## 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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## 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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## 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

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

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