# Sum Capacity for Single-Cell Multi-User Systems with M-Ary Inputs

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## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. Multiple Assess Channel

#### 2.2. Broadcast Channel

## 3. Entropy Power and the Parallelization of MAC and BC

#### 3.1. Entropy Power

#### 3.2. Parallelization for MAC

#### 3.3. Parallelization for BC

## 4. Sum Capacity for MAC with Different Power Allocation Strategies

#### 4.1. Equal Power Distribution

#### 4.2. Power Allocation for Equal Capacity

#### 4.3. Optimal Power Allocation for Maximum Sum Capacity

Algorithm 1 Optimal Power Allocation Algorithm. |

Step 1: initialize: set $\Delta $, set ${P}_{1}={P}_{2}=\cdots ={P}_{K}=P/K$. |

Step 2: Calculate ${\lambda}_{i},\forall i=1,2,\cdots ,K$. |

Step 3: Let ${\lambda}_{i}$ and ${\lambda}_{j}$ be the maximum and minimum values of $[{\lambda}_{1},{\lambda}_{2},\cdots ,{\lambda}_{K}]$. |

Step 4: ${P}_{i}={P}_{i}+\Delta $ and ${P}_{j}={P}_{j}-\Delta $. |

Step 5: Goto Step 2 if the incremental of ${C}_{\mathrm{sum}}$ is large than a threshold. |

## 5. Numerical Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Table 1.**Approximation parameters of (9) for QPSK, 8PSK, 16QAM modulations.

Modulation | a | b | N |
---|---|---|---|

QPSK | 1 | 0.6507 | 1 |

8PSK | 0.6130 | 0.1681 | 2 |

0.3855 | 0.8992 | ||

16QAM | 0.7177 | 0.1225 | 2 |

0.2804 | 0.8702 |

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**MDPI and ACS Style**

Yang, P.; Wu, Y.; Jin, L.; Yang, H.
Sum Capacity for Single-Cell Multi-User Systems with *M*-Ary Inputs. *Entropy* **2017**, *19*, 497.
https://doi.org/10.3390/e19090497

**AMA Style**

Yang P, Wu Y, Jin L, Yang H.
Sum Capacity for Single-Cell Multi-User Systems with *M*-Ary Inputs. *Entropy*. 2017; 19(9):497.
https://doi.org/10.3390/e19090497

**Chicago/Turabian Style**

Yang, Pei, Yue Wu, Liqiang Jin, and Hongwen Yang.
2017. "Sum Capacity for Single-Cell Multi-User Systems with *M*-Ary Inputs" *Entropy* 19, no. 9: 497.
https://doi.org/10.3390/e19090497