The 2Dwhitenoise model has been extended to represent a modified power law that is realistic. It allows for finite moments for the interference.The white noise processes with a decaying power law.Impulse response functions are ideally suited for modeling the network self-interference in an ad hoc network.The nodes are distributed in a plane according to a Poisson point process. A stochastic impulse response function is used to model different random parameters like channel fluctuation, variable transmission power of the nodes etc. For a decaying power law, all the moments of the interference diverge.We have presented performance curves for the additive white Gaussian noise (AWGN) channel with and without variable transmission power at the nodes.We have imposed a guard zone around each receiver node in the network to modify the shot noise model to this channel access scheme and demonstrate the improvement in pernode throughput the guard zone.