Communications and Network, 2013, 5, 161-165
http://dx.doi.org/10.4236/cn.2013.53B2031 Published Online September 2013 (http://www.scirp.org/journal/cn)
Performance Analysis of Multiband Impulse Radio UWB
Communication System Based on PSWF
Lili Chen, Zheng Dou
Information and Communication Engineering College, Harbin Engineering University, Harbin, China
Email: douzheng@hrbeu.edu.cn
Received May, 2013
ABSTRACT
To improve the data transmission rate and use spectrum flexibly, a new spectrum allocation method for Multiband Im-
pulse Radio UWB (MB-IR-UWB) is proposed in this paper based on the band-limited and orthogonal characteristics of
Prolate Spheroidal Wave Function (PSWF). The system model is built and the bit error rate (BER) formula is deprived
by binary time hopping pulse po sition modulation under additiv e white Gaussian noise. Moreover, the system perform-
ance is analyzed via MATLB simulation. The results indicate that MB-IR-UWB system performance of BER is the
same with single-band UWB. However, in the proposed scheme the data can be transmitted in multiple parallel bands,
which enjoys much higher transmission rate. In addition, PSWF pulse duration affects the BER performance.
Keywords: IR-UWB; Multiband; PSWF; Performance Analysis
1. Introduction
Ultra-wideband (UWB) is an emerging technology that
offers great promises to satisfy the growing demand for
low cost and high-speed digital wireless home networks.
By using ultra short impulse pulse to convey information
[1], Impulse Radio allows remarkable data rates of Gbit/s.
However, conventional single-band UWB signal has a
wide fixed spectrum, which made the receiver lack the
flexibility of spectrum utilization and restricted the im-
provement of the system transmission performance. In
2004, Stkphane Paquelet proposed the idea of multiband
in [2,3], and proved that the method can effectively im-
prove the transmission rate. Later in [4] Martin Mittel-
bach modified the model and concluded that extending
the basic architecture to a multiband system could allow
remarkable data rates in the order of several hundred
Mbit/s up to almost a Gbit/s. Multiband Impulse Radio
UWB (MB-IR-UWB) scheme divides the allocated
UWB frequency range into several subbands and trans-
mit information in multiple parallel band, which would
not only expand the capacity of the system, but also im-
prove the flexibility of spectrum utilization. By using
soft-spectrum adaption (SSA) [5], it can avoid some cer-
tain narrow-band interference and improve the perform-
ance of receiver. Therefore, this scheme will become a
new direction of future technologies.
According to preceding researches, we know tradi-
tional MB-IR-UWB systems use band-pass filter to ar-
range for the spectrum, and use incoherent energy detec-
tion in the receiver, but the filter design is more co mplex.
Based on the band-limited and orthogonal characteristics
of PSWF, it can be equivalent to the ideal band-pass fil-
ter, and the coherent demodulation can be applied to get
better performance.
In this paper, Section II makes a brief introduction of
MB-IR-UWB architecture. The detailed description of
waveform choice, band allocation, and system model is
developed in Section III. The simulation result and
analysis of transmission performance based on PSWF is
presented and discussed in Section IV. Finally, Section V
concludes this paper.
2. MB-IR-UWB System Overview
A block diagram of entire system model is depicted in
Figures 1 and 2. These two diagrams contain the major
components of this architecture [6,7].
The basic working method of MB-IR-UWB system is
as follows. A mono-band pulse generator is to generate a
number of pulses where each pulse occupies a specific
frequency band. The relatively narrow-band pulses are
referred to as subband or monoband pulses. Each sub-
band pulse is modulated with different data according to
a specific modulation scheme. Prior to modulation the
coded bit stream is convert into a block of M Nband bits
that is partitioned into Nband groups of M bits. After
modulation, this sum of subband pulses forms the MB-
IR-UWB transmit signal and is transmitted via the sing le
UWB antenna. After experiencing a multi-path and
thermal noise channel, on the receiver side, a coherent
C
opyright © 2013 SciRes. CN
L. L. CHEN, Z. DOU
162
demodulation is considered, ensuring the optimum re-
ception. At first, the received multi-band signal is de-
composed by multiplying the orthogonal mono-band
pulse to its subbands and subsequent operations are per-
formed per band. And then, make the received data par-
allel to serial conversion and make a soft or hard bit de-
cision depending on the type of channel decoder. At last,
we can get the original data. Theoretically multi-band
technology can improve the system capacity N times (N
is the sub-band number), but it is still far from this limit.
3. MB-IR-UWB System Model Building
3.1. Prolate Spheroidal Wave Function Set
Prolate Spheroidal Wave Function (PSWF) has the ad-
vantage of time-limited and band-limited. It was first
proposed by D.Slepian and H.O.Pollack of Bell Lab in
the late 1950s [8]. It is a complete set of orthogonal func-
tion, which is time-limited in [/ and band-
limited in . It has the maximum energy concen-
tration on the interval [-T, T] as a band limited function.
The PSWF pulses are orthogonal both in time and fre-
quency domain. We can shift its spectrum and control its
bandwidth easily by adjusting the pulse parameters.
Therefore it is often applied in UWB communication.
2,/2TT]
][, 
As is well-known, it’s difficult to calculate the clos ed-
form solution of PSWF. So the discrete approximation
solving method has been used, which can be regarded as
follows. The signal ()t
, whose time duration is T, goes
through an ideal band-pass filter that the upper cut-off
Figure 1. Multi-band pulse generator and MB-IR-UWB
transmitter.
Figure 2. MB-IR-UWB receiver block diagram.
frequency is u
f
and lower cut-off frequency is l
f
, the
output signal is ()t
. So the N base frequency bands
can be regarded as N ideal band-pass filter. The template
of N spectrum is as follows.
,,,
,,
()2sin (2)2sin (2)
1
() (1,)
0
iiu iuil i
il i iu
htfc ftfcft
fff
Hfi N
others
,l


(1)
where ,il
f
and ,iu
f
respectively means the lower cut-
off frequency and upper cut-off frequency of the ith base
frequency band. Using discrete solution respectively in
each band, the corresponding PSWF pulses of all orders
can be attained. In this paper, we choose the first order
PSWF pulses of each band as the base pulses.
For two band-limited PSWF pulses ,()
ik t
and ,()
jl t
,
in different sub-bands, they don’t overlap each other in
the frequency domain. By the Parseval’s theorem, it can
be easily proved that
2
,, ,
/2
1
() ()0
T
ikjli j
ij
ttdt ij
 

(2)
So the band pass PSWFs in different sub-bands are
orthogonal [9]. Due to the double orthogonal characteris-
tic, two PSWF pulses have the same time duration and
subbands are orthogonal. Therefore, all the pulses in the
set are mutually orthogonal.
In this paper, we divide the UWB spectrum (from 3.1
GHz to 7.5 GHz) into several subbands, and then use the
corresponding PSWF time domain impulse as the infor-
mation carrier of MB-IR-UWB. The multiband spectrum
allocation is given in Figure 3. In order to meet the re-
quirements of ultra-wideband communications, the
bandwidth of each band should be greater than or equal
to 500 MHz.
05 10 15
-150
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Fr equen cy [ G Hz]
PSD [dBm/GHz]
.......
Figure 3. The multiband spectrum allocation diagram.
Copyright © 2013 SciRes. CN
L. L. CHEN, Z. DOU 163
3.2. MB-IR-UWB System Model Building
Consider a single-user MB-IR-UWB, with the binary
orthogonal TH-PPM modulation, it is assumed that the
pulse repetition time is Ts and every Ns pulses are used to
transmit one bit information. So the binary symbol rate
s
bps. The transmitted signal can be ex-
pressed as:
1/
b
RNs
T
j
11
00
() ()()
0,1, 1
NN
iisjc
iij
Sts tp tjTcTa
iN


 


(3)
where ()
i
s
t is transmitted signal of the ith band,
is the pulse waveform of the ith band, ()
i
pt
j
c defines the
jitter of the pulse with respect to the timing of the integer,
cT
j
a
is the time shift caused by PPM modulation.
Trough AWGN channel, the received signal can be
written as:
()() ()rt Stnt
 (4)
Channel gain
and channel delay
depends on the
propagation distance between the transmitter and receiver.
is additive white Gaussian noise with zero mean
value and variance
()nt
02N.
As stated earlier, the pulses between each sub-band are
orthogonal, the optimum receiver under the AWGN can
be considered, the received signal goes into the correla-
tors, multiplying correlation mask of each band ,
and into the integrator, then into the decision unit for
judgment. The correlation mask of the ith band is
()
i
vt
()() ()
ii jci jc
vt ptcTptcT
 
(5)
For each band is independent, separate judgments can
be made in each branch. The detection is a standard hy-
pothesis testing problem. While the decision variables
() ()0
s
T
ii
Zrtvtdt
(6)
it will be judged bit ‘0’,othervise bit ‘1’.According to the
receive form of binary determinate signal, usually in the
case of equal priori probability, we can obtain the aver-
age error probability
11
Prob( >0<1)+Prob( <0>1)
22
= Prob(<0>1)
PeZ ZZ Z
ZZ
││
(7)
Define 01
0
1[()()]
T
bRX
ptptdt
E
is the normalized
correlation coefficient of the received signal and
, where , it’s the energy of each
0()pt
1()pt 2
=
bRXs TX
ENE
received bit information. After some calculus operations,
yield
2
0
2
(1 )
0
1
= 2
(1 )
1
=erfc()
22
bRX
u
E
N
bRX
Pee du
E
N

(8)
For binary orthogonal PPM signal, we can easily ob-
tain that
00
0
1() ()0
T
bRX
ptpt dt
E


(9)
Thus, the average error probability of binary orthogo-
nal PPM for MB-IR-UWB system is:
0
1erfc( )
22
bRX
E
Pe N
(10)
where 2
+-
2
erfc( )=u
y
y
edu
.
4. Simulations and Performance Analysis
4.1. Performance Comparison of Single-band
and Multiband IR-UWB
The following parts analyze MB-IR-UWB system per-
formance from two views of reliability and validity.
First, for the reliability, Figure 4 shows the perform-
ance comparison of the single-band UWB and MB-IR-
UWB system, assumed the conditions of the same wave-
form, the same data transmission rate.
It can be seen from Figure 4 that the BER curves of
MB-IR-UWB and single-band UWB almost completely
overlap. This is because that each band can be equivalent
to a single-band UWB, and in white Gaussian noise
channel bit error rate is only related to signal-to-noise
ratio. So in terms of reliability, multiband UWB system
did not enjoy the advantage.
-5 05 10 15
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/N0(dB)
BER
BER of M B- IR- UW B in t heory
BER of s in g l eba nd base d on PSWF
BER of M B- IR- U W B based on PSWF
Figure 4. The performance comparison of multiband and
single-band UWB.
Copyright © 2013 SciRes. CN
L. L. CHEN, Z. DOU
164
Second, for the validity, the transmission rate of the
two systems is compared. When the operating frequency
occupied the entire 7.5 GHz band, the single-band PSWF
pulse duration 1, multiband PSWF pulse dura-
tion 2. Therefore, if other conditions are the
same, the pulse repetition period 12 2
4
m
Tn
ns s
4
m
T
s
sshm
.
Suppose the transmission rate of single-band UWB is
1b, and the transmission rate of MB-IR-UWB is ,
we can see that
TT NNT
2b
RR
112 2
1/, (1/ )
bssb ss
RNTR NTN sub
Therefore, theoretically in equal time, compared with
single-band UWB, the multi-band scheme can increase
the transmission rate by N times. Thus, multi-band UWB
communications technology plays an important role in
satisfying the increasingly high data transmission rate.
4.2. The Impact of Pulse Duration on System
Performance
Due to the advantage of PSWF’s high energy concentra-
tion, it is of great significance to increase the transmis-
sion rate as much as possible. From the analysis above,
we can conclude that the pulse duration affects the data
transmission rate indirectly. The following part will fo-
cus on the analysis of the effect of different m on sys-
tem performance. In the simulation, the number of pulse
per bit , the cardinality of the TH code
T
5
s
N3
h
N
.
The corresponding relation between different values
and is shown as Table 1. m
T
b
It can be seen from Figure 5 that the BER curves are
very close when m equals to 8ns, 4ns, 2ns.Under this
circumstance, the system performance is the best. When
m is 1.5ns, the system performance deteriorates seri-
ously, and when m
T is 1ns, the system performance
becomes worst. It is because that the larger m is, the
higher energy concentration of pulse in particular fre-
quency band is. So the less energy loss is, the better the
system performance is. Thus, the validity and reliability
is a pair of mutually contradictory unity. To improve the
reliability of the system, it would inevitably lead to a
decline in the validity. In our simulation, in order to en-
sure the system performance, the pulse duration which
corresponds to = 66.7 Mbps is the best, i.e. = 2
ns.
R
T
b
T
T
TR m
5. Conclusions
This paper takes the MB-IR-UWB communication system
Table 1. Corresponding relation between different Tm val-
ues and Rb.
Pulse duration Tm/ns 8 4 2 1.5 1
Bit rate Rb/Mbps 16.7 33.3 66.7 88.9 133.3
02468 10
10
-4
10
-3
10
-2
10
-1
10
0
Eb/N0(dB)
BER
R b= 16.7 M bit /s
R b= 33.3 M bit /s
R b= 66.7 M bit /s
R b= 88.9 M bit /s
R b =1 33 .3 Mb it/s
Figure 5. The performance comparison in different data
rate.
based on PSWF pulse as the research object, proposes a
new way of multi-band spectrum arrangement and uses
coherent demodulation method to achieve the best recep-
tion. Through system model building and simulation
analysis, we draw the conclusion that MB-IR- UWB
system has the same bit error rate performance with sin-
gle-band UWB. But in the MB-IR-UWB, the data can b e
transmitted in parallel, which can improve the transmis-
sion rate of information. In addition, PSWF pulse dura-
tion affects the BER performan ce. The simulation results
show that the shorter PSWF pulse duration is, the larger
the transmission rate is, but the system performance be-
comes worse. Therefore, in actual communication, we
should make a tradeoff between the validity and reliabil-
ity to a best choice.
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