An achievable degree of freedom for multi-hop wireless networks under layered TDD constraint

We investigate the degrees of freedom (DoF) issue for multi-hop wireless networks with multiple-node layers under layered time-division-duplex (TDD) constraint. Our recent work about cascaded linear networks shows that the number of feasible network states is related to the famous Fibonacci sequence and the maximum achievable decode-and-forward (DF) rate is r*= min {C₁C₂/C₁+C₂, C₂C₃/C₂+C₃,⋯, C_K-1C_K/C_K-1+C_K} for K-hop networks, where C_k; ∀k = 1, 2, ..., K, is the capacity of each hop. Based on these results, we studies the DoF aspect of multi-hop networks with multiple-node layers, mainly about achievable lower bound on the sum DoF, by viewing the network as cascaded X channels (XC). Then we analyze the ultimate case where the number of antennas at each relay layer goes to infinity, from which we find that compared with two-hop networks, larger sum DoF can be obtained if the number of hops is no less than three.