# Antenna Selection Based on Matching Theory for Uplink Cell-Free Millimetre Wave Massive Multiple Input Multiple Output Systems

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## Abstract

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## 1. Introduction

- For all APs in the cell-free network, we propose an assignment optimization problem to accomplish matching between RF chains and several sets of selected antennas based on channel conditions. Then, we propose the Hungarian method to solve this optimization problem based on maximum weight matching in order to maximize energy efficiency. In contrast to [22], instead of assuming that all RF chains in the AP have the same fixed active switches, we exploit the advantages of the matching theory based on the Hungarian algorithm to assign each RF chain at each AP in the cell-free network to the optimal number of activated switches depending on AP channel condition in order to maximize energy efficiency.
- Simulation results demonstrate the performance of the proposed antenna selection strategies under an extensive set of cell-free mm-wave massive MIMO scenarios. In particular, the number of APs, the number of antennas, and the number of users in the network are analysed in terms of energy efficiency. In addition, computational complexity of the proposed algorithms is studied in this work.

## 2. System Model

#### 2.1. Channel Model

#### 2.2. Analog Combining Design

#### 2.3. Uplink Channel Estimation

#### 2.4. Uplink Data Transmission

## 3. Problem Formulation and Proposed Solution

#### 3.1. Problem Formulation

#### 3.2. Problem Solution

Algorithm 1: Matching strategy for RF chain-subset selected antennas based on the Hungarian algorithm. |

## 4. Power Consumption and Energy Efficiency Models

## 5. Simulation Results and Discussions

## 6. Complexity Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Hybrid beamforming structure for each AP in uplink cell-free massive MIMO systems with CPSs connected to RF chains via switch network.

**Figure 2.**Proposed matching strategy for RF chain-subset selected antennas for each AP diagram with flowchart of the Hungarian algorithm.

**Figure 3.**EE versus number ${N}_{r}$ of antennas, where $M=80$ APs, ${N}_{Q}=8$, $\rho =23$ dBm, and $K=8$ UEs.

**Figure 4.**Total power consumption versus number ${N}_{r}$ of antennas, where $M=80$ APs, ${N}_{Q}=8$, $\rho =23$ dBm, and $K=8$ UEs.

**Figure 5.**EE versus number of APs, where ${N}_{r}=48$ APs, ${N}_{Q}=8$, $\rho =23$ dBm, and $K=8$ UEs.

**Figure 6.**Total power consumption versus number of APs, where ${N}_{r}=48$ APs, ${N}_{Q}=8$, $\rho =23$ dBm, and $K=8$ UEs.

**Figure 8.**Total power consumption versus the number of UEs, where $M=80$ APs, ${N}_{Q}=8$, $\rho =23$ dBm, and ${N}_{r}=48$.

**Figure 9.**Complexity analysis based on floating-points operations (FLOPs) with different scenarios of uplink cell-free mm-Wave massive MIMO systems. (

**a**) FLOPs versus M APs for a system with ${N}_{r}=48$, $K=8$, $\rho =23$ dBm, and ${N}_{Q}=8$ CPSs. (

**b**) FLOPs versus ${N}_{r}$ antennas with $M=80$, $K=8$, $\rho =23$ dBm, and ${N}_{Q}=8$ CPSs. (

**c**) FLOPs versus the number of K UEs with, $M=80$, ${N}_{r}=48$, $\rho =23$ dBm, and ${N}_{Q}=8$ CPSs.

**Figure 10.**EE and SE and the complexity tradeoff as a function of the number M of APs when $M=\{16,32,48,64,80\}$, $K=8$, $\rho =23$ dBm, ${N}_{Q}=8$ CPSs, and ${N}_{r}=\{48,80\}$ for the proposed matching scheme in uplink cell-free mm-Wave massive MIMO systems.

Parameter | Value |
---|---|

Carrier frequency (f) | 28 GHz [25] |

Bandwidth (B) | 500 MHz [25] |

Antenna gain (${G}_{a}$) | 15 dBi [18,26] |

Noise figure ($\mathit{NF}$) | 9 dB [6,18] |

Coherence interval length (${\tau}_{c}$) | 200 samples |

Length of pilot sequence (${\tau}_{p}$) | 20 samples |

Pilot transmit power (${\rho}_{p}$) | 100 mW |

Quantization bits (${\alpha}_{m}$) | 2 bits [36] |

Fronthaul capacity (${C}_{FH}$) | 100 Mbps [39] |

Amplifier efficiency ($\eta $) | 0.3 [5] |

Coherence time (${T}_{c}$) | 2 ms [36] |

Power components: | ${P}_{m}^{\mathrm{FH},\mathrm{fix}}=5$ W, ${P}_{\mathrm{FH}max}=50$ W, ${P}_{\mathrm{CP}}=1$ W, ${P}_{\mathrm{RFC}}=40$ mW, ${P}_{\mathrm{LNA}}=20$ mW, ${P}_{\mathrm{SP}}=19.5$ mW, ${P}_{\mathrm{SW}}=5$ mW, ${P}_{\mathrm{CPS}}=5$ mW, ${P}_{\mathrm{C}}=19.5$ mW, and ${P}_{\mathrm{ADC}}=200$ mW. |

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**MDPI and ACS Style**

Al Ayidh, A.; Sambo, Y.; Olaosebikan, S.; Ansari, S.; Imran, M.A.
Antenna Selection Based on Matching Theory for Uplink Cell-Free Millimetre Wave Massive Multiple Input Multiple Output Systems. *Telecom* **2022**, *3*, 448-466.
https://doi.org/10.3390/telecom3030024

**AMA Style**

Al Ayidh A, Sambo Y, Olaosebikan S, Ansari S, Imran MA.
Antenna Selection Based on Matching Theory for Uplink Cell-Free Millimetre Wave Massive Multiple Input Multiple Output Systems. *Telecom*. 2022; 3(3):448-466.
https://doi.org/10.3390/telecom3030024

**Chicago/Turabian Style**

Al Ayidh, Abdulrahman, Yusuf Sambo, Sofiat Olaosebikan, Shuja Ansari, and Muhammad Ali Imran.
2022. "Antenna Selection Based on Matching Theory for Uplink Cell-Free Millimetre Wave Massive Multiple Input Multiple Output Systems" *Telecom* 3, no. 3: 448-466.
https://doi.org/10.3390/telecom3030024