A least squares approach to joint beam design for interference alignment in multiuser interference channels

The problem of interference alignment for K-user time-invariant multi-input multi-output (MIMO) interference channels is considered. A sufficient condition for perfect interference alignment is converted to a linear system of equations which is overdetermined for K≥ 4. It is shown that this linear system is infeasible almost surely. To obtain the approximate solution to this problem, we use a least squares (LS) approach. Various constraints are considered for the LS formulation, including the total signal power, individual user power and individual user beam power constraints. Numerical results are provided to evaluate the proposed design method.