Articles

The Use of Kullback–Leibler Divergence in Processing Pulse Signals Received from a Sea-Based RadarGerman Babin

This paper deals with the problem of processing radar signals in the presence of space-distributed interference including sea cutter. An algorithm was developed to discriminate distinctive signal amplitudes attributable to targets. The method is based on the use of the Kullback–Leibler information distance. The algorithm was validated both with real signal records from a sea-based pulse radar and with data obtained by simulation.

 

I. INTRODUCTION

The main radar engineering problem is detection, recognition and characterization (in terms of position, speed and geometry) of ground, air and sea targets. In practice, the detection problem is complicated by the presence of natural noises, which include echoes from ground and sea surfaces, from various weather formations and atmospheric irregularities, as well as from different ground features within the radar's field of view [1]. When the strength of reflections from natural scatterers is comparable to or exceeds the strength of reflection from a potential target, this target cannot be practically detected without using special signal filtering methods. Moreover, even when target

Radar picture of stormy sea and coast
Fig. 1. Radar picture of stormy sea and coast

detection itself is possible, high noise level considerably increases the computing load on the secondary processing unit of the radar system.

A considerable part of the natural noise is of the stochastic nature, i.e. its frequency responses can be described by the probability laws. A matched whitening filter widely used in radar engineering is an optimal aid to reject noises described by either uniform or Gaussian distribution [2]. However, sea clutter features a different statistical structure, and this kind of noise is among the most difficult to reject. This difficulty is attributed to non-stationary nature of frequency response of the radar echoes from waves and to interference of scattered electromagnetic radiation. Moreover, the sea wave pattern depends on wind direction and velocity, proximity of shoreline, time of day, presence of currents, water chemistry and many other parameters. Figure 1 clearly shows the complexity of the radar picture obtained from radar echoes from the sea surface.

Depending on external conditions, sea clutter can be described by the K-distribution [3-5] or the Weibull distribution [6]. Therefore, other filtering methods and techniques shall be used to reject sea clutter.

In addition to coherent filtering algorithms which require a priori information on spectral correlation characteristics of the clutter, adaptive algorithms [7] are widely used in practice. This paper describes an adaptive algorithm, which compares the true and anticipated distributions of the measured signal amplitudes using the Kullback–Leibler information distance to reject sea clutter.

II. ADAPTIVE SEA CLUTTER REJECTION ALGORITHM

Algorithms used in sea clutter rejection problems can be generally divided into deterministic and adaptive ones. To apply deterministic algorithms effectively, we shall have a priory information on clutter frequency response. As applied to sea-based radars, values of clutter frequency response depend on various external and internal factors. The external factors are wind velocity, angle between wind direction and main antenna lobe, and peculiarities of electromagnetic propagation, scattering and absorption. The internal factors include antenna height above sea, slant range, transmitted pulse duration, carrier frequency, radio frequency emission power, and radar resolution. In view of the above sea-based radar operation peculiarities, the use of deterministic algorithms seems not enough to solve sea clutter rejection problems. Other filtering methods shall be applied to solve this problem duly. One of such methods is adaptive algorithm-based filtering which enables solving the problem when the clutter frequency response is a priori uncertain.

Since measured signal amplitudes are random, mathematical statistics shall be used to process them effectively. Spatial distribution of received signal amplitudes seems the most suitable statistic parameter for adaptive algorithms for filtering at the primary processing stage. Both local and global amplitude distribution shall be considered to develop the algorithm. This shall be done to account for spatial and angular dependence of the received signal on sea wave parameters.

To describe distribution of the measured target signal amplitudes, we use the Rayleigh distribution in this paper. Based on the fact that signal amplitude distribution parameters depend on type of electromagnetic scatterer, we will use the Kullback–Leibler divergence [4-6], which is defined as follows:

Kullback–Leibler divergence



where parametric densities p(x) and q(x) of the selected competing distributions are defined by the following expressions:

Parametric densities p(x) and q(x) of the selected competing distributions are defined by the following expressions



Parametric densities p(x) and q(x) of the selected competing distributions are defined by the following expressions

In expressions (1-3), D is the Kullback–Leibler information measure, x is signal amplitude, and σ is a distribution scale parameter. Having defined the threshold for information measure D in each range quantum, we can perform local rejection of sea clutter with a specified probability.

The proposed algorithm can work correctly only if scale parameter σ of the used distributions is known. To evaluate scale parameters σi and σj of distribution densities p(x) и q(x), we use the modified exponential smoothing method:

To evaluate scale parameters σi and σj of distribution densities p(x) и q(x), we use the modified exponential smoothing method

where l and k are indexes of range channel and azimuth angle, respectively, and Slk(R), Slk(L), Slk(F), Slk(B) are averaged amplitudes of signal in range quanta passing in the selected directions. The walking senses are denoted by symbols R, L, F and B indicating the walk from the first to the last range channel at a fixed azimuth angle, from the last to the first range channel at a fixed azimuth angle, through azimuth angles in the scanning direction at a fixed distance, and through azimuth angles against the scanning direction at a fixed distance, respectively. Parameter xlk describes the array of amplitudes obtained over one radar scan, and coefficients αlkij and γlkij are calculated in each averaging iteration using the following expressions:


where the elements with indexes i and j correspond to the respective competing distributions.

The coefficients defined by (5) are obtained by solving the following system of equations:




and the values of scale parameters σ are linearly expressed through the values of function S at the previous iteration. The signal amplitude's threshold value Slk(G) for each range channel is determined after screening the indexes l and k using the following expression:

 

III. EXPERIMENTAL VALIDATION OF THE ALGORITHM

To validate the algorithm, we simulated radiation scattering from sea surface for radar with antenna directivity pattern 1ᵒ wide and in the presence of two targets at different ranges within the radar coverage. The sea surface was simulated through a discrete spectrum simulation approach using the Pierson–Moskowitz frequency spectrum [3, 4]. Uniform and Gaussian noise was additively admixed to echo signals.

Pulse picture before (upper figure) and after (lower figure) processing at the signal-to-noise ratio equal to 3.
Fig. 2. Pulse picture before (upper figure) and after (lower figure) processing at the signal-to-noise ratio equal to 3.



Pulse picture before (upper figure) and after (lower figure) processing at the signal-to-noise ratio equal to 1.
Fig. 3. Pulse picture before (upper figure) and after (lower figure) processing at the signal-to-noise ratio equal to 1.



Fig. 4. The real radar pulse records before (upper figure) and after (lower figure) processing
Fig. 4. The real radar pulse records before (upper figure) and after (lower figure) processing



Figures 2 and 3 show the space-distributed pulse amplitudes simulation and the result of application of the developed filtering algorithm. Each of the figures consists of two parts; the upper part represents the radar picture before applying the rejection algorithm, and the lower one, after applying the rejection algorithm. The radar picture data were obtained from several radar scans at a fixed azimuth angle. The targets were at the distances equal to 50 and 100 simulation range quanta. Figures 2 and 3 were plotted for cases with different signal-to-noise ratios (SNR=3 in Fig. 2 and SNR=1 in Fig. 3).

Fig. 4 shows a real record of pulses obtained from a sea-based radar with antenna directivity pattern 1ᵒ wide for a fixed azimuth angle, and the result of the developed algorithm applied to them. The detected target was at the distance of 122 range quanta. Comparing the results of application of the developed adaptive algorithm to the simulated data (Figs. 2, 3) and to the real radar records (Fig. 4), we can conclude that the algorithm is able to discriminate the distinctive amplitudes related to targets and to reject the sea clutter effectively.

IV. CONCLUSION

This paper presents an adaptive algorithm for sea clutter rejection under conditions when the clutter frequency response is a priori uncertain. The developed algorithm is based on the use of the Kullback–Leibler information measure. The algorithm includes estimation of the signal amplitude distribution parameters using a modified exponential smoothening method. The algorithm was validated with both simulated and real data. The validation proved the presented algorithm to be able to reject sea clutter effectively even at low signal-to-noise ratios. If used, the proposed algorithm will reduce the computing load on the secondary processing unit of the radar and make the radar picture more meaningful for operator.

ACKNOWLEDGMENT

This work was supported by the AstroSoft Company. We also thank our colleagues, especially PhD. Balabanov Mikhail, who have been involved in this project and who have helped in the experimental trials.

REFERENCES

[1] P.A. Bakulev. Radar systems // Moscow, Radioteknika, 2004 – 320 p.
[2] M.T. Ivanov, A.B. Sergienko, V.N. Ushakov. Radar circuits and signals // Saint-Petersburg: Piter, 2014 – 336 p.
[3] Antipov I. Analysis of sea clutter data // Salisbury: DSTO Electronic and Surveillance Research Laboratory, p. 46, 1998.
[4] Antipov I. Analysis of sea clutter data // Salisbury: DSTO Electronic and Surveillance Research Laboratory, p. 46, 1998.
[5] Antipov I. Simulation of sea clutter returns // Salisbury: DSTO Electronic and Surveillance Research Laboratory, p. 71, 1998.
[6] Ward K., Tough R., Watts S. Sea clutter: scattering the K distribution and radar performance // 2nd edition – Croydon: CPI Group Ltd, p. 586, 2013.
[7] Y.A. Melaschenko, V.G. Valeev. Prediction of coherent pulse radar's sea target detection performance considering non-Gaussian sea clutter // Electronics Magazine, #3, p.17, 2014
[8] A.E. Maniukhin. Algorithm for two-channel noise rejection with lack of intercorrelation between channels // Proceeding of the Moscow Aviation Institute, #50, 2012



German Babin, Igor Sidorov, Ilya Shabayev
Software Development Department, AstroSoft
B.Sampsonievskiy Ave, 3 /11 “D”, 194044, Saint-Petersburg, Russia
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