Deterministic annealing design and analysis of the noisy MIMO interference channel

We consider the Noisy MIMO Interference Channel (IFC) with linear transmitters and receivers and full CSI. The maximization of the Weighted Sum Rate (WSR) or transceiver design for Interference Alignment (IA) lead to cost functions with many local optima. Deterministic annealing is an approach that allows to track the variation of the known solution of one version of the problem into the unknown solution of the desired version by a controlled variation of a parameter called temperature. When the temperature parameter is chosen as inverse SNR (or noise power), the transceiver design for maximum WSR is known at low SNR and can be tracked to any desired SNR, yielding an elegant technique to find the global optimum. The solution includes filter design for the progressive switching on of streams as the SNR increases. For IA on the other hand, IA feasibility is unchanged when the MIMO crosslink channel matrices have a reduced rank equal to the maximum of the number of streams passing through them in forward and dual IFC (this would correspond to LOS channels in the case of single streams). The rank reduction simplifies IA design and feasibility analysis, and allows in particular a counting of the number of IA solutions. By choosing now the temperature parameter to be a scale factor for the remaining channel singular values, the solution for reduced rank channels can be evolved into that for arbitrary channels.