In wireless ad hoc network communications, both the network interference and the thermal noise should be considered in receiver design, due to the strong impairments each may cause on the quality of the reception at the destination. Since the closure under convolution of stable distributions only holds for the same stability index members, in general the additive convolution of the impulsive stable interference and lighter tailed Gaussian thermal noise will not result in a stable pattern. It is therefore a challenge to adequately model the distribution of such a process. In this context we consider an optimal receiver design and develop an importance sampling approach to perform estimation of the optimal receiver in the presence of convolved stable and Gaussian noises. Such an approximation approach to the optimal receiver is computationally expensive, hence we also develop as comparisons several suboptimal realizations of linear and non-linear receivers, including an approximation approach based on the Normal Inverse Gaussian (NIG) distribution. We demonstrate that the computationally efficient NIG receiver provides an alternative solution for the optimal receiver approx- imation. In addition we show that the p-norm receiver appears to have robust performance no matter what kind of noise is dominant.