The Pareto distribution for low grazing angle and high resolution X-band sea clutter

A radar pulse that impinges upon a radar resolution area of the sea surface produces backscattered returns which are called sea clutter. For low grazing angles and very fine radar cell resolution areas, the clutter intensity distribution departs significantly from the exponential distribution. In this case, the clutter is said to display spiky behavior and the distribution of the intensity develops a much longer tail relative to the exponential distribution. Statistical analysis of collected data near a grazing angle of 0.2° at X-band from the sea off the coast of Kauai, Hawaii are examined relative to the log-normal, Weibull and K distributions. Based on an analogy of sea clutter and other disciplines including computer networks and finance, we also apply the Pareto distribution to the collected data. We also compare the data to the WW and KK two-population mixture distributions. Maximum likelihood estimation of the parameters of the distributions are obtained from the measured data. In all cases, the two population mixture distributions and the Pareto distribution are more accurate than the three classical distributions. However the Pareto distribution has the advantage of being an analytically tractable two parameter distribution while having similar accuracy to the five parameter WW and KK at critical values.

I. Introduction

The performance of high resolution radars at low grazing angles has been a topic of research for the last several decades. Extensive surveys of many of the experimental and theoretical developments are given in [1] [2]. Despite the extensive number of studies, the current phenomenological understanding of sea clutter modeling is incomplete. Partially due to this incomplete knowledge, a variety of statistical models have been proposed for the distribution of the sea clutter. An accurate sea clutter model allows for the optimization of the radar detector chain including its CFAR processor. This in turn allows for enhanced target detection and better control of the false alarm rate. In this paper we assess the accuracy of some new and unexamined mixture distributions for the low grazing angle sea clutter data of [4]. Maximum likelihood estimation (MLE) of the parameters of the distributions are obtained and the results are compared to the actual data's distribution. In Section II of this paper we briefly review the measurement parameters, the collected data and sea conditions of the experiment. In Section III, we overview the traditional models as well as the mixture models [5] and Pareto distribution [7]. In Section IV we estimate the parameters of the distributions using the MLE and compare their respective CDFs. Conclusion of this paper is given in Section V.