# Group Sparse Precoding for Cloud-RAN with Multiple User Antennas

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model and Problem Formulation

**Lemma**

**1.**

**Proof.**

## 3. Reweighted ${\ell}_{\mathbf{1}}$ Based Algorithm

Algorithm 1 Reweighted ${\ell}_{1}$ Norm Based Sparse Precoding Design. |

Initilization: Set iteration counter $t=1$, Lagrangian dual variable ${\mathit{\lambda}}^{\left(0\right)}>0$, $l=1,\cdots ,L$.Repeat:- Update $\left\{{\lambda}_{l}\right\}$ according to (28).
- Update the iteration counter $t\leftarrow t+1$ and$$r=\sum _{l\in \mathcal{L}}{|{\lambda}_{l}\sum _{k\in \mathcal{K}}\mathrm{Tr}\left(\right)open="\{"\; close="\}">{\mathbf{B}}_{l}{\tilde{\mathbf{V}}}_{k}{\mathbf{Q}}_{k}{\tilde{\mathbf{V}}}_{k}^{\u2020}}^{|}2$$
Stop if $r<\epsilon $, where $\epsilon $ is a pre-defined tolerance threshold. |

## 4. Complexity Analysis

## 5. Simulation Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Proof of Lemma 1

## Appendix B. Derivation of (24)

## References

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**Figure 1.**Graphic illustration of a Cloud radio access network (C-RAN); BBU: baseband unit; RAP: remote antenna port.

**Figure 2.**An example of a randomly generated system configuration. The active RAPs at the converged state with $\eta =0.5$ are highlighted in red.

**Figure 3.**Convergence behavior of the proposed algorithm under the antenna and user layout shown in Figure 2 with randomly generated small-scale fading coefficients. $L=10$. ${N}_{c}=2$. $K=2$. $N=3$. $\eta =0.5$.

**Figure 4.**Number of active RAPs under the antenna and user layout shown in Figure 2 with randomly generated small-scale fading coefficients. $L=10$. ${N}_{c}=2$. $K=2$. $N=3$.

**Figure 5.**Transmit power of the RAPs under the antenna and user layout shown in Figure 2 with randomly generated small-scale fading coefficients. $L=10$. ${N}_{c}=2$. $K=2$. $N=3$. $\eta =0.5$.

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**MDPI and ACS Style**

Liu, Z.; Zhao, Y.; Wu, H.; Ding, S.
Group Sparse Precoding for Cloud-RAN with Multiple User Antennas. *Entropy* **2018**, *20*, 144.
https://doi.org/10.3390/e20020144

**AMA Style**

Liu Z, Zhao Y, Wu H, Ding S.
Group Sparse Precoding for Cloud-RAN with Multiple User Antennas. *Entropy*. 2018; 20(2):144.
https://doi.org/10.3390/e20020144

**Chicago/Turabian Style**

Liu, Zhiyang, Yingxin Zhao, Hong Wu, and Shuxue Ding.
2018. "Group Sparse Precoding for Cloud-RAN with Multiple User Antennas" *Entropy* 20, no. 2: 144.
https://doi.org/10.3390/e20020144