
1.1 Concept of OFDM
OFDM is a modulation technique used in multi-carrier communication. In this serial data is
converted into parallel and this parallel data symbol modulates a set of regularly spaced orthogonal
sub-carriers. The sub-carriers have minimum frequency separation required to maintain
orthogonality. The spectral overlap results in a waveform that uses the available bandwidth with a
very high spectral efficiency. Due to large symbol duration, OFDM is simple to use on channels that
exhibit delay spread or frequency selectivity. OFDM can be used to convert frequency selective
channel into a parallel collection of flat frequency sub-channels.
1.1.1 OFDM Concept
Basic arrangement used in OFDM transmitter is shown in Fig 1. OFDM modulator is
implemented as an N-point inverse discrete Fourier transform (IDFT) on a block of N information
symbols. Then these IDFT samples are followed by digital-to-analog converter (DAC). IDFT is
implemented using inverse fast Fourier transform (IFFT). A block of N complex symbols with an
appropriate signal constellation such as Quadrature phase shift keying (QPSK) or Quadrature
Amplitude Modulation (QAM) can be represented by {sk, k = 1,2,… , N}. The IDFT of the data
block can be written as
N −1
 j 2π nk 
Sn = ∑ sk exp 
 , n = 0,1,..., N − 1,
 N 
k =0
(1)
yielding the time domain sequence {Sn, n = 1, …, N}. Guard interval in the form of few samples (Ng)
is also introduced in the form of cyclic prefix (CP) at the end of each block of OFDM symbol to
mitigate the effects of ISI. The length of cyclic prefix is kept larger than delay of a communication
channel.
Fig.1 Block diagram of basic OFDM transmitter.
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
At the receiver, the received complex baseband signal is sampled with an analog-to-digital
converter (ADC). After ADC, the guard interval of each OFDM symbol is removed. Then each
block of N received samples is converted back to the frequency domain using discrete Fourier
transform, as shown in Fig. 2.
Fig. 2 Block diagram of basic OFDM receiver
The FFT operation performs baseband demodulation. The N frequency domain samples are
processed with a simple one-tap Frequency Domain Equalizer (FDE) to recover the data symbols.
Superimposition of large number of statistically independent sub-carriers results in large
envelope variation and high peak values. Every transmission system is peak-power limited and is
having non-linear characteristics. Nonlinear characteristics cause spectral widening of the transmit
signal resulting in unwanted out-of-band (OOB) noise causing adjacent channel interference (ACI)
and the transmit signal itself is degraded due to nonlinearities, resulting in large bit error rate (BER).
In this research work an attempt has been made to propose techniques that will reduce large peaks.
Thus avoiding nonlinear distortion we can improve BER performance.
2. PAPR REDUCTION USING DUMMY COMPLEMENTARY SEQUENCE
A new distortion-less technique is proposed to reduce the PAPR and to overcome problem of
large envelope variation by adding redundancy in the form of dummy sequence in the OFDM
symbol. This dummy sequence is determined by performing number of iterations in such a way that
the PAPR of the signal is reduced. Combinations of dummy sequence along with partial transmit
sequence results in reduced peaks and lowers BER. As compared to conventional PTS technique the
proposed technique requires half the IFFT operations only. Complementary sequence is used as
dummy and this sequence does not work as the side information unlike the PTS and SLM methods.
BER Performance of DSI is better than the PTS and SLM since there is no degradation due to error
in side information [4]. If the PAPR of IFFT output is lower than a certain prescribed PAPR
threshold level, the IFFT output data is transmitted. Otherwise, dummy sequence is inserted to lower
the PAPR. Reduction in PAPR also makes transmitter amplifier design much simpler. This technique
escalates the processing speed. Additional null symbols can be added for synchronization purpose.
2.1 Generation of Complementary Sequence
In the proposed DSI technique Golay complementary sequences are used as dummy sequence
in the form of pair of binary codes, which consists of two codes of the same length n, whose autocorrelation function have side-lobes equal in magnitude but opposite in sign. Summing these side
lobes result in a composite auto-correlation function with peak value of 2n and zero side-lobes [5].
Let ai and bi (i=1, 2, ….,n) be the elements of two complementary series, such as
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
A = a1 , a2 , a3 ,..., an
and
B = b1 , b2 , b3 ,..., bn
(2)
The ordered pair (A:B) are Golay sequences of length n if and only if their associated polynomials
B)
are:
(3)
A ( x ) = a1 , a2 x, a3 x 2 ,...an x n −1
B ( x ) = b1 , b2 x, b3 x 2 ,...bn x n −1
and satisfy the identity
−1
−1
A ( x ) A ( x ) + B ( x ) B ( x ) = 2n
(4)
and
, corresponding to the sequences A and B respectively,
The auto-correlation functions
can be defined by the following expression
N A ( j ) = ∑ ai ai + j
i∈z
(5)
N B ( j ) = ∑ bi bi + j
j∈z
If we put the condition (5.2) in equation (5.3) we get
)
(
2
N A ( j ) + N B ( j ) = {0,N ,
j=0
j≠0
(6)
The sum of both autocorrelation functions is 2N at j=0 and zero otherwise. From equation (6)
complex valued dummy sequences are generated first and then added to the vector of data sub
carriers. The addition of dummy sequences and data sub carriers is shown in Fig. 3.
carrie
X1 D1
X2
D2
X3
D3
X4
D4
Fig.3 Arrangement of Dummy Sequence and Data Symbols
In above figure X represents data subcarriers and D represents Dummy sequence [6]. Thus we get
new vector S (new symbol) is given by (7).
S = [ X k , DL ]
(7)
Where Xk (X1, X2, X3, X4) is the number of groups into which the subcarriers are partitioned and DL
into
pa
(D1, D2, D3, D4) is the dummy sequence added to reduce large peaks. After insertion of dummy
sequence PAPR of the resulting signal is checked with that of acceptable threshold that is pre
pre-defined.
If the PAPR value is less than the threshold then the OFDM signal is transmitted otherwise the
dummy sequence is regenerated with the help of number of iterations. From the block dia
generated
diagram in
Fig.2, X is the input signal with length N, after that dummy sequence is added. The dummy sequence
,
at the receiver can be replaced by zeros in the data samples. This makes the IFFT length without
change and decoding of the samples in receiver simpler. Now the signal is partitioned into M disjoint
simpler.
blocks becomes,
S m =  S1, S 2 , S3 ,..., S M 


133
(8)

5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Such that
M
S = ∑ Sm
(9)
m =1
Then, these sub-blocks are combined to minimize the PAPR in time domain. However in time
domain the signal Sm is oversampled L times which is obtained by taking an IFFT of length LN on Xm
concatenated with (L-1)N zeros. After partitioning the signal and performing the IFFT for each part,
the phase factors given by
bm = e jΦm ,
(10)
m = 1, 2, 3,..., M
are used for optimizing the Sm in time domain. Then the OFDM signal becomes:
M
S ' ( b ) = ∑ bm S m
(11)
m =1
This OFDM signal results in PAPR reduction. Simulation results show considerable decrease in
PAPR. This simplifies the design of high power transmitter amplifier.
3. PROPOSED CSI-PTS TECHNIQUE
The block schematic of complementary sequence insertion technique is shown in Fig. 3.
Complex complementary dummy sequence is first generated and then added to the OFDM symbol.
The new data symbol in the frequency domain is generated from k data and L-dummy subcarriers,
respectively. L can be any number less than the number of data symbols. The new vector S is given
by [7]:
S = [Xk, W ᶩ]
where Xk = [Xk,0, Xk,1,… , Xk,N-L-1], k = 1,2,…,K is data sub-carrier vector and W ᶩ is thedummy
signal vector W ᶩ = [W l,0,W l,1,W l,2,W l,L-1], ᶩ = 1, 2,…,L is complementary dummy sequence. After
successive iterations dummy complementary sequence is added to the OFDM symbol. If PAPR value
is greater than the threshold then complementary sequence is generated again. After adding the
dummy sequence the signal is partitioned into M disjoint block
M
SM = [S1, S2, …, SM] such that
∑S
m
= S and then these sub-blocks combined to lower PAPR of
m =1
the transmit signal in time domain. After partitioning the signal and performing and performing IFFT
on each sub-block, the phase factors bm = e jφm , m = 1, 2,... M are used for optimizing each sub-block. In
time domain each sub-block can be represented as [8]:
M
s’(b) =
∑b s
m m
T
'
'
Where s’(b) =  s0 ( b ) , s1' ( b ) ,..., s NF −1 ( b )  . Minimum of s’(b) can be determined by


m =1
iterations. The length of the input signal remains same after addition of complementary sequence.
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Fig. 4. Block dig for complementary dummy sequence insertion
The process of determination of dummy signal continues, till the minimum or the value equal
to or less than threshold is reached and the signal is transmitted. As the dummy signal do not carry
any information, it is removed at the receiving end. The effect on bandwidth efficiency depends upon
the length of complementary sequence.
Computational Complexity
As no side information needs to be transmitted, and it can be reduced in terms of sub-block
partition as less number of IFFT computations is required. And this is due to the addition of dummy
sequence. In many wireless applications number of zeros is added before transmission. Some of
these zeros can be replaced by this complementary sequence which reduces PAPR and hence design
of transmitter amplifier gets simplified and fewer distortions will occur in the signal at less
complexity.
However, addition of complementary sequence affects bandwidth efficiency.
Spectral Efficiency Loss = =
4.
Number of data subcarriers
× 100%
Number of data scbcarriers + Number of dummy sequences
RESULTS AND CONCLUSIONS
Matlab simulation of dummy complementary sequence for 256 sub-carrier system using
different lengths of complementary sequences was performed using different modulation techniques.
We employed QPSK modulation with oversampling factor D = 4. Ten thousand random OFDM
symbols were simulated for determining CCDF. Simulation results in Fig.5. shows considerable
improvement in PAPR for dummy sequence of length 4 and 8 with subcarriers divided into four
partitions of 64 subcarriers each. It can be observed that as compared to conventional PTS proposed
scheme shows an improvement of the order of 5-6 dB at CCDF of 10-2. PAPR reduction is achieved
without any transmission of side information with low computational complexity.
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Fig.5. PAPR Reduction for various length of complementary sequences
Fig. 6. And Fog. 7 shows an improvement in BER. It is observed that for SNR of 12dB there is
considerable improvement in BER for the dummy sequence length of 4 and 8. These results show
considerable reduction in PAPR without significant spectral efficiency loss. Since dummy
Fig. 6 BER vs SNR plot for dummy sequence length DS = 4
Fig. 7 BER vs SNR plot for dummy sequence length DS = 8
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8. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
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