281 
PERFORMANCE OF SYNTHETIC NEURAL 
NETWORK CLASSIFICATION OF NOISY 
RADAR SIGNALS 
S. C. Ahalt 
F. D. Garber I. Jouny 
Department of Electrical Engineering 
The Ohio State University, Columbus, Ohio 
A. K. Krishnamurthy 
43210 
ABSTRACT 
This study evaluates the performance of the multilayer-perceptron 
and the frequency-sensitive competitive learning network in iden- 
tifying five commercial aircraft from radar backscatter measure- 
ments. The performance of the neural network classifiers is com- 
pared with that of the nearest-neighbor and maximum-likelihood 
classifiers. Our results indicate that for this problem, the neural 
network classifiers are relatively insensitive to changes in the net- 
work topology, and to the noise level in the training data. While, 
for this problem, the traditional algorithms outperform these sim- 
ple neural classifiers, we feel that neural networks show the poten- 
tial for improved performance. 
INTRODUCTION 
The design of systems that identify objects based on measurements of their radar 
backscatter signals has traditionally been predicated upon decision-theoretic meth- 
ods of pattern recognition [1]. While it is true that these methods are characterized 
by a well-defined sense of optimality, they depend on the availability of accurate 
models for the statistical properties of the radar measurements. 
Synthetic neural networks are an attractive alternative to this problem, since they 
can learn to perform the classification from labeled training data, and do not require 
knowledge of statistical models [2]. The primary objectives of this investigation are; 
to establish the feasibility of using synthetic neural networks for the identification 
of radar objects, and to characterize the trade-offs between neural network and 
decision-theoretic methodologies for the design of radar object identification sys- 
tems. 
The present study is focused on the performance evaluation of systems operating on 
the received radar backscatter signals of five commercial aircraft; the Boeing 707, 
727, 747, the DC-10, and the Concord. In particular, we present results for the 
multi-layer perceptron and the frequency-sensitive competitive learning (FSCL) 
synthetic network models [2,3] and compare these with results for the nearest- 
neighbor and maximum-likelihood classification algorithms. 
In this paper, the performance of the classification algorithms is evaluated by means 
282 Ahalt, GarbeL Jouny and Krishnamurthy 
of computer simulation studies; the results are compared for a number of conditions 
concerning the radar environment and receiver models. The sensitivity of the neural 
network classifiers, with respect to the number of layers and the number of hidden 
units, is investigated. In each case, the results obtained using the synthetic neural 
network classifiers are compared with those obtained using an (optimal) maximum- 
likelihood classifier and a (minimum-distance) nearest-neighbor classifier. 
PROBLEM DESCRIPTION 
The radar system is modeled as a stepped-frequency system measuring radar backscat- 
ter at 8, 11, 17, and 28 MHz. The 8-28 MHz band of frequencies was chosen to 
correspond to the "resonant region" of the aircraft, i.e., frequencies with wavelengths 
approximately equal to the length of the object. The four specific frequencies em- 
ployed for this study were pre-selected from the database maintained at The Ohio 
State University ElectroScience Laboratory compact radar range as the optimal 
features among the available measurements in this band [4]. 
Performance results are presented below for systems modeled as having in-phase and 
quadrature measurement capability (coherent systems) and for systems modeled as 
having only signal magnitude measurement capability (noncoherent systems). For 
coherent systems, the observation vector X -- [(Xl , xlQ), (x, x?), (xa, x?), (x4 , x4Q)] T 
represents the in-phase and quadrature components of the noisy backscatter mea- 
surements of an unknown target. The elements of X correspond to the complex 
scattering coefficient whose magnitude is the square root of the measured cross 
section (in units of square meters, m2), and whose complex phase is that of the 
measured signal at that frequency. For noncoherent systems, the observation vec- 
tor X -- [al, a2, a3, a4] T consists of components which are the magnitudes of the 
noisy backscatter measurements corresponding to the square root of the measured 
cross section. 
For the simulation experiments, it is assumed that the received signal is the result 
of a superposition of the backscatter signal vector $ and noise vector W which is 
modeled as samples from an additive white Gaussian process. 
COHERENT MEASUREMENTS 
In the case of a coherent radar system, the k th frequency component of the obser- 
vation vector is given by: 
where s and s Q are the in-phase and quadrature components of the backscatter 
signal, and W and W Q are the in-phase and quadrature components of the sample 
of the additive white Gaussian noise process at that frequency. Each of these com- 
ponents is modeled as a zero-mean Gaussian random variable with variance (r2/2 
Performance of Synthetic Neural Network Classification 283 
so that the total additive noise contribution at each frequency is complex-valued 
Gaussian with zero mean and variance r 2. 
During operation, the neural network classifier is presented with the observation 
vector, of dimension eight, consisting of the in-phase and quadrature components 
of each of the four frequency measurements; 
Typically, the neural net is trained using 200 samples of the observation vector X 
for each of the five commercial aircraft discussed above. The desired output vectors 
are of the form 
d i = [di,1,... ,di,5] 
(3) 
where di,j = 1 for the desired aircraft and is 0 otherwise. Thus, for example, the 
output vector di for the second aircraft is 0, 1, 0, 0,0, with a i appearing in the 
second position. 
The structure of the neural nets used can be represented by [8, n,..., nh, 5], where 
there are 8 input neurons, ni hidden layer neurons in the h hidden layers, and 5 
output neurons. 
The first experiment tested the perceptron nets of varying architectures, as shown 
in Figures 1, and 2. As can be seen, there was little change in performance between 
the various nets. 
The effects of the signal-to-noise ratio of the data observed during the training 
phase on the performance of the perceptron was also investigated. The results are 
presented in Figure 3. The network showed little change in performance until a 
training data SNl of 20 dB was reached. 
We repeated this basic experiment using a winner-take-all network, the FSCL net 
[3]. Figure 4 shows that the performance of this network is also effected minimally 
by changes in network architecture. 
When the FSCL net is trained with noisy data, as shown in Fig. 5, the perfor- 
mance decreases as the SNR of the training data increases, however, the overall 
performance is still very close to the performance of the multi-layer perceptron. 
Our final coherent-data experiment compared the performance of the multi-layer 
perceptron, the FSCL net, a max-likelihood classifier and the nearest neighbor 
classifier. The results are shown in Figure 6. For this experiment, the training data 
had no superimposed noise. These results show that the max-likelihood classifier 
is superior, but requires full knowledge of the noise distribution. On average, the 
FSCL net performs better than the perceptron, but the nearest neighbor classifier 
performs better than either of the neural network models. 
284 Ahalt, Garber, Jouny and Krishnamurthy 
lOO 
80 
7o 
6o 
5o 
4o 
3o 
2o 
lO 
o 
8x5x5 
--. ..... 8x10x5 
8x20x5 
-- 8x30x5 
.......... 8x40x5 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR [db] 
Figure 1' Performance of the perceptron with different number of hidden units. 
100 
40 
30 
2O 
10 
0 
8x10x5, 200 
-- _ ..... 8x10x10x5, 1800 
8x10x10x10x5,1800 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR rdb] 
Figure 2: Performance of the perceptron with 1, 2 and 3 hidden layers. 
Performance of Synthetic Neural Network Classification 285 
lOO 
9o 
8o 
7o 
60 
5o 
40 
3o 
2o 
lO 
o 
I I I I 
Noise Free 
-- . ..... -5 db 
0 db 
- 6 db 
.......... 12db 
...... 20db 
: \ 
..................... '2-..--..."-._. J .,,, ,,,, 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR rdbl 
Figure 3: Performance of the perceptron for different SNR of the training data. 
100 
40 
30 
2O 
10 
0 
I I I 
8x 10x5 
--_ ..... 8x20x5 
8x30x 5 
--._ 8x40x5 
.......... 8x50x5 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR rdbl 
Figure 4: Performance of FSCL with varying no. of hidden units. 
286 Ahalt, Garber, Jouny and Krishnamurthy 
4O 
3O 
2O 
10 
0 
Noise Free 
-- _ ..... -5 db 
0 db 
-- 6db 
.......... 12db 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR [db] 
Figure 5: Performance of the FSCL network for different SNR of the training data. 
lOO 
9o 
80 
7o 
60 
50 
40 
30 
2o 
lO 
o 
I I I I 
FSCL 8x10x5 
 . ..... perceptron 8x10x5 
max. likelihood 
--  ..... nearest neighbor 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR [db] 
Figure 6' Comparison of all four classifiers for the coherent data case. 
Performance of Synthetic Neural Network Classification 287 
NONCOHERENT MEASUREMENTS 
For the case of a noncoherent radar system model, the k th frequency component of 
the observation vector is given by: 
(4) 
where, as before, s and s? are the in-phase and quadrature components of the 
backscatter signal, and W[ and W Q are the in-phase and quadrature components 
of the additive white Gaussian noise. Hence, while the underlying noise process 
is additive Gaussian, the resultant distribution of the observation components is 
Rician for the noncoherent system model. 
For the case of noncoherent measurements, the neural network classifier is presented 
with a four-dimensional observation vector whose components are the magnitudes 
of the noisy measurements at each of the four frequencies; 
X -- [al,a2,a3,a4] T 
(5) 
As in the coherent case, the neural net is typically trained with 200 samples for 
each of the five aircraft using exemplars of the form discussed above. 
The structure of the neural nets in this experiment was [4, n,..., nh,5] and the 
same training and testing procedure as in the coherent case was followed. Figure 7 
shows a comparison of the performance of the neural net classifiers with both the 
maximum likelihood and nearest neighbor classifiers. 
As before, the max-likelihood out-performs the other classifiers, with the nearest- 
neighbor classifier is second in performance, and the neural network classifiers per- 
form roughly the same. 
CONCLUSIONS 
These experiments lead us to conclude that neural networks are good candidates 
for radar classification applications. Both of the neural network learning methods 
we tested have a similar performance and they are both relatively insensitive to 
changes in network architecture, network topology, and to the noise level of the 
training data. 
Because the methods used to implement the neural networks classifiers were rela- 
tively simple, we feel that the level of performance of the neural classifiers is quite 
impressive. Our ongoing research is concentrating on improving neural classifier per- 
formance by introducing more sophisticated learning algorithms such as the LVQ 
algorithm proposed by Kohonen [5]. We are also investigating methods of improving 
the performance of the perceptron, for example, by increasing training time. 
288 Ahalt, Garber, Jouny and Krishnamurthy 
lOO 
8o 
7o 
6o 
o 
40 
o 
2o 
lO 
o 
I I I I I 
FSCL 4x20x5 
 . ..... perceptton 4X20x5 
....... max-likelihood 
-30 -25 -20 -15 -10 -5 0 5 10 15 20 
SNR 
Figure 7: Comparison of all four classifiers for the noncoherent data case. 
References 
[1] B. Bhanu, "Automatic target recognition: State of the art survey," IEEE Trans- 
actions on Aerospace and Electronic Systems, vol. AES-22, no. 4, pp. 364-379, 
July 1986. 
[2] R. R. Lippmann, "An Introduction to Computing with Neural Nets," IEEE 
ASSP Magazine, vol. 4, no. 2, pp. 4-22, April 1987. 
[3] S.C. Ahalt, A. K. Krishnamurthy, P. Chen, and D. E. Melton, "A new compet- 
itive learning algorithm for vector quantization using neural networks," Neural 
Networks, 1989. (submitted). 
[4] F. D. Garber, N. F. Chamberlain, and O. Snorrason, "Time-domain and 
frequency-domain feature selection for reliable radar target identification," in 
Proceedings of the IEEE 1988 National iadar Conference, pp. 79-84, Ann Ar- 
bor, MI, April 20-21, 1988. 
[5] T. Kohonen, Self-Organization and Associative Memory, nd Ed. Berlin: 
Springer-Veralg, 1988. 
