Communications and Network, 2013, 5, 98-102
http://dx.doi.org/10.4236/cn.2013.53B2019 Published Online September 2013 (http://www.scirp.org/journal/cn)
Impulse Radio UWB Signal Detection Based on
Compressed Sensing
Xing Zhu, Youming Li, Xiaoqing Liu, Ting Zou, Bin Chen
Institute of Communication Technology, Ningbo University, Ningbo, China
Email: liyouming@nbu.edu.cn
Received June, 2013
ABSTRACT
The extremely high sampling rate is a challenge for ultra-wideband (UWB) communication. In this paper, we study the
compressed sensing (CS) based impulse radio UWB (IR-UWB) signal detection and propose an IR-UWB signal detec-
tion algorithm based on compressive sampling matching pursuit (CoSaMP). The proposed algorithm relies on the fact
that UWB received signal is sparse in the time domain. The new algorithm can significantly reduce the sampling rate
required by the detection and provides a better performance in case of the low signal-to-noise ratio when comparing
with the existing matching pu rsuit (MP) based detection algorithm. Simulation results demonstrate the effectiveness of
the proposed algorithm.
Keywords: IR-UWB; Compressed Sensing; C oSaM P; MP; Si gnal Det ect i on
1. Introduction
UWB is one of the key technologies in the short-range
broadband wireless communication. With the character-
istics of high data rates, low power, and low cost, UWB
can be applied to many scenarios such as high-speed
short-range wireless personal area networks (WPAN),
ranging, positioning, monitoring, and wireless sensor
networks (WSN) [1]. In some of these applications,
UWB signal detection is a very important component.
Hence there is a need to study th e UWB signal detection
to make it more practical.
However, when using the traditional algorithm for
UWB signal detection, a very high sampling rate is re-
quired according to Shannon-Nyquist sampling theorem
for the UWB signal’s high bandwidth that is up to sev-
eral gigahertzes. This is difficult to implement with a
practical analog-to-digital converter (ADC) [2]. The
emerging theory of CS enables the reconstruction of
sparse or compressible signals from a small set of ran-
dom measurements. If adopted by the signal detection,
the CS theory will make the sampling rate much lower
than the Nyquist rate. The authors in [3,4] proved that it
is effective to detect signal by processing the sampling
values of compressed sensing directly. Reference [5]
proposed a MP based signal detection algorithm. In [2],
the authors proposed a CS based system for UWB echo
signal detection at a sampling rate much lower than Ny-
quist rate. This study indicates that the low-dimensional
random measurement method based on the CS theory can
be used to sample UWB signal. A UWB signal detection
method based on MP algorithm was developed in [6].
Whereas in a circumstance with low signal-to-noise ratio
(SNR), the performance of the MP based detection algo-
rithm is not good. Thus, it leaves room for improvement.
In [7], the authors demonstrated that CS theory is par-
ticularly suitable to IR-UWB signal detection, and a gen-
eralized likelihood ratio test (GLRT) detector was pro-
posed. However, the GLRT UWB receiver needs the
pilot symbol assisted modulation, leading to high system
complexity. Furthermore, in order to reach a high per-
formance, the number of mixer-integrators employed by
the receiver is too large to be realized.
In this paper, we propose a CoSaMP [8] based IR-
UWB signal detection method. Without other extra
processes, the method is formed from extracting infor-
mation directly from sampling values acquired by CS.
The complexity of the proposed detection method is re-
duced dramatically when comparing with the GLRT de-
tector. Moreover, computer simulation results are pro-
vided to verify the performance of the proposed method,
which show that the performance of the new method is
superior to that of the MP based detection algorithm,
especially in low signal-to-noise ratio.
The remainder of the paper is organized as follows. In
Section II, the background of CS is depicted. Section III
provides the principle for generating IR-UWB signal.
Section IV presents a CS based IR-UWB signal detection
principle and proposes a CoSaMP based IR-UWB signal
detection algorithm. Simulation results are provided in
Section V. Finally, conclusions are drawn in Section VI.
C
opyright © 2013 SciRes. CN
X. ZHU ET AL. 99
2. Compressed Sensing Background
CS is a technology that can recover the high-dimensional
signals from the low-dimensional and sub-Nyquist sam-
pling data with the prior information that the signals are
sparse or compressible [9]. The mathematical model of
CS can be described as
yAx (1)
where is a signal which can be sparsely rep-
resented in a basis matrix
N1
xRNN
12
{,, ,}
N
 
φR
TN
12
[, ,,]
N
 
,
that is, , the vector
xφθ 1
θR
MN
AR
θ
x
consists of K (K<<N) nonzero elements (we often say
that is K-sparse). Th e vector (K<M<<N)
is a random measurement matrix that is uncorrelated with
. denotes the M samples obtained by CS.
Our purpose is to recover the sparse coefficient vector
from the M samples, and then multiply it by the basis
matrix , thus recovering the original signal .
θ
φM1
yR
φ
In order to figure out the sparse coefficient vector ,
we need to find the solution to the following norm
optim i zat i on p r ob l em [10]
θ
0
l
0
argmin. .st
θθyAφθ (2)
Unluckily, solving the optimization problem (2) is
prohibitively complex for it is an NP-hard nonconvex
optimization problem. A modified problem is to replace
the restrict with the restrict
0
l1
l
1
argmin. .st
θθyAφθ (3)
This optimization problem transforms (2) into a con-
vex optimization problem which can be easily solved by
linear programmi ng.
3. Impulse Radio UWB Theory
The US Federal Communications Commission (FCC)
provided a definition that a signal can be classified as an
UWB signal if its fractional bandwidth is greater than 0.2
or its bandwidth is 500MHz or more [1]. According to
this definition, there are several ways to generate UWB
signals, among which impulse radio is the most common
method. In this paper, we focus on the impulse radio
UWB (IR-UWB) signal.
IR-UWB communication is based on transmitting ul-
tra-short (typically on the order of a nanosecond) dura-
tion pulses that are subsequently modulated by the binary
information symbols. The two most popular modulation
schemes are pulse amplitude modulation (PAM) and
pulse posit i o n modulat i o n ( PPM).
Owing to different approaches are employed to gener-
ate the pulse train, the UWB systems can be divided into
two main categories: time hopping UWB (TH-UWB) and
direct sequence UWB (DS-UWB). To take a specific
case, we will discuss the PAM-DS-UWB signal and its
detection in the following. A block diagram of the
PAM-DS-UWB transmitter [1] is shown in Figure 1.
In Figure 1,
01 1
,,,,, ,
kk
bb bb
 b is a binary
sequence to be sent and generated at a rate of 1/
bb
RT
(bits/s). After passing through the repeat encoder, every
bit of the sequence is repeated
b
s
N times, therefore
we get a new s e q u ence
000111
(,,, ,,,, ,, ,,, ,,)
kk k
bbbbb b bbb
 b*
where has a rate of (bits/s).
Then the second system of the block diagram converts
into a sequence 01 1
b* /1/
cbs bs
RNT T
(,,,,,mmm
b* , ,)
jj
m

11
*
21(
jj
mb 
m
)j 
m
that contains two kinds of elements,and . The con-
version equation of this is .
When the sequence enters the transmission encoder,
a binary zero correlation duration (ZC D ) co de
01 1
(,,,,,,)
jj
aa aa
a
composed of 1
’s is applied to it [11] and the output of
the transmission encoder is a new sequence , which
can be expressed as *m
00 010
10 111
01
01
*(,, ,,,
,,,,,
,,,,,
(,,,,,)
j
j
jj jj
j
ma mama
ma mama
ma mama
mmm
 
)




m
(4)
The period of the ZCD code
01 1
(,,,,,,)
jj
aa aa
a
is
p
N, we often assume that
s (a more general
hypothesis is that NN
p
N is an integer multiple of
s
N).
The rate of sequence is bs
(bits/s).
Next, the sequence goes into the PAM modulator,
and a sequence of unit pulses (Dirac pulses
*m
*m
/1/T T
cs
RN
()t
) lo-
cated at times
s
jT
1
are generated by the PAM modulator
[1,11]. The rate of the sequence of unit pulses is
/ /
p
sb s
RNT T
T
(pulses/s). At last, the output of the
PAM modulator passes through the pulse shaper, whose
impulse response is. The duration of is ,
and ms
()pt ()pt m
T
T
. Thus, we get the final output signal ()
s
t,
which is given by
*
()( )
j
s
j
s
tmptj



T (5)
where often has the following form
()pt
2
2
2
2
2
()(1 4)
t
t
pt e
 (6)
Figure 1. Block diagram of PAM-DS-UWB transmitter.
Copyright © 2013 SciRes. CN
X. ZHU ET AL.
100
where 2
42

is the pulse shap er facto r, and 2
is
the variance.
In practice, a PAM-DS-UWB transmitter’s parameters
set by the user are: the average transmit power , the
number of bits generated by the binary source 0, the
sampling frequency
0
P
n
c
f
,
p
N,
s
T,
s
N, , and
m
T2
[1].
Figure 2 shows an example of the PAM-DS-UWB
signal. From this figure, we can see that PAM-DS-UWB
signal presents an intuitive sparse characteristic in the
time domain. That is, the signal has only a few nonzero
values. Thus, according to the Section II, the basis matrix
of the PAM-DS-UWB signal can be an identity matrix.
Based on the above, we can apply the CS theory into
the PAM-DS-UWB signal detection.
4. CS Based IR-UWB Signal Detection
4.1. The Signal Detection Model
We implement the detection by distinguishing between
the following two hypotheses
0
1
:
:(
H
H

yAn
)
y
Axn (7)
where denotes the PAM-DS-UWB signal to
be detected, and
N1
xR 2
~(0, )
N
N
n
M1
I
is the independent and
identically distributed additive white Gaussian noise.
(M<<N) is a known random measurement
matrix, and is the sample obtained by the de-
tector. Next, we let
MN
yR
AR
11
10
Pr( chosen when true )and
Pr( chosen when true)
d
f
PH H
PH H
denote the probability of detection and the probability of
false alarm respectively [3].
Figure 3 illustrates the principle block diagram of the
IR-UWB signal detection based on CS.
4.2. The Proposed IR-UWB Signal Detection
Algorithm
In this section, we propose an IR-UWB signal detection
algorithm based on CoSaMP [8]. The procedure of the
algorithm is as follows:
00.5 11. 5
x 10
-8
-5
0
5
x 10
-3
Time[s ]
Am plitude[V ]
PAM-DS-UW B
Transmitter Sparse Signal
Reconstruction Decision Output
Detector
Random
Samplin g
Figure 3. IR-UWB signal detection principle block diagram.
Let
MN
ΦR
ometr denote the measurement matrix with
restricted isy constant 2sc
(c is a constant),
u denote the noisy sample . Furthermore, the
arsity level (the number of the nonzero values) is s, and
the -s pa rse
vector
sp
s
approximation of the target signal is a.
a)ze the approximation 00a and resid Initiali ual
vu. Initialize the iteration cou nter.
Find a proxy *
yΦv for the c
1k
b) urrent residual and
locate the 2
s
largens of the prox y
()
st colum
2
s
supp
y
2
()
s
supp
y
means the index set of the 2
s
where larg-
est columns of
y
.
c) Merge the index set of the newly identified compo-
nents with that of the largest components of the current
approximation
1
(a )
k
Tsupp
d) Solve a least squares problem to make an estimation
of
0
the signal
|; |
c
TT T
bΦub
†1
()
TTTT

ΦΦΦΦ.where For an arbitrary N1
bR,
assume {1,2,,N}, we define
that T is a subset of
,
|0,otherwise
i
TbiT
b.
e) Reserve the
s
largest components in the approxima-
tio h
f) Update the residual
n obtained by te step d) to produ ce a new approxima-
tion
ks
ab
k
a
uΦ v
, if 2
v,
Figure 2. PAM-DS-UWB signal.
g) 1kk
where
sis a known con-
stant, the b); or en go to steplse , go totep h).
h) If a
, where
is a threshold value, then
detect 1
H
; otherwise, choose 0
H
.
5. Simulation Results
In this section, the performance of the proposed detection
algorithm and the MP based detection algorithm are
compared. First, we set the parameters of the PAM-DS-
Copyright © 2013 SciRes. CN
X. ZHU ET AL. 101
UWB transmitter as follows: 030 (dBm)P , 02n
,
509 (Hz)
c
fe, 10 (s)
p
N,
39(s)
s
Te ,5
s
N
,
), lef
Btected is
01500
scs
NnN fT  [12
0.59(s
m
Te
the PAM-DS-U
20.25e
signal to be 9. Hence the
de ngth o
W].
We set the sparsity level of the signal. The
the measurement matrix
as s250
signal is shown in Figure 4.
In simulation, we let
MN
R be an independent and identically distributed
andom matrix with zero-mean and unit vari-
ance. Further, the mean and variance of the additive
white Gaussian noise are 0 and 1, respectively. For the
proposed detection algorithm, we let constant 5
10
A
Gaussian r
.
For the MP based detection algorithm [5], we
number of iterations as 10. Suppose that the prior prob-
abilities of the two hypotheses are equal, that is,
r0 r1
P()P()0.5HH. The probability of detection is
000 trials. In order to demonstrate
the effectiveness of the proposed algorithm, we have
implemented the following three simulations.
Figure 5 illustrates d
P as a function of M
set the
the statistic result of 10
which is
the number of measurents. We set the S as -2dB,
and 0.01
f
P. M ranges [150, 750].The threshold
value
me NR
and theeshold value of MP based detection
algorithm are both chosen by Monte Carlo simulations
[5]. The number of Monte Carlo simulations is 2000. If
we use the traditional detection algorithm, the number of
measurements should be 01500
scs
NnN fT 
according to the Shannon-Nyq
we can see from this figure, the proposed algorithm can
acquire a very high probability of detection at about 20%
of the sampling rate required by the Shannon-Nyquist
theorem. What’s more, in this condition, the proposed
algorithm is superior to the MP based detection algo-
rithm.
Figu
thr
uist samporem. Asling the
re 6 shows as a function of the SNR which
ra d
P
e cnges [-10, 5]. Wonsider M 300 and M 500
respectively. Let 0.01
f
P. The threld valu
two algorithms unent SNRs are also acquired
by the same means as in Figure 5. According to Figure
6, we can see that the perf ormance of the proposed algo-
rithm is better than that of the MP based detection algo-
rithm when the SNR is less than -1 dB.
shoes of the
der differ
00.5 11.5 22.5 3
x 10
-8
-5
0
5
x 10
-3
Time[s]
Amplit ude[V]
200 300 400500 600 700
0. 5
0. 55
0. 6
0. 65
0. 7
0. 75
0. 8
0. 85
0. 9
0. 95
1
Number of measurements (M)
P robabilit y of det ec t ion
MP-based
proposed a l gori thm
Figure 5. Probability of detection comparison of the
proposed algorithm and the MP based detection algorithm
under different number of measurements, SNR=-2 dB and
Pf = 0.01.
-10 -50 5
0
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
0. 8
0. 9
1
SNR(dB)
Probability of detec tion
MP-base d, M =300
MP-base d, M =500
propos ed al gorithm, M = 300
propos ed al gorithm, M = 500
Figure 6. Probability of detection comparison of the
Figure 7 illustrates as a function of
proposed algorithm and the MP based detection algorithm
under different SNRs, M = 300 or M = 500, Pf = 0.01.
d
P
f
P which
ranges [0, 0.2]. Let M150
and SNR= -2B. The
threshold values of thlgorithms under different
probabilities of false alarm are chosen by using the
method in Figure 5 and Figure 6. As we can see from
Figure 7, the proposed algorithm is superior to the MP
based detection algorithm in this situation.
According to Figure 5, Figure 6 and Fig
d
e two a
ure 7, we can
speculate that the performance of the proposed IR-UWB
signal detection algorithm is better than that of the MP
based detection algorithm in case of the low SNR.
Meanwhile, the proposed algorithm needs a much lower
sampling rate than the Nyquist rate.
Figure 4. The PAM-DS-UWB signal of interest.
Copyright © 2013 SciRes. CN
X. ZHU ET AL.
Copyright © 2013 SciRes. CN
102
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00.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180.2
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0. 8
0. 9
1
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Figure 7. Probability of detection comparison of the
6. Conclusions
esent a CS based IR-UWB signal
7. Acknowledgements
art by the National Science
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