1. PAPR Reduction Technique Using Tone
Reservation Scheme along with Gradient
Algorithm
Sunjeev Kumar Gupta
Telecommunication Department of Nepal Telecom (NTC),
URL: www.ntc.net.np, Kathmandu, Nepal
PH: +977-9855068555, E-mail: sk.gupta@ntc.net.np /4u.gupta@gmail.com
components such as power amplifiers (PAs). The nonlinear
Abstract-As we know multi carrier signal can support effects on the transmitted OFDM symbols are spectral
high transmission data rate in wireless channel environments spreading, intermodulation, and changing the signal
but meanwhile, large number of subchannels in the multi constellation. Some recent work have investigate OFDM
carrier signals cause large Peak to Average Power Ratio reduction technique via selected mapping(SLM), Partial
(PAPR) when using multi carrier modulation technique like
Transmit Sequence(PTS), Repeated Clipping and Filtering
OFDM which substantially reduces efficiency of transmit high
power amplifier. In this Paper, we are greatly concerned with (RCF), Block coding, Interleaving, Active Constellation
Tone Reservation technique (TR) applied for complex Extension (ACE), Nonlinear Companding Transform
baseband signals of OFDM systems with N subcarriers, L (NCT), Tone Injection and Tone Reservation.
reserved subcarriers don’t carry any data information, are
only used for PAPR reduction and further elaborates gradient
Though any of the methods is implemented, they
algorithm after N-point IFFT computation iteratively for phase have the same disadvantages in common that additional
appraisal simultaneously by using subset of the sub-carriers power is needed. So it is obvious that this additional power
called the peak reduction tones (PRT). must be weakest possible so that the method is viable in
practice. I this paper, a set of tones in each sub band of
1. INTRODUCTION system OFDM is allocated in order of improve reduction of
Orthogonal Frequency Division Multiple(OFDM), PAPR without any degradation of BER and data bit rate
which is a multi-carrier communication technique, has degradation and without sending any SI. For this I will use
become widely accepted primarily because of its robustness unused carriers to generate the corrective signal [2].
against frequency selection fading channels which are Among the schemes using PRT, the most widely
common in broadband mobile wireless communications [1]. used Tone Reservation scheme which is one of good PAPR
In OFDMA, closely spaced and overlapped subcarriers are reduction performance when operating with optimized PRT
divided into groups and assigned to multiple users for positions. In this, I present complementary cumulative
simultaneously transmissions. distribution function (CCDF) for measurement of PAPR
Comparing to frequency division multiple access reduction.
(FDMA), where any overlapping of the frequency spectrum 2. PAPR DERIVATION PATTERN
of different users introduces multiple-access interference
(MAI), Orthogonality of subcarriers guarantees that there is Let there is N subcarriers in which there is L
no intercarrier interference (ICI), which prevents MAI reserved unused subcarriers computed under N-point IFFT
among users in OFDM systems. In OFDM, closely spaced and FFT for modulation and demodulation. The OFDM
multiple subcarriers are assigned to different users for samples dn at the output of the IFFT are given by:
parallel signal transmissions. Generally concerned here
about the interleaved subcarriers assignment scheme is
preferred because it provides maximum frequency diversity
and increases the capacity in frequency-selective fading
channels.
While OFDM has great advantage of having simple For n= 0,1….N-1, where Dk is the quadrature
equalization, it has inherent drawbacks of PAPR which phase shift keying (QPSK) or quadrature amplitude
distorts the signal if the transmitter contains nonlinear modulation (QAM) data symbol transmitted through the Kth
sub-carriers.

2. The PAPR of an OFDM symbol is defined as the
ratio of the maximum to the average power of the OFDM
Memory
symbol and can be expressed as the ratio: Controller
Reserved
Tone
(L)
Where PAPR () represents PAPR calculation, d=
(d0, d1, d2…..dN-1) and E[] denoted the expectation. Transmitted
Tone Signal
N point S/P Gradient
It has assumed that Dk implies {1,-1, j,-j} (i.e Dk is Allocation
IFFT Converter Algorithm
to be a QPSK data symbol). From the central limit theory, (N)
Informat
the real and imaginary values of dn become Gaussian
(N-L)
Data
ion
distributed for N>>1, each with mean zero and variance
½.Thus the amplitude of dn has a Rayleigh distribution
while the power distribution becomes a central chi-square
distribution with two degree of freedom [3].
Figure 1. Structure of OFDM transmitter using Tone Reservation.
3. PROPOSED TRANSMITTER
FOR TONE RESERVATION (TR) SCHEME
NO
In the structure of OFDM system transmitter,
tones are reserved for PAPR reduction and are assigned for
data information. All tones are allocated according to
YES
predetermined tone locations and after that IFFT is executed PAPAR
Contr
and the gradient algorithm is operated. IFFT Adder Calculat
Output oller
ion
The structure of TR scheme is composed of three Transmitted
parts: PRT reservation, IFFT, and IGA. First, is the PRT Signal
reservation, it is considered to have L sub-carriers out of N
sub-carriers are reserved for PAPR reduction. Subsequently,
the data and null symbols are modulated by IFFT on (N-L)
Scaling
and L sub-carriers respectively. Finally the transmitted Peak Circul &
portion is x (tr) with PAPR reduced via Gradient Algorithm Detect ar Phase
(IGA). ion Shift Rotatio
n
Details operation of IGA are as follow: First, the
index of the OFDM sample with the maximum absolute
amplitude (i.e. arg[max[dn]] is detected, and then a
predetermined peak reduction kernel (PRK), denoted by P, Figure 2. Procedure of Gradient Algorithm.
is an impulse like time domain signal and can be obtained
by setting all the PRTs to a constant. The circularly shifted If the number of Iteration reaches predetermined
PRK is scaled by a given step size and by the difference maximum iteration number, control escapes the process and
between the maximum absolute amplitude if the OFDM resulting signal is transmitted. If not clipping operation is
sample and a desired threshold. The PRK is then phase- executed iteratively [4].
rotated in such a way that the phase of the PRK is the
opposite to that of the OFDM sample with the maximum 4. MATHEMATICAL DERIVATION
absolute amplitude. Finally, the modified PRK c is added to FOR PAPR REDUCTION
the OFDM symbol d and the PAPR of the modified OFDM The idea behind in this paper is to add an artificial
symbol d+c is calculated. If the PAPR is smaller than the signal to unused carriers. The signal addition is frequency
desired threshold, xth is transmitted; otherwise the above domain. Thus, the PAPR of the resulting signal is given by:
procedure is repeated iteratively.
Where x (m) is multi-carrier signal of user m and
c (m) is an additive corrective signa and E [] denoted the
expectation l. In this portion, I introduce a PAPR reduction

3. scheme for mobile users sharing an OFDM uplink. In this
method of Tone reservation of OFDM, I propose to allocate Figure 4. Simulation Parameters
a set of tones in each of interleaved subbands. All users and
the base station (BS) know the positions of the reserved IFFT size (nFFT.): 128
tones. The set of tones reserved, no data is transmitted and Symbols (s): 10000
the reserved tones do not interface with data transmission. Modulation: BPSK
Each user can design its compensating signal Cm without Total subcarriers used (N): 100
knowledge of other users’ compensating signals [5]. Total unused carriers (L): 28
However, adding a signal Cm to Xm to reduce the PAPR
Figure 5. Simulation Parameters
increases, the transmit power. The relative increase mean
power delta E due to PAPR reduction as [8]:
IFFT size (nFFT.): 128
Symbols (s): 10000
Modulation: BPSK and QPSK
Total subcarriers used (N): 128
Total unused carriers (L): 0
The parameter must be as small as possible in Figure 6. Simulation Parameters
order to be compatible with current power amplifiers [7].
Indeed, it is easy to understand that if one increases IFFT size (nFFT.): 128
indefinitely the average power of the signal Xm+Cm one Symbols (s): 10000
would have obviously PAPR=0dB but a signal which can’t Modulation: BPSK and QPSK
be transmitted, Thus the relative mean power must be upper Total subcarriers used (N): 100
bounded and can be written as: Total unused carriers (L): 28
is a constant closely
related to the characteristic of the amplifier.
5. SIMULATION RESULTS
For evaluating the performance of the proposed
method, CDF curves of OFDM signal is presented. In my
simulation, the bandwidth is 10MHz is divided into N=128
subcarriers and purposed unused subcarriers L=28 as the
reserved tone for PAPR reduction. To evaluate the PAPR
reduction performance, I concentrate on the complementary
cumulative distribution function of the user’s PAPR, in all
the cases the maximum computation IFFT size is 128 and
gradient algorithm used 30 iteration for computation of each
simulation result given below.
Matlab simulation for this purpose is presented sequentially
as below [6]: Figure 3. PAPR Performance measurement with BPSK
modulation without using unused carriers L=0.
Figure 3. Simulation Parameters
As seen to the simulated Figures, It is concluded
that, for BPSK and QPSK modulation pattern, Tone
IFFT size (nFFT.): 128
Reservation offers remarkable PAPR reduction when
Symbols (s): 10000
reserving reasonable amount subcarriers (L). The amount of
Modulation: BPSK
reserved Tones resembles the tones don’t contain “Actual”
Total subcarriers used (N): 128
information data but this gives us enhancement of PAPR
Total unused carriers (L): 0

4. reduction. In fig. 3 and 4, CDF shows at one of its point,
probability 0.8, PAPR is reduced to 7 dB instead of 7.9 dB
under BPSK modulation when L=28 unused subcarriers is
used. Likewise, in fig 5 and 6, CDF shows at one of its
point, probability 0.5, PAPR is reduced to 6.6 db instead of
7.4 db under QPSK modulation when L=28 unused
subcarriers is used.
6. CONCLUSIONS
In this paper. I have proposed PAPR reduction
using Tone Reservation (TR) along with Gradient
Algorithm which is one of the promising techniques in
terms of Performance and Complexity enhancement. Taking
into account the importance of total subcarriers used and
substantially taking care towards to the unused reserved tone
(L) which plays vital role for PAPR reduction as clearly
justified in Simulation results in both case of Modulation
techniques BPSK and QPSK.
7. REFERENCES Figure 4. Performance of Tone Reservation with BPSK modulation using
unused carriers L=28.
[1]S. Zid, and R. Bouallegue, “Reducing PAPR of OFDM signal using
Partial Transmit Signal (PTS) and Selected Mapping (SLM)”, IEEE
ISIVC Bilbao, Spain, July 2008.
[2]Seungsoo Yoo and Sun Yong,”PAPR reducing scheme for OFDM
system: selecting mapping of partial tones (SMOPT)”, IEEE
Transactions, Feb 2006.
[3]Kelvin Huang, SUID,”Reducing the Peak to Average Power Ratio in
OFDM”, Dec 5th, 2003.
[4]Sung Eun Park,Jae YoelKim and Suwon-si,”Tone Reservation
Methodfor PAPR Reduction Scheme”,IEEE 802.16 Broadband
Wireless Access Working Group,31th,2003.
[5] Zid and Bouallegue,”SOCP approach for reducing PAPR for
different kind of allocations OFDM in Uplink via Tone Reservation”,
SUP’ COM, 6’Tel Laboratory.
[6] Google Search on www.dsplog.com and use of Language of
Technical Computation “MATLAB”.
Figure. 5 PAPR Performance measurement with BPSK and QPSK
modulation without using unused carriers.
Figure 6. Performance of Tone Reservation with BPSK and QPSK
modulation using unused carriers L=28.