Degrees of Freedom of Two-Hop Wireless Networks: Everyone Gets the Entire Cake

• Published in: IEEE transactions on information theory Vol. 60; no. 5; pp. 2417 - 2431
• Main Authors: Shomorony, Ilan, Avestimehr, Amir Salman
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-05-2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Channels; Constants; Degrees of freedom; Electrical engineering; Exact sciences and technology; Hops; Information theory; Information, signal and communications theory; Interference; Linear transformations; Mathematical analysis; MIMO; Networks; Relays; Spread spectrum communication; Telecommunications and information theory; Time-varying channels; Vectors; Wireless networks; relays; wireless networks; Two-hop communications; degrees of freedom; MIMO system; Diagonalization; Time variable channel; Relay; Wireless telecommunication; Nodes; Multihop network; Linear transformation; Wireless network
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2308172

We show that fully connected two-hop wireless networks with K sources, K relays, and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new achievability scheme which we call Aligned Network Diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. In addition, we extend our scheme to multihop networks with fully connected hops, and multihop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.