Range resolution for given radar can be significantly improved by using very short pulses. But utilization of short pulse decreases the average transmitted power. The average transmitted power is directly linked to the receiver SNR, so it is desirable to increase the pulse width while simultaneously maintaining adequate range resolution. This requirement is achieved by pulse compression technique. Pulse compression is a method which combines the high energy of a longer pulse width with the high resolution of a narrower pulse width. Important aspects considered for a pulse compression technique are signal to sidelobe ratio performance, noise and the Doppler shift performance. In pulse compression technique a pulse having long duration and low peak power is modulated either in frequency or phase before transmission and the received signal is passed through a filter to accumulate the energy in short pulse. Pulse compression ratio (PCR) is given as

The block diagram of a pulse radar system is shown in the figure 1.

Figure.1: Block diagram of pulse compression radar

Usually, a matched filter is used for pulse compression to achieve high signal-to-noise ratio (SNR). However, the matched filter output- autocorrelation function (ACF) of modulated signal is associated with range sidelobes along with the mainlobe. These sidelobes are unwanted outputs from the pulse compression filter and may mask a weaker target which is present nearer to a stronger target. Hence, these sidelobes affect the performance of the radar detection system. In phase coded signals a long pulse is divided into a number of sub pulses each of which is assigned with a phase value. The phase value should be such assigned that the ACF of the phase coded signal attain lower sidelobes. Radial basis function (RBF) structures are proposed as mismatch filters to achieve better PSR values under various noisy conditions, under Doppler shift condition and the multiple target environment.

I. RADIAL BASIS FUNCTION NETWORK:

The radial basis function network can be viewed as a feed forward neural network with a single hidden layer which computes the distance between input pattern and the center. It consists of three layers, an input layer, hidden layer and an output layer. The input layer connects network architecture to the environment. The second layer is obviously hidden layer responsible for transfer of the input space nonlinearly using radial basis function. The hidden space is greater than the input space in most of the applications. The response of the network provided by the output layer which is linear in nature. The RBF network is suitable for solving function approximation, system identification and pattern classification because of its simple topological structure and their ability to learn in an explicit manner.

Figure 2 Architecture of Radial Basis Function network

The basic architecture of RBF network is shown in Figure 2. Here x(n) is the input to the network and φ represents the radial basis function that perform the nonlinear mapping and M represents the total number of hidden units. Each node has a center vector c_k and spread parameter σ_k, where k = 1, 2, ....M.

Learning algorithm for RBF network:

The error for the n^thpattern is obtained as

where d(n) is the desired output. If the Gaussian function chosen as the radial basis function

The cost function is defined as

where n₁ is the number of training patterns. It is required to adjust the free parameters such as weight, center and spread so as to minimize ξ. According to the gradient descent algorithm the free parameters for m^thepoch are updated as

where μ_w, μ_c and μ_σ are learning parameters and k =1, 2...M. Finally the updation equations are defined as

where,

II. COMPARISIONS:

The simulation results for various cases indicate that the performance of the proposed RBFN algorithm is much better than techniques such as MLP, RNN learning algorithms and the conventional ACF approach. All the networks are trained with time shifted sequences of the 13-bit and 35-bit Barker codes. The desired output of the pulse compression filter for an input sequence is modeled as a all zero vector except at one point at which the desired response is nonzero corresponding to the presence of the target. The numbers of input neurons are same as the length of the input code i.e.13 for 13-bit Barker code and 35 for 35-bit Barker code. After completion of the training, the neural network can be used for pulse radar detection by using various set of input sequences.

1) Convergence performance:

The mean square error (MSE) of all the networks for 13-bit and 35-bit Barker codes is depicted in Figure 3.

Figure 3 Convergence graph of (a) 13-bit (b) 35-bit Barker codes

2) PSR performance:

Ratio of peak sidelobe power to the mainlobe power. The compressed output of different networks for 13-bit Barker code is shown in Figure 4. The table shows that the proposed RBF network have achieved highest PSR magnitude for both 13-bit and 35-bit Barker codes compared to all other approaches.

3) Noise performance:

The inputs having different SNR ranging from 0 dB to 20 dB are applied to the networks and the output PSR for 13-bit and 35-bit Barker codes.

4) Doppler shift performance:

The influence of Doppler shift should be accounted for evaluating the detection performance for a moving target. The Doppler tolerance measures the Doppler sensitivity of the pulse compression technique. The Doppler sensitivity is caused by the shifting in phase of the individual elements of the code by the target Doppler. In extreme case the phase shift across the code will be 180⁰, the last subpulse in the received code is effectively inverted. For 13-bit Barker code at extreme case the input will change from “1 1 1 1 1 -1 -1 1 1 -1 1 -1 1” to “-1 1 1 1 1 -1 -1 1 1 -1 1 -1 1”. 13-bit and 35-bit Barker code, extreme case, Doppler shift PSR values for different types of network are listed in Table

III. CONCLUSION

In this paper RBF network is proposed for the radar pulse compression technique and RBF network is compared with other neural networks and the mathematical analysis and results show that RBF network yields better performance characteristics, higher Doppler shift tolerance, better convergence speed and the range resolution ability of RBF is far better than MLP,RNN networks.

Figure 4: Compressed waveforms for 13 bit Barker code using (a) MLP (b) RNN (c) RBF

IV. REFERENCE

[1] Merrill I. Skolnik, Introduction to radar systems, McGraw Hill Book Company Inc.,1962.

[2] D.K. Barton, Pulse Compression. Artech House, 1975.

[3] A.W. Rihaczek, Principle of high resolution radar. McGraw Hill, New York,1969.

[4] Ajit Kumar Sahoo, Ganapati Panda and Babita Majhi, A Technique for Pulse RADAR Detection Using RRBF Neural Network, Proceedings of the World Congress on Engineering 2012 Vol II WCE 2012, July 4 - 6, 2012, London, U.K

[5] K. H. Kwan and C. K. Lee, A neural network approach to pulse radar detection IEEE Transactions on Aerospace and Electronic Systems, vol. 29, no. 1, pp. 9{21, January 1993.

[6] Ackroyd, M.H. and Ghani, F. “Optimum Mismatch Filters for Sidelobe Suppression”, IEEE Transactions on Aerospace and Electronic Systems, Vol.9, No.2, March 1973, pp.214-21

[7] A. Zhu, R. Mason, Member, IEEE, and W. Stehwien, Member, IEEE, Maritime Radar Target Detection Using Neural Networks, IEEE Wescanex ’95 Proceedings,1995

[8] “Radial basis function neural network for pulse radar detection,” IET Radar, Sonar and Navigation, vol. 1, no. 1, pp. 8–17, February 2007.

[9] K. D. Rao and G. Sridhar, “Improving performance in pulse radar detection using neural networks,” IEEE Transactions on Aerospace and Electronic Systems, vol. 31, no. 3, pp. 1193–1198, July 1995.

[10] Y. M. Reddy, I. A. Pasha, and S. Vathsal, “Design of radial basis neural network filter for pulse compression and sidelobe suppression in a high resolution radar,” in Proceedings of the International Radar Symposium, Krakow, Poland, May 2006, pp. 1–46

[11] Ajit Kumar Sahoo, “Development of Radar Pulse Compression Techniques Using Computational Intelligence Tools,” Ph.D. dissertation, NIT, Rourkela, Orissa,2012

[12] Babita Mahji On Applications of New Soft and Evolutionary Computing Techniques to Direct and Inverse Modeling Problems, Ph.D. Thesis, NIT, Rourkela, Orissa, India, 2010

Received on 28.02.2013 Accepted on 26.03.2013

Research J. Science and Tech 5(3): July- Sept., 2013 page 331-334