Statistical Shaping of Interference to Maximize Capacity in Cognitive Random Wireless Networks

It is known that in a cognitive random wireless network, the aggregate interference from secondary network is not Gaussian. Using Shannon's bound for the capacity of general additive channels, Gaussian interference/noise is the worst case due to its maximum entropy property which leads to minimum capacity. Therefore, it is favorable to have the distribution of interference as far from Gaussian as possible. In this paper, we seek to deviate the statistics of secondary interference from Gaussianity by maximizing its kurtosis while a regulatory constraint is satisfied to keep the interference power below a threshold. For this purpose, we use power control for statistical shaping of interference. Considering a Gaussian and a non-Gaussian interference zone around primary receiver and assigning a fixed power level for the interfering nodes inside each zone, we show that optimum power levels are found by solving a constrained nonlinear optimization problem. The results show that using optimum power levels, the kurtosis increases significantly compared to the no power control case. Moreover, considering a generalized Gaussian model for interference, we show that the capacity of primary link improves dramatically by using the optimum power levels.