2005 RISP International Workshop on Nonlinear
Circuit and Signal Processing (NCSP'05)
Hawaii, USA, Mar. 4-6, 2005.

Research on Clutter Reduction Methods of a UWB Chaotic Radar
Natsumi Dake† , Yoko Uwate† , Yoshifumi Nishio† and Takaya Yamazato‡† Dept. of Electrical and Electronic Eng., Tokushima University, Japan
Email: {dakera55, uwate, nishio}@ee.tokushima-u.ac.jp‡ Center for Information Media Studies, Nagoya University, Japan
Email: yamazato@nuee.nagoya-u.ac.jp

1. Introduction
Chaos is nonperiodic and could generate sequences withinfinite length theoretically. Although the sequences appear
like noise, the values can be predicted exactly if the dynamics
and the initial value are provided. If the feature of chaos is exploited well, some engineering systems with a new excellent
performance could be invented.
On the other hand, a random noise radar using theUWB (Ultra Wide Band) technology has been proposed [1].
The motivation to use UWB stems from the need to have highrange and velocity resolution, unambiguous range and velocity estimates, low probability of intercept, and immunityfrom interference. The random noise radar system transmits
1-2GHz UWB Gaussian random noise wave and the target isdetected by a heterodyne correlation receiver. We have proposed a UWB chaotic radar [2] based on the random noiseradar. The transmitted signal is replaced by a chaotic sequence generated by a simple chaotic map.
In this study, we focus mainly on removal of clutters byapplying three clutter reduction methods. We apply the minimum distance approximation method, the maximum likelihood decoding method [3] and the affordable neural network
method [4]. When we carried out computer simulations aschanging the signal-to-noise ratio (S/N ), probability distributions of recovered signals are shown.

top coordinate of the skew tent map at (a, 0.5), where a isa parameter having the range in [−0.5, 0.5]. The equation
describing the skew tent map is as

⎧
xta
⎪
⎪
+ 0.5 −⎪⎪
0.5 + a0.5 + a⎪⎪⎨(−0.5 ≤ xt ≤ a)(1)
xt+1 =
⎪axt⎪⎪
0.5 +−⎪⎪⎪
0.5 − a0.5 − a⎩(a < xt ≤ 0.5).
A block diagram of the UWB chaotic radar system isshown in Fig. 2. The detection is accomplished by a heterodyne correlation receiver.
OSC 1
ChaoticSequence
Source

PD1

AMP1

XYDL

AMP2Transmit
Receive

BPF1
OSC 2
160MHzI.FClutterReduction

MXR1

MXR2
AMP3

2. UWB chaotic radar

BPF2Detector

X t+1
0.5
0.4

Figure 2: UWB chaotic radar.

0.3
0.2
0.1
0

At first, we give an initial value x 1 to the skew tent map
with a constant parameter a. The generated chaotic sequence,
which has a spectrum in 1-2GHz frequency range, passes
through PD1 to duplicate signals. One is amplified and transmitted toward targets and the other is delayed and multipliedwith the 160MHz sinusoidal signal generated by OSC2. The
received echo signal Y including many clutters is expressed
as follows;
Y = [y1 , y2 , · · ·, yN +1 ]
(2)

-0.1
-0.2
-0.3
-0.4
-0.5
-0.5

-0.4

-0.3

-0.2

-0.1

0a 0.1

0.2

0.3

0.4

0.5

Xt

Figure 1: Skew tent map.

We use the skew tent map, which is known as the simplest chaos-generating map, to generate a chaotic sequence
by OSC1. The skew tent map is shown in Fig. 1. We set theyt = xt + ωt

(1 ≤ t ≤ N + 1).

(3)

where xt is a generated chaos and ω t is clutter. Clutter is an
unnecessary reflection signals from the surface of the sea, the- 367 -rain, the cloud, and the obstacle such as buildings. In thissimulation, AWGN (Additive White Gaussian Noise) is used
to express all of the clutters.
In this study, we consider to remove clutters by using clutter reduction algorithms explained in the next section. The received echo signals Y are filtered and fed into a clutter reduction algorithm. At last, the output of clutter reduction is thenmultiplied with the delayed and up-converted chaotic signaland passes BPF having a center frequency of 160MHz and abandwidth of 5MHz.

3.2. Maximum likelihood decoding method
Secondly, we consider a method using the maximum likelihood decoding. In this method, the skew tent map is divided
into M states, and the dynamics is approximated by a Markov
chain with transition probabilities corresponding to the mapping of each state.
The trellis diagram for the case of M = 4 is shown inFig. 4.
state

3. Clutter reduction methods

S3

We consider three kinds of clutter reduction methods.

p24
p23
p12

S2

3.1. Minimum distance approximation method

S1

At first, we consider a method using the minimum distance approximation. This method is the simplest noise cleaning method of chaotic signals. By using the two successive signals, the transmitted signal and the received signal(S/N 20dB) can be plotted on the 2-dimensional plane asFig. 3.

.....

p11

1.....

2N+1 Sequence

Figure 4: Trellis diagram (omit paths with probability=0).
where si is the quantized state and p ij means the transition
probability from the state i to the state j.
The maximum likelihood decoding algorithm carries out tofind the best path in the trellis diagram.
1) Initialization : t = 1

0.6
Transmitted signal
Received signal

0.4x(t+1) ,y(t+1)

.....

p42

S40.2

δ1j = |yˆ1 − sj |0(6)2) Forward pass : 2 ≤ t ≤ N + 1

−0.2

−0.4

−0.6
−0.6

−0.4

−0.2

00.2

0.4

δtj = min

0.6

1≤i≤Mx(t), y(t)The transmitter signals should be on the skew tent map described by Eq. (1). However, the received signals are not on
the map because of the clutters. This method is to modify
the received signal into the point on the skew tent map whichis the nearest to the received signal. The x-coordinate of thepoint can be calculated from the values of the received signals
as follows;⎧0.5 + a⎪⎪·⎪⎪a + (0.5 + a)2⎪⎪⎪⎪a⎪⎪yt+1 + yt (0.5 + a) − 0.5 −⎪⎪0.5 + a⎪⎪⎨(yt ≤ a)vt =(4)⎪ (0.5 − a)2 + 1⎪⎪·−⎪⎪⎪
0.5 − a
⎪⎪
⎪a⎪
⎪
y−y(0.5−a)−
0.5+t+1t⎪⎪
0.5 − a⎪⎩(yt > a).
V = [v1 , v2 , · · ·, vN ].

φjt = arg[δtj ](7)3) Termination : t = N + 1

Figure 3: The transmitted signal and the received signal.

The output signal of this algorithm is given by V .

iδt−1|yˆt − sj |,pijwN = argjmin [δN]

1≤j≤M

(8)

4) Backward passwt+1wt = φt+1t = N − 1, N − 2, · · · , 1.

(9)This algorithm computes the hamming distance of each state
and the quantized received signal ŷ t . We calculate δtj andpreserve a minimum value in φ jt by the forward pass. And
the minimum value is chosen by the termination t = N + 1,
the operation is executed by the backward pass. As a result,the best pass W can be chosen.
W = [w1 , w2 , · · ·, wN ].

(10)

3.3. Affordable neural network method

We consider a method using the affordable neural network,
which has been proposed by the authors recently. The affordable neural network is one of feedforward neural network thatapplies the back propagation learning. Some extra neurons in
the hidden layer are prepared in advance. For learning pro(5) cess, all of the neurons in the hidden layer are not used, and- 368 -operating neurons in the hidden layer changes at every updating.
By giving a certain amount of chaotic sequences obtained
from the skew tent map as teacher signals, we train the network to output chaotic sequences generated by only the skew
tent map. After the learning, we input the received signal into
the network. If the learning of the network can be achieved
completely, the clutter in the received signals should be removed. The output of the network is given by Z.

affordable neurons is set to 10. From Figs. 6(a), (b) and (c),we can say that the distributions of all three methods shift tothe right compared with the result of N o Reduction. Thismeans that the wrong warning probability decreases and thedetection probability increases. From Fig. 6(d), for 20dB, thefour distributions are almost same. This is why the received
signals are almost the same as the transmitted signal.
In order to confirm the clutter removal ability of the threemethods, the distances between the transmitted signals andthe recovered signals are calculated. The results are shown(11) in Fig. 7. Figure 7(a) and (b) show the results for small S/Nand for large S/N , respectively. The distance are calculatedby the following equations;

Z = [z1 , z2 , · · ·, zN ].
4. Simulation result

In the following computer simulations, the parameter ofthe skew tent map is fixed as a = 0.01, and the chaotic
sequence length is fixed as N = 50. The target detections
using the three methods are carried out.
(1) The minimum distance approximation method(M ethod 1),(2) The maximum likelihood decoding method (M ethod 2),(3) The affordable neural network method (M ethod 3).
For comparison,(4) Without any clutter reduction methods (N o Reduction)is also carried out.
At first, we carried out computer simulations for the caseof N o Reduction. The probability distribution of power after passing BPF2 is shown in Fig. 5, when 10,000 chaotic
sequences with different initial values are transmitted. Thehorizontal axis is the power and the vertical axis is probability. The left graph shows the result for the case that thereceived signal is only clutters. While the right graph shows
the result for the ideal case of no clutters. From the figure,
we can say that the detection probability of a target is 100%
if the threshold is set between 13 and 18.
0.12

Probability [%]0.1ND1 =2(vt − xt ) ,
t=1
N

D3 =

2(zt − xt ) ,N

D2 =(wt − xt )2 ,t=1
N

DN o =

t=1(12)2(yt − xt ) .
t=1

From Fig. 7(a), for small S/N , the M ethod 2 achieves
the best performance to remove clutters. The performance ofthe M ethod 1 is worse than the M ethod 2. This is because
M ethod 1 uses only two values in each removing process.
However, the M ethod 1 is very simple, computational cost issmall even for long N . The performance of the M ethod 3 isnot very good. However, it is difficult to find a good parameter set of the M ethod 3. We still believe that the well-tuned
M ethod 3 could remove the clutters effectively.
From Fig. 7(b), for large S/N , the M ethod 1 achieves
the best performance to remove clutters. On the other hand,the performance of the M ethod 2 does not become less thanaround 0.05. This is because M ethod 2 includes unavoidable
quantization errors.
Finally, we investigated the detection probability when thethree clutter reduction methods are applied by computer simulations as changing S/N . The threshold of the probability ofP ower is set 20 and 25. From the results, we can say that all
three reduction methods contribute to increase the detection
probability as shown in Fig. 8, especially for smaller S/N .

0.08

5. Conclusions

0.06

In this study, the three clutter reduction methods have been
applied to the chaotic UWB radar. The basic properties of themethods have been investigated by computer simulations.

0.04

0.02

005101520253035References

PowerFigure 5: Probability distribution of P ower.
Next, we carried out computer simulations as changing
S/N from 5dB to 20dB. Figure 6 shows the probability distributions after passing BPF2. For M ethod 2, the quantizationof the skew tent map is M = 64. For M ethod 3, the number of learning pattern is set to 1000. Further, the parameterof the inertia rate is fixed as η = 0.02 and initial values of
the weights are given between -1.0 and 1.0 at random. The
learning time is set to 50,000. We prepare 50 neurons in input layer, 100 neurons in hidden layer, and the number of[1] M. Dawood, Ram R. Narayanan, “Receiver operating characteristics for the coherent UWB random noise radar,” IEEE
Trans. Aerospace Electronic Syst., vol. 37, no. 2, pp. 586-594,
2001.
[2] N. Dake, Y. Nishio, T. Yamazato, “UWB radar system using
chaotic signal,” Proc. IEICE General Conference, no. SA-2-6,
pp. S11-S12, 2004.
[3] A. Kisel, H. Dedieu, T. Schimming, “Maximum Likelihood
Approaches for Noncoherent Communications with ChaoticCarriers,” IEEE Trans. Circuits and Syst., vol. 48, no. 5, pp.
533-542, 2001.
[4] Y. Uwate, N. Dake, Y. Nishio, “Back propagation Learning ofan Affordable Neural Network for Chaotic Time Series,” Proc.
NCSP’05, 2005 (to appear).

- 369 -0.12

6Method1
Method2
Method3
No Reduction

Method1
Method2
Method3
No Reduction

540.08Distance

Probability [%]

0.1

0.06

320.0410.02
050051015202530101520

Power(a)(a) 5dB.

0.12
Method1
Method2
Method3
No Reduction

0.12
Method1
Method2
Method3
No Reduction

0.1

0.08

Distance

Probability [%]

0.1

0.08

0.06

0.04

0.06

0.02

0.04

0250.020025

S/N[dB]

3530354045

S/N[dB](b)
5101520253035PowerFigure 7: Distance between the transmitted signals and therecovered signals.

(b) 10dB.
0.12

10.9

Detection Probability [%]Probability [%]0.1

Method1
Method2
Method3
No Reduction

0.08

0.06

0.04

0.8
0.7
0.6
0.5
0.4
0.3
0.2

0.02

Method1
Method2
Method3
No Reduction

0.1

005

1015202530

0535

101520Power3540

Method1
Method2
Method3
No Reduction

Detection Probability [%]

0.45

0.08

0.06

0.040.40.35
0.3
0.25
0.2
0.15
0.1

Method1
Method2
Method3
No Reduction

0.05

0.02

05101520253035

40

S/N[dB]
0045

0.5

0.12

Probability [%]30(a) Threshold: 20.

(c) 15dB.

0.1

25

S/N[dB]

51015

202530(b) Threshold: 25.

35

PowerFigure 8: Detection Probability.

(d) 20dB.
Figure 6: Probability distribution of P ower.

- 370 -45