Unsaturated Throughput Analysis of Physical-Layer Network Coding Based on IEEE 802.11 Distributed Coordination Function

In this paper, we investigate the throughput performance of \rev{physical-layer network coding} (PNC) under the IEEE 802.11 distributed coordination function (DCF). We consider the wireless network that two client groups communicate with each other across one relay node, and focus on the unsaturated network case. The difficulty in modeling the relay systems under the IEEE 802.11 DCF is that the minimum contention window sizes of the client nodes and the relay node may be different, which makes the traditional throughput analysis methods for the non-relay wireless networks inapplicable. Fortunately, we find that the relay system can be decomposed into four parts and respectively modeled. Analytical results show that the throughput gain of PNC scheme is heavily affected by the probability that a transmitted network-coding (NC) packet contains the information of two packets. The implication is that the throughput benefit of PNC is more significant for bidirectional isochronous traffic with rate requirements. \rev{We further derive an approximate closed-form solution of the optimal transmission probability of client nodes that maximizes the PNC network throughput.} We validate our analytical model through extensive simulations and discuss the relationship between the PNC network throughput and other system parameters, such as the minimum contention window sizes of both the client nodes and the relay node.