Degrees of Freedom for the MIMO Multi-Way Relay Channel

This paper investigates the degrees of freedom (DoF) of the L-cluster, K-user MIMO multiway relay channel, where users in each cluster wish to exchange messages within the cluster, and they can only communicate through the relay. A novel DoF upper bound is derived by providing users with carefully designed genie information. Achievable DoF is identified using signal space alignment and multiple-access transmission. For the two-cluster MIMO multiway relay channel with two users in each cluster, the DoF is established for the general case when users and the relay have arbitrary number of antennas, and it is shown that the DoF upper bound can be achieved using signal space alignment or multiple-access transmission, or a combination of both. The result is then generalized to the three user case. For the L-cluster K-user MIMO multiway relay channel in the symmetric setting, conditions under which the DoF upper bound can be achieved are established. In addition to being shown to be tight in a variety of scenarios of interests of the multiway relay channel, the newly derived upperbound also establishes the optimality of several previously established achievable DoF results for multiuser relay channels that are special cases of the multiway relay channel.

[1]  Tobias Weber,et al.  Pair-Aware Interference Alignment in Multi-User Two-Way Relay Networks , 2013, IEEE Transactions on Wireless Communications.

[2]  Min Chen,et al.  Multiuser two-way relaying: detection and interference management strategies , 2009, IEEE Transactions on Wireless Communications.

[3]  Joohwan Chun,et al.  Degrees of Freedom of the MIMO Y Channel: Signal Space Alignment for Network Coding , 2010, IEEE Transactions on Information Theory.

[4]  Syed Ali Jafar,et al.  Interference Alignment and Degrees of Freedom of the $K$-User Interference Channel , 2008, IEEE Transactions on Information Theory.

[5]  Uri Erez,et al.  Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding , 2004, IEEE Transactions on Information Theory.

[6]  Min Chen,et al.  Power allocation for F/TDMA multiuser two-way relay networks , 2010, IEEE Transactions on Wireless Communications.

[7]  Syed Ali Jafar,et al.  Degrees of Freedom of the K User M×N MIMO Interference Channel , 2008, ArXiv.

[8]  Aydin Sezgin,et al.  Divide-and-Conquer: Approaching the Capacity of the Two-Pair Bidirectional Gaussian Relay Network , 2012, IEEE Transactions on Information Theory.

[9]  Aydin Sezgin,et al.  On the sum capacity of the Y-channel , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[10]  Andrea J. Goldsmith,et al.  The multi-way relay channel , 2009, 2009 IEEE International Symposium on Information Theory.

[11]  Shlomo Shamai,et al.  Degrees of Freedom Region of the MIMO $X$ Channel , 2008, IEEE Transactions on Information Theory.

[12]  Sae-Young Chung,et al.  Capacity of the Gaussian Two-Way Relay Channel to Within ${1\over 2}$ Bit , 2009, IEEE Transactions on Information Theory.

[13]  Aylin Yener,et al.  Degrees of freedom optimal transmission for the two-cluster MIMO multi-way relay channel , 2013, 2013 IEEE International Conference on Communications (ICC).

[14]  Inkyu Lee,et al.  Degrees of Freedom on MIMO Multi-Link Two-Way Relay Channels , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[15]  Alexander Sprintson,et al.  Joint Physical Layer Coding and Network Coding for Bidirectional Relaying , 2008, IEEE Transactions on Information Theory.

[16]  Lawrence Ong,et al.  The Capacity Region of Multiway Relay Channels Over Finite Fields With Full Data Exchange , 2011, IEEE Transactions on Information Theory.

[17]  Aydin Sezgin,et al.  The capacity region of the linear shift deterministic Y-channel , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[18]  Syed Ali Jafar,et al.  Degrees of Freedom of the K User M times N MIMO Interference Channel , 2008, IEEE Trans. Inf. Theory.

[19]  Claude E. Shannon,et al.  Two-way Communication Channels , 1961 .

[20]  Sae-Young Chung,et al.  Capacity of the Gaussian Two-way Relay Channel to within 1/2 Bit , 2009, ArXiv.

[21]  Syed Ali Jafar,et al.  Degrees of Freedom for the MIMO Interference Channel , 2006, IEEE Transactions on Information Theory.

[22]  Aydin Sezgin,et al.  Information Theory Capacity of the two-way relay channel within a constant gap , 2010, Eur. Trans. Telecommun..

[23]  Andrea J. Goldsmith,et al.  The Multiway Relay Channel , 2013, IEEE Transactions on Information Theory.

[24]  Fan Sun,et al.  Degrees of freedom of asymmetrical multi-way relay networks , 2011, 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications.

[25]  Inkyu Lee,et al.  Achievable Degrees of Freedom on K-user Y Channels , 2012, IEEE Transactions on Wireless Communications.

[26]  Aylin Yener,et al.  Degrees of Freedom for the MIMO Multi-Way Relay Channel , 2014, IEEE Trans. Inf. Theory.

[27]  Raymond Knopp,et al.  Multi-Pair Two-Way Relay Channel with Multiple Antenna Relay Station , 2010, 2010 IEEE International Conference on Communications.

[28]  Lawrence Ong,et al.  On the Equal-Rate Capacity of the AWGN Multiway Relay Channel , 2012, IEEE Transactions on Information Theory.

[29]  Tobias Weber,et al.  Interference Alignment in Multi-User Two Way Relay Networks , 2011, 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring).

[30]  Aylin Yener,et al.  Signal space alignment and degrees of freedom for the two-cluster multi-way relay channel , 2012, 2012 1st IEEE International Conference on Communications in China (ICCC).

[31]  Syed Ali Jafar,et al.  Interference Alignment and the Degrees of Freedom of Wireless $X$ Networks , 2009, IEEE Transactions on Information Theory.