Optimal waveforms design for ultra-wideband impulse radio sensors.

Abstract

Ultra-wideband impulse radio (UWB-IR) sensors should comply entirely with the regulatory spectral limits for elegant coexistence. Under this premise, it is desirable for UWB pulses to improve frequency utilization to guarantee the transmission reliability. Meanwhile, orthogonal waveform division multiple-access (WDMA) is significant to mitigate mutual interferences in UWB sensor networks. Motivated by the considerations, we suggest in this paper a low complexity pulse forming technique, and its efficient implementation on DSP is investigated. The UWB pulse is derived preliminarily with the objective of minimizing the mean square error (MSE) between designed power spectrum density (PSD) and the emission mask. Subsequently, this pulse is iteratively modified until its PSD completely conforms to spectral constraints. The orthogonal restriction is then analyzed and different algorithms have been presented. Simulation demonstrates that our technique can produce UWB waveforms with frequency utilization far surpassing the other existing signals under arbitrary spectral mask conditions. Compared to other orthogonality design schemes, the designed pulses can maintain mutual orthogonality without any penalty on frequency utilization, and hence, are much superior in a WDMA network, especially with synchronization deviations.

Full text

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Sensors, 2010, 10, 11038-11063; doi:10.3390/s101211038

sensors
ISSN 1424-8220
www.mdpi.com/journal/sensors
Article
Optimal Waveforms Design for Ultra-Wideband Impulse Radio
Sensors
Bin Li 1,2,*, Zheng Zhou 1,2, Weixia Zou 1,2, Dejian Li 1,2 and Chong Zhao 2
1 Key Lab of Universal Wireless Communications, Ministry of Education (MOE), Inner Box. 96,
BUPT, Beijing 100876, China
2 Beijing University of Posts and Telecommunications (BUPT), Inner Box.96, BUPT, Beijing
100876, China; E-Mails: zzhou@bupt.edu.cn (Z.Z.); zwx0218@bupt.edu.cn (W.X.Z.);
dejian021@163.com (D.J.L.); Emmacinderey@gmail.com (C.Z.)
* Author to whom correspondence should be addressed: E-Mail: stonebupt@gmail.com;
Tel.: +86-010-6228-3093.
Received: 20 October 2010; in revised form: 25 November 2010 / Accepted: 27 November 2010 /
Published: 6 December 2010

Abstract: Ultra-wideband impulse radio (UWB-IR) sensors should comply entirely with the
regulatory spectral limits for elegant coexistence. Under this premise, it is desirable for UWB
pulses to improve frequency utilization to guarantee the transmission reliability. Meanwhile,
orthogonal waveform division multiple-access (WDMA) is significant to mitigate mutual
interferences in UWB sensor networks. Motivated by the considerations, we suggest in this
paper a low complexity pulse forming technique, and its efficient implementation on DSP is
investigated. The UWB pulse is derived preliminarily with the objective of minimizing the
mean square error (MSE) between designed power spectrum density (PSD) and the emission
mask. Subsequently, this pulse is iteratively modified until its PSD completely conforms to
spectral constraints. The orthogonal restriction is then analyzed and different algorithms have
been presented. Simulation demonstrates that our technique can produce UWB waveforms
with frequency utilization far surpassing the other existing signals under arbitrary spectral
mask conditions. Compared to other orthogonality design schemes, the designed pulses can
maintain mutual orthogonality without any penalty on frequency utilization, and hence, are
much superior in a WDMA network, especially with synchronization deviations.
Keywords: UWB-IR sensors; waveform design; orthogonality; waveform division
multiple access

OPEN ACCESS

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1. Introduction
Ultra-wideband impulse radio (UWB-IR) is a promising technique in short-range high-data-rate
communication scenarios, such as wireless personal area networks (WPANs) [1]. Meanwhile, UWB-IR
sensors have also been employed in military applications such as high-precision radar and through-wall
target detection owing to their exceptional multipath resolution and material penetration capability [2-5].
Most recently, the emerging body area network (BAN) field also considers UWB as an appealing
solution for health monitoring. These advantages of UWB-IR are mainly attributed to the enormous
bandwidth of its transmitted pulses, which may occupy several gigahertz (GHz). However, on the other
side, UWB also has long been confronted with rigorous application restrictions, because of its potential
interference to other existing vulnerable wireless systems, such as Global Positioning System (GPS)
and Universal Mobile Telecommunications System (UMTS) [6]. The first UWB emission mask was
set out by U.S. Federal Communications Commission (FCC) in 2002, accompanying the authorization
of its unlicensed use in the 3.1–10.6 GHz band [7].
For thorough spectral compatibility between those systems sharing the same band, the released
UWB emission limits are very strict; for example, the FCC allowable equivalent isotropically radiated
power (EIRP) for UWB transmitted signals is below −41.3 dBm/MHz. Hence, with respect to this
EIRP mask, only when the transmitted pulses make full use of the regulated spectral energy, can a
sufficiently high signal to noise ratio (SNR) be obtained in UWB receivers, which in turn enhances
transmission reliability. Although the traditional Gaussian monocycle has been widely used in the early
stages because of its simple realization, its frequency utilization is quite limited [8], so many
publications have focused on this issue in recent years. In [9,10], Parr constructed an equivalent
channel matrix from the sampled mask, and generated orthogonal UWB pulses from its dominant
eigenvectors. However, the frequency utilization remains rather low, and the required 64 GHz
sampling frequency makes it comparatively hard to implement. The Finite Impulse Response (FIR)
filter based technique adopting Parks-McClellan (PM) algorithm has been presented in [11].
Unfortunately, the spectral mismatch between the designed PSD and emission mask is remarkable near
the sharp spectral discontinuities. Davidson et al. [12] applied linear matrix inequalities (LMI) theory
to design FIR filter, which could conform to piecewise constant and piecewise trigonometric
polynomial masks. Later, a FIR-based pulse shaper has been fully extended by using second order cone
programming (SOCP) and it achieved relatively high frequency utilization [13,14]. However, their
expected filter orders may be comparative large in order to achieve an acceptable frequency utilization,
and the pulses still cannot use the lower frequency region (0–0.9 GHz) entirely. In [15], Ohno and
Ikegami synthesized an interference mitigation waveform. Such a UWB pulse can use one single band
only and its realization is very complicated given the dozens of carrier generators required both in
transmitters and receivers. Other UWB waveform optimization techniques, such as the optimal
waveform designing based on Gaussian functions or Rayleigh functions, can match the whole spectral
mask to some extent [16,18]. Nevertheless, the frequency utilization of these optimal pulses is still far
from satisfactory.
In addition, modern communication design has gradually paid attention to resolving the spectrum
scarcity, so that the orthogonal waveform multiplexing have been widely adopted to further improve
the frequency efficiency, which can also eliminate mutual interference or provide considerable

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waveforms diversity gain in UWB sensor networks [19]. Therefore, an orthogonal waveform set
becomes indispensable in system design. The Hermite-Gaussian function and wavelet have been
introduced to design mutually orthogonal UWB waveforms; however, their frequency utilization
cannot been further optimized [20,21]. Although spectrally efficient orthogonal waveforms have been
devised based on the FIR filter [13,14], the complexity of this sequential algorithm may grow with the
increasing number of orthogonal users. More importantly, the frequency utilization of subsequent
derived pulses undergoes an obvious degradation. Besides, these designed orthogonal pulses are rather
sensitive to synchronization deviations, which imposes stringent requirements on receiving timing and
hence increases complexity [14,20].
In this paper, we propose a novel pulse forming technique for UWB-IR sensors. The frequency
domain representation of the emission pulse is firstly derived from the product of a weight vector and
the cyclic shift matrix (CSM) constructed from the basis waveforms. As a result, the spectral shaping
problem is transformed to an optimization of the corresponding weight vector. With the permission
that the designed PSD can temporarily outstrip UWB spectral masks, the design process can be
simplified greatly. Later, this preliminary waveform would be further modified iteratively to lower the
excess PSD until UWB pulses totally conform to emission constraints. Numerical evaluations indicate
that our pulse can match the arbitrary spectral constraint much more completely than the other existing
schemes. The proposed structure can also be viewed as a versatile pulse generator which can be
efficiently implemented for digital signal processing (DSP). Hence, it can be directly applied to
arbitrary UWB masks. We also design UWB waveforms with spectrum notch attenuated nearly 50 dB
in specific bands, which is of great significance for cognitive radios (CRs) considering spectral
avoidance to primary users.
Based on this already proposed algorithm, the constraint on orthogonal waveforms has also been
derived. In order to obtain orthogonal pulses, schemes both from time domain and frequency domain
have been addressed. We demonstrate that our designed orthogonal waveforms can use spectral mask
as entirely as a single pulse. It is shown through analysis and simulation evaluations that the designed
orthogonal pulses outperform other UWB waveforms in a WDMA network if mutual interference from
nearby sensors is taken into account, especially when the synchronization deviation exists.
The rest of this paper is organized as follows: Section 2 elaborates on the design algorithm in detail.
The orthogonal UWB pulses with efficient frequency utilization will be analyzed in Section 3. In
Section 4, we discuss and evaluate the performance of UWB pulses in WDMA network with different
degree of timing accuracy. At last, we conclude the paper in Section 5.
2. UWB Waveform Design
In order to eliminate potential interference from UWB sensors to the other vulnerable wireless
systems sharing the same frequency band, the emission power of transmitted UWB pulses has been
rigorously limited in different frequencies [6]. The regulatory FCC spectral mask for indoor UWB
devices can be shown as:

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41.3
75.3
53.3
51.3
41.3
51.3







[0, 0.96]
[0.96, 1.61]
[1.61, 1.99]
[1.99, 3.1]
[3.1, 10.6]
[10.6,

( )
f
FCC
dBm MHz
dBm MHz
dBm MHz
dBm MHz
dBm MHz
dBm MHz
f
f
f
f
f
f
GHz
GHz
GHz
GHz
GHz
]
GHz
M





















(1)
Thus, UWB sensors in preparation for data transmissions should make sure that their power
spectrum density (PSD) remains below MFCC(f). For the time-hopping pulse position modulation
(TH-PPM) and pulse amplitude modulation (TH-PAM) based multiple-access system, the accumulated
PSD of multiusers can be approximated well by K|S(f)|2 [11,13,22]. S(f) represents the Fourier
transform (FT) of baseband pulse s(t), while K is a constant related to the specific time-hopping (TH)
code [22], which has no relation with the pulse designing. To simplify elaborations, we directly set
K = 1 in our following analysis so the designed pulse should satisfy an important confinement
|S(f)|2 ≤ MFCC(f). When we adopt a more general emission limits, denoted by M(f) which is regulated
by different countries, the corresponding confinement can be further modified to |S(f)|2 ≤ M(f).
To improve SNR in receivers, on the other hand, the transmitted UWB pulse is also supposed to use
the regulatory spectral power as fully as possible. The spectral utilization efficiency of UWB signals is
always measured in terms of the normalized effective signal power (NESP) [13], which is defined as:


2
( )
S f
100%
( )
B
B
f
f
df
NESP
M f df


(2)
Where M(f) is the spectral mask regulated by the radio management and fB denotes the authorized
band. As a consequence, the consolidated objective of UWB waveform designing is to maximize the
NESP subject to |S(f)|2 ≤ M(f). Traditionally, the NESP optimization is mainly focused on two
techniques, that is, the UWB pulse shaping filter design and waveform optimization. Basically, both
two techniques can only concentrate on devising appropriate time sequences which are expected to
exhibit specific spectrum shapes, including the impulse response of FIR filters and UWB waveforms.
These design methods are usually either complicated in their realizations or inefficient in NESP. In this
paper, our new scheme will handle the UWB signal design directly in the transform domain, which is
much more competitive from the aspect of its substantivity of maximizing the NESP.
2.1. Design Algorithm
To begin this goal-directed design algorithm, we may select specific waveform meeting the
following two restrictions as the basis waveform in frequency domain:
(1) The basis waveform should be symmetric. Actually, the symmetry waveform is much suitable
in the sense that the UWB spectrum mask remains constant in most frequency range. Besides, it
is easy to generate an even symmetry waveform from the classical FIR filter [23].
(2) The basis waveform is also supposed to attenuate fast. This is mainly because the regulatory
UWB spectral masks always contain sharp stairs or narrow notches, whereas the long trailing
of basis waveform may destroy the chop features of UWB mask.

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In general, the energy concentration of the basis/windowing waveforms can be used to essentially
reflect their attenuation characteristic, which can be usually defined as ∫f1|w(f)|2df/∫fw|w(f)|2df. Here, w(f)
is the basis waveform in frequency domain; f1 represents frequency range limited by the −10 dB cutoff
points, while fw denotes the interested frequency ranges. It is clearly seen that the higher the energy
concentration is, the faster the waveform attenuation is. So, the conventional Gaussian waveform and
the raised cosine function are both good candidates for the basis waveforms, whose energy
concentrations can basically approach 99.8% and 99.4%, respectively. Some familiar basis waveforms
meeting the challenges have been shown in Figure 1.
Figure 1. Basis waveforms meeting the requirements.
-0.5-0.4-0.3 -0.2-0.1
Frequency /GHz

0 0.1 0.2 0.3 0.40.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Magnitude


Gaussian waveform
Hamming waveform
Blankman waveform

However, it should be noted that although the rectangular waveform has an ideal energy
concentration, the corresponding infinite waveform in time domain may prevents it from being applied.
In our following analysis, we adopt the Gaussian monocycle as the basis waveform because of its
simple realization on hardware. So, we have:
2
2
1
2
( )
w f
exp
2
f
s
s









(3)
where s is the shaping parameter which determines the waveform shape, including the height and width
of w(f). The corresponding sample basis sequence w(k) can be given by:
( )
w f
0,1,, -1
2
( )
() , 1,, -1
22
s
s
kf
s kf
N
k
w k
NN
w f NfkN









(4)
where fs represents the sample interval in frequency domain; N is the length of the basis sequence. A
cyclic shift matrix (CSM), W, can be then constructed from this basic sequence w(k) above:
(0) (
(1) (0)

( 2) (
( 1) (
w Nw N

1) (1)
(2)

w N
w
3) (
2) (0)
1)
w
w
w N
w
w
w
w Nw N


















W




(5)
We denote the first column of W with w0:
0
[ (0) (1)
w
( 2) (1)]T
w w Nw N

w


(6)
After the cyclic shift of i samples have been performed on w0, we have: