Cooperative communication is known to be one of the most effective techniques to improve the coverage and capacity of wireless networks. An Orthogonal Multiple Access Multiple Relay Channel (OMAMRC) is considered in the paper, where several nodes cooperate to send their messages to a single destination (typical uplink context in traditional wireless networks). The destination, as a central node, schedules the cooperative re-transmissions and allocates the transmission rates to the sources. The Link Adaptation (LA) is designed to optimize the spectral efficiency of the system. In our previous work, two LA algorithms were studied: Slow LA (SLA) and Fast LA (FLA). SLA relies on the Channel Distribution Information (CDI) of all links at the destination, while FLA relies on the Channel State Information (CSI) of all links. Clearly, SLA is less demanding in terms of channel information acquisition control overhead while FLA provides closer-to-optimum scheduling decisions. In this work, we propose and analyze a novel practical link adaptation algorithm combining the benefits of both. It is based on a FLA strategy with partial CSI. Our numerical results show that the proposed algorithm achieves a spectral efficiency that is close to the one achieved by FLA while demanding less CSI acquisition control overhead.