# Precoding Design and Power Allocation in Two-User MU-MIMO Wireless Ad Hoc Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model and Problem Formulation

## 3. Feasibility Proof and Optimal Solution

#### 3.1. A Feasibility Analysis of Problem P2

#### 3.2. The Optimization Algorithm for Problem P1

#### 3.3. The Optimization Algorithm for Problem P2

## 4. Two Suboptimal Solutions

#### 4.1. Sub-Optimal Algorithm with SVD in the First Timeslot

**Proposition**

**1.**

#### 4.2. Sub-Optimal Algorithm with BD in the Second Timeslot

## 5. Simulation Results

- (1)
- The higher the rate requirement is for the main user, U1, the smaller the achievable rate is for the secondary user, U2. This is because for U1 to achieve a high rate, the RN can harvest less energy in the first timeslot; consequently, less energy is allocated to U2 in the second timeslot.
- (2)
- The precoding design that uses the BF algorithm at both the first and second timeslots achieves the optimal performance; however, considering the high complexity of the optimization algorithm, we proposed two sub-optimal algorithms: SVD and BD.
- (3)
- When there are fewer receiving antennas than transmitting antennas, the performance of the sub-optimal precoding design with the BD algorithm achieves a performance close to that of the optimal precoding design with the BF algorithm. This occurs because the interference signals can effectively map to the null space of the useful signal with the BD algorithm; thus, it achieves an excellent performance in cancelling interference effects. In contrast, the performance with the SVD algorithm significantly impacts the performance of the sub-channel; its effect is relatively poor, but the receiver is simple to design.

- (1)
- Increasing the number of antennas in a user’s receiving terminal effectively increases the system’s capacity. The optimized beamforming scheme is not affected by the performance of the separated sub-channels nor by the number of receiver antennas; therefore, it achieves the maximum rate, and the optimization effect is remarkable.
- (2)
- When the number of receiver antennas is larger than the number of transmitter antennas, the channel dimensions also increase, and BD can no longer effectively eliminate the signal interference between users, therefore, its performance is the worst among the three tested precoding designs.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Proof of Theorem 1

## References

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**Figure 2.**When N = 4, M = 2, the second user’s rates with different precoding designs based on different rate requirement for the main user.

**Figure 3.**When N = 4, M = 4, the second user’s rates with different precoding designs based on different rate requirements for the main user.

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**MDPI and ACS Style**

Chen, H.; Xiao, L.; Li, Y.; Yang, D.; Zhou, X.
Precoding Design and Power Allocation in Two-User MU-MIMO Wireless Ad Hoc Networks. *Symmetry* **2017**, *9*, 247.
https://doi.org/10.3390/sym9110247

**AMA Style**

Chen H, Xiao L, Li Y, Yang D, Zhou X.
Precoding Design and Power Allocation in Two-User MU-MIMO Wireless Ad Hoc Networks. *Symmetry*. 2017; 9(11):247.
https://doi.org/10.3390/sym9110247

**Chicago/Turabian Style**

Chen, Haole, Lin Xiao, Yinfeng Li, Dingcheng Yang, and Xiaoxiao Zhou.
2017. "Precoding Design and Power Allocation in Two-User MU-MIMO Wireless Ad Hoc Networks" *Symmetry* 9, no. 11: 247.
https://doi.org/10.3390/sym9110247