Peak to Average Power Ratio Performance of a 16-QAM/OFDM System with Partial Transmit Sequence

IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
e-ISSN: 2278-2834,p- ISSN: 2278-8735. Volume 7, Issue 6 (Sep. - Oct. 2013), PP 17-19
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Peak to Average Power Ratio Performance of a 16-QAM/OFDM
System with Partial Transmit Sequence
Amritbir Kaur1
, Er. Harshit
2
1
(Mtech Student, ECE Department, DIET, Kharar, Mohali)
2
(HOD and AP, ECE Department, DIET, Kharar, Mohali)
Abstract : Orthogonal Frequency Division Multiplexing is a spectral efficient transmission format. But it
suffers from the problem of high Peak to Average Power Ratio. This high Peak to Average Power Ratio leads
the power amplifier into saturation and results in non-linear distortion at the output of power amplifier.
Different peak to average power ratio reduction techniques are available in literature. This paper computes the
performance of partial transmit scheme, which is one of the important peak to average power ratio reduction
technique
Keywords: Orthogonal Frequency Division Multiplexing, Partial Transmit Sequence, Peak to Average Power
Ratio, Power Amplifier, Scrambling Techniques.
I. INTRODUCTION
R.W. Chang proposed the first Orthogonal Frequency Division Multiplexing (OFDM) technique in
1966 for fading limited channels. Since then it has emerged as a very attractive and powerful transmission
technique. It provides transmission of multiple signals simultaneously, over a single transmission path. In
OFDM a high rate data stream is divided into many low data streams these steams are then multiplied by
corresponding carrier frequency signals that are orthogonal to each other. A composite signal so formed by
multiplexing these modulated signals is called the OFDM signal. For the understanding purpose, OFDM can be
thought of as a special case of Frequency Division Multiplexing (FDM) with the subcarriers which are
orthogonal to each other. The lower rate data stream so formed from the higher rate data stream (after serial to
parallel conversion) has large symbol duration so Inter Symbol Interference (ISI) is reduced in OFDM. In other
words, there is less dispersion in time domain due to multipath delay spread as in Time Division Multiplexing
(TDM) [1].
The condition for maintaining the orthogonality is that the frequency spacing between the carrier
signals must be an integer multiple of the lowest carrier frequency. That is, each subcarrier has an integer
number of cycles in time period T. The numbers of cycles in adjacent subcarriers differ by exactly one. This
technique provides high data rate even if relatively small frequency bandwidth is available. Also, OFDM based
system has other favorable properties such as high spectral efficiency, robustness to channel fading and impulse
interference. Because of these advantages, OFDM has been adopted in both wireless and wired applications in
recent years. OFDM-based systems are more immune to impulse noise, fast fades and can be of greater pursuit
for wireless applications as they eliminate the need for equalizers. Also, efficient hardware implementations can
be realized using Fast Fourier Transform (FFT) techniques for small numbers of carriers. So, OFDM has
emerged as the standard of choice in a number of important high data applications in past few decades.
High Peak to Average Power Ratio is one of the major practical complications of the uncoded OFDM
signals. PAPR is defined as the ratio between the instantaneous power of the peaks and the average power of the
signal. Mathematically,
PAPR =
max x t 2
E{ x t 2}
(1)
Where E {.} is the expectation operator. Also,
Crest Factor = 𝑃𝐴𝑃𝑅 (2)
PAPR is usually analyzed by using statistical parameter called complementary cumulative distribution function
(CCDF). CCDF shows the probability that PAPR is above a threshold level. CCDF is defined as
𝑃(𝑃𝐴𝑃𝑅 ≥ 𝑧) = 1 − ((1 − exp −z )N
(3)
When the N sinusoidal signals after modulation by their carriers, adds mostly constructively the peak
envelop power is as much as N times the mean power. As a result the amplitude of such a signal can have very
large values. When high-peak power signals pass through power amplifiers, Analog to Digital (A/D) and Digital
to Analog (D/A) converters, peaks are distorted non-linearly because of amplifier and converters imperfection
thus, the output signal will suffer from intermodulation distortion resulting in energy being generated at
frequencies outside the allocated bandwidth. Therefore average signal power must be kept low in order to

Peak to Average Power Ratio Performance of a 16-QAM/OFDM System with Partial Transmit
prevent the transmitter amplifier and other circuitry limiting. Minimizing the PAPR allows a higher average
power to be transmitted for a fixed peak power, improving the overall signal to noise ratio at the receiver [2].
PAPR reduction methods can be categorized as distortion type and non-distortion type methods. Distortion type
techniques reduce the PAPR by reducing the higher peaks in the signal and thereby distorting the signal. In
other words, these methods modify the signals in time domain to reduce the PAPR so that a certain level of
distortion is introduced. These methods cause an increase in both In-Band Radiation (IBR) and Out of Band
Radiation (OBR) and Bit Error Rate (BER). Example: clipping, peak windowing, peak cancellation etc.Non-
distortion type techniques include coding and data scrambling methods. These methods do not introduce any
distortion, but they also do not ensure reduced PAPR. So they must be used along with other distortion type
techniques. They do not cause high OBR and BER. Example: peak reduction carrier, selective level mapping
(SLM), partial transmit sequence (PTS) and block coding [3].
II. PARTIAL TRANSMIT SEQUENCE
The partial transmit sequence (PTS) technique partitions an input data block of N symbols into V
disjoint subblocks as follows:
0 1 2 1
, , ,...,X
Tv
X X X X 
    (4)
where Xi
are the subblocks that are consecutively located and also are of equal size. Unlike the SLM technique
in which scrambling is applied to all subcarriers, scrambling (rotating its phase independently) is applied to
each subblock [5] in the PTS technique. Then each partitioned subblock is multiplied by a corresponding
complex phase factor v j v
b e 
 , 1,2,...,v V , subsequently taking its IFFT to yield
 
1 1 1
.
V V V
v v v v v v
v v v
X IFFT b X b IFFT X b X
  
 
   
 
   (5)
Figure 1 Block diagram of partial transmits sequence (PTS) technique for PAPR reduction.
where  v
X is referred to as a partial transmit sequence (PTS). The phase vector is chosen so that the PAPR
can be minimized [6], which is shown as
 1
1 argmin max
0,1,..., 1,...,
1
,..., V
V
V v v
n Nb b
v
b b b x n 

 
     
 
  (6)
Then, the corresponding time-domain signal with the lowest PAPR vector can be expressed as
1
V
v v
v
X b X

   (7)
In general, the selection of the phase factors   1
V
v
v
b

is limited to a set of elements to reduce the search
complexity [4]. As the set of allowed phase factors is  2 / 1
0,1,..., 1 ,j i w V
b e i W w 
   sets of phase
factors should be searched to find the optimum set of phase vectors. Therefore, the search complexity increases
exponentially with the number of sub blocks.
The PTS technique requires V IFFT operations for each data block and 2log v
W   bits of side
information. The PAPR performance of the PTS technique is affected by not only the number of sub blocks, V,

Peak to Average Power Ratio Performance of a 16-QAM/OFDM System with Partial Transmit
and the number of the allowed phase factors, W, but also the subblock partitioning. In fact, there are three
different kinds of the subblock partitioning schemes: adjacent, interleaved, and pseudo-random. Among these,
the pseudo-random one has been known to provide the best performance [7].
III. PTS ALGORITHM
To As discussed in section II, the PTS technique suffers from the complexity of searching for the
optimum set of phase vector, especially when the number of subblock increases. In the literature [8, 9], various
schemes have been proposed to reduce this complexity. One particular example is a suboptimal combination
algorithm, which uses the binary phase factors of  1, 1 [8]. It is summarized as follows:
1. Partition the input data block into V subblocks as in Equation (4).
2. Set all the phase factors bv
= 1 for v = 1 : V, find PAPR of Equation (5), and set it as PAPR_min.
3. Set v = 2.
4. Find PAPR of Equation (3.27) with bv
= -1.
5. If PAPR> PAPR_min, switch bv back to 1. Otherwise, update PAPR min=PAPR.
6. If v < V, increment v by one and go back to Stepu.Otherwise, exit this process with the set of optimal phase
factors b .
IV. Simulation Results
An The number of computations for Equation (5) in this suboptimal combination algorithm is V, which
is much fewer than that required by the original PTS technique (i.e., V <<Wv
.
Figure 3 PAPR performance of a 16-QAM/OFDM system with PTS technique when the number of
subblocks varies.
Figure 3 shows the CCDF of PAPR for a 16-QAM/OFDM system using PTS technique as the number of
subblock varies. It is seen that the PAPR performance improves as the number of subblocks increases with V =
1, 2, 4, 8, and 16.
V. Conclusion
Signal scrambling techniques work with side information which minimized the effective throughput
since they commence redundancy. The signal scrambling techniques can be classified as Block coding, Partial
Transmit Sequences (PTS), Tone Reservation (TR) and Tone Injection (TI), Selective Mapping (SLM),
Interleaving and Active Constellation Extension (ACE). In this paper PTS technique has been implemented for
different number of subblocks. From simulation results it has been concluded that as the number of subblocks
increases, the value of PAPR decreases
REFERENCES .
[1] Gordan A. Gow, Richard K. Smith (2006), Mobile and Wireless communications: An Introduction, New York: Mc Graw-Hill
International.
[2] P. Muthu Chidambara Nathan (2008), Wireless Communications, New Delhi: PHI Learning Private Limited.
[3] N.Revueto (2008) PAPR reduction in OFDM systems. Master Thesis, Polytechnic University of Catalonia, Spain.
[4] Han, S.H. and Lee, J.H. (2005) An overview of peak-to-average power ratio reduction techniques for multicarrier transmission. IEEE
Wireless Commun., 12(2), 56–65.
[5] Muller, S.H. et al. (1997) OFDM with reduced peak-to-average power ratio by multiple signal representation. In Annals of
Telecommun., 52(1–2), 58–67.
[6] Muller, S.H. and Huber, J.B. (1996)OFDMwith reduced peak-to-average power ratio by optimum combination of partial transmit
sequences. Electron. Lett., 32(22), 2056–2057.
[7] Muller, S.H. and Huber, J.B. (Sep. 1997)Anovel peak power reduction scheme for OFDM. PIMRC’97, vol. 3, pp. 1090–1094.
[8] Cimini, L.J. Jr (2000) Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences. IEEE Commun.
Letters, 4(3), 86–88.
[9] Tellambura, C. (1998) A coding technique for reducing peak-to-average power ratio in OFDM. IEEE GLOBECOM’98, vol. 5, pp.
2783–2787.

Peak to Average Power Ratio Performance of a 16-QAM/OFDM System with Partial Transmit Sequence

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Peak to Average Power Ratio Performance of a 16-QAM/OFDM System with Partial Transmit Sequence