Degrees of freedom of general symmetric MIMO interference broadcast channels

In this paper, we study the maximal achievable degrees of freedom (DoF) for G-cell, K-user M×N symmetric multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients by linear interference alignment (IA). We start by analyzing the sufficient and necessary conditions of the IA feasibility, which are associated with generalized Fibonacci sequences. Except for the well-known proper condition, we find another condition necessary to ensure a kind of irreducible interference to be eliminated, denoted as irreducible condition. We proceed to find the minimal number of antennas at each base station and each user to support a required number of interference-free data streams, from which we obtain the maximal achievable DoF. We find that the feasibility conditions in terms of the required antenna resources can be divided into two regions according the ratio of ρ = M/N. If ρ falls into the region that characterized by the proper condition, the achievable DoF per user with spatial extension is (M + N)/(GK + 1). If ρ lies in the region that characterized by the irreducible condition, the DoF is a piecewise linear function of M or N alternately.