Tree Search Algorithms Applied to the BD-RIS Configuration in MU-MISO Communication Systems

The reconfigurable intelligent surface (RIS) has attracted considerable attention of both academia and industry in recent years, given its capacity to dynamically manipulate the reflection of incident electromagnetic waves. Although the research developed for the RIS may have reached its maturity, there are still contentious aspects and limitations regarding its potential benefits for the next generation of wireless communications. In order to improve upon the the RIS technology, the beyond diagonal reconfigurable intelligent surface (BD-RIS) was recently proposed as an promising alternative. The BD-RIS boasts a more sophisticated circuit topology that is capable of providing more combinations of different adjustments or configurations for signal reflection. However, to aptly reap the benefits of the BD-RIS, the added degrees-of-freedom of its configuration must be leveraged accordingly. Therefore, in this work we propose a depth-first tree search algorithm for configuring the BD-RIS in multi-user multiple-input single-output (MU-MISO) communication systems. Taking advantage of the tree search exploration, the proposed algorithm achieves a remarkable trade-off between channel strength maximization performance and computational complexity scalability.