Algorithms for improper single-stream MIMO interference networks

The “max-SINR” algorithm and a number of related algorithms have been shown to be very useful for determining good strategies in MIMO interference networks and achieving spatial interference alignment at high SNR. These algorithms, however, rely on being initialized with a “proper” configuration of streams per user, as they do not have the capability of reducing a user\´s power or deactivating users completely. Alternatively, algorithms for MIMO interference networks can be designed to perform power control, so that interference alignment can be achieved even from an improper initialization. In this paper, we examine one particularly promising such design. We discuss in detail an update procedure based on maximizing the own rate minus a linearized cost of causing interference to other users, a technique known as "interference pricing" for simplicity, we restrict our attention to the case of one stream per user. As previously proposed, we combine the pricing updates with a gradual increase of the transmit power or SNR, which greatly improves the numerical properties. We show with numerical experiments that in an improper system our proposed pricing algorithm with incremental SNR achieves better performance than other algorithms with power control; the fixed-power algorithms, such as the max-SINR algorithm, perform poorly at high SNR.