Application of the support function and the steiner point on the study of interference alignment channel

Interference is usually viewed as an obstacle to communication in wireless networks. Therefore, we describe a way to find a doubly infinite nested lattice partition chain for the real dimension 2 in order to realize interference alignment onto these lattices and a procedure to find the minimum solution of the mean square error related to the corresponding channel quantization. Besides, we propose a new methodology based on the support function and Steiner points of fuzzy vectors to find the closest point of a coset in a lattice. Such a methodology is flexible enough to combine the fuzzy characterization with the geometric insights and it is able to maintain the inherent stochastic nature of the wireless communication networks.