Fronthaul-aware superposition coding for noncoherent transmission in C-RAN downlink

Abstract

Cloud radio access network (C-RAN) has arisen as a promising architecture for the 5G wireless communication system. Among many advantages, C-RAN is known to enable large-scale interference management by migrating baseband processing functionalities from radio units (RUs) to a control unit (CU) with the aid of fronthaul links. Most of literatures prescribe that perfect synchronization is available among distributed RUs and fronthaul links are equipped with infinite capacities. Since these assumptions are far from practical situations, this work proposes a more practical noncoherent transmission strategy, in which synchronization is not needed among the RUs, by means of a novel superposition, or broadcast, coding. Under the proposed superposition coding scheme, the problem of maximizing the weighted sum of per-user achievable rates is tackled while satisfying per-RU transmit power and fronthaul capacity constraints. Some numerical results are provided to validate the effectiveness of the proposed scheme.

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References

  1. 1.

    Checko A, Christiansen HL, Yan Y, Scolari L, Kardaras G, Bergerand MS, Dittmann L (2015) Cloud RAN for mobile networks - a technology overview. IEEE Comm Surveys Tutorials 17:405–426

    Article  Google Scholar 

  2. 2.

    Simeone O, Maeder A, Peng M, Sahin O, Yu W (2016) Cloud radio access network: virtualizing wireless access for dense heterogeneous systems. J Commun Netw 18:135–149

    Google Scholar 

  3. 3.

    Heo E, Simeone O, Park H (2015) Optimal fronthaul compression for synchronization in the uplink of cloud radio access networks. arXiv:1510.01545

  4. 4.

    Park S-H, Simeone O, Sahin O, Shamai S (2014) Fronthaul compression for cloud radio access networks: signal processing advances inspired by network information theory. IEEE Sig Proc Mag 31:69–79

    Article  Google Scholar 

  5. 5.

    Xu M, Guo D, Honig ML (2013) Downlink noncoherent cooperation without transmitter phase alignment. IEEE Trans Wireless Comm 12:3920–3931

    Article  Google Scholar 

  6. 6.

    Sangiamwong J, Saito Y, Miki N, Abe T, Nagata S, Okumura Y (2011) Investigation on cell selection methods associated with inter-cell interference coordination in heterogeneous networks for lte-advanced downlink, In: Proceeding European wireless conference sustainable wireless technology, pp 1–6

    Google Scholar 

  7. 7.

    Guvenc I (2011) Capacity and fairness analysis of heterogeneous networks with range expansion and interference coordination. IEEE Comm Lett 15:1084–1087

    Article  Google Scholar 

  8. 8.

    Cover TM (1998) Comments on broadcast channels. IEEE Trans Inf Theory 44:2524–2530

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Shamai S, Steiner A (2003) A broadcast approach for a single-user slowly fading MIMO channel. IEEE Trans Inf Theory 49:2617–2635

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Park S-H, Simeone O, Sahin O, Shamai S (2014) Robust layered transmission and compression for distributed uplink reception in cloud radio access networks. IEEE Trans Veh Technol 63:204– 216

    Article  Google Scholar 

  11. 11.

    Yemini M, Somekh-Baruch A, Leshem A (2015) On the multiple access channel with asynchronous cognition. arXiv:1503.08413

  12. 12.

    Cover TM, Thomas JA (1991) Elements of information theory. Wiley

  13. 13.

    Gamal AE, Kim Y-H (2011) Network information theory. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  14. 14.

    Thi HAL, Tao P (2005) The DC programming and DCA revised with DC models of real world nonconvex optimization problems. Ann Oper Res 133:23–46

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Grant M, Boyd S (2013) CVX: Matlab software for disciplined convex programming, ver. 2.0 beta, http://cvxr.com/cvx

  16. 16.

    Gaubock G (2012) Complex-valued random vectors and channels: Entropy, divergence, and capacity. IEEE Trans Inf Theory 58(5):2729–2744

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgments

S.-H. Park was supported by the National Research Foundation of Korea grant funded by the Korea government (Ministry of Science, ICT &Future Planning) [2015R1C1A1A01051825]. The work of C. Song was supported by the National Research Foundation of Korea within the Ministry of Science, ICT, and Future Planning through the Korean Government under Grant NRF-2015R1C1A1A02036927.

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Correspondence to Changick Song.

Appendix 1: Proof for Eq. 9

Appendix 1: Proof for Eq. 9

In this appendix, we show that, under the assumption that UE k jointly decodes the submessages \(\{M_{k,i}\}_{i\in \mathcal {N}_{R}}\) based on the received signal y k , the mutual information quantity \(I(\mathbf {s}_{k,\mathcal {S}} ; \mathbf {y}_{k} | \mathbf {s}_{k,\mathcal {S}^{c}})\) in Eq. 8 can be calculated as Eq. 9.

By the property I(X; Y ) = h(Y ) − h(Y |X) of mutual information, we can write

$$\begin{array}{@{}rcl@{}} &&I(\mathbf{s}_{k,\mathcal{S}} ; \mathbf{y}_{k} | \mathbf{s}_{k,\mathcal{S}^{c}}) =h(\mathbf{y}_{k} | \mathbf{s}_{k,\mathcal{S}^{c}}) - h(\mathbf{y}_{k} | \mathbf{s}_{k,\mathcal{S}}, \mathbf{s}_{k,\mathcal{S}^{c}})\\ &&=\log_{2}\det\left( E\left[\mathbf{y}_{k} \mathbf{y}_{k}^{\dagger} | \mathbf{s}_{k,\mathcal{S}^{c}}\right]\right) - \log_{2}\det\left( E\left[ \mathbf{y}_{k}\mathbf{y}_{k}^{\dagger} | \mathbf{s}_{k,\mathcal{S}}, \mathbf{s}_{k,\mathcal{S}^{c}} \right]\right), \end{array} $$
(13)

where the second equality is obtained by considering the fact that the differential entropy of circularly symmetric complex Gaussian vector \(\mathbf {v}\sim \mathcal {CN}(\mathbf {0}, \mathbf {R})\) is given as log 2 det(π e R) [16, Th. 4.4].

By direct calculation, the covariance matrices appearing in the log-det functions in Eq. 13 can be written as

$$\begin{array}{@{}rcl@{}} &&E\left[\mathbf{y}_{k} \mathbf{y}_{k}^{\dagger} | \mathbf{s}_{k,\mathcal{S}^{c}}\right] = \mathbf{N}_{k}(\mathbf{B}) + \sum\limits_{i\in\mathcal{S}}\tilde{\mathbf{H}}_{k,i}\mathbf{B}_{k,i}\tilde{\mathbf{H}}_{k,i}^{\dagger}, \end{array} $$
(14)
$$\begin{array}{@{}rcl@{}} &&E\left[ \mathbf{y}_{k}\mathbf{y}_{k}^{\dagger} | \mathbf{s}_{k,\mathcal{S}}, \mathbf{s}_{k,\mathcal{S}^{c}} \right] = E\left[ \mathbf{y}_{k}\mathbf{y}_{k}^{\dagger} | \mathbf{s}_{k,\mathcal{N}_{R}} \right] = \mathbf{N}_{k}(\mathbf{B}), \end{array} $$
(15)

where we recall that N k (B), which measures the covariance matrix of the interference-plus-noise signals at UE k, is given as Eq. 7. Substituting Eqs. 14 and 15 into Eq. 13 results in the expression (9), which concludes the proof.

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Park, SH., Song, C. Fronthaul-aware superposition coding for noncoherent transmission in C-RAN downlink. Ann. Telecommun. 72, 661–667 (2017). https://doi.org/10.1007/s12243-017-0594-3

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Keywords

  • Cloud radio access network
  • Constrained fronthaul
  • Noncoherent transmission
  • Superposition coding