Conference PaperPDF Available

OFDM Pulse Design with Low PAPR for Ultrasonic Location and Positioning Systems

Authors:

Abstract and Figures

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.
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.
KeywordsUltrasounds, 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 fork≠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 5.61011 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
(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
(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
... Also, to solve the multiple-access problem in the field of UPSs, narrowband 2 signal-based modulation schemes such as orthogonal-frequency division multiplexing (OFDM) [30]- [33] have been presented. However, such OFDM-based systems suffer from high peak-to-average power ratios (PAPRs) [34]- [38] although, there are techniques for designing OFDM pulses with good PAPRs, including iterative ones such as those in [34], [39] . Recently, we [41], [42] as well as the authors of [43] proposed chirp-based multiple-access UPSs. ...
... Also, to solve the multiple-access problem in the field of UPSs, narrowband 2 signal-based modulation schemes such as orthogonal-frequency division multiplexing (OFDM) [30]- [33] have been presented. However, such OFDM-based systems suffer from high peak-to-average power ratios (PAPRs) [34]- [38] although, there are techniques for designing OFDM pulses with good PAPRs, including iterative ones such as those in [34], [39] . Recently, we [41], [42] as well as the authors of [43] proposed chirp-based multiple-access UPSs. ...
Article
Full-text available
In ultrasonic positioning systems (UPSs) chirp waveforms have attracted much attention due to its high range resolution. However, the multiple-access schemes for chirp-based UPS are limited. In its application to multiple-access ultrasonic positioning, effective waveform diversity design is a prerequisite. In a multiple-access UPS, each transmitter should transmit a unique waveform with impulse-like auto-correlation and relatively flat cross-correlations to the waveforms transmitted by other transmitters. Proposed in this paper is a methodology whereby multiple transmitters can transmit chirp signals simultaneously. The chirp waveforms are constructed by concatenating a number of linear sub-chirps of the same durations and bandwidths but different starting and stopping frequencies. This process is optimized by selecting sequences with impulse-like auto-correlations and relatively flat cross-correlations. Firstly, the efficiency of the proposed methodology is evaluated by several metrics and then, in an indoor environment, through simulations and experiments for ultrasonic positioning.
... Nevertheless, the longer duration of these signals, as well as the capability to simultaneously emit them following a Code Division Multiple Access (CDMA) method, magnified the problems derived from multipath propagation. Some authors have mitigated this problem by using an OFDM modulation scheme [33], estimating the line-of-sight TOA with a Matching Pursuit algorithm [34], or introducing a validation method based on the repetition of the same code [35]. ...
Article
Current ultrasonic Local Positioning Systems (LPS) based on an infrastructure of beacons can provide centimeter-level accuracy employing the spread spectrum technique, which also adds robustness against noise. However, the strong attenuation of the acoustic waves at high frequencies, the high directionality of ultrasound transducers, and the Doppler effect caused by moving targets still affect the correct performance of LPS. These phenomena reduce the availability of these systems in weak signal coverage areas, as they are no longer able to distinguish weak arrivals from spurious peaks, failing to calculate the position of the target. In this work, the aforementioned problems are dealt with by transmitting Doppler resilient waveforms together with a validation code based on Complementary Set of Sequences. This validation code is leveraged at the receiver after Doppler compensation to reduce the number of spurious arrival candidates and therefore increase the system availability. Compared to a system with no validation, experimental tests with a moving robot have shown that the proposed system increased the availability in weak coverage areas between 20 and 25%. The robot’s average 2D positioning error at rest and in motion was 4.6 cm and 6 cm, respectively.
... Cross correlation between the transmitted and received signals is commonly used in LPSs to maximize the signal-to-noise ratio (SNR) at the output of the correlator. The development of mobile communications Proceedings of the IEEE 5 in recent years and the interest of large companies has boosted the promotion of new encoding schemes and modulations [28], [29]. ...
Article
Acoustic local positioning systems (ALPSs) are an interesting alternative for indoor positioning due to certain advantages over other approaches, including their relatively high accuracy, low cost, and room-level signal propagation. Centimeter-level or fine-grained indoor positioning can be an asset for robot navigation, guiding a person to, for instance, a particular piece in a museum or to a specific product in a shop, targeted advertising, or augmented reality. In airborne system applications, acoustic positioning can be based on using opportunistic signals or sounds produced by the person or object to be located (e.g., noise from appliances or the speech from a speaker) or from encoded emission beacons (or anchors) specifically designed for this purpose. This work presents a review of the different challenges that designers of systems based on encoded emission beacons must address in order to achieve suitable performance. At low-level processing, the waveform design (coding and modulation) and the processing of the received signal are key factors to address such drawbacks as multipath propagation, multipleaccess interference, near-far effect, or Doppler shifting. With regards to high-level system design, the issues to be addressed are related to the distribution of beacons, ease of deployment, and calibration and positioning algorithms, including the possible fusion of information obtained from maps and onboard sensors. Apart from theoretical discussions, this work also includes the description of anALPS that was implemented, installed in a large area and tested for mobile robot navigation. In addition to practical interest for real applications, airborne ALPSs can also be used as an excellent platform to test complex algorithms (taking advantage of the low sampling frequency required), which can be subsequently adapted for other positioning systems, such as underwater acoustic systems or ultrawideband radio-frequency (UWB RF) systems.
Article
Currently, most acoustic positioning strategies are based on broadband coding and the pulse compression technique to obtain better accuracy and robustness against in-band noise. However, the accuracy and robustness of these systems is often seriously damaged in areas of low coverage and/or affected by multipath. This work proposes a High Availability Positioning Algorithm (HAPA) that optimally processes the received signal to improve positioning results throughout the whole location area. This algorithm validates the Time-of-Arrival (ToA) from each beacon, corrects their Doppler shift and compensates for multipath when it exists. If the number of validated beacons is enough to obtain a position, the algorithm tries to position with their optimal combination; if not, it tries to position by incorporating additional ToA candidates for the non-validated beacons. The HAPA performance has been evaluated through a set of experimental tests to compare its results with those obtained by the Robust Positioning Algorithm (RPA) developed by the authors in a previous work, and by a Classical Positioning Algorithm (CPA) based on the emission of chirps. In particular, when using a mobile robot to follow trajectories that cross areas with low coverage and affected by multipath, the HAPA maintains an availability of 97.89%, while the RPA drops to 83.25% and the CPA to 50.19%.
Article
Narrowband ultrasonic sensors can be used for motion tracking and small scale localization. Moving sensor nodes emitting ultrasonic waves produce a Doppler shift in the received signals. Doppler correction methods in narrowband ultrasonic motion tracking systems are explained in this work. Two methods are suggested for Doppler compensation for small-scale localization using ultrasonic sensors. One of the methods requires a pilot carrier to be added to the transmitted signal and the other method exploits range-Doppler coupling for Doppler correction. In the simulation experiments, we compare the performance of the two methods with the traditional methods. We implement both the methods on hardware and compare the performance of the methods for ranging and localization in the presence of Doppler shift.
Article
The task of determining the physical coordinates of a target in indoor environments is still a key factor for many applications including people and robot navigation, user tracking, location-based advertising, augmented reality, gaming, emergency response or ambient assisted living environments. Among the different possibilities for indoor positioning, Acoustic Local Positioning Systems (ALPS) have the potential for centimeter level positioning accuracy with coverage distances up to tens of meters. In addition, acoustic transducers are small, low cost and reliable thanks to the room constrained propagation of these mechanical waves. Waveform design (coding and modulation) is usually incorporated into these systems to facilitate the detection of the transmitted signals at the receiver. The aperiodic correlation properties of the emitted signals have a large impact on how the ALPS cope with common impairment factors such as multipath propagation, multiple access interference, Doppler shifting, near-far effect or ambient noise. This work analyzes three of the most promising families of codes found in the literature for ALPS: Kasami codes, Zadoff-Chu and Orthogonal Chirp signals. The performance of these codes is evaluated in terms of time of arrival accuracy and characterized by means of model simulation under realistic conditions and by means of experimental tests in controlled environments. The results derived from this study can be of interest for other applications based on spreading sequences, such as underwater acoustic systems, ultrasonic imaging or even Code Division Multiple Access (CDMA) communications systems.
Article
Distance-based ultrasonic positioning systems (UPSs) using trilateration have been adopted in various types of applications across a wide variety of fields. Recently, the use of a chirp signal in conjunction with cross correlation has drawn a considerable amount of attention for UPSs. However, when a chirp signal is used for positioning, these algorithms suffer from problems due to signal interference. In this paper, to solve this problem, we propose using four sets of orthogonal chirps, each of which contains three waveforms. The first three sets use chirp rates as a mechanism for assigning uniquely modulated chirp signals to transmitters while the basic idea behind the last one is to exploit the orthogonality of the subcarriers of a chirp waveform, i.e., the discrete frequency components of a chirp waveform. All the waveforms contained in each set have good orthogonality (i.e., the waveforms contained in sets 1 to 3 and set 4 are, respectively, quasi-orthogonal and perfectly orthogonal) and also have all the advantages of a classic chirp waveform. First, the performance of the waveforms is investigated through correlation analysis and then, in an indoor environment, evaluated through simulations and experiments for ultrasonic positioning. For sets 1 to 4, for an operational range of approximately 1000 mm, the positioning root-mean-square-errors & 90% error were 6.20 & 9.13 mm, 6.05 & 8.90 mm, 7.38 & 10.85 mm, and 4.54 & 6.68 mm, respectively.
Article
Full-text available
One of the challenging issues for Orthogonal Frequency Division Multiplexing (OFDM) system is its high Peak-to-Average Power Ratio (PAPR). In this paper, we review and analysis different OFDM PAPR reduction techniques, based on computational complexity, bandwidth expansion, spectral spillage and performance. We also discuss some methods of PAPR reduction for multiuser OFDM broadband communication systems.
Article
A new view of the problem of continuing a given segment of the spectrum of a finite object is presented. Based on this, the problem is restated in terms of reducing a defined ‘error energy’ which is implicit in the truncated spectrum. A computational procedure, which is readily implemented on general purpose computers, is devised which must reduce this error. It is demonstrated that by so doing, resolution well beyond the diffraction limit is attained. The procedure is shown to be very effective against noisy data.
Conference Paper
In this paper we evaluate the probability of detection and the probability of false alarm for an OFDM pulse over AWGN channel. This type of pulse is useful for indoor location systems using ultrasounds due to the ability to accurately measure the time of flight by pulse detection while transmitting some data. Moreover, we can avoid the RF auxiliary channel by using an OFDM-based sync. The probability of OFDM pulse detection over white Gaussian noise will be presented as function of the probability of false alarm when a threshold technique is employed at the receiver. Furthermore, the pulse detection probability will be compared with a chirp pulse.
Article
High peak-to-average power ratio of the transmit signal is a major drawback of multicarrier transmission such as OFDM or DMT. This article describes some of the important PAPR reduction techniques for multicarrier transmission including amplitude clipping and filtering, coding, partial transmit sequence, selected mapping, interleaving, tone reservation, tone injection, and active constellation extension. Also, we make some remarks on the criteria for PAPR reduction technique selection and briefly address the problem of PAPR reduction in OFDMA and MIMO-OFDM.
Article
An algorithm is presented to minimize the peaks in the time domain of bandlimited Fourier signals. This method has the ability to compress signals effectively without disturbing their spectral magnitudes. A computationally efficient algorithm is presented that leads to strongly compressed signals (crestfactors of 1.41 compared to 1.67). The method is applicable not only to flat spectrum magnitudes but to any frequency domain energetic distribution
Theory and Applications of OFDM and CDMA
  • Henrik Schulze
  • Christian Luders
Henrik Schulze and Christian Luders, Theory and Applications of OFDM and CDMA, John Wiley & Sons, first edition, 2005.
A new algorithm in spectral analysis and bandlimited extrapolation
  • Athanasios Papoulis
Athanasios Papoulis, "A new algorithm in spectral analysis and bandlimited extrapolation," Circuits and Systems, vol. 22, no. 9, 1975.
  • Nadav Levanon
  • Eli Mozeson
Nadav Levanon and Eli Mozeson, Radar Signals, JOHN WILEY & SONS, 2004.