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In this paper, we analyze the throughput of multi-hop amplify and forward (AF) relay networks in delay-constrained scenario. Using quantized channel state information (CSI), the transmission rates and powers are discretely adapted with individual average power constraint on each node. A sub-gradient projection-based algorithm is utilized, by which there is no need for probability density functions (PDFs) to solve the optimization problem. Our numerical evaluations show that the sub-gradientdoi:10.1186/s13638-019-1423-3 fatcat:i5w7tikht5dedcdp57acjh2bxy