Optimal opportunistic scheduling and adaptive modulation policies in wireless ad-hoc networks with network coding

In this paper, we study an opportunistic scheduling and adaptive modulation scheme for a wireless network with an XOR network coding scheme, which results in a cross-layer problem for MAC and physical layers. A similar problem was studied in [2] which considered an idealized system with the Shannon capacity. They showed that it may not be optimal for a relay node to encode all possible native packets and there exists the optimal subset of native packets that depends on the channel condition at the receiver node of each native packet. In this paper, we consider a more realistic model than that of [2] with a practical modulation scheme such as M-PSK. We show that the optimal policy is to encode native as many native packets as possible in the network coding group into a coded packet regardless of the channel condition at the receiver node for each native packet, which is a different conclusion from that of [2]. However, we show that adaptive modulation, in which the constellation size of a coded packet is adjusted based on the channel condition of each receiver node, provides a higher throughput than fixed modulation, in which its constellation size is always fixed regardless of the channel condition at each receiver node.