In this paper, we consider a cognitive multi-hop relay secondary user (SU)
system sharing the spectrum with some primary users (PU). The transmit power as
well as the hop selection of the cognitive relays can be dynamically adapted
according to the local (and causal) knowledge of the instantaneous channel
state information (CSI) in the multi-hop SU system. We shall determine a low
complexity, decentralized algorithm to maximize the average end-to-end
throughput of the SU system with dynamic spatial reuse.