The actual noise environment is often non-Gaussian in nature. In this case, the conventional detector (CD) based on the Gaussian assumption suffers significant performance degradation. To avoid such degradation, an asymptotically optimum detector (AOD) is used. The structure of the AOD is based on an asymptotic expression of the log-likelihood ratio and the functional form of zero memory non linearity (ZMNL), which depends on the noise statistics. In this paper, we calculate the functional form of ThINL for three different probability density functions (Gaussian, log-normal, and Weibull distribution). The structure of the AOD has been introduced when the probability density function of the noise is either unknown or known. This structure can be used to improve the radar performance.