A Novel Gamma Distributed Random Variable (RV) Generation Method for Clutter Simulation with Non-Integral Shape Parameters

Abstract

Sea clutter simulation is a well-known research endeavour in radar detector analysis and design, and many approaches to it have been proposed in recent years, among which zero memory non-linear (ZMNL) and spherically invariant random process (SIRP) are the most two widely used methods for compound Gaussian distribution. However, the shape parameter of the compound Gaussian clutter model cannot be a non-integer nor non-semi-integer in the ZMNL method, and the computational complexity of the SIRP method is very high because of the complex non-linear operation. Although some improved methods have been proposed to solve the problem, the fitting degree of these methods is not high because of the introduction of Beta distribution. To overcome these disadvantages, a novel Gamma distributed random variable (RV) generation method for clutter simulation is proposed in this paper. In our method, Gamma RV with non-integral or non-semi-integral shape parameters is generated directly by multiplying an integral-shape-parameter Gamma RV with a Beta RV whose parameters are larger than 0.5, thus avoiding the deviation of simulation of Beta RV. A large number of simulation experimental results show that the proposed method not only can be used in the clutter simulation with a non-integer or non-semi-integer shape parameter value, but also has higher fitting degree than the existing methods.Sensors 2020, 20, 955 2 of 11 of its large computation. A method based on zero memory non-linear (ZMNL) is proposed in [12]. The ZMNL is suitable for non-coherent clutter model, and the principle of it is simple. However, the main drawback of ZMNL is that the shape parameter of the clutter model must be an integer or semi-integer. If the shape parameter does not satisfy the requirement, the ZMNL method will lead to clutter simulation error. What's worse, the ZMNL cannot control the power spectrum and amplitude independently. With the principle that each quadrature component of K-distributed clutter can be modelled, exactly or approximately, by a weighted sum of products of two independent Gaussian variables in [13], a new method for modelling and simulation of correlated K-distributed clutter is proposed in [14]; the new method can simulate the clutter with arbitrary and specified power spectrum, and is a much more simple calculation compared with the traditional ZMNL and SIRP, which makes it easier to realize both in software and hardware. Nevertheless, an approximate approach is made for the simulation when the shape parameter is non-integer or non-semi-integer. Besides, a method of simulation of coherent compound Gaussian clutter based on memorials non-linear transformation (MNLT) is proposed in [15]. Through the generation of arbitrary correlated Gamma random variable (RV) by MNLT, this method can simulate clutter specifically. However, similar to SIRP method, the computational complexity of MNLT is high due to nonlinear computation.To solve this problem, the additive property of Gamma RV is used to improve the ZMNL and SIRP methods in [16,17...