# Transceiver Design and Power Allocation for SWIPT in MIMO Cognitive Radio Systems

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## Abstract

**:**

## 1. Introduction

#### 1.1. Related Works

#### 1.2. Motivation and Contributions

- The transceiver design and power allocation problem in a MIMO CR network is studied, and an interference-alignment-based precoder design scheme for the SUs is proposed to protect the priority of the PU. This problem is solved by alternating optimization and convex optimization. The minimum transmit power, optimal transceiver and power splitting ratio of the PU are derived to guarantee its SINR and harvested energy constraints by using the SDR technique.
- The precoder of the SUs is analyzed by the theory of minimum squared Euclidean distance. The precoder of the SUs is obtained by eigenvalue decomposition of the interference covariance matrix.
- We propose a PA algorithm to maximize the sum rate of SUs. As the sum rate maximization power allocation algorithm may compromise some user’s performance, we further propose a PA algorithm to maximize the minimum SINR of the SUs.
- The approaches proposed can be implemented in the CR network especially the unlicensed spectrum CR where a PU’s interest must be protected. Moreover, our solutions can be extended to traditional communication network without WPT.

#### 1.3. Organization and Notation

## 2. System Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Problem Formulation

## 3. Alternating Optimization

#### 3.1. Transceiver Design and Power Allocation for PU

**Proposition**

**1.**

- 1.
- ${\mathbf{X}}_{1}^{\ast}$ satisfies $\mathrm{Rank}\left({\mathbf{X}}_{1}^{\ast}\right)=1$.
- 2.
- ${\mathbf{X}}_{1}^{\ast}$ and ${\rho}_{1}^{\ast}$ satisfy SINR and EH constraint of the problem in Equation (14) with equality.

**Proof**

**of Proposition 1.**

#### 3.2. Transceiver Design and Power Allocation for SUs

**Proposition**

**2.**

Algorithm 1: Sum rate maximization algorithm. | |

1: | Initialize: give initial feasible ${Q}_{\mathrm{SUs}-\mathrm{PU}}$ and ${\mathbf{U}}_{1}$ |

2: | repeat |

3: | solve The problem in Equation (13) by CVX with ${\mathbf{U}}_{1}$; |

4: | obtain ${\mathbf{V}}_{1}$ by EVD of ${\mathbf{X}}_{1}$; |

5: | update ${\mathbf{U}}_{1}$ by (11); |

6: | until converge or maximum number of iterations |

7: | Output ${P}_{1}^{\ast}=\mathrm{Tr}\left({\mathbf{X}}_{1}\right)$ |

8: | calculate ${\mathbf{V}}_{k}$ by (17) |

9: | obtain ${\mathbf{U}}_{k}$ by (19) |

10: | given a ${\rho}_{k}$; |

11: | repeat |

12: | $\left\{{P}_{k}\right\}$← solve the problem in Equation (22) by CVX with given ${\rho}_{k}$ |

13: | update ${\rho}_{k}$ |

14: | until converge or maximum number of iterations; |

15: | Update ${Q}_{\mathrm{SUs}-\mathrm{PU}}$; |

16: | Repeat 2–15 until convergence or maximum number of iterations. |

#### 3.3. Maximize Minimum SINR Solution for SUs

**Proposition**

**3.**

**Proof**

**of Proposition 3.**

**Proposition**

**4.**

**Proof**

**of Proposition 4.**

#### 3.4. Solution Discussion

## 4. Simulation Results

## 5. Conclusions

- Robust design: This paper considers a perfect CSI among all users, thus extending the results in our work to the more general imperfect CSI case is an interesting topic.
- Massive MIMO: Massive MIMO is a promising technology in the 5G communication network, but more effort is needed to design the transceiver for a Massive MIMO case.
- Nonlinear energy harvesting model: In practice, the energy harvesting model is a nonlinearity model; in the near future, we will pay attention to transmission strategies design for nonlinear energy harvesting model.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Proof of the Proposition 1

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**MDPI and ACS Style**

Wu, F.; Xiao, L.; Yang, D.; Cuthbert, L.; Liu, X.
Transceiver Design and Power Allocation for SWIPT in MIMO Cognitive Radio Systems. *Symmetry* **2018**, *10*, 647.
https://doi.org/10.3390/sym10110647

**AMA Style**

Wu F, Xiao L, Yang D, Cuthbert L, Liu X.
Transceiver Design and Power Allocation for SWIPT in MIMO Cognitive Radio Systems. *Symmetry*. 2018; 10(11):647.
https://doi.org/10.3390/sym10110647

**Chicago/Turabian Style**

Wu, Fahui, Lin Xiao, Dingcheng Yang, Laurie Cuthbert, and Xiaoping Liu.
2018. "Transceiver Design and Power Allocation for SWIPT in MIMO Cognitive Radio Systems" *Symmetry* 10, no. 11: 647.
https://doi.org/10.3390/sym10110647