Content uploaded by Sérgio Ivan Lopes

Author content

All content in this area was uploaded by Sérgio Ivan Lopes on Sep 04, 2015

Content may be subject to copyright.

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

34/278

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.

35/278