Distributed wireless systems offer several advantages over their traditional wired and centralized counterparts, e.g., flexibility, easy installation, reconfiguration, and scalability. Although the resources in these distributed systems are often limited in order to achieve costeffective operation, the concept of distributed system design is in the focus of intensive research even in those application fields that are extremely susceptible against the uncertainties caused by decentralized operation. Such applications are closed-loop signal processing systems where signals are fed back through a shared communication channel. There are three challenging problems of distributed closed-loop signal processing systems: bandwidth limit of the communication medium, synchronization of sensor nodes and data loss in communication. The paper introduces these problems and proposes some possible solutions.