On the Pareto Boundary for the Two-User Single-Beam MIMO Interference Channel

We consider a two-user multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream is transmitted and each receiver applies the minimum mean square error (MMSE) filter. In this paper, we study an open topic on the Pareto boundary of the rate region. The Pareto boundary is divided by two turning points into the weak Pareto boundary (including the horizontal part and vertical part) and the strict Pareto boundary (including the upper-right part and turning points). The weak Pareto boundary and turning points can be computed exactly. For the strict Pareto boundary, we propose a computationally efficient method called iterative alternating algorithm (IAA) for maximizing the rate of one user while the rate of the other user is fixed. To deal with the difficult coupling of the two transmit beamformers in this optimization problem, we convert it into two single-beamformer optimization problems. Then, by certain equivalent transformations, each problem becomes a quadratically constrained quadratic programming (QCQP) problem, which can be optimally solved by the semidefinite relaxation (SDR) technique in combination with a matrix rank-one decomposition. Furthermore, convergence of the proposed IAA is guaranteed. Numerical simulations show that the IAA provides a better lower bound on the strict Pareto boundary compared with the existing methods.