We consider the utility maximization problem in wireless multi-hop networks with unicast and multicast communication and jointly optimize routing or network coding together with the physical layer. Since for any communication demands the performance is predominately determined by the region of achievable rates on edges between nodes, we provide a framework for including advanced physical layer methods in wireless networks by means of factorizing the achievable rate region into a set of advanced elementary rate regions. Various advanced physical layer operations such as broadcast and multiple access channels are included. Additionally, the wireless multicast advantage is efficiently modeled for degraded channels, namely broadcast and multicast, to improve performance of multicast sessions. Numerical examples show the impact of the physical layer onto the optimal routing or network coding solution and the benefits of advanced physical layer operations.
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