The capacity of wireless ad hoc networks is constrained by the interference of concurrent transmissions among nodes. Instead of only trying to avoid the interference, physical-layer network coding (PNC) is a new approach that embraces the interference initiatively. We employ a network form of interference cancellation, with the PNC approach, and propose the multihop, broadcastrelay transmission strategy in linear, rectangular, and hexagonal networks. The theoretical analysis shows that it gains

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... the transmission efficiency by the factors of 2.5 for the rectangular networks and 2 for the hexagonal networks. We also propose a practical signal recovery algorithm in the physical layer to deal with the influence of multipath fading channels and time synchronization errors, as well as to use media access control (MAC) protocols that support the simultaneous receptions. This transmission strategy obtains the same efficiency from one-to-one communication to one-to-many. By our approach, the number of the users/terminals of the network has better scalability, and the overall network throughput is improved. Since we will discuss the transmission strategy in linear, rectangular, and hexagonal networks for the unicast, multicast, and broadcast cases, for preliminaries, we present some basic definitions first. Definition 1 (distance). The distance between two nodes is the minimum number of hops between these two nodes in an ad hoc network. Definition 2 (distance-n-network). The distance-n-network is an ad hoc network with one source in which all the distances between the source node and the other nodes are not larger than n. Definition 3 (full distance-n rectangular network). The full distance-n rectangular network is a rectangular distance-nnetwork that contains 2n(n + 1) + 1 nodes. All the possible 4 EURASIP Journal on Wireless Communications and Networking nodes with distance-n to the source in the rectangular network topology exist in this network.