# Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. System Overview

#### 2.2. Channel Model

#### 2.3. Noncoherent Detection

#### 2.4. Digital Beamspace Preprocessing

#### 2.4.1. Full-Array

#### 2.4.2. Sub-Array

## 3. Numerical Results

#### 3.1. Full-Array vs. Sub-Array Architecture

#### 3.2. Influence of Propagation Channel

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Digital beamspace preprocessing in noncoherent massive multiple-input/multiple-output (MIMO) systems: (

**a**) Full-array and (

**b**) sub-array architecture.

**Figure 2.**Spatial power distribution at ${N}_{\mathrm{rx}}$ = 12 receive branches (×) in case of Bartlett beamforming ( ) and in case of a combination with eigenspace-based post-processing ( ) considering two incident waves ( / ) and a field of view (FoV) of $\Phi $ = $\pi /2$.

**Figure 3.**User and base station (BS) arrangement to evaluate the noncoherent massive MIMO system with digital beamspace preprocessing.

**Figure 4.**Full-array architecture: Power-space profile and symbol error rate performance. Colors correspond to users: user 1 ( ), user 2 ( ), user 3 ( ). Gray plots ( ) represent results without digital beamspace preprocessing for each user.

**Figure 5.**Sub-array architecture of ${N}_{\mathrm{sub}}$ = 8 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 16: Power-space profile and symbol error rate performance. Colors correspond to users: user 1 ( ), user 2 ( ), user 3 ( ). Gray plots ( ) represent results without digital beamspace preprocessing for each user.

**Figure 6.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 for the full-array system ( ) and for different sub-array configurations (${N}_{\mathrm{sub}}$ = 4 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 32 ( ), ${N}_{\mathrm{sub}}$ = 8 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 16 ( ), ${N}_{\mathrm{sub}}$ = 16 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 8 ( )).

**Figure 7.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 at different LMR considering the full-array architecture: $\mathrm{LMR}$ = $0\mathrm{dB}$ ( ), $\mathrm{LMR}$ = $10\mathrm{dB}$ ( ), $\mathrm{LMR}$ = $20\mathrm{dB}$ ( ).

**Figure 8.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 at different spatial spread ${\sigma}_{\mathrm{s}}$ considering the full-array architecture: ${\sigma}_{\mathrm{s}}$ = ${2}^{\xb0}$ ( ), ${\sigma}_{\mathrm{s}}$ = ${4}^{\xb0}$ ( ), ${\sigma}_{\mathrm{s}}$ = ${8}^{\xb0}$ ( ).

**Table 1.**System configuration and parameterization of propagation channel and noncoherent detection.

System Configuration | |

number of users ${N}_{\mathrm{u}}$ | 3 |

number of BS antennas ${N}_{\mathrm{rx}}$ | 128 |

BS antenna spacing ${d}_{\mathrm{a}}$ | $\lambda /2$ |

FoV $\Phi $ | $\pi /2$ |

user antenna type | omni-directional |

BS antenna type | patch [15] |

angle ${\varphi}_{u}$ of user | ${\varphi}_{1}$ = $-{30}^{\xb0}$, ${\varphi}_{2}$, ${\varphi}_{3}$ = ${30}^{\xb0}$ |

Noncoherent Detection | |

modulation alphabet | 4-ary DPSK |

block length ${N}_{\mathrm{bl}}$ | 201 |

Propagation Channel | |

cluster types | local |

number of multi-path components ${N}_{p}$ | 3 |

angular spread ${\sigma}_{\mathrm{s}}$ at BS | variable |

LOS-to-MPC ratio (LMR) | variable |

number of different channel realizations ${N}_{\mathrm{ch}}$ | $50,000$ |

channel normalization (power control) | ${\left|\right|H\left|\right|}_{\mathrm{F}}^{2}$ = ${N}_{\mathrm{u}}$ |

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**MDPI and ACS Style**

Bucher, S.; Waldschmidt, C.
Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing. *Telecom* **2020**, *1*, 211-227.
https://doi.org/10.3390/telecom1030015

**AMA Style**

Bucher S, Waldschmidt C.
Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing. *Telecom*. 2020; 1(3):211-227.
https://doi.org/10.3390/telecom1030015

**Chicago/Turabian Style**

Bucher, Stephan, and Christian Waldschmidt.
2020. "Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing" *Telecom* 1, no. 3: 211-227.
https://doi.org/10.3390/telecom1030015