An inverter/cycloconverter system for variable frequency, variable voltage, ac power supplies. In Proceedings of IEEE IAS International Semiconductor.
Bhat, A. K. S. (1991) A unified approach for the steady-state analysis of resonant converters. IEEE Transactions on Industrial Electronics, 38, 4 (Aug. 1991), 251-259. Jain, P. (1989) A 20 kHz hybrid resonant power source for the space station. IEEE Transactions on Aerospace and Electronic Systems, 25, 4 (July 1989), 4914%. Jain, P., Bannard, D., and Cardella, M. (1992) A phase-shift modulated double tuned resonant DC/DC converter: Analysis and experimental results. In Proceedings of IEEE Applied Power Electronics Conference, (1992), 90-97. Rosenberg, S. A., and Dewan, S. B. (1977) An inverter/cycloconverter system for variable frequency, variable voltage, ac power supplies. In Proceedings of IEEE IAS International Semiconductor Power Conference, (1977), 247-255. Baterseh, I., and Lee, C. Q. (1991) Steady-state analysis of the parallel resonant converter with LLCC-type commutation network. IEEE Transactions on Power Electronics, 6, 3 (July 1991), 525-538. Bhat, A. K. S., and Dewan, S. B. (1989) A generalized approach for the steady-state analysis of resonant inverters. IEEE Transactions on Industry Applications, 25, 2 (Mar./Apr. 1989), 326-338. Bhat, A. K. S. (1990) Analysis and design of a modified series resonant converter. In IEEE Applied Power Electronics Conference Record, (WO), 594-600. Bhat, A. K. S. (1991) Analysis and design of a parallel resonant converter with the resonating capacitor placed on a tertiary winding. In IEEE Industry Application Society Conference Record, (Oct. 1991), 99&995. Biswas, A. (1993) Analysis and design of (LC)(LC)-type series-parallel resonant converter. M.E. project report, Department of Electrical Engineering, Indian Institute of Science, Bangalore, Feb. 1993. Bhat, A . K. S. (1991) Analysis and design of a series-parallel resonant converter with capacitive output filter. IEEE Transactions on Industry Applications, 27, 3 (May/June 1991), 523430. Severns, R. (1990) Topologies for three element resonant converters. In IEEE Applied Power Electronics Conference Record, (Mar. 1990), 712-722. Schmidtner, E. G. (1988) A new high frequency resonant converter topology. In High Frequency Power Conversion Conference Record, (1988), 390-403. Bhat, A. K. S. (1990) Analysis and design of LCL-type series resonant converter. In Proceedings of IEEE International Telecommunications Energy Conference (INTELEC), (1990), 172-178.
Improving Performance in Pulse Radar Detection Using Neural Networks
A new approach using a multilayered feed forward neural
network for pulse compression is presented. The 13 elemenl Barker code was used as the signal code. In training this network, the extended Kalman filtering (EKF)-based learning algorilhm which has faster convergence speed than the conventional backpropagation (BP) algorithm was used. This approach has yielded output peak signal lo sidelobe ralios which are much superior to those obtained with the BP algorithm Further, for use of this neural network for real time processing, parallel implementation of lhe EKF-based learning algorilhm is indispensable. Therefore, parallel implementation of the EKF-based learning algorithm on a network of lhree transputers also has been developed.
I.
INTRODUCTION
Pulse compression technique [l] is always used to improve the performance in pulse radar detection. In practice, two different approaches are used to obtain the pulse compression. The first one is to use a matched filter, in which codes with small sidelobes in their autocorrelation functions are used. The second approach is to use inverse filters of two kinds, viz., nonrecursive time invariant causal filter [2] and recursive time variant filter [3]. A new approach using a multilayered neural network that yields much better signal-to-sidelobe ratio (the ratio of peak signal to maximum sidelobe) than the traditional approaches has been reported in [4]. This approach also has an advantage of robustness that is typical of multilayered neural networks. In this approach, the 13 element Barker code [l] which has the sequence [l, 1,1,1,1,-1,-1,1,1, -1,1, -1,1] and the maximum length sequences (m-sequences) of lengths 15, 31, and 63 (all of them are single period) [l] were used as the signal codes, and four networks were implemented, respectively. Each of the networks used had n input nodes (where n is the code length), three hidden nodes, and a single output node. The BP algorithm, which is the most popular learning algorithm for training neural networks, was used for training the network. The training set for each network comprised of just the time-shifted sequences with magnitudes k1 of the code adopted. The desired Manuscript received October 20, 1993; revised July 27, 1994. IEEE Log No. T-AES/31/3/12744.
0018-9251/95/$4.00 @ 1995 IEEE
CORRESPONDENCE
1193
(or target) output was 1when the whole code was the input, and it was zero otherwise. However, convergence speed of the BP algorithm is inherently slow. A better algorithm for training multilayered neural networks, based on the extended Kalman filter (EKF), was presented in [5],which was shown to be much faster than the BP algorithm. In this work, the new EKF-based algorithm is extended for training the neural network used for pulse radar detection and the 13 element Barker code was used as input to the neural network. It is found that this new algorithm has a much better signal-to-sidelobe ratio than the BP algorithm. Further, for use of this network for real time processing, parallel implementation of the EKF-based learning algorithm is indispensable. Therefore, parallel implementation of the EKF-based learning algorithm on a network of three transputers has been developed and the results of single and three transputer implementations are reported.
II. EKF-BASED LEARNING ALGORITHM
In the multilayered neural network, each node which is connected by the links with all nodes in the adjacent layer computes a weighted sum of inputs, and then adds an offset to the sum. The computed result is output through a nonlinear function. The ith node in the nth layer is denoted by node(n,i). The structure of the network considered here is illustrated in Fig. 1. In this network,the node in the input layer is assumed to do no operation, that is,
TABLE I
The derivative of f ( x ) is given by
f ' W = (1 - ( f 2 W / 2 )
where N, is the total number of nodes in the nth layer, x ( t ) is the input, x;(n) is the output of the node(n,i), a i j is the linkweight from the node(n,j) to the node(n l,i), and 0; is the offset of the node(n,i). Since the EKF is a method of estimating the state vector, the unknown linkweights can be put as the state vector a = [(a')T,(a2)T]T, ( L x 1) (8)
+
where anr = [an i,1~'~2"'u~N,,]T
(1)
Further,the offset is treated as the linkweight by setting X;;"(t)
aZN,
15 n < 3
=1
or+',
=
(Nn
l)
1)Tx , 1) an = [ < ~ ~ > T , ( ~ ~ ) T ~ ' . ( a ~(Nn(Nn+l"+,-l)T~ for an =
15 i 5 N I - I.
x!(t) = xi(t)
(7)
n =1
n =2
for
where L indicates the total number of linkweights as defined by 2
(2)
15 i 5 N n + 1 - 1,
L = C N n ( N n + l- 1)+ N2.
(9)
n=l
Let the output vector of the nodes in the nth layer be
(3) when
n=l,
i = 1 when
The operation of the node(n characterized by
n=2.
xn(t) = t x ; ( t > , x 2 n ( t ) , . . . ~ ~ " ( t )(Nn l ~ , x 1) (10)
+ 1,i) is then
and the desired output be d ( t ) . The multilayered neural network is then expressed by the following nonlinear system equations: a(t + 1) = a ( t ) d(t) = x?(t)
x;+'(t) = f
CUijX?(t)
1: (
)
.
The function f(.) is chosen by the following sigmoid function: 1 - e-"
f(x)
1194
=
1+e-W'
(6)
(11)
+V(t)
(12)
where x ? ( t ) is the output of the node in the output layer. The observation is represented by the desired output d ( t ) , and ~ ( tis) assumed to be a white noise with covariance R(t). Applying the extended Kalman filtering to (11) and (12) and following the procedure adopted in [5] leads to the following EKF-based learning algorithm as shown in Table I.
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 31, NO. 3 JULY 1995
x,(t)
L8y8r
'
-QA
Fig. 1. Structure of multilayered neural network.
Ill. TRANSPUTER IMPLEMENTATION OF EKF-BASED LEARNING ALGORITHM
The EKF-based learning algorithm, used in training the multilayered network, was implemented on a network of three transputers in a configuration as shown in Fig. 3. For the computation of the outputs of the nodes in the feedforward process and for updating the connection weights, the following distribution of nodes among the three transputers was used.
T1: Nodes 1 through
N21 in the hidden layer. Root: Nodes N21 + 1 through N21 + N22 in the hidden layer and the output node. T2: Nodes N21+ Nz + 1 through N21+ NE NU (= N2 - 1) in the hidden layer.
+
In each iteration,using the currently updated weights, the outputs of the neural network are computed and the distribution is as follows.
Second layer: 2;(t) 15 i 5 N21 are computed on T1 2?(t) (N21 + 1) 5 i 5 (N21 + Nz)are computed on
Root (TO)
+ N22 + 1)5 i 5 N2 - 1 are computed N21 + NE + NU = N2 - 1.
i ? ( t ) (N21
on T2 where
Third layer (output layer): i ? ( t ) is
computed on Root(T0)
The weights to the third layer were updated by the Root(T0). For updating the weights to the second layer, i.e., ii;(t) 15 i 5 Nn+l- 1 for n = 1, the latest estimates of the neural network outputs, i.e., i);(t) 1 5 CORRESPONDENCE
i 5 Nn+l - 1 for n = 1 are required. j l ( t ) for a node is computed using the updated weight of the previous node,and thus, updating of the weights to the second layer can be done sequentially. Therefore, $: ( t ) , a!(t),P!(t), 8f(t), and p ! ( t ) for i = 1 to N2 - 1 are computed in parallel by the three transputers. Using these,the weights to the second layer are updated for all the nodes sequentially-as follows. a f ( t ) for i = 1 to N21 are updated on T1 a;'(t) for i = (N21 1) to (N21 NE)are updated
on Root(T0) a:(t) for i = (N21 on T2.
+ + + NE + 1) to N2 - 1 are updated
In the next iteration, these updated weights are used in computing the neural network output, i.e., ,?:(t) and for updating the weights.
IV.
PERFORMANCE OF THE APPROACH
The performance of the approach was studied using the neural network shown in Fig. 1 with N I = 14 and N2 = 4. The input patterns to the neural network used for training it were the time-shifted sequences of the Barker code assuming there are strings of zeroes on either side of the 13 element code. This makes 26 input patterns, including a null sequence. The desired output when the correct Barker code was the input was 1, and -1 when the input was any other time shifted sequence. But using only these 26 input patterns made convergence very difficult, as there was only one input pattern among these 26 input patterns whose desired output was 1; the rest being -1. To overcome this problem, the correct Barker sequence was given after 1195
YE@#1)
Fig. 2. Configuration for using NN after training.
every other input pattern, thus making the number of occurances of the correct sequence in one epoch 25, and the total number of input patterns per epoch 50. After training is complete, a linear system as shown in Fig. 2 was connected at the output of the
Fig. 3. Transputer configuration.
f i 10
m
30
50
40
m Fig. 4. Error convergence trajectory with BP algorithm.
10
20
30
40
50
I
Egoclr
Fig. 5. Error convergence trajectory with EKF algorithm.
1196
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 31, NO. 3 JULY 1995
m80-
70-
60-
m-
__________________------------______------
40-
_.-_.-
/---
30-
I 0
10
m
30
I 40
U)
Epoch
Fig. 6. Output peak signal-to-sidelobe ratio versus epochs.
w80-
m60-
1
so
-
.i 10
I
0
I SNR- lodB
SNR= SdB
9
/
10
m
30
40
so
I
E#
Fig. 7 . Performance of EKF approach at different noise levels.
neural network, so that the output is close to 1 when the correct sequence was the input and close to zero otherwise. From Figs. 4 and 5, the EKF-based algorithm was found to converge much faster than the BP algorithm, when the Barker code was used as the signal code. The effect of the training epochs on output peak signal-to-sidelobe ratio and the superiority of the EKF approach to BP algorithm is illustrated in Fig. 6, when no input noise was added. Further, the performance of the EKF approach with different input signal-to-noise ratios is shown in Fig. 7. CORRESPONDENCE
The transputer implementations are all written in ANSI “c” language and run using a mother board with 3 T R A M S each containing one T800 transputer. The results of three and single transputer implementations are listed in Table 11, where the efficiency is measured with reference to the fastest implementation obtained on one processor. It may be observed from Table I1 that the speed up rate is not 3 but 1.9. This may be attributed to the nature of the EKF-based learning algorithm. The feedforward process (i.e., computation of the outputs of the nodes) and the computation of qi, 1197
TABLE I1 B-ansputer Implementations of EKFBased Learning Algorithm 1 tmnsputa JhMpIlter
@w
dlicimcy
Qi,
An Improved LMS Adaptive Algorithm for Narrowband Interference Suppression in Direct Sequence Spread Spectrum
568.195 298.021 1.9085736 63.61911%
pi, Ai,and pi are performed in parallel on the
three transputers. Since the computation of weight updates requires the weight updates of the previous nodes, the weight updates are computed sequentially as mentioned in Section 111.
In 1990 Viayan and Poor proposed nonlinear predictive methods for suppressing narrowband interference in spread spectrum (SS) system with a significant increase in signal-to-noise ratio (SNR) improvement The main drawback of their adaptive nonlinear filter is its slow convergence rate. A new adaptive least mean squares (LMS) algorithm to increase the slow convergence rate of their nonlinear adaptive filter is
V.
described. Computer simulation results are presented to support
CONCLUSIONS
the advantages of the new filter.
A new approach using neural networks for pulse compression has been presented. The EKF-based learning algorithm which has much faster convergence speed than the conventional BP algorithm has been extended for training the neural network. This approach has a much superior output signal-to-sidelobe ratio than those of the approaches existing in the literature. Further, parallel implementation of the EKF-based learning algorithm has been carried out on a network of 3 transputers which may make the neural network useful for real time processing. K. DEERGHA RA0 R & T Unit for Navigational Electronics Osmania University Hyderabad-500 007 India G. SRIDHAR Dept. of Electrical Engineering Indian Institute of Technology Bombay400 076 India
REFERENCES Nathanson, E E. (1969) Radar Design Principles. New York McGraw-Hill, 1969, 4521469. Ackroyd, M. H., and Ghani, E (1973) Optimum mismatched filters for sidelobe suppression. IEEE Transactions on Aerospace and Electronic Systems, AES-9, 2 (Mar. 1973), 214-218. Mese, E. D., and Giuili, D. (1977) Optimal recursive phase-coded waveform radars. IEEE Transactions on Aerospace and Electronic Systems, AES-13, 2 (Mar. 1977), 163-171. Kwan, H. K., and Lee, C. K. (1993) A neural network approach to pulse radar detection. IEEE Transactions on Aermpace and Electronic Systems, 29, 1 (Jan. 1993), 9-21. Iiguni, Y., Sakai, H., and 'Ibkumaru, H. (1992) A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter. IEEE Transactions on Signal Processing, 40, 4 (Apr. 1992), 959-966. 1198
I.
INTRODUCTION
The burgeoning field of personal communication has led to the ever greater demand on an already crowded spectrum. The use of spread spectrum (SS) signaling for these services has been proposed to share the frequency allocations with existing users. SS has inherent noise suppression capability (it is the characteristic of SS that suggests the new application). This work discusses a new adaptive algorithm which converges much faster, and further attenuates the interference and slightly improves the signal-to-noise ratio (SNR) at the input of the correlation receiver. Narrowband interference suppression in SS systems utilizes the spectral property viz. the SS is wideband (hence unpredictable), whereas the interference is confined to a narrow bandwidth and is peaky (i.e., can be predicted accurately). Hence, any estimate of a signal which comprises both the above mentioned signals, will be the estimate of the interference. This estimated interference can be subtracted from a delayed version of the received signal, and thereby suppress the interference. In the past, several linear prediction techniques were used for interference suppression in SS [1-4]. When the statistics of the interference are not known, several adaptive techniques exist. Among these, the least mean squares (LMS) is used most frequently due to its ease of analysis and implementation. The nonlinear adaptive filter proposed by Vijayan and Poor [5] performs better than the linear LMS prediction filter. A modification of the nonlinear filter is proposed here and extensive computer simulations are carried Manuscript received December 30, 1992; revised December 18, 1994. IEEE Log NO. T-AES/31/3/12743.
0018-9251/95/$4.00 @ 1995 IEEE
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 31, NO. 3 JULY 1995
