Achievable DF rate for cascaded undirected wireless networks with TDD and hidden-terminal

This paper investigates general Z-hop cascaded undirected wireless relay network, where the source, the relays, and the destination form an undirected chain, and each node receives radio waves from its two neighboring upstream and downstream nodes in the chain. We focus on the effect of time-division duplex and hidden-terminal constraints from two aspects: 1) finding all feasible network states (FNS) and determining the amount; 2) scheduling among FNS to maximize the transmission rate of the whole network when the decode-and-forward (DF) relay strategy is used. Firstly we define a new S sequence, which is proved to exactly characterize the number of all FNS. We provide a simple recursive construction method to get all FNS and discuss its properties. Then we formulate the scheduling problem into linear program which can be efficiently solved, and find the maximum achievable DF rate is: r* = min {1/1/c_j-1 + 1/c_j + 1/c_j+1 | ∀j =2, 3, ..., K - 1}, where C_k, ∀k = 1, 2, ..., K, denote thecapacity of component hops.