There are many future directions going forward. For example, the beamforming matrices used in our simulation studies could be further optimized. In addition, the setting in which there are unequal amounts of traffic between stations will be interesting to explore. A lso, this paper has only considered switch matrices those realize full permutations in which all stations participate in transmission and reception in each slot; it will be interesting to explore switch matrices that realize connectivities among stations that are not a full permutation. Finally, future work could also explore the case where the number of antenna at the relay is not exactly N . 

## REFERENCES 

[1] T. Cover and A. Gamal, “Capacity theorems for the relay ch annel,” Information Theory, IEEE Transactions on , vol. 25, no. 5, pp. 572–584, 1979. 

[2] D. Gunduz, A. Yener, A. Goldsmith, and H. Poor, “The multi -way relay channel,” in Information Theory, 2009. ISIT 2009. IEEE International Symposium on , 2009, pp. 339–343. 

[3] Y. Mohasseb, H. Ghozlan, G. Kramer, and H. El Gamal, “The M IMO wireless switch: Relaying can increase the multiplexing gain,” in Information Theory, 2009. ISIT 2009. IEEE International Symposium on , 2009. 

[4] T. Cui, T. Ho, and J. Kliewer, “Space-time communicationprotocols for n-way relay networks,” in IEEE Global Telecommunications Conference, 2008. , 2008. 

[5] F. Gao, T. Cui, B. Jiang, and X. Gao, “On communication pro tocol and beamforming design for amplify-and-forward n-way relay networks,” in Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009 3rd IEEE International Workshop on , 2009. 

[6] R. Ahlswede, N. Cai, S.-Y. Li, and R. Yeung, “Network info rmation flow,” Information Theory, IEEE Transactions on , vol. 46, no. 4, pp. 1204–1216, 2000. 

[7] S.-Y. Li, R. Yeung, and N. Cai, “Linear network coding,” Information Theory, IEEE Transactions on , vol. 49, no. 2, pp. 371–381, 2003. 

[8] S. Zhang, S. C. Liew, and P. P. Lam, “Physical-layer netwo rk coding,” in ACM Mobicom , 2006. 

[9] S. Katti, S. Gollakota, and D. Katabi, “Embracing wirele ss interference: Analog network coding,” in ACM SIGCOMM . MIT, 2007, pp. 397–408. 

[10] M. Hassani, “Derangements and applications,” Journal of Integer Sequences , vol. 6, no. 1, 2003. 

[11] A. U. T. Amah and A. Klein, “Non-regenerative multi-wayrelaying with linear beamforming,” in Proc. 20th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications Symposium , 2009. 

