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2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31st October 2013
OFDM Pulse Design with Low PAPR for Ultrasonic
Location and Positioning Systems
Daniel F. Albuquerque, Jos´
e M. N. Vieira, S´
ergio I. Lopes, Carlos A. C. Bastos, Paulo J. S. G. Ferreira
Signal Processing Lab – IEETA/DETI – University of Aveiro
3810-193 Aveiro, Portugal
{dfa, jnvieira, sil, cbastos, pjf}@ua.pt
Abstract—In this paper we propose an iterative algorithm
to design ultrasonic orthogonal frequency division multiplexing
(OFDM) pulses with low peak-to-average power ratio (PAPR),
increasing, not only, the probability of pulse detection, but also,
the system power efficiency. The algorithm is based on the
Papoulis-Gerchberg method, where in each iteration the PAPR
of the resultant pulse is reduced while keeping the spectrum
flat and band limited. On each iteration the amplitude of the
OFDM carriers are kept constant and only the phases of carriers
are optimized. The experimental results have shown that for
ultrasonic OFDM pulses with a large number of carriers it is
possible to design pulses with a PAPR of 1.666. The designer
pulse is ideal for time of flight (TOF) measurement purposes.
Keywords—Ultrasounds, Ultrasonic Pulse, Pulse Design, Time
of Flight, Pulse Detection, OFDM, PAPR, Papoulis-Gerchberg.
I. INTRODUCTION
The OFDM is a method of data transmission that uses
multiple carriers at a very low rate [1]. The main advantage
of using OFDM is its robustness to some adverse indoor
ultrasonic (US) channel conditions, such as strong multipath
and different equalization along the frequency [1]. Due to this
advantages, the authors have proposed an ultrasonic pulse that
uses OFDM pulses to measure the TOF and transmit data
simultaneously [2]. However, one of the major drawbacks
of using OFDM pulses to measure the TOF is the high
PAPR when comparing to other types pulses, such as chirps.
The PAPR is defined as the ratio between the peak power
to the mean power of the OFDM pulse. On the one hand,
the probability of pulse detection increases with the signal
energy [3]. On the other hand, if the transmission system
uses a power amplifier it is important to increase the signal
energy and reduce the signal amplitude peak in order to
increase the power amplifier efficiency [1]. Therefore, the pulse
used for TOF measurement should present a PAPR as low as
possible [1]. The literature usually covers the PAPR problem
for communication purposes [4], [5] but for TOF measurement,
where the quest for the best pulse is the goal, the typical
solutions are not for the PAPR problem but for a similar
one, the peak-to-mean envelope power ratio (PMEPR) [3]. The
PMEPR instead of measuring the ratio between the peak power
and mean power of the real transmitted signal it computes the
ratio using the signal envelope. For narrow-bandwidth signals1
the PMEPR provides a good approximation of the PAPR value
(typical radar case) [3], [5]. However, for typical US signals
1Narrow-bandwidth signals are signals whose carriers’ frequency is much
greater that the signal bandwidth.
(up to 100 kHz) the narrow-bandwidth model it is not well
suited.
II. PROPO SED ALGORITHM
The algorithm to optimize the PAPR of OFDM pulses
is presented in Fig. 1 and it is adapted from the algorithm
proposed in [6] which is based on the Papoulis-Gerchberg
algorithm [7], [8]. The algorithm starts by computing the
Compute:
(k)
from Newman method
Compute: S(k) = e j
(k)
S(k) = 0 fork≠k0..kNc-1
IFFT
Clip the signal peaks
Compute:
(k)
from X(k)
Compute the real part
x(n) = 2 x Re{s(n)}
FFT
Fig. 1: Proposed iterative algorithm to decrease the PAPR.
carrier phases, ✓(k)=(k1)2⇡/Nc, using the Newman
method, where Ncis the number of carriers. After it is
computed the frequency carriers information, S(k)=ej✓(k),
with amplitude one which results into an OFDM pulse with
a PAPR around 3.5. The resultant signal is then converted to
the time-domain and the double of its real part is computed.
Note that the double is only important to keep the carriers
amplitude equal to one. Therefore, from the resultant signal,
x(n), the peaks are removed by clipping the maximum and
the minimum of the signal. Note that the clipping process
must be between 75% to 95% from the maximum amplitude
of the signal to ensure that the algorithm converges and that
the PAPR is reduced as fast as possible [6]. After passing
the clipped signal to the frequency-domain the new carriers
phases are obtained and the first iteration is completed. For
each iteration, the carriers phase from the last iteration must
be kept.
III. ALGORITHM RESULTS
This section presents the results of the proposed algorithm
for two types of OFDM pulses, a short pulse, with 100 ms, and
a long pulse, with 20 s. Both pulses performance are compared
with a chirp signal2with the same characteristics.
2The term chirp is sometimes used interchangeably with sweep signal and
linear frequency modulation signal.
978-1-4673-1954-6/12/$31.00 c
2012
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2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31st October 2013
A. Short Pulse
For the short pulse an 100 ms OFDM pulse with 1000
carriers from 20 kHz to 30 kHz was used. The algorithm was
ran one million times and the clipping process started at 0.8 of
the maximum signal value. If the PAPR during one iteration is
not reduced, the clipping value for the next iteration changes to
80% of the previous clipping value plus 0.2. For example if a
clipping of 0.8 does no reduce the PAPR the clipping changes
to 0.84 and after that to 0.872 and so on. The result for this
test is presented in Fig. 2. As can be seen the PAPR reduces
to the value of 2 in just 3980 iterations. The problem is to
reduce the PAPR bellow 2. After one million of iterations the
PAPR is only 1.945 and it is only reduced by 5.6⇥1011 in
each iteration.
100101102103104105106
1.7
2
2.3
2.6
2.9
3.2
3.5
Iteration
PAPR
Fig. 2: Algorithm results after 1 million iterations for an
100 ms OFDM pulse with 1000 carriers.
The resultant OFDM pulse will be compared with a chirp
pulse with the same main characteristics: amplitude, duration
and bandwidth. The probability of detection as a function of
the signal’s amplitude for the last pulse sample using a matched
filter and considering a threshold that produce a probability of
false alarm of 106is depicted in Fig. 3. One can observe
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
0.2
0.4
0.6
0.8
1
(Max. Amplitude)/(Noise std.)
Probability of Detection
OFDM pulse
Chirp pulse
Fig. 3: Probability of detection for an OFDM and a chirp pulse
as a function of the signal amplitude.
that the OFDM pulse detection is slightly better than the chirp
pulse detection for the same amplitude.
B. Long Pulse
For the long pulse a 20 s OFDM pulse with 2 million
carriers from 0 Hz to 100 kHz was used. The algorithm was ran
10 million times and the clipping process was manually tuning
between 80% and 99.999%. Fig. 4 presents the instantaneous
power for the resultant OFDM pulse and for a chirp with
similar characteristics: energy, duration and bandwidth. The
PAPR reducing technique shows up its value, the OFDM pulse
presents a PAPR of 1.666 against 2 for the chirp. As a result
of this, the OFDM pulse has a considerable better efficiency.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
10
20
30
Occurences (%)
Instantaneous Power (Normalized to Chirp Peak Power)
(a) OFDM Instantaneous Power Distribution.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
10
20
30
Occurences (%)
Instantaneous Power (Normalized to Chirp Peak Power)
(b) Chirp Instantaneous Power Distribution.
Fig. 4: Instantaneous Power Distribution for a 20 s OFDM
pulse with 2 million carriers and a chirp pulse with a bandwidth
of 100 kHz. The instantaneous power was normalized to the
peak power of the chirp.
IV. CONCLUSION
Using the proposed algorithm it is possible to design
OFDM pulses that present a low PAPR. The results show that
it is only needed some thousand iterations to obtain an OFDM
pulse with a PAPR of 2, however to go beyond this value it
will be necessary to iterate the algorithm millions of times.
Additionally, the results also show that it is easy to obtain an
OFDM pulse with low PAPR for long pulses than for short
pulses. It was possible to design an OFDM pulse with 20 s of
duration that presents a flat spectrum between 0 and 100 kHz
and a PAPR of 1.666. This result represents a 16.7% energy
gain when compared with the chirp pulse having the same
amplitude, length and bandwidth.
REFERENCES
[1] Henrik Schulze and Christian Luders, Theory and Applications of OFDM
and CDMA, John Wiley & Sons, first edition, 2005.
[2] Daniel F Albuquerque, Jos´
e M N Vieira, Carlos A C Bastos, and Paulo
J S G Ferreira, “Ultrasonic OFDM Pulse Detection for Time of Flight
Measurement Over White Gaussian Noise Channel,” in 1st internation
conference on Pervasive and Embedded Computing and Communication
Systems, Vilamoura, Portugal, 2011.
[3] Nadav Levanon and Eli Mozeson, Radar Signals, JOHN WILEY &
SONS, 2004.
[4] Seung Hee Han and Jae Hong Lee, “An overview of peak-to-average
power ratio reduction techniques for multicarrier transmission,” IEEE
Wireless Communications, vol. 12, pp. 56–65, 2005.
[5] Jiang Tao and Wu Yiyan, “An Overview: Peak-to-Average Power Ratio
Reduction Techniques for OFDM Signals,” Broadcasting, vol. 54, no. 2,
pp. 257–268, 2008.
[6] Edwin Van der Ouderaa, Johan Schoukens, and Jean Renneboog, “Peak
factor minimization using a time-frequency domain swapping algorithm,”
Instrumentation and Measurement, vol. 37, no. 1, pp. 145–147, 1988.
[7] Athanasios Papoulis, “A new algorithm in spectral analysis and band-
limited extrapolation,” Circuits and Systems, vol. 22, no. 9, 1975.
[8] R. W. Gerchberg, “Super-resolution through Error Energy Reduction,”
Optica Acta: International Journal of Optics, vol. 21, no. 9, 1974.
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