Abstract: Zero memory nonlinearity(ZMNL)and spherically invariant random process(SIRP)are two mainly used methods in compound Gaussian clutter simulations. Aiming at the problem that the shape parameters in the K and Pareto distributed radar clutter simulation based on the traditional ZMNL and SIRP methods can only be integer or semi-integer， by adding branches and using the additivity of the second parameter of Gamma function， it is proposed to transform the probability density function(PDF)of the Gamma function into second-order nonlinear ordinary differential equation. Furthermore， it is solved to generate Gamma distributed random numbers under arbitrary parameters， and the shape parameters of compound Gaussian distribution clutter is extended to general real numbers. The simulation experiments show that the proposed method is not only suitable for clutter simulation with non-integer or non-semi-integer shape parameter values， but also further improves the fitting degree.

Key words: clutter simulation; Gamma distribution; compound Gaussian distributed; zero memory nonlinearity(ZMNL); spherically invariant random process(SIRP)