Robust optimization of an amplify-and-forward relay network in impulsive noise environment

This paper proposes a robust algorithm for the optimization of an amplify-and-forward relay network in impulsive noise environment. Mixture of Gaussian (MoG) variable is used to model the impulsive noise. The characteristic function of the MoG variable is computed, and it is used to derive the Probability Density Function (PDF) of the linear combination of impulsive noises. Using the derived PDF, an objective function is designed and the maximum likelihood criterion is used to optimize the beamforming weight vector of the relay network. Because the objective function does not have a concave-convex structure, gradient descending technique is applied to find the solution of the optimization problem. Computer simulations are conducted to show the validity of the proposed algorithm. It is shown that, in the presence of impulsive noise, the proposed algorithm reduces the bit error rate by one order of magnitude compared to the minimum mean square error technique.