SCIENCE CHINA Information Sciences, Volume 59, Issue 8: 082306(2016) https://doi.org/10.1007/s11432-015-0772-6

## Achievable degrees of freedom of MIMO two-way X relay channel with delayed CSIT

• AcceptedJan 21, 2016
• PublishedJun 7, 2016
Share
Rating

### Abstract

The previous work on interference alignment for multiple-input-multiple-output (MIMO) two-way X relay channel assumes perfect channel state information at the transmitter (CSIT), which is reasonable in slow fading channel. However, in fast fading scenario, this assumption is impractical. In this paper, assuming that each node has delayed CSIT, we study the achievable degrees of freedom (DOF) for MIMO two-way X relay channel in frequency division duplex (FDD) systems. Specifically, in the broadcast (BC) phase, we propose a new multiple-stage transmission (MST) scheme, which utilizes retrospective interference alignment for physical layer network coding (PLNC). We show that MST can achieve significant DOF gain and tremendous power gain over other schemes. When the number of antennas for each user, $N$, is smaller than the number of the relays, $M$, the time division multiple access (TDMA) scheme can only achieve an ergodic sum-rate increase by $N$ bps/Hz for every increasing of 3 dB of signal-to-noise power ratio (SNR), while the proposed MST scheme can achieve an ergodic sum-rate increase by $M$ bps/Hz.

### Funded by

Regional Cooperation Project of MOST of China(2014DFT10290)

### Acknowledgment

Acknowledgments

This work was supported by Regional Cooperation Project of MOST of China (Grant No. 2014DFT10290).

### References

[1] Hossain E, Rasti M, Tabassum H, et al. Evolution toward 5G multi-tier cellular wireless networks: an interference management perspective. IEEE Wirel Commun, 2014, 21: 118-127 Google Scholar

[2] VanderMeulen E. Three-terminal communication channels. Adv Appl Prob, 1974, 3: 120-154 Google Scholar

[3] VanderMeulen E. A survey of multi-way channels in information theory: 1961--1976. IEEE Trans Inf Theory, 1977, 23: 1-37 CrossRef Google Scholar

[4] Cover T, Gamal A. Capacity theorems for the relay channel. IEEE Trans Inf Theory, 1979, 25: 572-584 CrossRef Google Scholar

[5] Xing C W, Li S, Fei Z S, et al. How to understand linear minimum-mean-square-error transceiver design for multiple-input multiple-output systems from quadratic matrix programming. IET Commun, 2013, 7: 1231-1242 CrossRef Google Scholar

[6] Xing C W, Ma S D, Fei Z S, et al. General robust linear transceiver design for multi-hop amplify-and-forward MIMO relaying systems. IEEE Trans Signal Proc, 2013, 61: 1196-1209 CrossRef Google Scholar

[7] Jafar S A, Shamai S S. Degrees of freedom region of the MIMO x channel. IEEE Trans Inf Theory, 2008, 54: 151-170 CrossRef Google Scholar

[8] Maddah-Ali M, Motahari A, Khandani A. Communication over MIMO x channels: interference alignment, decomposition, and performance analysis. IEEE Trans Inf Theory, 2008, 54: 3457-3470 CrossRef Google Scholar

[9] Zhang S L, Liew S C, Lam P P. Hot topic: physical-layer network coding. In: Proceedings of the 12th Annual International Conference on Mobile Computing and Networking. New York: ACM, 2006. 358--365. Google Scholar

[10] Xiang Z Z, Tao M X, Mo J H, et al. Degrees of freedom for MIMO two-way x relay channel. IEEE Trans Signal Proc, 2013, 61: 1711-1720 CrossRef Google Scholar

[11] Maddah-Ali M, Tse D. Completely stale transmitter channel state information is still very useful. IEEE Trans Inf Theory, 2012, 58: 4418-4431 CrossRef Google Scholar

[12] Maleki H, Jafar S A, Shamai S S. Retrospective interference alignment over interference networks. IEEE J Sel Topic Signal Proc, 2012, 6: 228-240 CrossRef Google Scholar

[13] Abdoli M, Ghasemi A, Khandani A. On the degrees of freedom of K-user SISO interference and x channels with delayed CSIT. IEEE Trans Inf Theory, 2013, 10: 6542-6561 Google Scholar

[14] Vaze C, Varanasi M. The degrees of freedom region of the two-user MIMO broadcast channel with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, 2011. 199--203. Google Scholar

[15] Yi X P, Yang S, Gesbert D, et al. The degrees of freedom region of temporally correlated MIMO networks with delayed CSIT. IEEE Trans Inf Theory, 2014, 60: 494-514 CrossRef Google Scholar

[16] Abdoli M, Ghasemi A, Khandani A. On the degrees of freedom of three-user MIMO broadcast channel with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory, Saint Petersburg, 2011. 209--213. Google Scholar

[17] Wang I H, Diggavi S. On degrees of freedom of layered two-unicast networks with delayed CSIT. In: Proceedings of IEEE International Symposium on Information Theory, Cambridge, 2012. 46--50. Google Scholar

[18] Tandon R, Mohajer S, Poor H, et al. On x channels with feedback and delayed CSI. In: Proceedings of IEEE International Symposium on Information Theory, Cambridge, 2012. 1877--1881. Google Scholar

[19] Li Q Y, Li H X, Wu G, et al. Achievable degrees of freedom of MIMO y channel with delayed CSIT. IEEE Commun Lett, 2014, 18: 1583-1586 CrossRef Google Scholar

[20] Li Q Y, Li H X, Wu G, et al. Retrospective network coding alignment over K-user MIMO y channel. IEEE Commun Lett, 2016, 20: 502-505 CrossRef Google Scholar

Citations

• #### 0

Altmetric

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有