Feasibility Condition for Interference Alignment With Diversity

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.